摘要:

Russian Chemical Reviews 70 (1) 1 ± 22 (2001) Correlation analysis in the chemistry of free radicals A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov Contents I. Introduction II. Correlation analysis for reactions involving free radicals III. The use of r72 analysis in free-radical chemistry IV. Conclusion Abstract. correlation of use the on available now data Published Published data now available on the use of correlation analysis systematically. discussed are chemistry free-radical in analysis in free-radical chemistry are discussed systematically. The The scales previously proposed substituents of of scales of `radical' `radical' s-constants -constants of substituents proposed previously are as applicable is them of none that shown is It analysed. are analysed.It is shown that none of them is applicable as a general scale because almost in all cases, it is impossible to general scale because almost in all cases, it is impossible to separate contributions polar and radical proper the correctly separate correctly the proper radical and polar contributions to to the the to approach new A substituents. of effect overall the overall effect of substituents. A new approach to the quanti- quanti- tative structure the between relationship the of estimation tative estimation of the relationship between the structure and and reactivity processes free-radical in molecules of reactivity of molecules in free-radical processes called called r72-analysis is 238 includes bibliography The proposed. is proposed.The bibliography includes 238 references. references. I. Introduction Correlation analysis is a widely used mathematical formalisation of the chemical similarity principle. The foundations of the analysis were laid by Hammett, who discovered a correlation between the rate constants (k) or equili- brium constants (K) of reactions involving benzene derivatives and the ionisation constants of benzoic acids 1 kH log kX à rlog KX à rs, KH where the subscripts X and H refer to substituted and unsubsti- tuted derivatives and r is the reaction constant for the given series. The reaction series of dissociation of benzoic acids in aqueous solutions at 25 8C was chosen as the reference series, described by r=1, and the ratio logKX , KH was introduced as the s-constant, reflecting the influence of the substituent X in a set of similar reaction series.This empirical approach, which is also known as sr-analysis, became one of the first quantitative methods for describing the structure ± reactivity relationship for compounds and has served as the basis for the A R Cherkasov, V I Galkin, R A Cherkasov Department of Chemistry, Kazan State University, ul. Kremlevskaya 18, 420008 Kazan, Russian Federation. Fax (7-843) 231 54 16. Tel. (7-843) 231 54 16. E-mail: vladimir.galkin@ksu.ru (V I Galkin); rafael.cherkasov@ksu.ru (R A Cherkasov) MJonsson Department of Chemistry, Royal Institute of Technology, Teknikringen 56, S-100 44 Stockholm, Sweden. Fax (46-8) 790 87 72. Tel.(46-8) 790 91 23. E-mail: matsj@nuchem.kth.se Received 2 February 2000 Uspekhi Khimii 70 (1) 3 ± 27 (2001); translated by Z P Bobkova #2001 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2001v070n01ABEH000574 12 11 20 subsequent development of the general formal theory of the influence of substituents. The principles of linear free energy (LFE) and polylinearity (PL) provide the physical grounds for this approach, according to which the increment of the Gibbs energy change (DG) in a reaction or of the activation energy caused by the introduction of a substituent is represented as the additive sum dDG=dDGI+dDGS+dDGR , each of the terms reflecting a particular type of substituent effects, namely, inductive (I), steric (S) or resonance (R) effect. The multitude of inductive, steric and resonance constants determined from diverse experimental sources, together with some specific constants (for example, `phosphorus' or `silicon' constants) form dozens of scales which are widely used to describe the influence of substituents on the reactivity at the group level of additivity.Various aspects of the determination and versatile practical application of steric and inductive constants of groups and the concept of electronegativity tightly connected to them have been described in detail in our previous reviews.2± 5 It should only be noted that modern correlation analysis has long overstepped the limits of a purely empirical approach. The group constants of substituents have provided the experimental basis for the physical interpretation and for the development of various quantitative models describing the steric and electronic effects.Certainly, some key problems of the formal theory of inter- action and correlation analysis are still to be ultimately solved. For example, the nature of the inductive effect and the mechanism of its transfer remain one of the most debatable and topical problems of physical chemistry 2 (the state-of-the-art in this line of research has been discussed comprehensively in recent review publications 5 ±8). Nevertheless, it can be stated with confidence that the theoretical grounds of modern correlation analysis provide in general a clear picture and give good grounds for the extensive use of the substituent constants for description of the structure ± property relationships in the chemistry of organic and heteroorganic compounds.Perhaps, the only field of chemistry in which the use of correlation analysis has not yet provided good results is free-radical chemistry. The application of LFE and PL principles in this field of chemistry is still limited to a rather narrow range of compounds (mainly, aromatics). In this review, the current state of the use of correlation analysis for radical reactions is considered for the first time. In addition, we thought it necessary to present the generalising results obtained by the new approach to the estimation of the structure ± reactivity relationship in free-radical reactions which we have developed and called `r72 analysis'.2II.Correlation analysis for reactions involving free radicals 1. Methods for the description of the effects of substituents in homolytic processes based on kinetic parameters. s -Scales Despite the fact that the applicability of the Hammett equation to homolytic processes is sometimes debated,9 there exist quite a few examples of successful use of various polar constants for the description of free-radical reactions.10 ¡¾ 28 In addition to the proper Hammett s-constants,18 ¡¾ 29 which reflect the overall effect of substituents in aromatic systems, so- called dual s+ and s7 parameters of substituents, which imply direct polar (mesomeric) interaction of +M or 7M substituents with the reaction centre, are also actively used in the analysis of homolytic processes.The scale of s+-constants proposed by Brown and Okamoto,30 which is based on the rates of solvolysis of para- and meta-substituted cumyl chlorides, is believed to be more adequate in describing the properties of aromatic radicals than the scale of Hammett s-constants.31 In our opinion, the use of s+-constants is really more effective as far as the properties of radical cations are concerned but this is not that obvious for neutral radicals. Never- theless, radical bromination of substituted toluenes with bro- mine,24 N-bromosuccinimide 24 and bromotrichloromethane 32 as well as the quantitative interpretation of abstraction of a hydrogen atom by alkoxy radicals,11, 12, 33 chlorine atoms,34 and peroxy radicals 34 have become classical examples of successful use of the s+ constants in free-radical chemistry.Experimental results obtained by one of the authors of this review have confirmed the exceptionally high efficiency of the s+ constants in correlations with single-electron reduction potentials of various aromatic molecules and radicals.35 ¡¾ 40 Other researchers 18, 41 have also considered the Brown ¡¾ Okamoto scale to be the most suitable scale for the description of properties of free radicals; it is the scale of s+constants that has served as the base for the introduction of several specific radical constants of substituents s (they will be considered in detail in the subsequent sections of this review).The s7-constants found from the pK values for ionisation of substituted anilines, N,N-dimethylanilines and phenols 42, 43 have also been used successfully to describe a number of radical processes.29, 44 However, polar constants are finding fairly limited application in free-radical chemistry. The scope of application of particular scales to the description of properties of free radicals remains obscure, identification of statistically significant correla- tions in each successful case being rather a matter of luck than of a systematic approach. Additional difficulties arise when the corre- lation analysis technique is employed to describe the properties of non-aromatic free radicals. The main problem in the quantitative estimation of the effects of substituents in homolytic processes is, undoubtedly, the neces- sity of adequate description of their ability to delocalise the unpaired electron.Currently, this is one of the most topical and ambiguous problems in free-radical chemistry (see, for example, a monograph 45 and references therein). There is a common opinion that both donors and acceptors are capable of stabilising a radical centre;45 this is often used as an argument in favour of the introduction of special radical s constants of substituents, which are expected to describe quanti- tatively the ability of substituents to delocalise spin density. The methods of determination of s -constants can be classified into three main types. The first type includes methods based on the use of kinetic parameters of homolytic processes; the second type comprises physicochemical methods which provide direct infor- mation on the spin density distribution in radicals; and thermody- namic approaches operating with energy characteristics belong to the third type.Below we consider the existing approaches in accordance with this classification. The methods based on the kinetic parameters of homolytic processes are used most widely in determining the s -constants of A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov substituents and are modifications of the classical correlation analysis, based on the use of the extended Hammett equation (1) log k a r1sX a r2s . k0 The essence of this approach is to separate the contribution of the proper radical stabilisation (s ) from the polar effect (sX); hence, it requires selecting a model reaction series in which the latter contribution would be small and could be determined reliably in terms of polar constants.The most widely used reactions involv- ing free radicals include electron transfer, free-radical transfer of a hydrogen atom and radical addition. The kinetic approach to the description of the effects of substituents in radical reactions was first employed by Alfrey and Price 46 in a study of the reactivity of vinylic monomers in copolymerisation. The researchers 46 did not use the classical logarithmic form of Eqn (1); however, the capacity of substituents for stabilisation of radicals was estimated quantitatively for the first time in terms of group constants Q, whereas the polar component was taken into account by the parameter e (the Q constants are given in Table 1) (2) k1 k2 a Q1 Q2 exp¢§e1Oe1 ¢§ e2U.A substantial disadvantage of this approach is the fact that the calculation of Q is based on the analysis of a set of data on copolymerisation, and introduction of new individual values requires a consistent procedure for recalculation of the whole array of Q. Walling et al.59 have critisised the theoretical substantiation of the Alfrey ¡¾ Price approach, which ignores the possibility of resonance stabilisation of a radical transition state. Later, the group parameters ER have been introduced using the relative reactivity of monomers (1/r) in the radical copoly- merisation of aryl-substituted methacrylates 47, 48, 60 (3) log 1r a rs a gER , R, where the g coefficient was taken to be 1, and the parameter ER was interpreted as the resonance component of the substituent effect in free-radical processes. Subsequently,49 this approach was subjected to severe criticism, the legitimacy of the ER and g values being prejudiced.The researchers 49 believed that the nature of ER is rather complex; therefore they proposed adjusted values, En free from the contribution of heterolytic resonance (see Table 1). A similar scale of resonance constants ED has been developed to describe the effects of para-substituents in the addition of trichloromethyl radical to substituted styrenes 53 (4) log kp a rsap OrspU a ED ; kH in this case, the polar effect was taken into account by both the Brown ¡¾ Okamoto constants and the Hammett sp-constants.Correspondingly, two sets of ED parameters for para-substituents (MeO, Cl, CN,NO2) in styrenes were obtained [ED(s) and ED(s+) in Table 1]. The ED constants of these substituents found using the s+ parameters are in good agreement with the Alfrey ¡¾ Price Q constants. A similar approach was used 54 to develop the t scale, which reflects the conjugation effects in radical arylation of substituted benzenes (5) log kp k a rsp a tp , where kp are the rate constants for the arylation into the para- position expressed in terms of the Hammett constants of para- substituents (sp) and the group parameters tp, which reflect the additional delocalisation effects of para-substituents.The r-con- stant appearing in Eqn (5) was determined on the basis of a similar reaction series of meta-arylation, the influence of substituentsTable 1. Constants characterising the radical-stabilisation properties of substituents (data of kinetic studies). R(p) logQ E Substituent see a 0.00 H 0.04 Me 0.13 OMe 0.21 NO2 0.27 CN ± ± ± ± ± ± ± ± 70.25 F 0.01 Cl 0.04 Br 0.07 I ± OH ± C(O)Me P(O)(OEt)2 ± ± ± ± ± ± ± ± ± ± ± 0.18 P(S)(OEt)2 ± ± ± ± ± ± ± ± ± ± ± 0.29 ± ± ± ± ± ± ± ± 0.12 PhSMe ± ± ± ± ± ± ± ± ± (0.49) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± SPhCF3 ± ± ± ± ± ± ± ± ± ± ± 0.08 ± OPh CO2Et ± ± ± ± ± ± ± ± ± ± ± 0.39 CO2Me ± ± ± ± ± ± ± ± ± ± ± 0.35 ± C(O)Ph But ±± ± ± ± ± ± ± ± ± ± ± ± ± 0.15 EtPri ±± SOMe ± SC(O)Me ± S(O)OMe SO2Ph ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± S(O)Ph SO3Me ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± OC(O)Me ± OC(O)Ph ± N=NPh NH2 ± ± ± ± ± ± ± ± ± ± ± 0.69 NMe2 ± SiMe3 ± ± ± ± ± ± ± ± ± ± ± 0.17 CH=CH2 ± ± ± ± ± ± ± ± ± ± ± 0.67 Note.The values which vary in original publications are given in parentheses. a From Ref. 46; b from Refs 47, 48; c from Refs 49 ± 52; d from Ref. 53; e from Ref. 54; f from Ref. 55; g from Refs 50 ± 52; h from Ref. 56; i from Ref. 57; j from Ref. 58. En ER(m) R see c see b see b 0.000 0.00 0.00 70.020 ± 0.03 70.008 ± 0.11 0.410 0.35 0.41 0.230 ± 0.24 0.062 0.08 0.10 0.072 ± 0.12 0.037 ± 0.12 ± ± 0.21 0.240 ± ± 70.147 ± 0.13 ± ± ± 0.014 ± 0.03 0.034 ± 0.03 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 70.110 ± 0.24 s s to tp ED(s+) ED(s) J FM see g see f see e see e see d see d 0.00 0.00 0.00 0.00 0.00 0.00 70.02 0.38(0.39) 0.50 0.09 0.11 0.16 70.12 0.31(0.42) ± 0.14 0.19 0.40 0.73(0.76) 0.27 0.88 0.90 0.27 0.27 (0.41) 0.34 ± ± 0.32 0.33 0.07(0.12) 0.06(0.18) 0.08 0.48 0.16 0.07 0.12 (0.20) ± ± ± ± 0.17 ± ± ± ± ± 0.16 ± ± 0.57 ± ± ± ± ± ± ± ± 0.53 0.39(0.42) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.13 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.18 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.18 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 70.11 ± ± ± ± ± ± ± ± ± ± ± ± 0.33 ± 0.90 ± ±± ± ± ± ± ± 0.535 js ¡ sj n s sC(p) C(m) see i see i see h 0.00 0.00 0.000 70.02(0.03) 0.11 0.170 70.02 0.24 0.250 70.11 0.57 0.440 70.12 0.46 0.260 70.05 70.08 0.065 70.04 0.12 0.065 ± 0.13 0.055 0.10 0.41 0.075 ± ± ± ± ± ± 70.11 70.06 ± 0.46 0.230 70.03 0.43 ± 70.07 ±±±0.01 70.07 ± 1.08 ± ±± 0.90 ±± s s JJ(m) JJ(p) see j see j 0.00 0.00 0.00 0.15 0.10 0.23 0.001 0.36 0.11 0.42 70.02 0.03 70.05 0.22 0.12 0.23 ± ± ± ± ± 0.54 ± ± ± ± ± 0.47 ± 0.62 70.07 70.01 ± ± 0.10 0.33 0.11 0.26 ±± 0.50 ± 0.38 70.10 ± ± ± ± ± 1.00 ± 0.31 ± ±4being entirely ascribed to the polar interaction.The parameters to for ortho-substitution were introduced by a similar procedure.The 4-XC6H4CH2 radicals, where X=H, NO2, Cl, Me, MeO, were investigated (regardless the nature of the attacking agent); in this case, the tp and to constants decreased in the series PhNO2 44 PhCl, PhOMe>PhMe (see Table 1). This model series has an important advantage: the measured kinetic param- eters vary over a broad range due to the direct conjugation of para-substituents with a cyclohexadienyl radical. R X +R H X However, it cannot be ruled out that, within the framework of the given reaction series, fairly reactive phenyl radicals would be involved with high probability in side homolytic properties. The methodology of the above approaches is evidently similar to that used in the classical equations of correlation analysis, which determine the inductive and resonance constituents of the polar effect of substituents in terms of Taft,42, 61 ¡À 63 Exner,64 ¡À 66 Yukawa ¡À Tsuno,67, 68 Swain ¡À Lupton,69 Dewar ¡À Grisdale,70 Charton 71 and Palm 72, 73 approaches.In all the studies described above, except for the study by Alfrey and Price,46 the researchers dealt only with aromatic systems. Therefore, the radical constants t, ER and ED are believed to contain a component due to the polar effect. Fisher et al.55, 74, 75 used radical bromination of 4-substituted 3-cyanotoluenes with N-bromosuccinimide as the model reaction to determine the `extra-resonance' (this name was proposed by the authors), i.e., the proper radical contribution (the polar contribu- tion is minimised).When considering the possible canonical forms of the transition state of hydrogen abstraction via the reaction YH+Z Y+H Z¡¦ 1b Y¡¦ HZ�¢ , 1c YHZ 1a the researchers suggested that the high electronegativity of the attacking bromine atom Z precludes a substantial contribution of structure 1c. In order to destabilise the polar form 1b to decrease its contribution, the electron-withdrawing CN group was intro- duced in the meta-position relative to the methyl group (substrate YH) of the substituted toluene. The radical intermediate 1a is stabilised additionally due to direct resonance. Assuming that the polar effects in the model system were thus minimised, Fisher et al.55, 74, 75 proposed a scale of s radical constants within the framework of a two-parameter equation including the Brown ¡À Okamoto constant s+ (6) log k �� rs�¢ �¢ s , k0 in which the parameter r was determined on the basis of a similar reaction series of 4-substituted toluenes.Fisher and Meierhoefer 55 did not use a series of meta- substituted toluenes as the standard for determining r on the ground that the corresponding parameter in Eqn (6) reflects, in their opinion, both the resonance and inductive polar effects. Thus, the differences between the effects of substituents in the free radical bromination of monosubstituted and 3-cyano-4-substi- tuted toluenes by N-bromosuccinimide were attributed to the stabilisation of the structure 1a; they were proposed as character- istics of the radical effects of para-substituents.In accordance with the results of this study, the ability of substituents to stabilise free radicals increases in the series F<OMe<Me<H<Cl<Ph< I <Br<NO2<N=NPh<CN<Ac, the s constants for F and MeO being negative [s (F)= 70.25, s (MeO)=70.12], which implies that these groups destabilise the radical reaction center (see Table 1).55 Meanwhile, it is obvious that the resonance stabilisatoion of substituted benzyl radicals by electron-withdrawing substituents (structures 2a and 2b) is similar to resonance delocalisation of the A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov negative charge.This accounts for the most pronounced radical- stabilisation properties of substituents such as Ac, CN, N=NPh and NO2, which also exhibit a negative mesomeric effect. X Y X Y CH2 CH2 2b 2a In the case of stabilisation of the benzyl radical by the donor mesomeric effect of some substituents such as halogens (except for F), the researchers cited 55 discussed the formation of three contributing structures 2c, 2d and 2e. +X X X CH¡¦ CH2 CH2 2 2c 2e 2d Structure 2e is characterised by substantial charge separation, which makes it energetically less favourable. The electrically neutral structure 2d implies delocalisation of the unpaired electron because it has been added to the electron octet of the X atom. As Tsuno et al.68 rightly noted, elements of Period II, O and F, are incapable of this type of interaction, which accounts for the negative values of the corresponding radical constants.The presence of negative s values in the Fisher ¡À Meierhoefer scale hampers its quantitative comparison with other known scales, in most of which the radical constants can be only positive, implying that the radical reaction centres are stabilised by both donors and acceptors. It should also be noted that in the model system of disubstituted toluenes proposed, the possibility of resonance effect of para-substituents is retained, despite the minimisation of polar effects. The search for standard reaction series with a clear-cut radical character of the transition state, which rules out a noticeable influence of polar interactions, has led al.50, 51, 56, 76, 77 to consideration of the thermal dissociation of dibenzylmercury derivatives in solution. ArCH2HgCH2Ar ArCH2 +HgCH2Ar HgCH2Ar Hg+ArCH2 .It was found that homolysis occurs in two stages. The first, rate-determining stage is generation of benzyl and benzylmercurio radicals;52, 78, 79 it was suggested that in the transition state, one C¡ÀHg bond has been cleaved almost completely, which corre- sponds to the formation of a nearly free benzyl radical. The conventional sr-analysis, which makes use of the first- order rate constants for the reaction under consideration and the Hammett s-constants (subsequently, the s0 parameters were used), identified a linear correlation for meta-derivatives, whereas para-substituents of both electron-donating and electron-with- drawing nature accelerate homolysis, due to an additional stabi- lisation of benzyl radicals.In the equation (7) log k �� rs �¢r s k0 resulting from the correlation procedure, the parameter r was taken to be unity for reactions giving rise to free benzyl radicals in the rate-determining step. In terms of the regression analysis performed, the constants which were later designated by sJ (see Ref. 45) and which reflect the stabilising effect of substituents in the para-position of the benzyl radicals were determined from the deviations from the meta-correlation (see Table 1). The sJ values were found to be in good agreement with the Q, t, ED and ER scales (the correlation coefficients r varied from 0.83 to 0.92); as regards the Fisher ¡À Meierhoefer constant (sFM), only some qual- itative correspondence was found in this case (r=0.63).It has been proposed 56 to use the |s7s|/n scale, where s is the s+ or s7 constant, as a measure of radical stabilisation; for substituents containing a lone electron pair n=2, while for groups with a multiple bond or any other p-system, n=1. ThisCorrelation analysis in the chemistry of free radicals scale correlates well with the sJ values. As drawbacks of this approach, the authors note the difficulty of preparing a broad range of dibenzylmercury derivatives and the limited solubility of these compounds in octanol, used as the reaction medium.An attempt to select a perfect free-radical transition state is also the central point in Creary's approach,57, 80 ± 84 in which thermal rearrangement of 3-aryl-2,2-dimethylmethylenecyclopro- panes 4 has been used as a standard reaction series to introduce the scale of radical constants sC. Me Me CH2 H H X 4 Me Me H Me H H Ar X=NO2, NMe2, CH=CH2, C(Me)=CH2, Ph, cyclo-C3H5, 6 CH2SiMe3, SiMe3, SnMe3, HgCl, B(OCH2CH2O). The transition state of the rearrangement is of biradical nature; this has been confirmed in a series of studies.85 ± 94 Proceeding from the assumption that the biradical nature of the transition state rules out the possibility of substantial charge separation in it, Creary suggested using the logarithm of the relative rate constant for the reaction, krel, as a measure for the ability of substituents to stabilise the benzylic radical centre sC =log krel .The kinetic parameters of thermal rearrangement of 2-aryl- 3,3-dimethylmethylenecyclopropanes 4 into 2-arylisopropylide- necyclopropanes 5 can be easily determined by gas chromatog- raphy or NMR; this permits determination of radical constants for meta- and para-substituents of the aromatic ring within the framework of this approach. It is also possible to evaluate the stabilising influence on the radical centre of heteroorganic sub- stituents.45 It was found 57, 84 that electronegative substituents in the meta- position retard the rearrangement, which might point to an electron-deficient character of the biradical transition state.Most para-substituents, both electron-donating and electron- withdrawing ones have positive values of sC constants. An exception is F, for which sC= 70.08 (see Table 1); this was explained by the destabilising influence of F caused by the enhanced inductive effect. The influence of the para-methoxy group was regarded as stabilisation (sC=0.24), caused by the contribution of the canonical forms 7a,b. CHR H3C:O H3C:O 7a + CHR F ¡ 8 A similar structure for the para-fluorine-substituted system appears less favourable because of the high electronegativity of fluorine. From the molecular-orbital standpoint, the stabilising effect of the para-methoxy group can be due to the interaction of the radical centre with the filled non-bonding orbital of oxygen; Me CMe X 5Me H H CHX (8) á CHR ¡ 7b 5 however, the low energy of the filled 2p orbital of fluorine precludes manifestation of the effects of this type.As has been noted in a monograph,45 synthesis of a broad range of methylenecyclopropanes 4 is quite difficult; therefore, the reaction series proposed by Creary has no advantages in this respect over thermal dissociation of mercury dibenzyl derivatives. In addition, it is not quite clear to what extent the centre in the transition state 6 is a radical centre. Nevertheless, this approach has been successfully developed; it was shown in a recent pub- lication 94 that the introduction of nitrogen-containing substitu- ents into the para-position of the substrate 4 provides considerable radical stabilisation.Moreover, some substituents, for example, CH=NNMe2, N=NPh, N=N(O)But and CH=N(O)But (sC=0.92, 1.08, 1.08 and 1.13, respectively), displayed extraordi- nary radical-stabilisation capacity; they were called super-stabil- isers. Afree-radical transition state in aliphatic systems 45, 95 ± 100 has been modelled by pyrolysis of substituted azopropanes 9. Me Me Me Me C Me N N C C Me X X X 10 9 According to the researcher's assumption, this reaction series is characterised by slight steric and inductive interactions; therefore, the pronounced difference between the reaction rates (the range of variation of the rate constants is 10 9) is interpreted as being due exclusively to resonance stabilisation. Later, the kinetic character- istics of pyrolysis of the azopropanes 9 were found to be well correlated with the Creary radical constants sC, despite the substantial difference between the structures of the radical sub- strates 6 and 10 and the fact that the extents of influence of substituents on the radical centres are difficult to compare.83 The series of model aryl-substituted azoalkanes has been markedly extended 101 by the inclusion of polycyclic azoalkane derivatives,102 symmetrical azopropanes,103, 104 azoethanes,105, 106 azomethanes,98 azoneopentanes 107 and 3,5-diaryl-1-pyrazo- lines,98, 108 for which the kinetic parameters of pyrolysis have been found. It is worth mentioning that, only in terms of two- parameter correlations including polar constants s, was it possible to attain satisfactory relationships between the experimental relative rate constants for the thermolysis of azo derivatives and the corresponding Creary parameters sC.84 The equilibrium constant of the dissociation of substituted hexaarylethanes to triarylmethyl radicals has been used success- fully as a measure of radical-stabilising capacity of substituents.109 An association reaction, namely, thermal [2+2]-cycloaddi- tion of substituted a,b,b-trifluorostyrenes 11 58 has been used as a model series for determination of spin-delocalisation group con- stants sJJ (see Table 1).DD(+ or 7 ) dd+ dd7 CF Y CF2 F1 F3 D(+ or 7) d7 d+ C 2Y C F2 11 CF Y CF2 d F F Ar F Y CF D CF2 F F F F Ar F F + F CF D Y dCF2 Ar F Ar F 12 An advantage of this model reaction is that no side radical processes are involved.In addition, charge distribution in the transition state 12 is symmetric, which eliminates additional polar effects. Study of the kinetics of this reaction gave a two-parameter correlation equation6 (9) log kY a rmbsmb a r sJJ, kH which was employed for the introduction of spin-delocalisation constants of substituents sJJ. The smb parameter in Eqn (9) is identical to the group constant proposed previously, which is determined on the basis of fluorine chemical shifts in the 19F NMR spectra of compounds 11.58, 110 ¡¾ 113 The mb (multiple bond) subscrflects the hypothetical additional repulsive component of interaction between the double bond and the electron lone pair or p-electrons in the Y substituent in the compound 11 (Jiang et al.113 consider this to be a fundamental feature distinguishing the scale of smb constants from the Brown ¡¾ Okamoto s+ constants).Equation (9) provided the possibility of determining the sJJ constants for 32 substituents (see Table 1) at five different temperatures; this allowed the researchers to verify the adequacy of the correlation parameters proposed and to introduce an averaged scale. JJ the two-parameter equations r as a measure of the relative r contributions of radical effects in the corresponding model series.By the use of the sJJ scale, together with the s+ parameters, the kinetic data underlying other scales of s radical constants have been reproduced with rather high accuracy within the framework of a two-parameter equation. Assuming that the s parameters reflect the real ability of substituents to delocalise spin density, Dust and Arnold 114 used the ratio of the coefficients of Thus it was shown that the ratio r for the reaction series of r monosubstituted toluenes used by Fisher and Meierhoefer 55 to determine polar effects amounts to 4.8, whereas an analogous model series of substituted toluenes containing a cyano group in the meta-position is described by a ratio of polar to resonance effect equal to 1 : 1.51; in addition, the accuracy to which each contribution has been determined does not provide the possibility of their correct separation.It should be noted that many researchers 4, 52, 77, 114, 115 pro- posed their own scales of s constants which they considered to be the most suitable for estimating the radical character of transition states. For instance, Jackson et al.56 used the sJ scale and demonstrated that in the transition states of the model homolytic reactions that underlay the Fisher ¡¾ Meierhoefer radical constants sFM and the ER and ED parameters, the fraction of structures corresponding to the proper benzyl radicals is not more than 50%. The authors of most of the approaches discussed above have attempted to formulate the requirements to an ideal model system to be used for kinetic determination of radical constants.1. The substituents should interact directly with the radical centre. 2. The mechanism of the model reaction should be as clear as possible. 3. Side reactions should be minimised. 4. Model systems should be preferred in which substituents have a strong influence on the reaction rate and for which accessible and precise methods for the determination of relevant kinetic parameters exist. 5. The polar effects should be either absent or minimised, or be reliably separated from the effect of radical stabilisation. 6. The model compounds should be readily available and should contain diverse substituents of both electron-donating and electron-withdrawing natures.7. The role of other external and internal factors, for example, the solvent and the steric effect, should be minimised. 8. One of the most important features required for a free- radical reaction to be used as a model to describe the radical effects of substituents is that the nature of the transition state should be as radical as possible. According to the Hammond postulate,116 the last-mentioned condition (this is very important to emphasise) implies a late A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov transition state of the process, which corresponds to a more endothermic generation of free radicals. This, in turn, stipulates a higher selectivity of the reaction.117 Therefore, the radical effects of substituents (in particular, the captodative effect { of radical stabilisation) are often considered in the context of selectivity of free-radical processes (see, for example, Refs 45, 118).It should be noted that in none of the above-listed approaches, the transition state can be considered completely radical�¢in any case, one should suggest the presence of charge separation and polar interactions. Therefore, the topicality of the question of to what extent a particular scale of radical constants is free from the polar constituent is beyond doubt. Apparently, the polar constit- uent can hardly be ruled out completely. 2. Spectroscopic determination of the capacity of substituents for delocalisation of spin density in free radicals Physicochemical methods such as EPR spectroscopy permit direct investigation of the properties of free radicals.According to the McConnel equation aH=QrpC, the hyperfine splitting (HFS) constants aH in the EPR spectra are directly proportional to r.118 For a number of compounds, the relative HFS constants have been found 119, 120 to correlate with the s and s7 polar constants; it was concluded 119 that delocalisation of an electron pair is a more substantial stabilising factor than spin density delocalisa- tion. A non-kinetic scale of the stability of alkyl radicals based on HFS constants of b-protons has been composed.121 The approach proposed by Arnold et al.122 ¡¾ 126 is best known of all; according to this approach, the HFS constants of a-protons are used as a measure of stabilisation energy, determined by delocalisation of spin density in substituted benzyl radicals 13 with respect to PhCH2.X1 CH2 13 X2 This method has obvious advantages, which include the absence of side radical reactions and the relative ease of generation of the required free radicals.45 In addition, the radical constants sa, defined by the equation (10) sa a 1 ¢§ aOHXU 0U , aOH where aOHXU and aOH0U are the HFS constants of the a-protons in the substituted and unsubstituted radicals, respectively, can be considered to be free from the polar effects characteristic of radical-like transition states and do not correlate with the sub- stituent effects in the corresponding diamagnetic initial com- pounds.The researchers 122 assumed that other factors which can potentially influence the HFS constants (hybridisation of the orbital bearing the unpaired electron, interaction with b-substitu- ents, steric effects reflected in the geometry of benzyl radicals 118) are insensitive to the substitution in the aromatic ring. The sa values thus obtained (Table 2) confirmed that the meta-substituents in the aromatic ring decrease delocalisation of the unpaired electron. The correlation established between the constants of meta-substituted benzyl radicals and the correspond- ing Hammett meta-constants (sm) made it possible to relate the destabilising effect of meta-substituents to their inductive elec- tron-withdrawing effect.45 However, it is not entirely clear why electronegative meta-substituents hamper delocalisation of spin density on the methylene carbon atom in the benzyl system.124 { Captodative effect is a joint influence of electron-donating and electron- withdrawing substituents on a radical reaction centre, resulting in a stabilisation greater than the sum of the two stabilising effects in the corresponding monosubstituted radicals.45Correlation analysis in the chemistry of free radicals Table 2.Constants characterising the radical-stabilisation properties of substituents (from EPR data and bond energies). Substituent HMe OMe NO2 CN FCl Br IOH C(O)Me P(O)(OEt)2 P(S)(OEt)2 Ph SMe SPh CF3 OPh CO2Et CO2Me C(O)Ph But Et Pri SOMe SC(O)Me S(O)OMe SO2Ph S(O)Ph SO3Me OC(O)Me OC(O)Ph N=NPh NH2 NMe2 SiMe3 CH=CH2 Note.Ed is the energy of homolytic dissociation of the C7X bond in substituted methanes. a From Refs 114, 125; b from Ref. 127; c from Ref. 45; d from Ref. 115. Presumably,124, 128 a decrease in the electron density by the inductive mechanism prevents the effective overlap of the inter- acting sites, i.e., of the orbital carrying the unpaired electron with the p-system of the benzene ring, or, in other words, it decreases the energy of the p-system and thus weakens the interaction between the CH2-group carbon and the aromatic ring. The effects of the OC(O)Me, CF3 and F groups located in the para-position were found to destabilise the radical centre, whereas other para-substituent according to the data obtained from EPR, favour spin density delocalisation.It has been suggested that a decrease in the spin density in the a-position of the benzyl radical would result in an increase in the p-resonance binding of the aromatic system with the methylene group and, correspondingly, in an increase in the barrier to rotation around the Carom±CH2 bond.45, 124 The p-component of the stabilisation energy (Es) of the p-radical was expressed via the rotation barriers of the CH2 group in the ZCH2 radicals with or without spin density delocalisation Es= V2(CH2)7V2 , where the corresponding rotation barriers (V2 and V 2 ) can be determined from EPR data. s DDp see b a(m) see a sa(p) see a 0.00 0.02 70.05 0.90 0.54 70.17 0.09 0.05 0.04 70.05 ± 0.000 70.001(0.002) 70.001 ± 70.039(70.026) 70.018(70.009) 70.001(70.007) ±±±± ±±± ±±± 0.11 ±± 70.014(70.017) 70.013(70.002) ± 70.004 ±±±±±±±±±± 0.53 ±±±±±±±±±±±±±0.30 0.000 0.015 0.034(0.018) ±0.043(0.040) 70.011 0.017(0.011) ±±±0.066 (0.060) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.063 0.058 0.001(70.009) 0.018 ±0.048(0.043) 0.064(0.055) 0.036(0.008) 0.012 0.009 0.006(0.018) 0.029 0.016(0.005) 0.018 0.026 0.003(0.013) 0.001(70.005) 0.000 ±±±±± 70.014 ±±±±±± ±±± 7 av RRSX see c Ed see c DDm see b ssee d 0.00 0.23 0.35 0.76 0.63 70.03 0.18 0.23 ±± 0.0 2.3 4.5 9.4 8.6 71.4 2.4 0.9 0.2 3.1 10.2 0.00 70.09 70.15 70.06 70.14 ± 70.08 ± 70.09 70.22 ± 0.58 104.4 100.3 93.3 ± 92.9 101.0 99.2 102.5 103.4 95.0 ± 0.59 0.55 ±0.09 ±± 11.2 10.7 10.7 70.3 4.9 ±7.9 9.3 3.0 1.5 ±4.1 6.7 3.6 4.5 5.9 2.9 0.9 0.0 ±8.4 8.9 3.5 12.8 0.54 0.65 0.13 ±±±±±±±±±±±±±±± 87.9 ±± 106.7 ±±±± 93.9 99.7 ±±±±±±±±±± 94.0 84.0 ± 86.7 ±±± 70.04 ±±±±±±±±±±±±±±±± 70.19 ±±± Jackson 129, 130 has noted that the range of HFS constants considered by Arnold et al.122 ± 126 is rather narrow and some individual values were determined with substantial errors.There- fore, he developed a new approach that provided more accurate determination of the HFS constants a(CH2) in the EPR spectra of benzyl radicals.116 The results 129, 130 are generally consistent with the sa scale. Yet another example of using quantitative parameters of EPR spectra is a study by Adam et al.,127, 131 ± 135 who made use of the electronic spin ± spin splitting parameters D. The parameter D is a sensitive function of the averaged distance between the unpaired electrons in a biradical (D!1/r3) which is proportional to the product of local spin densities in the triplet biradicals 14 and 15, chosen as the reference species to determine the capacity of the substituent X for spin density delocalisation.130 ± 132 3 3 X X X 14 158 Proceeding from the assumption that specific electronic effects (captodative stabilisation, spin polarisation, etc.) are relatively insignificant in 1,3-biradicals,136 Adam et al.127, 132 ± 134 proposed the scale of DD= DH7DX values (where H corresponds to the unsubstituted radical), which reflects delocalisation of the unpaired electron by the aryl group. Negative DD values, which should correspond to electron-donating groups, were found for all meta-substituents (including charged ones, viz., NHá3 , O7) and for para-substituents such as F, OMe, OC(O)Me and OH.The para-substituents NO2, CN, C(O)OMe, NH2 and CF3 exhibit the highest capacity for spin density delocalisation (see Table 1). The additivity of DD values found for monosubstituted and symmetrically disubstituted triplet biradicals 14 and 15 served as the basis for the assumption that each of them can be represented as composed of two fixed fragments of the cumyl radical. Hence, the researchers suggested 127, 132 that the DD scale could also be used for adequate description of benzyl monoradicals. This suggestion is supported by the fact that the parameters D for triplet biradicals are correlated with the a-spin densities and the energies of resonance stabilisation of the corresponding cumyl radicals.127, 132 ± 134 Comparison of the DD scale with known radical constants based on the properties of benzyl radicals revealed a relatively good correlation of this scale with the Fisher data (the correlation coefficient squared is r2=0.92); however, the discrepancies with the sJ , sC , and sJJ arrays are quite substantial (r2=0.33 ± 0.60).Subsequently, this approach has been extended to heteroaromatic p-systems such as pyridine and furan derivatives and some other.135 3. Thermodynamic approaches to the estimation of radical stabilisation. Bond energy as a measure of radical stabilisation Study of the effects of substituents in free radicals is tightly connected with the problem of quantitative evaluation of the energies of dissociation of chemical bonds. The energy of anR7R0 bond is known 136 to be determined by the enthalpy DH0 1 of homolytic dissociation of this bond, giving rise to free radicals R and R0 R+R0 .R7R0 In turn, the DH0 1 value is determined by the standard enthal- pies of formation of RR0, R and R0 DH10= DH0(R)+DH0(R0)7DH0(RR0) . Thus, the relative energies of the homolytic dissociation of bonds can serve as a measure of radicals stabilisation. On the basis of the foregoing, Benson and O'Neal 137, 138 have proposed estimating the stabilisation energy for p-resonance delocalised radicals R(p-CH2) as the difference between the dissociation energies Ed of the corresponding derivatives Es[R(p-CH2)]=Ed[R(CH27H)]7Ed[R(p-CH27H)]. Subsequently, the C7H bond energies have been widely used to estimate the stabilisation energies for carbon-centred radicals.For example, the resonance stabilisation energy of the benzyl radical can be represented as the difference between the energy of the benzylic bond in toluene and the energy of the C7H bond in ethane.45, 139, 140 The enthalpy of dissociation of the C7Hbond in the methane molecule Ed(CH3 ±H)=439 kJ mol71 is used most often as the reference value.140 ± 145 In one of the first studies dealing with this topic, the enthalpy of the isodesmic reaction (i.e., a reaction in which the number and character of bonds do not change on passing from the initial compounds to the products) 146 RH+ CH3 R +CH4 was identified as the stabilisation energy ER of the R radicals 146 ER(R )=DH0 2 =Ed(CH3±H)7Ed(R ± H).A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov Subsequently, stabilisation energies of radicals expressed in terms of Ed , i.e., Es(R )=Ed(CH3±H)7Ed(R ± H), have been widely used for various correlations.138 ± 145 Bordwell et al. 147, 148 have proposed a scale of redox poten- tials IAO, which is also actually based on the relative energies of dissociation of bonds in substituted fluorenes. H H OMe OMe H7 +OMe The potentials were determined using the thermodynamic cycle (pKa) (Eox) H++A7 A +e7 H (Ered) HA A7 H+ + e7 H +A HA (Ed), in which the proton reduction potential Ered is a constant and the sum pKHA+Eox=IAO can be regarded as a measure of relative radical stability of the radical A.The oxidation potentials Eox of substituted fluorenide ions were determined experimentally in DMSO solutions, and the pK values of the conjugate acids were established on the basis of their correlation with Eox; this gave rise to a scale of IAO values for a number of substituents at the 2-, 4- and 7-positions expressed in kJ mol71 and reflecting the ability of these substituents to delocalise the unpaired electron in fluorenes. The application of this approach to 9-substituted fluorenes and to 3- and 4-substituted phenylacetonitriles has made it possible to analyse a wide spectrum of radical-stabilisation and -destabilisation effects.149, 150 Comparison of the IAO values for 4-substituted arylacetonitriles with the sJJ constants within the framework of a two-parameter equation containing the s+-parameter showed that the contributions of the polar and radical constituents to IAO are approximately equal.58 It has been proposed to use the Eox oxidation potentials of 3- and 9-substituted fluorenes 150, 151 and of a-substituted acetone and acetophenone derivatives 152 in DMSO as the basis for determination of the stabilisation energies ERS of the correspond- ing radicals DEd=1.37DpKHA +23.1DEox(A7)=ERS. The resulting values point to a stabilising effect of substituents at the 3-position in substituted fluorenyl radicals, except for F and PhSO2.Substitution into the 9-position both by donors and by acceptors results, as a rule, in system stabilisation. Most of 4-substituents (except for F and CF3) also exhibit pronounced stabilising properties.148 In general, it was concluded 150 that the majority of substituents play a dual role in the stabilisation of a free radical: they destabilise the radical due to the electron- acceptor influence and stabilise it due to delocalisation.In some studies, the radical-stabilisation energy of substituent X was set identical to the covalent component of the dissociation energy of the XR7Z bond, where R is a permanent molecular fragment (for example, the aromatic ring), while R7Z is the `indicator' bond.140, 153 ± 156 The notion `indicator' bond was introduced back in Pauling's studies;151 the stabilisation energy ERS was defined via the relative dissociation energies of bonds in symmetrically substituted molecules ERS=0.5 Ed(XR ± RX)70.5 Ed(HR ± RH).Correlation analysis in the chemistry of free radicals A similar approach has been proposed by Leroy,157, 158 who used the enthalpies of atomisation DHa together with the standard bond energy EAB to define the stabilisation energy Es Es=DHa7SNABEAB , where NAB is the number of AB bonds.This procedure was applied successfully both to free radicals and to diamagnetic molecules. Thermochemical and kinetic investigations of the rupture of the C7C bond have been employed to define the parameter ERS, introduced to reflect the difference between the stabilities of the hydrocarbon radical 16a and the corresponding substituted rad- ical 16b.117, 156, 159 ± 161 Z S Y C Y C X X 16a 16b X, Y, Z are hydrogen atoms or alkyl substituents and S is a functional group.Asubstantial drawback of the approaches in which the radical stabilisation is defined in terms of the relative bond energies and the reason why these approaches are severely criticised is the fact that the energy of homolytic dissociation of a bond is a relative value, i.e., the difference between the energies of the molecule and the corresponding radicals; therefore, the substituent effect can- not be attributed to the properties of the free radical alone.117, 143, 162, 163 It is well known that the dissociation energies of bonds depend on steric effects 116 and on polar effects;164 the presence of numerous correlations between Ed(CH) and the `ionic' constants of substituents s+ (see publications 23, 147, 165) is com- mon knowledge.In our opinion, this virtually rules out a legitimate separation of the polar and radical effects in this type of approach. Moreover, it was shown that in some cases, the effect of substituents can even prevail in the ground state; then the corresponding DEd values reflect destabilisation of the molecule rather than stabilisation of the free radical.163 It has been clearly demonstrated 143 using, among other reasons, vast literature data that relative bond energies cannot be related directly to the stability of radicals. 4. Calculation of the energies of stabilisation of radical centres Apart from experimental methods, there also exist theoretical methods for the determination of group parameters of substitu- ents reflecting their capacity for stabilisation of radical centres.Modern quantum-chemical approximations permit direct calculation of quantitative characteristics of radicals such as the total energy, the standard enthalpy of formation, the energy of the orbital with the unpaired electron and the spin and charge density, which make it possible to judge the stabilising influence of substituents. Many quantitative parameters employed to deter- mine the radical-stabilisation effects in terms of the experimental approaches described above such as the kinetic parameters of free- radical reactions and the overall thermodynamic characteristics, spin densities and rotation barriers in free radicals can be calculated quite reliably by quantum-chemical methods.Cer- tainly, any general description of theoretical approaches requires separate consideration. Within the framework of this review, we shall dwell only on those of them that have served as the base for the introduction of sets (scales) of energetic parameters of substituents reflecting their radical-stabilisation influence and implying consistent utilisation of the LFE principle. In studies by Pasto et al.,166, 167 the change in the total energy of species participating in the free-radical transfer of a hydrogen atom has been identified with the stabilisation energy ERS of the corresponding substituted methyl radical. The ERS values were calculated for a large number of substituents.The captodative 9 effect of radical stabilisation and the influence of the substituents attached to the reaction centre containing an unpaired electron were analysed from the additivity standpoint.166 The comparison of the calculated ERS values with the known scales demonstrated a relatively good quantitative agreement with the IAO parameters for 3- and 9-substituted fluorenes and 4-substituted phenylaceto- nitriles,148 with the relative constant of the thermal rearrangement of 3-aryl-2,2-dimethylmethylenecyclopropanes 57, 82, 83 and a-spin density in 4-substituted benzyl radicals.114 Within the framework of this approach, it was found that the radical-stabilisation effect markedly increases on passing from F- to O- and N-containing substituents.In the series Cl, S, P, the capability for spin density delocalisation increases due to the decrease in the energy gap between the vacant MO of the methyl radical and the MO occupied by the unpaired electron. Study of the effects of substitution with charged (+NR3, +SR2, +PR3) or electro- negative non-charged (CF3, SOR, SO2R) groups showed that they destabilised the radical. In addition, it was found that the energies of stabilisation of the radical centre calculated in terms of the approach proposed are exceptionally sensitive to the confor- mation of the free radical and the corresponding diamagnetic molecule. Isodesmic reactions (see Section II.3) proved convenient for the calculation of ERS(R ).44, 144, 168 ± 173 The enthalpy of hydrogen atom detachment in these reactions is a measure of the energy of stabilisation of the radical centre; the use of this value decreases the errors related to the basis set chosen and to electron correla- tion effects.174 The stabilisation energies of the radical centre ERS correlated with the barriers to rotation around the C7C bond in benzyl radicals were calculated by quantum-chemical methods, as well as the difference between the energies of the conformers correspond- ing to angles of rotation around the s-bond equal to 90 8 and 08.175 ± 177 ERS=DHf(90)7DHf(0). The ERS values thus obtained are well correlated with the parameters D of the biradicals 14 and 15 determined experimen- tally by EPR.127 5. Critical analysis of the existing approaches The attempts at systematisation of the existing radical scales of substituents made previously can be classified, in our opinion, into two main types, namely, the choice of the s -scale describing most accurately the standard homolytic reaction series and the develop- ment of a quantitative approach integrating the accumulated arrays of `radical' constants and combining them into some universal scale. We have already mentioned that the authors of many of the studies presented in the previous Sections proposed their own standard series; the corresponding arrays of the group parameters were regarded as most suitable for developing a scale that could be used as the reference in analogous approaches.However, the search for this optimal scale did not reveal obvious advantages of any of the known sets of radical parameters; therefore, in some cases, it was concluded 9 that development of universal radical constants s is impossible in principle. The attempts to find multiparameter correlations with the use of various combinations of polar and radical scales did not produce a satisfactory general result either. Moreover, the methodology of using the extended Hammett equation for the description of radical-stabilisation effects has been criticised.49 In view of the difficulty of using group radical constants to describe homolytic processes, Hansch and Leo 178 proposed that the polar parameters s should be used for this purpose whenever possible. Exner 179 also suggested that the sáp and sm,p constants suffice for interpretation of the free-radical reactivity.In another study,180 radical-stabilisation effects of substituents are described in terms of the quadratic function s2; this, in principle, contradicts the LFE formalism.10 Several prominent researchers attempted, in a joint review,45 to devise a universal scale of relative radical stabilisation (RRS), based on averaging of the above-mentioned scales of the Creary (sC ),57, 80 ± 84 Jackson (sJ ) 51, 52, 56, 76 ± 79 and Arnold (sa) con- stants,114, 122 ± 125 the kinetic parameters of radical fragmentation of bis-azo derivatives 96 ± 100 and a number of other analogous characteristics of free-radical reactions.45, 180 ± 184 It was suggested that statistical averaging would eliminate the errors inherent in each of basic experimental approaches.In addition, the average group RRS parameters are expected to reflect the degree of additivity of the group influences upon multiple substitution at the carbon radical centre and to describe the effect of captodative radical stabilisation. Positive averaged RRSX values (see Table 2), which imply radical-stabilisation properties, were found for a large number of diverse substituents. The only exceptions were F and CF3, for which the RRSX(F) values were71.4 and70.3, respectively. By means of the scale of averaged RRSX, the researchers 45 were able to identify a number of interesting correlations which point, in particular, to underestimation of the radical-stabilisation properties of electron-withdrawing substituents and overestima- tion of the role of electron donors in terms of some s -approaches.av scale was based 115 on two sets of The averaged radical s EPR characteristics of benzyl radicals taken from the litera- trure 115, 124 and on three `kinetic' arrays, namely, scales of the sC (see Refs 57, 80 ± 84) and sJ (see Refs 50 ± 52, 56, 76 ± 79) constants and kinetic data taken from the literature.101 The sav values (see Table 1) confirmed the radical-stabilisation properties of the vast majority of para-substituents including CF3. Only the averaged constant for p-F was found to be negative (sav =70.02). This deviation was explained by assuming that, under the action of the electronegative F atom, hybridisation of the carbon atom at the 4-position changes somewhat towards sp3; this disturbs the aromaticity of the benzene ring and, hence, destabilises the radical centre.Each of the definitions of the radical s constants character- ised in this Section suffers from its own specific disadvantages. They were noted above whenever appropriate. In addition, the methods of description of the radical effects of substituent can be subjected to a common criticism. It is expedient to arrange critical remarks in accordance with the above classification. 1. Kinetic methods. It is known that the classical s-constants of electron-withdrawing substituents, which stabilise an electron- enriched reaction centre, are positive, whereas electron-donating groups, which stabilise electron-deficient systems, have negative polar constants.In turn, the sign of the parameter r of the correlation equation reflects the character (either electrophilic or nucleophilic) of the reaction, while the magnitude of r shows the degree of charge separation in the transition state. It is commonly known that the polar constants of substituents correlate equally adequately with the properties of the transition state and the ground state (numerous polar scales are based on the physico- chemical, for example spectroscopic, properties of neutral mole- cules). Thus, successful description of energy characteristics of heterolytic processes in terms of group constants is normally explained by assuming either that the substituent effects in the transition and ground states are correlated or that the latter can be neglected.The kinetic methods of determination of substituent effects in homolytic processes also deal with the difference between the energy of the ground and radical-like transition states. However, a significant specific feature of free-radical reactions is that the natures of the initial species (or products) and the transition state in any homolytic process are fundamen- tally different because of the presence of an unpaired electron; the effects of substituents on the energies of the ground and transition states differ not merely quantitatively, as in the case of heterolytic processes, but also qualitatively.Furthermore, the numerous examples cited in the preceding Sections point to the importance of substituent effects in the ground state of homolytic processes, which precludes the possibility of neglecting them. In addition, A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov even if the polar interactions in the ground state are assumed to be proportional to those in the radical-like state, their role in delocalisation of the proper unpaired electron still remains obscure. Strictly speaking, the magnitudes of radical s parameters established by kinetic methods often reflect the differences between the influence of substituents on the initial and transition states of a particular reaction but not the effectiveness of delocal- isation of the unpaired electron by one or another substituent.In this connection, the numerous examples of successful use of polar constants alone for the description of free-radical processes seem quite obvious and the lack of correlation between radical scales is quite logical. Thus, reasonable separation of the effects related to charge stabilisation and to delocalisation of the unpaired electron within the framework of kinetic approaches appears unlikely, if achievable at all. It is also worthy of note that the role of other factors (steric effects and, especially, solvent effects) has been interpreted fairly arbitrarily in most of the approaches considered. As a rule, the authors assumed that the homolytic mechanism of the standard reaction allows the solvent effects to be completely neglected.However, as has already been noted, in reality, none of the kinetic approaches allows complete elimination of the influence of polar interactions (which can depend substantially on the properties of the medium); this casts doubt on the proper methodology of determination of many s -scales. 2. Spectroscopic methods. Methods based on the use of EPR for determination of the spin density distribution are free from the drawbacks associated with the substituent effects in the corre- sponding molecules. Meanwhile, the question of whether spin density delocalisation follows a linear correlation with the stabi- lisation energy of a free radical remains relevant.In addition, it is unclear to what degree the spin density distribution is governed by the delocalisation contribution and to what degree, by the spin- polarisation contribution.45 And, finally, what is the role of polar effects (for example, resonance effects) in the spin density distri- bution? Is it proper to consider them insignificant and related exclusively to charge stabilisation? In our opinion, the following circumstance is also rather important. Let us assume that the spectral s -constants do actually reflect the capacity of substituents for delocalisation of the unpaired electron. Then it is clear that valid considerations about the mechanisms of delocalisation of an unpaired electron by substituents can be constructed on their basis and the s values can be used to verify the adequacy of similar approaches to the solution of problems for which the correlation analysis methods are meant. However, the scope of applicability of these spectral radical scales still remains vague, while their predictive capacity and practical application hardly possess considerable advantages.In any case, when describing real homolytic reaction series, the presence of polar interactions (which are always quite probable, as we have repeatedly emphasised above) implies the use of a two- parameter correlation equation containing both radical and polar constants. One or another polar scale can be preferred and the relationship between the polar and radical components of the stabilisation effect can be identified only on the basis of a statistical selection procedure.From a practical point of view, this brackets the s constants obtained by spectroscopic methods with those determined by kinetic methods. 3. Thermodynamic methods. The approaches based on the use of thermodynamic methods are criticised especially vigo- rously. As has been mentioned above, determination of radical- stabilisation effects in terms of thermodynamic parameters (bond energies) corresponding to diamagnetic substrates does not permit one to rule out the substituent effects related to the molecules or to distinguish the proper radical stabilisation from polar or steric factors. Strictly speaking, these approaches are rather suitable for discussing the relative effects of substituents on the energies of covalent bonds; this, in itself, is a complex problem not ultimately solved.It is also noteworthy that, within the framework ofCorrelation analysis in the chemistry of free radicals thermodynamic approaches, the radical stabilisation effect is largely replaced by the notion of radical stability. Strictly speak- ing, this is not the same; below we shall consider this point in more detail. To conclude this section, it can be stated that none of the existing methods of sr-description of substituent effects in free- radical processes is free from serious drawbacks and, as a rule, each method operates within a narrow reaction series. The lack of correspondence between radical scales and the different in kind interpretations of the radical-stabilisation properties of the same substituents in terms of different approaches make difficult the understanding of the physical meaning of radical constants and preclude the possibility of their joint application. It cannot be ruled out that the correlation analysis formalism cannot, in principle, be applied in full measure to the description of homolytic processes because the additivity of group interac- tions is there violated. An especially clear example is the captoda- tive stabilisation effect, or push ± pull effect, repeatedly mentioned above.4. Captodative effect. The existence of an extra-stabilisation effect peculiar to bifunctional radicals was first assumed by Dewar.185 A quantitative proof of the unusual stability of these radicals was later presented in studies by Balaban et al.,186, 187 who used the term `push ± pull resonance.' Later, Katritzky et al.188 ± 190 arrived at the conclusion that radical centres bearing simultaneously an electron-donating and an electron-withdraw- ing group are subject to an extra-stabilisation effect, which was called merostabilisation (later, captodative effect).45,191 ± 194 Asimple substantiation of the captodative stabilisation can be derived from the numbers of contributing structures [in the example presented below, there are two structures for the amino- (17) or the cyano-derivative (18)] corresponding to monosubsti- tuted radicals and to a disubstituted radical containing both electron-donating and electron-withdrawing groups [five contri- buting structures are presented for the amino-cyano-substituted radicals 19].+ N C N C¡, 17 C C N , C C N 18 + 7 N C N C N C N C N C N C 19 C C N +C N+ C N¡. N¡ For disubstituted radicals containing either only amino- (20) or only cyano groups (21), three contributing structures can be proposed + 7 7 C C N N N C N N N+ , 20 N C C C N N C C C N 21N C C C N . Thus, stabilisation of these species due to delocalisation would be somewhat weaker than is expected based on the sum of the substituent effects in the monosubstituted analogues. The over-additive stabilisation effect in radical species con- taining both electron-donating and electron-withdrawing groups has been repeatedly confirmed experimentally.The enhanced reactivity of captodative alkenes has been noted in radical 193 ± 199 and [2+2]-cycloaddition 45, 199 ± 202 reactions. The captodative acceleration was considered to be the reason explaining the results 11 obtained in studies of cyclisation of 6-substituted hex-5-en-1-yl radical,203 homosolvolysis of some alkyl bromides on treatment with di-tert-butylnitroxide,204 thermal rearrangement of substi- tuted 2-arylmethylenecyclopropanes,205 isomerisation of diaste- reomeric substituted cyclopropanes 206, 207 and thermal homolysis of the C7C bond in hexa-1,5-dienes 207 and dibenzyls.208, 209 EPR data for substituted benzyl radicals point to enhanced stabilisation of those radicals that contain both electron-donating and electron-withdrawing substituents, whereas two identical substituents decrease radical stabilisation.114 Analysis of the barriers to internal rotation and the energy barriers to E,Z- isomerisation of substituted allylic radicals determined from EPR data also attests in favour of captodative interactions.210 Study of the barriers to rotation around the C7N bond in substituted aminoalkyl radicals has led to similar conclusions.211 In several publications,161, 212, 213 the captodative effect was sub- stantiated from the standpoint of orbital views.Calculations of the stabilisation effects in free radicals also predict an enhanced stabilisation of captodatively substituted derivatives.45, 163, 214, 215 However, a number of experimental and theoretical studies have not elucidated any significant distinctive features of capto- datively substituted radicals and demonstrated strictly additive influence of the corresponding substituents at a radical reaction centre.216 ± 219 Moreover, some researchers cast doubt on the existence of an additional captodative stabilisation.Within the context of the present consideration, we would only like to mention that, under the assumption of the existence of captoda- tive stabilisation of free radicals, the use of additive correlation equations based on LFE and polylinearity principles to describe homolytic processes should be subject to certain, perhaps quite substantial, constraints. Thus, analysis of the published data available to date provides grounds for the following conclusions.1. The classical polar constants s are not fully applicable to the description of free-radical processes and do not reflect the radical-stabilisation effects of substituents. In all probability, one can speak about a disproportion of substituent effects in hetero- lytic and homolytic processes. Although quite a few examples of successful use of polar constants in free-radical chemistry have been reported, the existing scales of specific radical constants s are not general. The lack of correspondence between the scales and vagueness of their physical meaning might be due to the constrains inherent in the use of the LFE principles and correla- tion analysis in free-radical chemistry and violation of the additvity of the group influence in paramagnetic systems rather than to the drawbacks of the methods of their determination.2. It is obvious that an approach, new in principle, to the description of substituent effects in free-radical systems needs to be developed. It is important that this approach should possess predictive capacity and provide a quantitative estimate of the character of interaction of substituents with the radical reaction centre. However, it is quite probable that the physical nature of this interaction would not be clarified completely but it would be possible to obtain a satisfactory quantitative description of the structure ± reactivity relationship as applied to the chemistry of free radicals.III. The use of r72 analysis in free-radical chemistry 1. Modelling of inductive and steric effects Previously, we have developed quantitative procedures for deter- mination of the steric and inductive effects of substituents in terms of discrete atomic contributions. Detailed description and theo- retical substantiation of the models proposed, aspects of their practical use and the inductive electronegativity concept based on them have been presented in our previous reviews.2±6 In the context of this review, we considered it pertinent to mention the main theses of these approaches.12 Steric interactions were determined in terms of the model of frontal steric effect in which the steric effect of a substituent is represented as a result of mechanical shielding of the reaction centre by the surrounding atoms ia1 Xn R2iR0S a , (11) 4r2i where R0S is the steric constant, n is the number of atoms in the substituent, Ri is the radius of an ith atom and ri is the distance from the ith atom to the reaction centre.It should be emphasised that in terms of this approach, the steric effect of any substituent at any reaction centre can be predicted with high accuracy on the basis of only fundamental parameters (the size and the distance to the reaction centre) of the atoms forming the substituent. The R0S parameters calculated for a broad range of the most frequently encountered groups follow a good correlation with the Taft steric constants (N=35, R=0.9854, S=0.141).In the model of inductive effect, the inductive constant s* of an n-atomic substituent was represented at the atomic additivity level (12) r2iia1 s aXn sAOiU , where sA is an empirical constant introduced in the model of inductive effect and reflecting the ability of an atom to exhibit the inductive effect, which depends on the nature and valence state of the atom. The sA values have been established for a wide range of elements; the inductive constants calculated theoretically using these values (altogether 426 substituents) have formed a high- quality correlation with the corresponding experimental data (N=426, R=0.9910, S=0.190). The practical use of this additive approach in the description of reactivity and investigation of the mechanisms of reactions involving organic and heteroorganic compounds proved fairly successful.This has also contributed to the solution of a number of important theoretical problems related to inductive interactions such as the inductive effect of alkyl substituents, the presence or absence of linearity in the inductive effects of substituents on carbon and heteroatom reaction centres and some others. The models developed make it possible to describe quantitatively only the inductive and steric effects; no approach based on the modelling principle for estimation of resonance interactions has been devised yet. Nevertheless, as shown in our study,4 the additive model of inductive effect describes rather adequately the electronic interactions in various conjugated systems and only some of them, subjected to the influence of direct polar conjuga- tion, can provide exceptions.2. Combinational approach. r72-Analysis. Ionisation energies of amines The new topological approach developed on the basis of the above models, which allows the substituent effect to be expressed in terms of discrete atomic contributions, was first reported in our publication and called r72-analysis.220 Since both the steric and inductive constants were expressed in Eqns (11) and (12) as functions of 1/r72, the two-parameter Taft equation (13) Y a r i i Xs a dXEs can be represented in terms of discrete atomic contributions (14) rc¢§i i6arc Y ¢§ Y0 aXN¢§1 ei , r2 where N is the number of atoms in the molecule, rc is the atom chosen as the reaction centre, rrc7i is the distance between atom i and the reaction centre.The dependent parameter Y can be A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov represented by any physical value which is used in terms of a general correlation equation (13) (the logarithm of the rate or equilibrium constant, the reaction or activation energy, etc.), Y0 is the same parameter for a compound chosen as the standard in this reaction series, and e is a parameter reflecting the capacity of an atom of a definite type for exhibiting intramolecular effects determining the Y values. The approximation we used permits one, first of all, to verify whether it is possible, in principle, to introduce the operational atomic constants ei corresponding to atoms of different types and depending on the nature and the valence state.The next step is to determine their physical meaning. The formalism of this approach implies that each atom encountered in all the molecules of the reaction series can, in principle, be regarded as a hypothetical reaction centre. In this case, for each molecule contained in the reaction series, the other N71 atoms are treated as a single sub- substituent. After the reaction centre for a given series has been chosen, the matrix of sums 1 , r2 k k rc¢§m X rc¢§mk corresponding to the types of atoms present should be composed. A table should be made up, containing N vertical matrix elements (rows), where N is the number of molecules in the reaction series, and M horizontal elements (columns),where M is determined by the types of atoms represented in the molecules of the series. The k value in the matrix of sums corresponds to the number of atoms of type m in molecule n, and r2 are the distances between type m atoms and the reaction centre rc in molecule n.If no type m atoms are present in molecule n, the corresponding matrix element is taken to be zero. As an example, Table 3 gives the r72-matrix for the reaction series including the MeH2C , ClH2C, and Me(NH2)HC radicals in which the carbon bearing the unpaired electron is chosen as the reaction centre. In real calculations, the number of horizontal elements should exceed the number of vertical elements; then the columns of this matrix can be regarded as sets of independent arguments and the Y7Y0 array can be regarded as an array of dependent values of multiparameter linear regression (14).Table 3. r72-Matrix for the reaction series containing the MeH2C , ClH2C and Me(NH2)HC radicals. Type of atom Radical H C(sp3) Cl N(sp3) 0 0 MeH2C 1 1:542 2 3 1:092 a 2:162 2 0 0 ClH2C 1 1:762 1:092 0 Me(NH2)HC 1 1:462 1 1:542 1 3 2 1:092 a 2:162 a 2:042 Thus, if the corresponding multiparameter correlation can be established with a satisfactory accuracy, its linear coefficients are the operational atomic constants ei corresponding to particular types of atoms. It is clear that this scheme should be effective in the description of those reaction series that can be analysed quantita- tively using inductive and steric group constants.The method developed for the description of substituent effects has several obvious advantages over classical correlation analysis. First, it is free from the restrictions associated with the choice of an appropriate scale of substituents because it deals directly with interatomic distances and is conformationally sensi- tive. Second, the use of a simple mathematical apparatus allows one to analyse quickly and effectively indefinitely large sets ofCorrelation analysis in the chemistry of free radicals parameters. Third, within the framework of this model, it becomes possible to consider all the potential reaction centres of the series, which can provide additional information on the mechanism of the process under study.This is important in those cases where interpretation of the mechanism does not appear unambiguous and variation of the reaction centre could permit decision in favour of one of the most probable mechanisms. We implemented the algorithm outlined above as a product called RMATRIX, which was developed on the basis of the MATLAB program.221 The RMATRIX program allows import- ing of intramolecular distances from HyperChem or from similar files containing data on the spatial structure of the molecules of a reaction series; then it composes the r72-matrix corresponding to the reaction centre chosen for each molecular series, and, finally, it establishes statistically the operational atomic increments e for the series.3. The physical meaning of the operational atomic parameters A drawback of r72-analysis is that it does not allow direct consideration of resonance interactions because they cannot be described certainly by any distance function. However, a more substantial problem is that the physical meaning of the opera- tional atomic parameters ei, defined by Eqn (14), remains vague and does not provide the possibility of resolving the substituent effects into the inductive and steric components. The analysis of the ei values presented below is pertinent in this connection. The correlations established previously in terms of the steric and inductive models can serve as the basis for this consideration.Thus it has been found 4 that the sA constants for a broad range of elements are correlated with the difference between Pauling's electronegativities Dwi ¡À rc of a given element A and the atomic reaction centre (rc) (this difference reflects the ability of atomAto displace electron density) and with the squared covalent radius of the A atom (which reflects its capacity for charge delocalisation) 4, 5, 222 sA �� 7:84Dwi¡¦rcR2i . The back calculation of the w values using this relation makes it possible to introduce a new scale of `inductive' electronegativ- ities, which is purely empirical because it is based on the inductive constants describing a huge array of reaction series.4, 5 This scale is, by definition, in good agreement with Pauling's electronegativ- ities, except that for carbon.According to the `inductive' scale, the electronegativity of carbon is 2.1. This value appears to be more plausible than wP=2.55 proposed in the Pauling scale.2, 223, 224 The latter value implies that carbon should be more electro- negative than, say, phosphorus (wP=2.2) or iodine (wP=2.4), which is not the case in reality. The low polarity of the C7Hbond also indicates that the Pauling wP value for carbon is overesti- mated. Subsequently, a scale of group inductive electronegativ- ities and the concept of inductive chemical hardness, which interpret a number of widely used reactivity indices using simple geometrical characteristics of bonded atoms, have been developed in terms of this approach.2 These concepts were considered in detail in our review 2 and in a number of publications.223 ¡À 231 On the basis of established correlations, the Taft inductive constant can be expressed in terms of fundamental characteristics of the atoms of substituents and the reaction centre, namely, electronegativities, radii and interatomic distances (15) r2ii s �� 7:84XDwR2i.By superposition of Eqns (11) ¡À (14), the atomic parameters ei can be represented as the sum of inductive and steric constituents(16) ei �� aDwi¡¦rcR2i �¢ bR2i . Evidently, if a satisfactory correlation of type (16) has been established, it becomes possible not only to calculate the unknown ei values on its basis but also to express the dependent parameters 13 Y in terms of inductive and steric Taft constants as an ordinary two-parameter equation (13).If the `inductive' electronegativity of the reaction centre atom is unknown, the e value can be found using the two-parameter correlation (17) ei �� a0wiR2i �¢ b0R2i , where the coefficient b0 includes the wrc value. It should be emphasised that correct separation of the inductive and steric effects requires that the nature (electronega- tivity) of the reaction centre be known exactly and, in any case, it implies certain assumptions. Nevertheless, the corresponding atomic operational constants ei still can be employed to predict the unknown Y values for related molecular systems consisting of atoms with known ei even in those cases where correlations (15) and (16) cannot be established. Except for the inapplicability for the description of the resonance effect, the method under discussion does not have any serious limitations and can be used successfully even in those cases where the standard empirical scales are ineffective.The quantita- tive description of the vertical and adiabatic ionisation potentials of amines performed in our study exemplifies the practical application of the r72-scheme.221 Previously, the dependence of the ionisation potentials of a limited range of amines on their structure has been interpreted with utilisation of a large number of independent parameters both those reflecting particular inductive, resonance and polarisation effects and those chosen rather arbitrarily.232 7e +N NWe attempted to consider the ionisation potentials of amines in terms of the unified approach developed and composed the corresponding r72-matrix in which the nitrogen atom was chosen as the reaction centre.The adiabatic and vertical ionisation potentials (I ad, I vert) of amines in the gas phase, taken from a publication,233 were analysed in terms of the parameters of the basic equation (14). As a result, reliable multiparameter correla- tions were established for the sets of adiabatic and vertical potentials IRvert 3N �� �¢ const1 (R=0.954, S=0.331, N=287), (18) XN¡¦1 i vert i i r2i IRad XN¡¦1 i ad ir2ii��1 i i 3N �� �¢ const2 (R=0.960, S=0.341, N=231), (19) where N is the number of atoms in the amine molecule and i vert and i ad are the operational atomic parameters reflecting the capacity of the atom of a definite type for participation in intra- molecular interactions, which determine the I vert and I ad values, respectively.The following fact attracts attention: although we analysed arrays of the absolute values of I ad and I vert not referred to any standard, the free terms of multiparameter correlations (18) and (19) determined statistically actually reproduced the correspond- ing ionisation potentials of the ammonia molecule. The values of the i ad/vert parameters were then analysed using Eqn (16); the following correlations were identified: (20) i ad=4.55 (w72.79)R2, (21) i vert=4.38 (w72.98)R2. Thus, the correlations found allow the calculation of the unknown parameters i ad/vert and, hence, the previously unknown ionisation potentials of amines from atom electronegativities and covalent radii.Moreover, if the role of steric effect during electron transfer is assumed to be insignificant (which appears quite reasonable), values of 2.790.7 and 2.980.7 found using these14 relations are in a fairly good agreement with the inductive electro- negativity of nitrogen (2.56, see Ref. 223). 4. Ionisation energies of free radicals The possibility of quantitative determination of the energies of oxidation of amines to the corresponding radical cations using the approach we developed points to its adequacy and applicability to free-radical processes.As noted above, the examples of quantita- tive interpretation of the reactivity of free radicals currently available are limited, as a rule, to aromatic systems. We attempted to apply the r72-analysis to electron transfer, which is one of the least studied homolytic reactions from the standpoint of `radical' effects of substituents. We did not restrict ourselves to narrow series of aromatic compounds but considered single-electron processO- centred radicals both belonging to aromatic and aliphatic ser- ies.233, 234 The single-electron ionisation potentials of free radicals in the gas phase were taken from a database 235 and analysed in terms of our approach.a. Carbon-centred radicals In accordance with the approach developed, the ionisation potentials (I ) and electron affinities (Ae) of carbon-centred radicals were analysed using the equations i and IR ¢§ IMe a r2ii(R Xea AeOR U ¢§ AeOMe U a i(R Xe¢§ in which the I and Ae values for the methyl radical are included as reference values provided that the carbon atom bearing the unpaired electron is taken to be the reaction centre. Table 4. Operational atomic parameters eaemp found from experimental ionisation potentials and the corresponding eacalc values calculated using correlation (17). Atom Radical centre CNO C(arom.) S CHC(arom.) C(sp2) C(sp) Cl Br FSONN(sp) CHNC(arom.) CHOCl FBr ICHSFC(arom.) (22) i (23) , r2i R2 wi 0.593 0.090 0.449 0.449 0.390 0.980 1.299 0.409 1.082 0.436 0.490 0.3025 0.593 0.090 0.490 0.449 0.593 0.090 0.436 0.980 0.410 1.300 1.769 0.449 0.593 0.090 1.082 0.410 0.449 2.10 2.10 2.45 2.25 2.65 3.09 2.97 3.93 2.67 3.05 2.56 6.76 2.10 2.10 2.56 2.45 2.10 2.10 3.05 3.09 3.93 2.97 2.80 2.45 2.10 2.10 2.67 3.93 2.45 A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov The multiparameter correlations (22) and (23) were estab- lished with high accuracy.The operational parameters e+ and e7 found from relations (22) and (23) are presented in Tables 4 and 5 together with the corresponding values for the inductive electro- negativities and the covalent radii of atoms.By comparing them in terms of a type (17) relation, we expressed the e+parameters in the formeai a O1:09 0:33UwiR2i ¢§ O5:49 0:97UR2i (the O, N and S atoms were not included in the correlation) or eai a 1:09Owi ¢§ 5:04UR2i . Thus, the ionisation potentials of C-centred radicals in the gas phase can be expressed in terms of fundamental parameters of atoms Owi ¢§ 5:04UR2i. I a IMe a 1:09 r2iia1 XN Relations (24) and (25) demonstrate that the vast majority of atoms [except highly electronegative ones such as sp-hybridised N atom (w=6.76)] introduced in the environment of the C reaction centre decrease the corresponding ionisation energy relative to that of the methyl radical.The deviation of the atomic parameters e+ for O,Nand S atoms from the general pattern of dependence is apparently due to the resonance effect, which cannot be described from the standpoint of the given approach, as has been repeatedly mentioned above. To elucidate the reasons for this deviation, a special detailed analysis is required; we plan to perform it subsequently. In addition, analysis of the predicted ionisation potentials demonstrates a substantial deviation of the Ipred value for the methyl radical, which is a typical problem for this type of approach. Since the methyl radical was chosen as the reference species (DI=0), its e+ parameter should, by definition, be equal eaemp eacalc 71.860.11 70.250.04 71.450.14 71.780.14 70.800.39 71.910.19 72.730.23 70.780.10 76.610.58 73.770.27 76.150.26 5.888 76.2021.361 70.2170.485 75.9962.652 71.9341.088 75.4070.534 0.0220.327 73.6630.799 76.3071.052 70.4980.748 78.9421.244 714.251.51 74.0710.348 73.3701.831 0.0031.089 78.6802.598 70.8141.848 71.90 70.29 71.27 71.37 70.55 72.09 72.94 70.50 72.78 70.95 71.33 0.562 75.70 70.87 74.46 74.14 76.22 70.94 72.93 76.45 71.34 79.17 713.66 74.09 74.57 70.69 77.25 71.88 73.19 72.4290.972 (24) (25) eaemp ¢§ eacalc 0.04 0.04 70.18 70.41 70.25 0.18 0.21 70.28 73.83 72.82 74.82 5.326 70.502 0.653 71.536 2.206 0.813 0.962 70.733 0.143 0.842 0.228 70.59 0.019 1.2 0.693 71.43 1.066 0.761Correlation analysis in the chemistry of free radicals Table 5.Operational atomic parameters e¢§emp found from experimental electron affinities and the corresponding e¢§calc values calculated using correlation (17). Atom Radical centre CNO C(arom.) S CHC(arom.) C(sp2) Cl Br FOCHC(arom.) CHOCl FBr ICHSOC(arom.) or nearly equal to zero, which is not always fulfilled. The e+(H) value found statistically is markedly smaller than zero, as well as the calculated DI(CH3) value. Taft 236 was faced with similar difficulties when using the methyl group as the reference for the scale of inductive constants s*.There are also other factors determining the so pronounced difference between the experimental and calculated ionisation potentials of methyl radicals in the construction of a scale of radical constants. Detailed analysis of these factors is beyond the scope of this review. When considering the e7 parameters found from the electron affinities of carbon-centred radicals, the following correlation was established: e¢§i a O1:64 0:43UwiR2i ¢§ O3:17 1:26UR2i or e¢§i a 1:64Owi ¢§ 1:93UR2i . As for ionisation potentials, this correlation permits the electron affinity parameters of carbon-centred radicals to be expressed at the atomic level on the basis of fundamental atomic characteristics, namely, electronegativities, sizes and interatomic distances Ae a AeOMe U a 1:64 ia1 XN The ionisation potentials and electron affinities of carbon- centred radicals calculated from the atomic inductive electro- negativities and covalent radii are listed in Tables 6 and 7; the statistical parameters of correlations are presented in Table 8, and the operational parameters e+ and e7 are given in Tables 4, 5.b. Deviations from the general dependence As noted above, the presence of substantial resonance interactions in radicals can result in deviation of their characteristics predicted in terms of the additive scheme in question from the correspond- R2 wi 0.593 0.090 0.449 0.449 0.980 1.299 0.409 0.436 0.593 0.090 0.449 0.593 0.090 0.436 0.980 0.410 1.300 1.769 0.449 0.593 0.090 1.082 0.436 0.449 2.10 2.10 2.45 2.25 3.09 2.97 3.93 3.05 2.10 2.10 2.45 2.10 2.10 3.05 3.09 3.93 2.97 2.80 2.45 2.10 2.10 2.67 3.05 2.45 (26) (27) Owi ¢§ 1:93UR2i.r2i e¢§emp e¢§calc 70.260.14 70.010.04 0.600.06 0.510.37 2.220.17 2.080.23 1.040.08 70.160.44 70.3960.255 70.0080.093 0.6870.091 70.1040.155 0.0250.098 71.6540.257 1.3280.340 0.9360.242 1.8390.402 2.3380.488 0.3790.111 70.410.386 0.17 0.03 0.38 0.24 1.87 2.22 1.35 0.80 70.39 70.059 0.69 0.19 0.029 0.66 1.527 1.07 1.83 2.11 0.34 70.008 70.001 72.09 71.36 70.52 70.120.261 71.840.457 71.950.482 70.020.236 ing experimental values.An alternative and, perhaps preferable, explanation of most of the deviations observed in the description of redox properties of carbon-centred radicals is that in some radicals, the carbon atom bearing the unpaired electron is not the ionisation centre. For example, in the case of ionisation potentials, the opera- tional atomic parameters e+ for S, N and O atoms deviate from the linear dependence (24), and the effects of the corresponding substituents observed experimentally exceed those predicted based on the e+ values. The experimental values of the ionisation potential Iexp might correspond to the I value of a heteroatom (S, N, O) present in the carbon-centred radicals and having a lone electron pair rather than to the I value of the radical centre.A similar deviation from the linear dependence has been observed in a study of the single-electron reduction potentials of arylmethyl- chalcogenide radical cations in aqueous solutions.40 In addition, electron-withdrawing substituents (NO2, CN, Hal) are able to enter into reduction processes and, hence, only for some of the carbon-centred radicals considered, do the Ae values correspond completely to the ionisation of the radical centre. For some strong electron acceptors, a saturation effect also cannot be ruled out. Thus, most of the observed deviations of the predicted ionisation potentials and electron affinities of substituted car- bon-centred radicals are most likely due to non-homogeneity of the data arrays considered.It should also be borne in mind that the ionisation potentials and the electron affinities of radicals match the energy differences between the radical and the corre- sponding cation in the former case and between the anion and the radical in the latter case. Hence, the energy effects of substituents described by Eqns (22) and (23) can refer both to the radical and to the corresponding ion. The positive values of e+ and e7 imply that the radical is stabilised by the substituent in question more efficiently than the cation as compared with the CH3/CHa3 pair (for ionisation potentials), and that the anion is stabilised by the given substituent more efficiently than the radical, compared with the CH¢§3 /CH3 system (in the case of electron affinity).Note that, the use of the notion of relative stabilisation can also imply lesser 15 e¢§emp ¢§ e¢§calc 70.43 70.04 0.22 0.27 0.35 70.14 70.31 70.96 70.006 0.051 70.003 70.294 70.004 72.314 70.199 70.134 0.009 0.228 0.039 70.403 70.121 0.263 70.596 0.50016 Table 6. Ionisation potentials (in eV) of C-, S-, N- and O-centred radicals determined experimentally (Iexp), predicted (Ipred) using relation (14) and calculated (Icalc) from Eqns (25), (28), (30), (32). Radical 3H5) MeNHCH2 Me(NH2)CH Me2NCH2 Me2(NH2)C (H2C=CH)2CH Me2(HC:C)C (cyclo-C5H9) HSCH2 MeSCH2 H3C Me3C MeEtCH PrnCH2 PriCH2 MeCH2 Me2CH EtCH2 HOCH2 Me(HO)CH MeOCH2 Me(MeO)CH NCCH2 H2NCH2 Cl3C Cl2HC ClH2C F3C F2HC FH2C Br3C Br2HC BrH2C MeCF2 MeCHF H2C=CHCH2 (cyclo-C CH2=C(Me)CH2 (H2C=CH)MeCH (cyclo-C4H7) H2C=CHCH2CH2 (cyclo-C5H9) H2C=CHCMe2 H2C=CHCHEt MeCH=CHCHMe H2C=CHCH(Me)CH2 H2C=C(Et)CH2 (C6H5) PhCH2 HO (ref) a HOO ClO FO BrO IO MeO EtO PrnO PhO HS (ref) a MeSS FS MeS EtS PrnS Iexp Ipred 6.1 5.72 5.74 4.98 7.3 7.44 7.22 7.32 7.07 9.21 77.41 87.81 8.47 7.74 8.14 7.51 6.77 7.13 6.4 9.9 6.45 7.99 8.4 8.8 8.57 8.79 97.59 8.13 8.67 8.05 8.26 8.25 7.87 7.95 7.52 7.41 8.05 7.11 6.78 7.19 7.39 7.71 7.66 8.31 7.24 13.04 11.35 10.89 12.78 10.46 9.66 10.39 9.47 9.1 8.56 10.43 8 10.16 9.38 8.92 8.73 5.9 5.7 5.7 5.4 7.25 7.44 77.54 6.85 9.84 6.7 7.25 8.02 7.93 8.12 7.37 8.09 7.56 6.85 6.9 6.5 9.9 6.29 8.06 8.32 8.75 8.76 8.78 9.04 7.5 8.3 8.61 7.92 7.93 8.18 8.18 7.9 7.49 7.54 8.04 7.21 7.13 7.3 7.07 87.9 8.32 7.24 13.017 11.35 10.885 12.78 10.46 9.66 10.72 9.11 9.2 8.56 10.429 8 10.16 9.262 9.6 8.2 A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov Iexp7Ipred 70.20 70.02 70.04 0.42 70.05 0 70.22 0.22 70.22 0.63 70.3 70.16 0.02 0.12 70.36 70.37 70.05 0.05 0.08 70.23 0.1 0 70.16 0.07 70.08 70.05 0.19 70.01 0.04 70.09 0.17 70.06 70.13 70.33 70.07 0.31 70.05 70.03 0.13 70.01 0.1 0.35 0.11 70.32 0.29 0.24 0.01 70.01 70.02 000000.33 70.36 0.11 0000 70.12 0.68 70.53 Icalc Iexp7Icalc 8.23 7.86 7.86 7.11 7.73 7.51 7.38 8.44 8.19 9.11 6.88 7.28 7.88 7.68 8.37 7.62 8.03 8.82 8.07 8.43 7.68 9.18 8.6 7.82 8.25 8.68 9.03 9.06 9.08 7.42 7.99 8.55 8.31 8.34 8.42 7.77 8.11 7.67 7.29 8.04 6.98 6.93 7.33 7.54 7.69 7.81 8.46 7.42 11.99 11.45 10.84 12.38 10.4 9.8 9.31 8.13 7.62 8.14 10.04 8.05 9.81 8.64 7.93 7.61 72.33 72.16 72.16 71.71 70.48 70.07 70.38 70.91 71.34 0.73 70.18 70.03 0.14 0.25 70.25 70.25 0.06 71.25 71.22 71.53 71.18 0.72 72.31 0.24 0.07 0.07 70.27 70.28 70.04 0.08 0.31 0.06 70.39 70.41 70.24 0.41 70.21 70.18 0.25 00.23 0.2 70.03 70.47 0.31 0.09 70.14 70.19 1.024 70.095 0.048 0.399 0.064 70.137 1.406 0.978 1.581 0.425 0.386 70.052 0.35 0.625 1.673 0.594Correlation analysis in the chemistry of free radicals Table 6 (continued).Radical PhS H2N (ref) a MeNH Me2N PhNH H2N7NH a The reference species in the corresponding reaction series. Table 7. Electron affinities (in eV) of C-, S-, N- and O-centred radicals determined experimentally [Ae(exp)], predicted [Ae(pred)] using relation (14) and calculated [Ae(calc)] from Eqns (27), (29), (31) and (33).Radical H3C MeCH2 MeCH2CH2 Me2CH MeEtCH Me3C H2C=CHCH2 PhCH2 Ph2CH Ph3C F3C F2HC FH2C Cl3C Cl2HC ClH2C Br3C BrH2C CF3CF2 MeOCH2 HO (ref) HOO ClO FO BrO IO MeO EtO PrnO PhO PriO ButO HS (ref) MeSS MeS EtS PrnS PhS HSS HOS PriS ButS H2N (ref) MeNH Me2N PhNH PhMeN Ph2N Iexp Ipred 8.63 10.36 7.55 4.75 8.26 7.61 8.63 10.78 6.7 5.17 8.26 7.61 Ae(pred) Ae(exp) 0.05 70.05 70.09 70.16 70.2 70.27 0.36 0.62 1.2 1.77 1.76 1.19 0.62 2.23 1.5 0.78 1.79 0.63 1.76 70.02 1.83 1.08 2.28 2.27 2.35 2.38 1.62 1.72 1.79 2.25 1.84 1.91 2.25 1.80 2.12 2.05 2.02 2.26 1.86 1.65 1.98 1.90 0.77 0.60 0.43 1.57 1.40 2.37 0.08 70.26 70.07 70.32 70.12 70.16 0.36 0.91 1.36 1.56 1.84 1.21 0.20 2.17 1.58 0.80 1.73 0.82 1.81 70.02 1.83 1.08 2.28 2.27 2.35 2.38 1.62 1.72 1.79 2.25 1.84 1.91 2.31 1.75 1.87 1.95 2.00 2.26 1.90 1.65 2.02 2.07 0.78 0.45 0.38 1.70 1.65 2.18 Iexp7Ipred 00.43 70.85 0.43 00Ae(exp)7Ae(pred) 0.03 70.21 0.02 70.16 0.08 0.11 0.00 0.29 0.16 70.21 0.08 0.02 70.42 70.06 0.08 0.02 70.06 0.19 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 70.05 70.25 70.10 70.02 0.00 0.05 0.00 0.04 0.16 0.01 70.15 70.05 0.13 0.25 70.19 17 Icalc Iexp7Icalc 0.81 1.698 70.003 0.846 3.442 0.222 7.82 9.08 6.7 4.32 4.82 7.39 Ae(calc) Ae(exp)7Ae(calc) 0.14 0.21 0.24 0.27 0.30 0.34 0.27 0.49 0.84 1.19 2.27 1.56 0.85 1.89 1.31 0.73 1.91 0.73 2.26 0.52 1.86 2.14 2.34 2.34 2.35 2.33 1.94 1.98 1.99 2.21 2.01 1.96 2.32 1.81 2.31 2.31 2.31 1.93 1.81 1.87 2.31 2.31 0.66 0.50 0.34 1.48 1.32 2.30 70.06 70.47 70.31 70.59 70.42 70.50 0.09 0.42 0.52 0.37 70.43 70.35 70.65 0.28 0.27 0.07 70.18 0.09 70.45 70.54 70.03 71.06 70.07 70.06 0.00 0.05 70.32 70.26 70.20 0.04 70.17 70.05 0.00 70.06 70.45 70.36 70.32 0.32 0.09 70.22 70.30 70.24 0.12 70.05 0.04 0.22 0.33 70.1218 Table 8.Statistical parameters for correlations of type (14) determined for various classes of free radicals. Series Type of radicals a and sC¢§, which N R S/ eV make it possible to calculate the I and Ae values for carbon- C-centred 0.2345 0.1995 0.9768 0.9816 48 20 IAe S-centred 0.6105 0.1491 0.9278 0.8390 7 10 IAe O-centred 0.3557 0.1150 0.9938 0.9836 10 12 IAe N-centred 1.041 0.2179 0.968 0.9744 56 IAe destabilisation. In a published discussion 9¡¾11 dealing with the influence of substituents on bond energies, similar considerations are presented concerning the situation where the effects observed can be attributed both to the RX molecule and the R radical.Equation (25) indicates that a substituent atom should have an abnormally high electronegativity (w >5.04) to stabilise a radical more effectively than the corresponding cation. In turn, relation (27) illustrates the fact that for most of atoms (w >1.93), stabilisation of anions predominates. Thus, it can be concluded that the described substituent effects which determine the electron potentials of free radicals refer to stabilisation of the correspond- ing ions. The role of steric interactions can be elucidated by comparing the adiabatic ionisation potentials, studied within the framework of the approach under discussion, with the corre- sponding vertical ionisation potentials.The adiabatic potentials reflect the difference between the energies of the radicals and the cation having the most favourable (equilibrium) spatial structure, whereas vertical potentials imply identical geometries of these species. Thus, the difference between the adiabatic and vertical potentials can be attributed to structural reorganisation of a free radical caused by its oxidation. The adiabatic and vertical potentials of the methyl radical are known to be equal. This is apparently due to the fact that both the radical and the cation are planar. The other primary, secondary and tertiary carbon-centred radicals are non-planar, unlike the corresponding cations.The difference between their adiabatic and vertical potentials remains approximately constant (0.3 ¡¾ 0.4 eV) and does not change significantly on passing from primary to secondary or tertiary radicals, i.e., the steric contribution to the adiabatic ionisation potentials is insignificant but they do contain a constant component due to the energy of spatial reorganisation. The absence of this component in the case of the methyl radical can be the main reason for the observed difference between the predicted and experimental I(CH3) values. The foregoing attests that steric interactions have no influence on the ionisation potentials and electron affinities of free radicals and the corresponding effect of substituents has a purely inductive nature.It is common knowledge that cations are stabilised by elec- tron-donating substituents and anions are stabilised by electron- withdrawing substituents. According to Eqn (15), the atomic inductive effect is proportional to the difference between the electronegativities of the given atom and the reaction centre. Hence, it is reasonable to assume that the electronegativity of the central atom (carbon) increases in the series anion < radical < cation, while the inductive effect of the substituent atoms switches from electron-withdrawing to electron-donating influence, and only in extreme cases [for example, for N(sp), which has wind=6.76], is the effect of the atom adjacent to the cationic centre maintained as the electron-withdrawing influence.Thus, parameters of 5.04 and 1.93 in Eqns (24) and (26) can actually be taken as the inductive electronegativity of the reaction centre, i.e., of positively and negatively charged carbon, respectively. A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov c. The group sCa and sC¢§ scales The empirical operational parameters e+ and e7 established have also been used to introduce group scales called sC centred radicals in terms of an additive scheme.233 a A 0 aPsC I a I e a A0e aPsC¢§ These parameters were calculated for the most frequently encountered organic substituents with the assumption of the standard geometries and using the e+ and e7 values for atoms contained in these substituents.These radical scales, based on electron transfer reactions and considering the substitution effect at the group level of additivity, reflect, as do the Hammett s-constants, the overall influence of substituents on a radical reaction centre without separation of the inductive, resonance, and steric constituents. The use of group sCa and sC¢§ scales simplifies the procedure of calculation of the ionisation energies of radicals and eliminates the necessity of determining interatomic distances. Similarly, we calculated the ionisation energies of O-, S- and N-centred radicals in terms of the basic equation (14). The atomic operational parameters e+ and e7 found in this way were then analysed using relation (16).The corresponding equations for radicals of various types are presented below in the same order which was accepted for carbon-centred radicals.234 d. Oxygen-centred radicals For oxygen-centred radicals, the operational parameters e+, which determine the relative contributions of atoms to the ionisa- tion energy of the system, are described with high accuracy by means of atomic electronegativities and the covalent radii in accordance with Eqn (16) eai a O3:94 1:01UwiR2i ¢§ O18:77 2:93UR2i or eai a 3:94Owi ¢§ 4:76UR2i . The corresponding atomic parameters e7 are determined in a similar way e¢§i a O1:25 0:27UwiR2i ¢§ O2:31 0:79UR2i or e¢§i a 1:25Owi ¢§ 1:84UR2i .Thus, the ionisation energy of the alkoxy radicals I(RO ) can be presented by the relation (28) , Owi ¢§ 4:76UR2iIORO U a IOHO U a 3:94 r2iia1 XN and the electron affinity of oxygen-centred radicals is determined in terms of atomic parameters A (29) Owi ¢§ 1:84UR2i. eORO U a AeOHO U a 1:25 r2iia1 XN e. Sulfur-centred radicals The atomic operational constants e+ and e7 of sulfur-centred radicals determined from the ionisation potentials and the elec- tron affinity correlate with the atomic electronegativities and atomic radii with a lower accuracy eai a O1:71 2:19UwiR2i ¢§ O11:29 5:93UR2i or eai a 1:71Owi ¢§ 6:61UR2i ,Correlation analysis in the chemistry of free radicals e¢§i a O¢§3:27 1:41UwiR2i a O6:84 3:68UR2i or e¢§i a ¢§3:27Owi ¢§ 2:09UR2i .Nevertheless, the expressions obtained which relate the ion- isation energies of sulfur-centred radicals to parameters of the atoms forming them appear well substantiated (30) Owi ¢§ 6:61UR2i. IORS U a IOHS U a 1:71 r2iia1 XN The electron affinity of sulfur-centred radicals is found from the relation A (31) Owi ¢§ 2:09UR2i. eORS U a AeOHS U ¢§ 3:27 r2iia1 XN ea f. Nitrogen-centred radicals A similar correlation obtained for nitrogen-centred radicals is unsatisfactory because of the deficiency and great inaccuracy of the corresponding experimental data; therefore, the available data on the ionisation of N-centred radicals cannot serve as the base for discussion.Nevertheless, we thought it fit to present the relations determining the e+ and e7 parameters for atoms making up N-centred radicals. As in the above cases, the electronegativities and the sizes of atoms forming the corresponding N-centred radical were used. i a O1:14 10:70UwiR2i ¢§ O12:01 24:9UR2i or ea e¢§i a 1:14Owi ¢§ 10:55UR2i , i a O6:24 0:41UwiR2i a O13:76 0:92UR2i , or e¢§i a 6:24Owi ¢§ 2:20UR2i . The ionisation energies and electron affinities of nitrogen- centred radicals can be written as follows: (32) Owi ¢§ 10:55UR2i, IOR2N U a IOH2N U a 1:14 r2iia1 XN A (33) Owi ¢§ 2:20UR2i. eOR2N U a AeOH2N U a 6:24 r2iia1 XN The ionisation potentials and the electron affinities of S-, N- and O-centred radicals calculated on the basis of the atomic inductive electronegativities and covalent radii are given in Tables 6 and 7.The electronegativities of ionic forms of the C, S, N and O atoms considered as reaction centres, obtained in accordance with the proposed procedure, are given in Table 9. Table 9. Electronegativities and statistical parameters for correlations of type (16) determined for various types of free radicals. N R S/ eV Type of radicals Parameter wrc e+ C-centred e7 0.9509 0.266 0.9502 0.328 8 a 7 b 5.04 1.93 e+ S-centred e7 0.9368 1.3768 0.8739 0.5329 55 6.61 2.09 e+ O-centred e7 0.9891 0.7342 0.9808 0.1975 87 b 4.76 1.84 e+ N-centred 10.55 2.20 e7 0.8393 1.9877 0.9977 1.041 43 a Except for parameters for the O, N, S and N(sp) atoms; b except for parameters for the O atom.19 The same Table contains the statistical parameters of the corre- sponding correlations of type (16) found for the the operational atomic parameters e+ and e7 of the series studied. 5. The stability of free radicals in redox processes We have already noted that the problem of radical stability, especially within the framework of the thermodynamic approaches proposed here, largely overlaps the problem of radical reactivity and is considered from the standpoint of the influence of substituents. The stability of free radicals itself in terms of the relative energies of covalent bonds in the corresponding systems with filled electron shells is normally considered separately from the known effect of steric shielding of the unpaired electron by the molecular environment, decreasing the reactivity of the radical.45, 114, 237 In our opinion, the concept of radical stability (reactivity) should be supplemented by one more type, namely, stability of free radicals in redox processes (subsequently referred to as redox stability).As has already been noted, single-electron transfer is one of the most frequently encountered types of reaction in homolytic chemistry. Meanwhile, neither kinetic nor thermodynamic methods for the description of the radical effects of substituents take into account the redox stability of free radicals or provide the possibility of quantitative interpretation of the corresponding single-electron potentials.However, it is absolutely clear that the lower the ionisation potential and the higher the electron affinity of a free radical, the more easily it would enter into single-electron transfer reactions. Thus, the redox stability of a free radical can be matched to its absolute chemical hardness (Z) Z a I ¢§ Ae, 2 where I and Ae are the single-electron ionisation potential and the electron affinity of the radical in the gas phase determined experimentally. Let us consider carbon-centred radicals. Using relations (25) and (26), we express the relative chemical hardness of a carbon- centered radical (Z) in terms of fundamental atomic characteristics used to describe its single-electron potentials. Owi ¢§ 4:22UR2iZORU a ZOMeU ¢§ 0:28 r2iia1 XN This relation reflects the trend of the redox stability of C-centred radicals to decrease under the influence of the vast majority of atoms present in the environment of a carbon reaction centre; only the most electronegative elements increase the ZORU value with respect to the chemical hardness of the methyl radical ZOMeU.As noted above, the stability of carbon-centred radicals is often expressed as a derivative of the dissociation energy of the C7H bonds. A lower energy implies higher radical stabillity. However, a low bond energy often corresponds to a low chemical hardness of the corresponding radical. In conformity with our approach, this, conversely, implies a lower redox stability of the radical.Hence, the criteria used to describe radical stability should be chosen with caution. 6. Energies of dissociation of C¡¾H bonds An attractive aspect of our approach is, in our opinion, the possibility of using it successfully to describe dissociation energies of bonds Ed. We demonstrated this taking carbon ¡¾ hydrogen bonds as an example.238 We obtained a large array of Ed(CH) values using the following relation i E (34) . dOR3CHU ¢§EdOCH4U a i C¢§i X d r220 Here Ed(CH4) is the energy of the C7H bond in the methane molecule, Ed(R3CH) is the energy of the C7H bond in the corresponding derivative; the correlation parameters are: N=72, R=0.9773, S=8.484 kJ mol71. Equation (34) allowed high-accuracy determination of atomic constants which were designated by d and corresponded to the operational parameters ei in the base equation (14).We were unable to determine the parameters d using the inductive and steric constituents and a correlation of type (15). Thus, the relationship between the redox and thermodynamic [expressed in terms of relative Ed(CH)] stabilities of free radicals remains uncertain. Nevertheless, the operational values d can be used successfully to calculate unknown energies of the C7H bonds. IV. Conclusion To summarise, it can be stated that the use of polar constants for the description of the reactivity and physicochemical properties of free radicals is rather limited, although in some cases, it is quite successful.The scales of specific radical constants s are not general either. The absence of coordination between them and the ambiguity of the physical meaning of the s radical constants might be due not only to the drawbacks of methods of their determination but rather to the limitations of principle inherent in the application of the linear methodology of correlation analysis to the free-radical chemistry and to the violation of additivity of the group influence in paramagnetic systems. Thus, the problem of using correlation analysis in the chem- istry of free radicals is far from being solved; in this respect `homolytic' chemistry is markedly inferior to the `heterolytic' chemistry of organic compounds. The new approaches to the quantitative description of the structure ± reactivity (property) relationships for the participants of homolytic processes which we propose give hope for elimination of this objectively formed unbalance and make the quantitative organic chemistry more harmonious in some respect. The model we developed, based on the consideration of discrete contributions of atoms, depending on the remoteness, to the substituent effects makes it possible to predict with high accuracy the quantitative characteristics of free radicals obtained experimentally.The method implies taking account of the influ- ence of the molecular environment on the reaction centre without preliminary resolution of the effect into electronic and steric constituents. This approach provides the possibility of analysing efficiently diverse experimental results, irrespective of the nature of reaction centres.Within the framework of our approach, we have considered only one of the three main types of free-radical processes. The quantitative description of the ionisation potentials and the electron affinities of diverse C-, N-, S- and O-centred radicals and the ionisation energies of aliphatic and aromatic amines permitted us to identify the physical nature of the corresponding substituent effects and to demonstrate the versatility of this approach in interpretation of the results of quantitative inves- tigations in the chemistry of organic and heteroorganic free radicals. In our opinion, of fundamental importance is the established fact that the substituent effects determining the electronic poten- tials of free C-, N-, O- and S-centred radicals are correlated with the stability of the corresponding ions and can be regarded as purely inductive.Nevertheless, correct quantitative determination of these values requires that the electronegativities of the ionic forms of C, N, O and S acting as the reaction centres be established. á and sC¡ scales introduced on the basis of atomic The sC operational parameters e+ and e7, which determine the overall effects of substituents in single-electron transfer reactions involv- ing C-centred radicals, exhibit high predictive capacity, although they do not clarify the physical nature of the corresponding interactions. A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov The approaches that we developed provide the possibility of describing a large array of dissociation energies of the C7H bonds and of determining operational atomic constants d, which are applicable for predicting unknown Ed(CH) values. The notion `redox stability of free radicals' also appears useful.It interprets this type of stability in terms of absolute hardness, without resorting to the approach according to which the relative bond energies are used as a measure of radical stability and which is criticised in the literature. Successful use of the developed approaches for the quantita- tive interpretation of the ionisation energies of free radicals and molecules with closed electron shells gives hope that they would also be employed to describe the effects of substituents in other types of free-radical processes.References 3. V I Galkin, R D Sayakhov, R A Cherkasov Usp. Khim. 60 1617 1. L P Hammett J. Am. Chem. Soc. 59 96 (1937) 2. A R Cherkasov, V I Galkin, E M Zueva, R A Cherkasov Usp. Khim. 67 423 (1998) [Russ. Chem. Rev. 67 375 (1998)] (1991) [Russ. Chem. Rev. 60 815 (1991)] 4. A R Cherkasov, V I Galkin, R A Cherkasov Usp. Khim. 65 695 (1996) [Russ. Chem. Rev. 65 641 (1996)] 5. V I Galkin J. Phys. Org. Chem. 12 283 (1999) 6. O Exner,M Charton, V Galkin J. Phys. Org. Chem. 12 289 (1999) 7. O Exner J. Phys. Org. Chem. 12 265 (1999) 8. M Charton J. Phys. Org. Chem. 12 275 (1999) 9. K Herberger J. Phys. Org. Chem.7 244 (1994) 10. K M Johnston, G H Williams. J. Chem. Soc. 1446 (1960) 11. R D Gilliom, B F Ward Jr J. Am. Chem. Soc. 87 3944 (1965) 12. B R Kennedy, K U Ingold Can. J. Chem. 44 2381 (1966) 13. H Sakurai, A Hosomi J. Am. Chem. Soc. 89 458 (1967) 14. H Sakurai, K Tokumaru (Eds) Chemistry of Free Radicals (Tokyo: Nankodo, 1967) Ch. 17 15. C Walling, J A McGuinness J. Am. Chem. Soc. 91 2053 (1969) 16. D A Pratt, J S Wright, K U Ingold J. Am. Chem. Soc. 121 4877 (1999) 17. J A Howard, J H B Chenier J. Am. Chem. Soc. 95 3054 (1973) 18. W A Pryor, W H Davis Jr, J P Stanley J. Am. Chem. Soc. 95 4754 (1973) 19. W A Pryor, T H Lin, J P Stanley, R W Henderson J. Am. Chem. Soc. 95 6993 (1973) 20. W H Davis Jr,W A Pryor J. Am. Chem. Soc. 99 6365 (1977) 21.I B Afanas'ev Int. J. Chem. Kinet. 13 173 (1981) 22. H R Dutsch, T H Fisher Int. J. Chem. Kinet. 14 195 (1982) 23. W A Pryor, F Y Tang, R H Tang, D F Church J. Am. Chem. Soc. 104 2885 (1982) 24. R E Pearson, J C Martin J. Am. Chem. Soc. 85 354 (1963) 25. R W Henderson J. Am. Chem. Soc. 97 213 (1975) 26. E V Blackburn, D D Tanner. J. Am. Chem. Soc. 102 692 (1980) 27. A Streitwieser Jr, C Perrin J. Am. Chem. Soc. 86 4938 (1964) 28. D D Tanner, J A Plambeck, D W Reed, T W Mojelsky J. Org. Chem. 45 5177 (1980) 29. C Hansch, H Gao Chem. Rev. 97 2995 (1997) 30. H C Brown, Y Okamoto J. Am. Chem. Soc. 80 4979 (1958) 31. C Hansch, A Leo, R W Taft Chem. Rev. 91 165 (1991) 32. E S Huyser J. Am. Chem. Soc. 82 394 (1960) 33. C Walling, B B Jacknow J.Am. Chem. Soc. 82 6113 (1960) 34. G A Russell, R C Williamson Jr J. Am. Chem. Soc. 86 2357 (1964) 35. M Jonsson, J Lind, G Merenyi, T E Eriksen J. Chem. Soc., Perkin 36. M Jonsson, J Lind, T E Eriksen, G Merenyi J. Chem. Soc., Perkin 37. M Jonsson, J Lind, T Reitberger, T E Eriksen, G Merenyi J. Phys. 38. M Jonsson, J Lind, T E Eriksen, G Merenyi J. Am. Chem. Soc. 116 39. M Jonsson, J Lind, G Merenyi, T E Eriksen J. Chem. Soc., Perkin Trans. 2 2149 (1994) Trans. 2 1567 (1993) Chem. 97 11 278 (1993) 1423 (1994) Trans. 2 61 (1995) 40. M Jonsson, J Lind, G Merenyi, T E Eriksen J. Chem. Soc., Perkin Trans. 2 67 (1995)Correlation analysis in the chemistry of free radicals 41. M J Jones, G Moad, E Rizzardo, D H Solomon J. Org.Chem. 54 1607 (1989) 42. S Eherson, R T C Brownlee, R W Taft Prog. Phys. Org. Chem. 10 1 (1973) 43. P R Wells Chem. Rev. 63 171 (1963) 44. A Zavitsas, J A Pinto J. Am. Chem. Soc. 94 7390 (1972) 45. H G Viehe, Z Janousek, R D Merenyi (Eds) Substituent Effects in Radical Chemistry (NATO SAD Ser.) (Dordrecht; Boston; Lancaster; Tokyo: Reidel, 1986) 46. T Alfrey Jr, C C Price J. Polym. Sci. 2 101 (1947) 47. T Otsu, T Ito, Y Fujii,M Imoto Bull. Chem. Soc. Jpn. 41 204 (1968) 48. T Yamamoto, T Otsu Chem. Ind. 787 (1967) 49. A P G Kieboom Tetrahedron 28 1325 (1972) 50. S Dinctmrk, R A Jackson,M Townson J. Chem. Soc., Chem. Commun. 172 (1979) 51. S Dinctmrk, R A Jackson,MTownson, H Agirbas, N C Brillingham, G March J. Chem. Soc., Perkin Trans.2 1121 (1981) 52. H Agirbas, R A Jackson J. Chem. Soc., Perkin Trans. 2 739 (1983) 53. H Sakurai, S-i Hayasaki, A Hosomi Bull. Chem. Soc. Jpn. 44 1945 (1971) 54. RIto, T Migita,NMorikawa,OSimamura Tetrahedron 21 955 (1965) 55. T H Fisher, A W Meierhoefer J. Org. Chem. 43 224 (1978) 56. S Dinctmrk, R A Jackson J. Chem. Soc., Perkin Trans. 2 1127 (1981) 57. X Creary J. Org. Chem. 45 280 (1980) 58. X-K Jiang, G-Z Ji J. Org. Chem. 57 6051 (1992) 59. C Walling, E R Briggs,K B Wolfstirn, F R Mayo J. Am. Chem. Soc. 70 1537 (1948) 60. T Otsu, T Yamamoto J. Soc. Org. Synth. Chem. Jpn. 23 643 (1965) 61. R W Taft Jr, I C Lewis J. Am.Chem. Soc. 80 2436 (1958) 62. R W Taft Jr, I C Lewis J. Am. Chem. Soc. 81 5343 (1959) 63. R W Taft Jr J. Phys.Chem. 64 1805 (1960) 64. O Exner Tetrahedron Lett. 815 (1963) 65. O Exner, J Lakomy Collect. Czeh. Chem. Commun. 35 1371 (1970) 66. K Kalfus,M Vecera, O Exner Collect. Czeh. Chem. Commun. 35 1195 (1970) 67. Y Yukawa, Y Tsuno Bull. Chem. Soc. Jpn. 32 971 (1959) 68. Y Tsuno,M Sawada, T Fujii, Y Yukawa Bull. Chem. Soc. Jpn. 48 3347 (1975) 69. C G Swain, E C Lupton Jr J. Am. Chem. Soc. 90 4328 (1968) 70. M J S Dewar, P J Grisdale J. Am. Chem. Soc. 84 3539 (1962) 71. M Charton J. Am. Chem. Soc. 97 1552 (1975) 72. V A Palm Osnovy Kolichestvennoi Teorii Organicheskikh Reaktsii (Foundations of the Quantitative Theory of Organic Reactions) (Leningrad: Khimiya, 1977) 73. V A Palm, A V Tuulmets, in Reaktsionnaya Sposobnost' Organiche- skikh Soedinenii (Reactivity of Organic Compounds) (Tartu: Tartu State University, 1964) Vol.1, No. 1, p. 33 74. T H Fisher, A W Meierhoefer Tetrahedron 31 2019 (1975) 75. T H Fisher, S M Dershem, M Lynn Prewitt J. Org. Chem. 55 1040 (1990) 76. R A Jackson, F Malek J. Chem. Soc., Perkin Trans. 1, 1207 (1980) 77. N M K El-Durini, R A Jackson J. Organomet. Chem. 232 117 (1982) 78. R A Jackson, D W O'Neill J. Chem. Soc., Perkin Trans. 2 509 (1978) 79. R A Jackson J. Organomet. Chem. 437 77 (1992) 80. X Creary, C C Geiger, K Hilton J. Am. Chem. Soc. 105 2851 (1983) 81. X Creary Acc. Chem. Res. 18 3 (1985) 82. X Creary, B Benage, M E Mehrsheikh-Mohammadi, J P Bays Tetrahedron Lett. 26 2383 (1985) 83. X Creary,M E Mehrsheikh-Mohammadi J. Org. Chem. 51 1110 (1986) 84.X Creary,M E Mehrsheikh-Mohammadi, S McDonald J. Org. Chem. 52 3254 (1987) 85. J P Chesick J. Am. Chem. Soc. 85 2720 (1970) 86. T C Shields, B A Shoulders, J F Krause, C L Osborn, P D Gardner J. Am. Chem. Soc. 87 3026 (1965) 87. J J Gajewski J. Am. Chem. Soc. 90 7178 (1968) 88. R Noyari, H Takaya, Y Nakanisi, H Nozaki Can. J. Chem. 47 1242 (1969) 89. J C Gilbert, J R Butler J. Am. Chem. Soc. 92 2168 (1970) 90. W von E Doering, H D Roth Tetrahedron, 26 2825 (1970) 91. J J Gajewski J. Am. Chem. Soc. 93 4450 (1971) 92. WKirmse, H-R Murawski J. Chem. Soc., Chem. Commun. 122 (1977) 93. X Creary J. Org. Chem. 43 1777 (1978) 21 94. X Creary, P S Engel,N Kavaluskas, L Pan,A Wolf J. Org. Chem. 64 5634 (1999) 95. J C Martin, J W Timberlake J.Am. Chem. Soc. 92 978 (1970) 96. J W Timberlake,M L Hodges Tetrahedron Lett. 4147 (1970) 97. J W Timberlake, A W Garner,M L Hodges Tetrahedron Lett. 309 (1973) 98. B K Bandlish, A W Garner,M L Hodges, J W Timberlake J. Am. Chem. Soc. 97 5856 (1975) 99. M F Dube, J W Timberlake Tetrahedron, 36 1753 (1980) 100. A E Luedtke, J W Timberlake J. Org. Chem. 50 268 (1985) 101. W M Nau, H M Harrer,W Adam J. Am. Chem. Soc. 116 10 972 (1994) 102. W Adam,H M Harrer,W M Nau,K Peters J. Org. Chem. 59 3786 (1994) 103. J R Shelton, C K Liang, P Kovacic J. Am. Chem. Soc. 90 354 (1968) 104. P Kovacic, R R Flynn, J F Gormish, A H Kappelman, J R Shelton J. Org. Chem. 34 3312 (1969) 105. J R Shelton, C K Liang Synthesis 204 (1971) 106.J R Shelton , C K Liang J. Org. Chem. 38 2301 (1973) 107. A Peyman, E Hickl, H-D Beckhaus Chem. Ber. 120 713 (1987) 108. J W Timberlake, B K Bandlish Tetrahedron Lett. 1393 (1971) 109. W P Neumann, A Penenory, U Stewen,M Lehnig J. Am. Chem. Soc. 111 5845 (1989) 110. G-Z Ji, X-K Jiang, Y-H Zhang, S-G Yuan, C-X Yu, Y-Q Shi, X-L Zhang, W-T Shi J. Phys. Org. Chem. 3 643 (1990) 111. X K Jiang, G-Z Ji, C-X Yu Acta Chim. Sin., Engl. Ed. 369 (1985) 112. X-K Jiang, G-Z Ji, C-X Yu Acta Chim. Sin., Engl. Ed. 82 (1984) 113. X-K Jiang, C-J Wu, X-X Wu Acta Chim. Sin., Engl. Ed. 42 (1983) 114. J M Dust, D R Arnold J. Am. Chem. Soc. 105 1221 (1983) 115. R A Jackson, M Sharifi J. Chem. Soc., Perkin Trans. 2 775 (1996) 116. G S Hammond J. Am. Chem.Soc. 77 334 (1955) 117. C RuÈ chardt Angew. Chem., Int. Ed. Engl. 9 830 (1970) 118. J E Wertz, J R Bolton Electron Spin Resonance (New York: McGraw-Hill, 1972) Ch. 6 119. R I Walter J. Am. Chem. Soc. 88 1923 (1966) 120. E G Janzen Acc. Chem. Res. 2 279 (1969) 121. I B Afanas'v Int. J. Chem. Kinet. 7 856 (1975) 122. J M Dust, D R Arnold J. Am. Chem. Soc. 105 6531 (1983) 123. W J Leigh, D R Arnold, R W R Humphreys, P C Wong Can. J. Chem. 58 2537 (1980) 124. D D M Wayner, D R Arnold Can. J. Chem. 63 2378 (1985) 125. D D M Wayner, D R Arnold Can. J. Chem. 62 1164 (1984) 126. A M de P Nicholas, D R Arnold Can. J. Chem. 64 270 (1986) 127. W Adam, H M Harrer, F Kita,W M Nau Pure Appl. Chem. 69 91 (1997) 128. A Pross, L Radom Prog. Phys. Org.Chem. 13 1 (1981) 129. R A Jackson J. Chem. Soc., Perkin Trans. 2 523 (1983) 130. R A Jackson J. Chem. Soc., Perkin Trans. 2 1991 (1993) 131. W Adam, L FroÈ hlich,W M Nau, H-G Korth, R Sustmann Angew. Chem., Int. Ed. Engl. 32 1339 (1993) 132. W Adam, F Kita, H M Harrer, W M Nau, R Zipf J. Org. Chem. 61 7056 (1996) 133. W Adam, C van Barneveld, O Emmert, H M Harrer, F Kita, A S Kumar, W Maas,W M Nau, S H K Reddy, J Wirz Pure Appl. Chem. 69 735 (1997) 134. W Adam, H M Harrer An. Quim. Int. Ed. 93 271 (1997) 135. W Adam, O Emmert, T Heidenfelder J. Org. Chem. 64 3417 (1999) 136. D A Dougherty Acc. Chem. Res. 24 88 (1991) 137. S W Benson J. Chem. Educ. 42 502 (1965) 138. H E O'Neal, S W Benson, in Free Radicals Vol. 2 (Ed. J K Kochi) (New York: Wiley, 1973) 139.M Rossi, D M Golden J. Am. Chem. Soc. 101 1230 (1979) 140. D J DeFrees, R T McIver Jr,W J Hehre J. Am. Chem. Soc. 102 3334 (1980) 141. D F McMillen,D M Golden Annu. Rev. Phys. Chem. 33 493 (1982) 142. D C Nonhebel, J C Walton J. Chem. Soc., Chem. Commun. 731 (1984) 143. A Mde P Nicholas, D R Arnold Can. J. Chem. 62 1850 (1984) 144. D D M Wayner, K B Clark, A Rauk, D Yu, D R Armstrong J. Am. Chem. Soc. 119 8925 (1997) 145. J Berkowitz,G B Ellison,D Gutman J. Phys. Chem. 98 2744 (1994) 146. M Szwarc J. Chem. Phys. 16 128 (1948) 147. X-M Zhang, F G Bordwell, J E Bares, J-P Cheng, B C Petrie J. Org. Chem. 58 3051 (1993)22 148. F G Bordwell, M J Bausch J. Am. Chem. Soc. 108 1979 (1986) 149. F G Bordwell, X-M Zhang, R Filler J.Org. Chem. 58 6067 (1993) 150. F G Bordwell, X-M Zhang Acc. Chem. Res. 26 510 (1993) 151. L Pauling The Nature of Chemical Bond (Ithaca, NY: Cornell University Press, 1960) 152. F G Bordwell, M J Bausch J. Am. Chem. Soc. 108 1985 (1986) 153. W M Nau J. Org. Chem. 61 8312 (1996) 154. W M Nau J. Phys. Org. Chem. 10 445 (1997) 155. GLeroy,MSana,CWilante J.Mol. Struct. (Theochem) 205 97 (1990) 156. C Ruchardt, H-D Beckhaus Top. Curr. Chem. 130 1 (1986) 157. G Leroy Int. J. Quantum Chem. 23 271 (1983) 158. G Leroy J. Mol. Struct. (Theochem) 93 175 (1983) 159. F M Welle, S P Verevkin, H-D Beckhaus, C RuÈ chardt Liebigs Ann. Chem. 155 (1997) 160. C RuÈ chardt Angew. Chem. 82 845 (1970) 161. FMWelle, H-D Beckhaus, C RuÈ chardt J. Org.Chem. 62 552 (1997) 162. A Mde P Nicholas, D R Arnold Can. J. Chem. 62 1860 (1984) 163. K B Clark, D D M Wayner J. Am. Chem. Soc. 113 9363 (1991) 164. A AZavitsas, C C Chatgilialoglu J.Am. Chem. Soc. 117 10 645 (1995) 165. W A Pryor, D F Church, F Y Tang, R H Tang, in Frontiers in Free Radical Chemistry (Ed. WA Pryor) (New York: Academic Press, 1980) p. 335 166. D J Pasto J. Am. Chem. Soc. 110 8164 (1988) 167. D J Pasto, R Krasnansky, C Zercher J. Org. Chem. 52 3062 (1987) 168. W J Hehre, L Radom P von R Schleyer, J A Pople Ab Initio Molecular Orbital Theory (New York: Wiley-Interscience, 1986) 169. M J S Dewar,M A Fox, D J Nelson J. Organomet. Chem. 185 157 (1980) 170. M Lehd, F Jensen J. Org. Chem. 56 884 (1991) 171.J D Goddard Can. J. Chem. 60 1250 (1982) 172. BS Jursic, JWTimberlake,P S Engel TetrahedronLett. 37 6473 (1996) 173. Y-D Wu, C-L Wong, K W K Chan, G-Z Ji, X-K Jiang J. Org. Chem. 61 746 (1996) 174. W J Hehre, R Ditchfield, L Radom, J A Pople J. Am. Chem. Soc. 92 4796 (1970) 175. A E Dorigo, Y Li, K N Houk J. Am. Chem. Soc. 111 6942 (1989) 176. F G Bordwell, X-M Zhang, M S Alnajjar J. Am. Chem. Soc. 114 7623 (1992) 177. D A Hrovat,W T Borden J. Phys. Chem. 98 10460 (1994) 178. C Hansch, A Leo Substituent Constants for Correlation Analysis in Chemistry and Biology (New York: Wiley, 1979) 179. O Exner Advances in Linear Free Energy Relationships (Eds N B Chapman, J Shorter) (London: Plenum, 1971) p. 1 180. A Cammarata, S J Yau J. Polym. Sci., A1 8 1303 (1970) 181. L Sylvander, L Stella, H-G Korth, R Sustmann Tetrahedron Lett. 26 749 (1985) 182. M C Flowers, H M Frey Proc. R. Soc. London, A Math. Phys. Sci., 257 122 (1960) 183. M Arai, R J Crawford Can. J. Chem. 50 2158 (1972) 184. WKirmse, MZeppenfeldt J. Chem. Soc., Chem. Commun. 124 (1977) 185. M J S Dewar J. Am. Chem. Soc. 74 3353 (1952) 186. A T Balaban Rev. Roum. Chim. 16 725 (1971) 187. A T Balaban,M T Caproiu, N Negoita, B Baican Tetrahedron 33 2249 (1977) 188. R W Baldock, P Hudson, A R Katritzky, F Soti Heterocycles 1 67 (1973) 189. R W Baldock, P Hudson, A R Katritzky, F Soti J. Chem. Soc., Perkin Trans. 1 1422 (1974) 190. A R Katritzky, F Soti J. Chem. Soc., Perkin Trans. 1 1427 (1974) 191. L Stella, Z Janousek, R Merenyi, H G Viehe Angew. Chem., Int. Ed. Engl. 17 691 (1978) 192. H G Viehe, R Merenyi, L Stella, Z Janousek Angew. Chem., Int. Ed. Engl. 18 917 (1979) 193. S Mignani,M Beaujean, Z Janousek, R Merenyi, H G Viehe Tetrahedron 37 (Suppl. 1) 111 (1981) 194. S Mignani, R Merenyi, Z Janousek, H G Viehe Bull. Soc. Chim. Belg. 93 991 (1984) 195. S Mignani, Z Janousek, R Merenyi, H G Viehe Bull. Soc. Chim. Fr. 1267 (1985) 196. S Mignani,R Merenyi, Z Janousek,H G Viehe Tetrahedron 41 769 (1985) 197. S Mignani, Z Janousek, R Merenyi, H G Viehe, J Riga, J Verbist Tetrahedron Lett. 25 1571 (1984) A R Cherkasov,MJonsson, V I Galkin, R A Cherkasov 198. F Lahousse, R Merenyi, J R Desmurs, H Allaime, A Borghese, H G Viehe Tetrahedron Lett. 25 3823 (1984) 199. C De Cock, S Piettre, F Lahousse, Z Janousek, R Merenyi, H G Viehe Tetrahedron 41 4183 (1985) 200. K D Gundermann, E Rohrl Liebigs Ann. Chem. 1661 (1974) 201. R M Moriarty, C R Romain, I L Karle, J Karle J. Am. Chem. Soc. 87 3251 (1965) 202. H K Hall Jr Angew. Chem. 95 448 (1983) 203. S-U Park, S-K Chung,MNewcomb J. Am. Chem. Soc. 108 240 (1986) 204. H Singh, J M Tedder J. Chem. Soc., Chem. Commun. 1095 (1980) 205. X Creary, Z Jiang, M Butchko, K McLean Tetrahedron Lett. 37 579 (1996) 206. A De Mesmaeker, L Vertommen, R Merenyi, H G Viehe Tetrahedron Lett. 23 69 (1982) 207. R Merenyi, A De Mesmaeker, H G Viehe Tetrahedron Lett. 24 2765 (1983) 208. M van Hoecke, A Borghese, J Penelle, R Merenyi, H G Viehe Tetrahedron Lett. 27 4569 (1986) 209. R Merenyi, V Daffe, J Klein,W Masamba, H G Viehe Bull. Soc. Chim. Belg. 91 456 (1982) 210. H-G Korth, P Lommes,WSicking,R Sustmann J. Am. Chem. Soc. 106 663 (1984) 211. I MacInnes, J C Walton, D C Nonhebel J. Chem. Soc., Chem. Commun. 712 (1985) 212. H G Viehe, Z Janousek, R Merenyi, L Stella Acc. Chem. Res. 18 148 (1985) 213. M Klessinger Angew. Chem., Int. Ed. Engl. 19 908 (1980) 214. G Leroy, D Peeters J. Mol. Struct. (Theochem) 85 133 (1981) 215. A R Katritzky,M C Zerner,M M Karelson J. Am. Chem. Soc. 108 7213 (1986) 216. H-G Korth, P Lommes,W Sicking, R Sustmann Chem. Ber. 188 4627 (1985) 217. H-G Korth, R Sustmann, R Merenyi, H G Viehe J. Chem. Soc., Perkin Trans. 2 67 (1983) 218. MZamkanei, J H Kaiser, H Birkhofer, H-D Beckhaus, C RuÈ chardt Chem. Ber. 116 3216 (1983) 219. H Birkhofer, J HaÈ drich, H-D Beckhaus, C RuÈ chardt Angew. Chem., Int. Ed. Engl. 26 573 (1987) 220. A Cherkasov,MJonsson, V I Galkin J. Mol. Graph. Model. 17 28 (1999) 221. MATLAB The Language of Technical Computing 5.2.0.3084, The MathWorks Inc., 1998 222. A R Cherkasov, V I Galkin, R A Cherkasov J. Phys. Org. Chem. 11 437 (1998) 223. A R Cherkasov, V I Galkin, E M Zueva, R A Cherkasov Zh. Obshch. Khim. 66 877 (1996) a 224. V I Galkin, A R Cherkasov, R D Sayakhov, R A Cherkasov Zh. Obshch. Khim. 65 458 (1995) a 225. A R Cherkasov, V I Galkin, E M Zueva, R A Cherkasov Zh. Obshch. Khim. 66 411 (1996) a 226. A R Cherkasov, V I Galkin, E M Zueva, R A Cherkasov Zh. Obshch. Khim. 67 92 (1997) a 227. A R Cherkasov, V I Galkin, R A Cherkasov Zh. Org. Khim. 35 163 (1999) b 228. A R Cherkasov, V I Galkin, R A Cherkasov J. Mol. Struct. (Theochem) 489 43 (1999) 229. A R Cherkasov, V I Galkin, R A Cherkasov J. Mol. Struct. (Theochem), 497 115 (2000) 230. V I Galkin, A R Cherkasov, R A Cherkasov Phosphorus Sulfur Silicon Relat. Elem. 144 ± 146 329 (1999) 231. A R Cherkasov, V I Galkin, R A Cherkasov Phosphorus Sulfur Silicon Relat. Elem. 144 ± 146 775 (1999) 232. I A Koppel, U H Molder, R I Pikver Org. React. 18 380 (1981) 233. A Cherkasov,M Jonsson J. Chem. Inf. Comput. Sci. 38 1151 (1998) 234. A Cherkasov,M Jonsson J. Chem. Inf. Comput. Sci. 39 1057 (1999) 235. NIST Standard Reference Database No. 69, November 1998, Release 236. R W Taft Jr J. Am. Chem. Soc. 75 4538 (1953) 237. D Griller, K U Ingold Acc. Chem. Res. 9 13 (1976) 238. A Cherkasov,M Jonsson J. Chem. Inf. Comput. Sci. 40 1222 (2000) a�Russ. J. Gen. Chem. (Engl. Transl.) b�Russ. J. Org. Chem. (Engl. Tran

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Russian Chemical Reviews 70 (1) 23 ± 44 (2001) Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them I G Panova, I N Topchieva Contents I. Introduction II. Rotaxanes III. Polyrotaxanes IV. Supramolecular devices based on rotaxanes and polyrotaxanes Abstract. and rotaxanes of synthesis the to approaches Various Various approaches to the synthesis of rotaxanes and polyrotaxanes are considered. The principles employed in the polyrotaxanes are considered. The principles employed in the design of highly organised structures comprising rod-shaped design of highly organised structures comprising rod-shaped polymeric molecules, complexes, inclusion macromolecular polymeric molecules, viz., ., macromolecular inclusion complexes, are discussed.In addition to the conventional (step-by-step) are discussed. In addition to the conventional (step-by-step) methodology which consists of polymerisation of monomers in methodology which consists of polymerisation of monomers in the presence of macrocycles, molecular self-assembly is gaining an the presence of macrocycles, molecular self-assembly is gaining an ever increasing significance. The main emphasis is laid on the ever increasing significance. The main emphasis is laid on the preparation and characterisation of inclusion complexes which preparation and characterisation of inclusion complexes which are polymers. synthetic linear and cyclodextrins on based are based on cyclodextrins and linear synthetic polymers. The The bibliography references 138 includes bibliography includes 138 references.I. Introduction Supramolecular chemistry as a new line of research has evolved and has developed intensively in the past few years. This inter- disciplinary science encompasses the chemistry of noncovalent interactions, molecular physics and molecular biology. Its main attention is focussed on the systems which are capable of self- organisation, i.e., spontaneous production of definite structures by self-assembly of constituents into supramolecular assemblies. The synthesis of such structures is based on the molecular recognition principle and is effected by the cooperation of various non-covalent interactions, e.g., electrostatic, hydrophobic, hydro- gen bonding, etc.The principle of molecular recognition can be exemplified in the formation of complexes of the `host ± guest' type. The role of `hosts', i.e., receptors, is played by cyclic molecules, e.g., crypt- ands, crown ethers, cyclodextrins and calixarenes. The chemical nature of `guests' is extremely diverse, they include both small particles (e.g., inert gas atoms, metal ions, etc.) and complex bulky molecules of the fullerene type. In the past few years, supra- molecular chemistry has been enriched by systems with polymers as the `guest' molecules, which underlies the supramolecular chemistry of polymers. This approach has made it possible to obtain such compounds as polyrotaxanes, catenanes, `molecular necklaces', dendrimers, I G Panova, I N Topchieva Department of Chemistry, M V Lomonosov Moscow State University, Leninskie Gory, 119899 Moscow, Russian Federation.Fax (7-095) 939 01 74. Tel. (7-095) 939 31 27. E-mail: vspan@redline.ru (I G Panova); kurganov@gagarinclub.ru (I N Topchieva) Received 2 June 2000 Uspekhi Khimii 70 (1) 28 ± 51 (2001); translated by R L Birnova #2001 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2001v070n01ABEH000608 23 23 30 41 etc., which possess novel, previously unknown structures and remarkable properties. This review is devoted to one type of polymeric supramolecular assemblies, viz., polyrotaxanes. In the latter, the macrocycles are `threaded' onto a polymeric molecule with bulky terminal groups. In addition to polyrotaxanes, their topological analogues, viz., pseudopolyrotaxanes including `molecular necklaces', are reviewed.Since these structures are synthesised using essentially the same procedures as for rotaxanes, the strategy of rotaxane synthesis is also discussed. II. Rotaxanes Rotaxanes (Rt) represent complexes comprising cyclic molecules (C) threaded onto linear molecules (L). Their characteristic feature is the lack of covalent binding between the components C and L. In order to prevent the dissociation of the complex into constituents, the `stoppers' (S), i.e., bulky molecules which are covalently linked to the ends of linear molecules, are used (Fig. 1 a, b). Similar structures in which the molecules S are absent are called pseudorotaxanes (pseudo-Rt) (Fig.1 c). The nomencla- ture used to describe such compounds takes account of the number of components involved in the complexation. Thus [2]-Rt (see Fig. 1 a) contains one L and one C molecule; [3]-Rt is comprised of one L and two C molecules (see Fig. 1 b), etc. a L C S S b L C C S S c L C Figure 1. A schematic representation of rotaxanes: (a) [2]-Rt, (b) [3]-Rt, (c) pseudo-Rt. 1. General approaches to the rotaxane synthesis It should be noted that the threading of cyclic molecules onto linear components, which forms the basis for all the strategies of the rotaxane synthesis (Fig. 2), is a reversible process which is described by the equilibrium constant Keq à âRtä=âLäâCä.24 Keq , + Rt L C Therefore, the creation of conditions where the equilibrium of the reaction is shifted towards complex formation is the key event in the assembly of rotaxane molecules.Quantitatively, this process can be described by standard thermodynamic equations: RTlnK (1) eq a ¢§DG a ¢§ODH ¢§ TDSU, (2) lnKeq a ¢§DH RT a DRS . As can be seen from Eqn (2), two extreme cases are thermo- dynamically possible. First, the so-called statistical threading, i.e., a random collision and interaction of molecules of different nature (e.g., L and C). The enthalpy of such a reaction, DH, is close to zero or is positive, i.e., the threading is determined by the entropy factor. Second, template-directed threading, which is based on the principle of molecular self-assembly where the reaction is energeti- cally favourable due to the existence of specific non-covalent interactions between the particles L and C (DH<0).Strategy I Strategy II 12 3 Strategy III + Figure 2. The strategies of the chemical synthesis of rotaxanes: (1) rod molecule, (2) macrocycle, (3) `stopper'. When considering the strategies of chemical synthesis of rotaxanes (see Fig. 2), one can distinguish three general approaches: 1 (1) threading of a macrocycle onto a rod molecule and subsequent interaction of the complex formed with the blocking reagents (strategy I); (2) cyclisation in the presence of compounds having a dumb- bell-like structure (strategy II); (3) temperature-induced `slipping' of the macrocycle onto bulky terminal groups of the dumbbell-shaped molecule (strategy III).2. The statistical approach to the rotaxane synthesis The first attempts to synthesise rotaxanes were based on statistical threading of a cyclic component onto linear molecules. The first report on a successful synthesis of such complexes,2 which consisted of random threading of a macrocyclic acyloin onto decane-1,10-diol using bulky trityl groups as stoppers, was pub- lished in 1967. After a 70-fold passage of the reaction mixture containing components L and S through a column with an immobilised cyclic component (C) and subsequent chromato- graphic separation of the eluate, the yield of rotaxane was as low as 6%. Further experiments 3, 4 were aimed at establishing a correlation between the efficiency of statistical threading, the properties of the reactants C, L and S and reaction conditions.The synthesis of rotaxanes from various dibenzocrown ethers, ethylene oxide oligomers (EOO) and trityl chloride by their joint fusion has been described.4 In this case, the efficiency of threading depended on the size of the ring, the L :C ratio, the length of the chains of the L-molecules and the total volume of the reaction I G Panova, I N Topchieva mixture, whereas temperature had no effect on the course of the reaction. The maximum degree of threading was achieved when a mixture of an ethylene oxide oligomer having a molecular mass (MM) of 1000 and crown ethers (on average, dibenzo-58.2-crown- 19.4) is used.Mixing of EOO (MM=400) with dibenzo-58.2- crown-19.4 at 130 8C and subsequent addition of triphenylchloro- methane gave the corresponding [2]-Rt in 15% yield. The intro- duction of bromomethyl substituents into each phenyl group of the blocking reagent and the reaction in the presence of the Zn/Cu couple in DMF resulted in [4]-Rt in 8% yield.5 The experiments 3 with statistical threading of cyclic hydro- carbons onto 1,10-bis(triphenylmethoxy)decane at 120 8C revealed that only rotaxanes comprising C29 rings were more or less stable at this temperature, although their yields did not exceed 1.6%. (H2C)n Ph3CO OCPh3 OCPh3 (CH2)10 Ph3CO (CH2)10 (CH2)n n=11 ¡¾ 39. Later, it was found 4 that a macrocycle which has to be threaded onto the methylene groups should contain no less than 22 carbon atoms.It was shown also that terminal trityl groups can hold the rings which contained no more than 29 carbon atoms. Bulkier tris(p-butylphenyl)methyl groups prevent the dissociation of the rings containing 42 carbon atoms. Thus, the statistical approach affords a mixture of starting compounds and rotaxanes; the isolation of the latter often presents a problem.2¡¾5 The efficiency of threading and the yields are controlled by varying the concentrations of the reactant and their molar ratios and by matching the geometric parameters of the molecules L, C and S. It is noteworthy that this approach gives relatively low yields of reaction products which at best do not exceed 15%. On the other hand, one of the benefits of the statistical approach to the rotaxane synthesis is the possibility of using a vast diversity of linear and cyclic molecules of different chemical nature which significantly expand the range of the structures that can be synthesised by this method.3. Template synthesis of rotaxanes Yet another approach to the rotaxane synthesis is based on the use of the fundamental principle of supramolecular chemistry, namely, the self-organisation of molecules due to specific non- covalent interactions. This approach is named template or directed synthesis, since in this case the process is directed by molecular recognition between two or more complementary frag- ments of the interacting molecules. Depending on the type of bonding, the following main routes to the rotaxane synthesis may be distinguished: (1) the formation of metal ¡¾ ligand coordination bonds; (2) donor ¡¾ acceptor interactions; (3) combined interac- tions which are observed in the formation of inclusion complexes based on cyclodextrins.a. The synthesis of rotaxanes using transition metal ions This strategy is based on the assembling and `orientational' properties of transition metals. The complexation of two 2,9- disubstituted 1,10-phenanthrolines 1a,b with the copper(I) ion was R R R [Cu(MeCN)4]+ N + N N Cu 2 N N N R R R 2a,b 1a,b R=OMe (a), OH (b).Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them O O O N 1b, [Cu(MeCN)4]+ N O O O3 first proposed as the template-based reaction.6 The complexes 2a,b formed have an ideal spatial structure for the synthesis of rotaxanes based on them. The synthesis of the macrocycle 3 incorporating one bidentate centre has been described.7 The reaction of compound 3 with [Cu(MeCN)4]+[BF4]7 and 2,9-bis(4-hydroxyphenyl)phenan- throline 1b affords the pseudorotaxane 4 (Scheme 1).7 Reactive phenolic groups can react with different stoppers.Modification of R R N+ N Au N N R N 3, [Cu(MeCN)4]+ N CHO 6 O O O N N +Cu N N O O O 8, 10 R=1,3-But2C6H3; M = 2H+ (8, 9), Zn2+ (10, 11).HO HO R N+ N Au N N R N N M N N O O O N N +Cu N N O O O 4 the terminal groups of the complex 4 with alkyl iodide containing the bulky triarylmethyl group has led to [2]-Rt 5.8 In order to remove CuI, the complex formed was passed through an ion- exchange resin.The structure of the individual [2]-Rt 5 isolated in 21% yield was confirmed by 1H NMR spectroscopy and mass spectrometry. Later, data on the synthesis of porphyrin-containing rotax- anes have been documented (Scheme 2).9±12 Initially, compound O O O N N +Cu N N O O O 7 O O R O NN O O O + R O Ar Ar Ph N N 1) I(CH2)3CAr2Ph, K2CO3 2) Amberlite (CN7) N N Ph Ar O Ar 5 (Ar=p-ButC6H4) R R N+ N Au N N R ; N N H H 3,5-But2C6H3CHO, CF3CO2H chloranil CHO R R N N Au+ N N R N Cu + N N N M N N N N +Cu N N R N+ N Au N N R 9, 11 R 25 Scheme 1 O O OO O O Scheme 2 O O OO O O26 OMe N 3, [Cu(MeCN)4]+ N N O N O MeO 12 6 which contained a porphyrin ± gold(III) complex as a stopper was prepared.This complex was added to the macrocycle 3 in the presence of a copper(I) complex. The intermediate product 7 formed reacted with 3,5-di-tert-butylbenzaldehyde and bis- (3-ethyl-4-methylpyrrol-2-yl)methane in the presence of trifluoro- acetic acid. The intermediate porphyrinogen was oxidised with chloranil. Chromatographic separation gave [2]-Rt (8) and [3]-Rt (9) in 25% and 32% yields, respectively.11 The rotaxanes 8 and 9 were converted into their Zn-analogues 10 and 11 by treatment with Zn(OAc)2 .2H2O. A 1H NMR spectroscopic study showed that demetallation of the phenanthroline moiety of [2]-Rt by ion exchange with KCN changes its structure so that the phenanthro- line fragment of the macrocycle lies outside the `cleft' formed by the porphyrin fragments.12 Several modifications of this synthetic procedure are known. In one of them, the blocking groups are represented by fuller- enes.13 It was suggested 14 to use linear molecules incorporating two (12) or three (13) 1,10-phenanthroline fragments for the synthesis of structurally more elaborate rotaxanes. Their interactions with the macrocycle 3 in the presence of [Cu(MeCN)4]+[BF4]7 have been studied (Scheme 3). It was shown that [3]-pseudo-Rt formed on the basis of compound 12 has the composition L :CuI :C=1 : 2 : 2.Compound 13, which contains three phenan- throline fragments, yields a complex with the composition L :CuI: C=1:2:1, i.e., [2]-Rt in which two phenanthroline frag- ments of the rod molecule interact both with each other and with CuI, rather than the expected complex with a L :CuI :C ratio of 1 : 3 : 3. This phenomenon was attributed to the flexibility of the stretched rod molecule. The ability for self-complexation must be taken into consideration in the synthesis of [3]- and [4]-Rt by this method. b. Rotaxane syntheses based on donor-acceptor interactions of L and C molecules This method consists in the interaction of electron-donor and electron-acceptor molecules or their fragments and results in p-bonding. Cyclobis(paraquat-p-phenylene) 14,15 which reacts with a variety of aromatic electron-donor substrates, and bis-p- phenylene-34-crown-10 (15),16 which forms a complex with para- quat bis(hexafluorophosphate), have received especially wide acceptance as receptors.Using X-ray diffraction analysis, it was shown 17, 18 that the complexes prepared on the basis of these compounds and the corresponding ligands have ordered struc- tures both in solution and in the solid phase and represent pseudorotaxanes. The aromatic rings of the `guest' molecules are accommodated inside the `host' molecules between the rings of the receptor, which are stacked parallel to one another. The com- MeO O O O N N + Cu N N O O O O O N N Cu + N N O O OMe OMe NN (H2C)6 NN (CH2)6 NN OMe 13 plexes have box-like structures, which are ideal for their conver- sion into rotaxanes. N+ N+ 4PF¡6 + + N N 14 The interaction of compounds 16 and 17 (Scheme 4) with the macrocycle 14 in acetonitrile followed by a reaction with triiso- propylsilyl triflate was studied.19 After purification of the reaction mixture by column chromatography on silica gel, [2]-Rt 16 0 and 17 0 were isolated in equal yields (22%).A similar compound, viz., [2]-Rt 17 0, was obtained in 14% yield using strategy II (see Scheme 2, Fig. 2).20 It was noted 19 that the reduction in the length of the oligoethylene oxide fragments of the rod molecules changes the arrangement of the p-dioxyphenyl- ene fragments relative to the plane of cyclophane and results in the increase in the distance between the complementary aromatic fragments of the L and C molecules.An increase in the number of electron-donor fragments in the rod molecule not only increases the yields due to the self- organisation of rotaxanes, but also enables the synthesis of the so-called molecular shuttles,21 ± 27 viz., the complexes in which the macrocycle can migrate from one part of the rod molecule to another (the so-called translocation isomers). For the first time, such rotaxanes were synthesised in 1991 21 by the reaction of the tetracationic cyclophane 14 with the dumbbell-shaped compound 18 (Scheme 5) containing two p-dioxyphenylene fragments.The corresponding rotaxane was obtained in 32% yield. A 1H NMR spectroscopic study revealed that the cyclophane migrated between the two aromatic fragments of the L molecule at a rate of 500 s71. The activation free energy of the migration observed (DG) is*13 kcal mol71. Strategy II was also used for the synthesis of a series of [2]-Rt 19 ± 22 (yields 1%, 25%, 29% and 40%, respectively).22 It is remarkable that in neither case [3]-Rt was obtained. Of the four rotaxanes isolated, only complex 22 exists in the form of two translocation isomers. Similar `molecular shuttles' were obtained by substitution of electron-donor (e.g., tetrathiofulvalene,23 ± 25 4,40-bisphenol, benzidine 26, 27) fragments for one of the p-dioxy- phenylene fragments of the rod molecule; the yields of the isolated rotaxanes did not exceed 9%.Presumably, this can be attributed I G Panova, I N Topchieva Scheme 3 (CH2)6N N +Cu N N 3, [Cu(MeCN)4]+ O O OMe O N N Cu + N N O O O OMe O O O O O O O O O O 15Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them O HO O n O O O O 16, 17 MeCN 14O O HO n ON + + + N N O O O n = 0 (16, 160), 1 (17, 170). O O O Pri3SiO +N + + N N O O O to the fact that in these cases the complexation largely involves one binding centre of the rod molecule. O N+ O RO +N O O O O O ; n = 0 (19), 1 (20), 2 (21), 3 (22). R= O The synthesis of rotaxanes based on crown ether 15 was carried out using strategies I and III.28 Thus the reaction of the +N OH n +N Pri3SiO +N + Pri3SiOTf, N N OH n O O O Pri3SiO O O O O 18 14, MeCN 7 days, AgPF6 + O O O OSiPri3 +N CD3COCD3 4PF¡6 O O O O O ON+ OR O n +N 4PF¡6 19 ± 22 dication 23 with the bulky blocking reagent 24 in the presence of an equimolar amount of the macrocycle 15 under high pressure (strategy I) (Scheme 6) has been described.The yield of the target product, viz., [2]-Rt, was 23%. Noteworthy, the rate of the translocation of the macrocycle between the two dications in this complex is *300 000 s71, which markedly exceeds that of rotaxanes based on cyclobis(paraquat-p-phenylene). By varying the size of the blocking group in the dumbbell- shaped molecule 25 (Scheme 7), it became possible to synthesise rotaxanes using thermodynamically more favourable slipping of the macromolecule 15 onto the bulky terminal groups of com- pound 25 (strategy III, see Fig.2). Compound 25 in which the terminal tert-butyl groups were replaced severally by isopropyl, ethyl and methyl groups as well as by hydrogen atoms were heated in acetonitrile with four equivalents of the macrocycle 15 at 60 8C.29 This resulted in the self-organisation of [2]-Rt of the type 26 (see Scheme 7) in 47%, 45% and 51% yields for R=Et, Me and H, respectively. The isopropyl groups appeared to be too bulky for the slipping of the macrocycle. All the rotaxanes thus prepared were stable at room temperature.Strategy III was also employed in the synthesis of [2]- and [3]-Rt containing two bipyridine fragments.30 It should be noted that such rotaxanes cannot be synthesised using strategies I and II, O O O Pri3SiO O O Br N ; MeCN, 7 days, AgPF6 N BrO + O n ON +N + N OSiPri O O O n 160, 170 O O OSiPri O 3 O O O O Pri3SiO +N O O 27 Scheme 4 OSiPri O 3 4PF¡6 3 Scheme 5 O O OSiPri O 3 +N 4PF¡6+ + N N O O O28 + N CH2 N CH2 23 2PF¡6 But But O O But But R O But But R But whereas slipping allows one to obtain them in 20% and 55% yields, respectively. An illustrative example of a successful application of strategy III has been described.31 Heating of a mixture containing com- 15 MeCN, 50 8C, 10 days 27 = 27 O MeC6H4(ButC6H4)2C Figure 3.The synthesis of dendrimeric rotaxanes using strategy III.31 But + But N N + But +N N +O CH2 4PF¡6 + + O O N CH2 N CH2 2PF¡6 25 (R=But, Pri, Et,Me,H) O O +NO O O CH2 OO O 26 (R=H, Me, Et) 28 (19%) O O O + N + + N N N + + N O O O O O 24 O O CH2 CH2 O O O O O O +N CH2 O O O 2PF¡6 pound 27 and the macrocycle 15 affords [2]-Rt 28 (yield 19%), [3]-Rt 29 (yield 41%) and [4]-Rt 30 (yield 22%) (Fig. 3). Such branched supramolecular assemblies are the first examples of dendritic rotaxanes. + + 29 (41%) C(C6H4But)2C6H4Me + N O 6PF¡6O O O O O O + O O Cl O O O O 15 O O O + + O N N CH2 O O O But MeCN, 60 8C R +15 But But O O O But 30 (22%) C(C6H4But)2C6H4Me I G Panova, I N Topchieva Scheme 6 NH4PF6, H2O DMF, 10 kbar, 30 8C, 36 h But O O O But ButScheme 7 RRotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them c.The synthesis of cyclodextrin-containing rotaxanes The use of cyclodextrins (CD) as cyclic components has marked a new step in the synthesis of rotaxanes. These compounds were first discovered in 1891 32 and represent cyclic oligosaccharides built up of D-glucopyranose units linked together by a-1,4-glucoside bonds. The shape of the cyclodextrin molecules resembles a torus.The structure of a-, b- and g-cyclodextrins is schematically represented in Fig. 4. The presence of a cylindrical hydrophobic cavity determines the ability of cyclodextrins to form inclusion complexes with molecules of different chemical nature in aqueous solutions. The synthesis and characteristics of such complexes have been outlined in numerous reviews and monographs.33 ± 39 Suffice it to say that the driving forces of this complexation are Coulombic, dipole ± dipole, hydrophobic and van der Waals interactions as well as hydrogen bonds between the CD and `guest' molecules. Matching of the geometrical characteristics of the cyclodextrin cavity and those of the `guest' molecule is an important prerequisite for the formation and stability of the inclusion complexes. The unique capacity of cyclodextrins to interact selectively with the substrate molecules which are com- plementary in size makes them attractive subjects of the supra- molecular chemistry.OH H 6 H2C O 5 4 H : : H 3 1 2 H HO OH O H n Figure 4. The structural formula of a- (n=6), b- (n=7) and g-cyclo- dextrins (n=8). Initially, syntheses of cyclodextrin-containing rotaxanes were based on the ability of CD molecules to be threaded onto polymethylene chains. It should be noted that the cavity of one macrocycle accommodates approximately five methylene units. The blocking groups were introduced into pseudorotaxanes by the reaction with the terminal functional groups of the rod molecules.The role of stoppers was played by transition metal complexes. This approach was used in the synthesis of [2]-Rt 31 ± 33 based on a- and b-CD.40 The maximum yield of the rotaxanes (19%) was obtained for the systems comprising a-cyclodextrin and linear molecules whose alkyl chains contained 12 carbon atoms (n=12). Similarly, [2]-Rt 34 was prepared by the reaction of the a-CD ± 1,10-nonamethylenebis(4,40-bipyridine) complex with cya- noferrate(II) in an aqueous solution.41 The rotaxane formed was kinetically labile, so it could not be isolated from the solution. 4+ H2N NH2 NH2 H2 N (CH2)n H2N NH2 Co Co Cl Cl NH2 H2N NH2 H2N 31 ± 33 n = 8 (31), 10 (32), 12 (33); =a-CD, b-CD. 47 NC NC CN CNCN NC N Fe N N Fe N (CH2)n NC NC CN CN 34 Ion-to-ion interactions were used to stabilise cyclodextrin- containing pseudorotaxanes.42 The role of the thread was played by molecules carrying terminal ammonium groups, heptakis(2,6- di-O-methyl)-b-cyclodextrin (DM-b-CD) was used as the cyclic component. Pseudorotaxane 35 was precipitated from the solu- tion by addition of tetraphenylborate; after isolation and purifi- cation, its yield was 71%.[3]-Rt 36 which can be regarded as an analogue of heme-containing proteins was synthesised in a similar way.43 + 7XH3N(CH2)3O + 7XH3N(CH2)3O + 7XH3N(CH2)3O X=Ph4B7; =DM-b-CD. Stable rotaxanes can only be obtained in those cases where stoppers are covalently bound to the termini of the `guest' molecule. The main difficulty is related to the choice of a solvent which must serve as a suitable medium for the chemical reaction of the terminal groups of the pseudorotaxane and simultaneously ensure stabilities of the inclusion complexes.Water, which is the best solvent for the interaction of cyclodextrins with the substrate, is most often inappropriate for the introduction of terminal groups, since these reagents are usually poorly soluble in water or undergo hydrolysis. To overcome this problem, it was sug- gested 44 to use strong nucleophiles (e.g., NH2) as the functional groups of the stoppers and aliphatic carboxylic acid derivatives as the rod molecules. This approach was used in the synthesis of two [2]-Rt, viz., 37a,b, and their orientational isomers 38a,b in 15% yield.45 Me +N (CH2)n Fe Me 37a,b Me +N (CH2)n Fe Me 38a,b n = 7 (a), 11 (b).It is remarkable that the isomer 37a remained stable, whereas the complex 38a dissociated into constituents. This example illustrates the strong dependence of the stability of the rotaxanes on the spatial orientation of the CD molecules threaded onto the `guest' molecules. A similar strategy of the rotaxane synthesis in aqueous solutions on the basis of rod molecules carrying terminal NH2 groups and di-O-methyl- and tri-O-methyl-a-cyclodextrins 29 + 7 O(CH2)3NH3X 35 + 7 O(CH2)3NH3X N NH + 7 O(CH2)3NH3X HN N 36 CONH SO¡3 Ká CONH SO¡3 Ká30 was used by Harada and Kamachi.46 In this study, 1,12-diamino- dodecane complexes with methylated cyclodextrins reacted with an aqueous solution of trinitrobenzenesulfonic acid, which resulted in the corresponding rotaxanes isolated in 42% and 48% yields.The formation of inclusion complexes based on cyclodextrins is often used for stabilisation of photosensitive compounds.34 ± 36 The conversion of such complexes into rotaxanes is a logical sequel of these studies. Thus an azo dye was synthesised from a bisdiazonium salt and a b-naphthol derivative in the presence of various cyclodextrins.47 Rotaxanes 39a,b were prepared from a- and b-CD in 12% and 15% yields, respectively. The formation of such water-soluble rotaxanes illustrates the possibility of an increase in the stabilities and solubilities of practically important synthetic dyes using this simple approach.It has thus been demonstrated that molecular self-assembly is an efficient tool for the design of new structures. SO3Na NaO3S N N OH N+Cl7 NN N N N SO3Na NaO3S HO , H2O±Na2CO3 N N+Cl7 H N N OSO3Na NaO3S 39a,b =a-CD (a), b-CD (b). III. Polyrotaxanes The strategies of rotaxane synthesis can also be applied to the development of procedures for the preparation of structurally more elaborate compounds, viz., polyrotaxanes (PRt or [n]-Rt) which represent supramolecular assemblies where multiple mac- rocycles are non-covalently bound with the polymeric chains. Two main types of such complexes are distinguished, viz., linear polyrotaxanes where the macrocycles are threaded onto the main chain (Fig.5 a) and comb-like polyrotaxanes (Fig. 5 b). There are several main approaches to the synthesis of poly- rotaxanes, namely, the formation of a polymer in the presence of a macrocycle (method 1); the formation of a ring in the presence of a macromolecule (method 2); polymerisation or polycondensation of a stable pseudorotaxane (method 3); self-organisation of a pseudopolyrotaxane (pseudo-PRt) due to specific non-covalent b a n n Figure 5. A schematic representation of polyrotaxanes: (a) linear, (b) comb-like. I G Panova, I N Topchieva interactions (method 4) and temperature-induced slipping of the macrocycles onto the stoppers, viz., terminal groups or those pertaining to the main chain (method 5).It should be noted that cyclisation is usually performed in dilute solutions. However, if polyrotaxanes are synthesised by the method 2, the Le Chatelier principle requires that the polymer was used as a solvent or was taken in excess. This results in a significant increase in the viscosity of the reaction mixture and, correspondingly, in a decrease in the rate of the reaction. For this reason, method 2 is virtually inapplicable to the synthesis of polyrotaxanes. The role of macro- cycles is usually played by synthetic or natural cyclic molecules, e.g., crown ethers 48 ± 59 or cyclodextrins.60 ± 117 1. Linear polyrotaxanes based on crown ethers The procedures used for the synthesis of polyrotaxanes which incorporate crown ethers have been studied in sufficiently great detail.48 ± 59 They are based on the statistical threading of macro- cycles onto the rod molecule in the course of polymerisation (method 1).The possibility of the use of virtually all (as regards their chemical nature) linear molecules for the rotaxane synthesis allows the design of a great diversity of pseudopolyrotaxanes. 36-Crown-12, 42-crown-14, 48-crown-16 and 60-crown-20 are usually used as crown ethers. Radical polymerisation was used for the synthesis of pseudo- polyrotaxanes 40 based on polyacrylonitrile.48, 49, 59 Polystyrene- based polyrotaxanes 41 were synthesised by anionic polymer- isation of styrene in the presence of 36-crown-12 and 42-crown-14.50 Pseudopolyrotaxanes and polyrotaxanes based on various polyesters (compound 42) and polyurethanes (com- pounds 43 and 44) were obtained by polycondensation and polyesterification.51 ± 58 CN Ph R R CH CH CH2 CH2 n l n l 40 41 R =(4-ButC6H4)3C(CH2)4 O O O R RO O C O C (CH2)m (CH2)4 (CH2)2 l n O 42 R=Ph3CCH2C O O C NH C NH O(CH2CH2O)2CH2CH2O (CH2)6 n l 43 O O NH C O(CH2CH2O)2CH2CH2O C NH CH2 n l 44 �30-crown-10, 42-crown-14, 48-crown-16, 60-crown-20.The isolation and purification of the polymers thus formed were carried out by multiple precipitation of the macrocycles using selective solvents. To ensure invariable composition, it is sufficient to repeat the procedure once or twice even in the case of pseudopolyrotaxanes. This suggests that the folded conformation of the macromolecules prevents the dissociation of the complex into the constituents.The properties of the polymers synthesised were studied by NMR spectroscopy, gel permeation chromatog- raphy (GPC), viscosimetry and differential scanning calorimetry (DSC). It was found that the molecular mass of the polyrotaxane formed and the degree of threading of the crown ether increase with an increase in the concentration of the macrocycle and depend on the ratio of the components in the original mixture. The maximum efficiency of threading of crown ethers is achieved where the latter are used as solvents or co-solvents for monomers in the course of polymerisation.Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them O O + + N N O O OH HO 45 2PF¡6O O O O O O 15 But O+ + O N O O Z (CH2)3O (CH2)3O Z O x 2PF¡ O But Z=OCHN NHCO The possibility of a template synthesis of polyrotaxanes was also studied using crown ether 15 as a template.Co-polymer- isation of N,N0-bis(2-hydroxyethyl)-4,40-bipyridinium bis(hexa- fluorophosphate) (45) with bis(p-isocyanatophenyl)methane (46) in the presence of the macrocycle 15 (Scheme 8) afforded a polyrotaxane with a high (54%) content of cyclic molecules.51, 55 To increase the flexibility of the synthetic polymer, small amounts of an ethylene oxide oligomer were added to the reaction mixture. It was found that the molecular mass and the amount of the macrocycle in polyrotaxane depend on the ratio of the starting components as well as by the amount of the stopper added.The incorporation of macrocycles into polymers causes sig- nificant changes in the physicochemical properties (e.g., solubility, thermal and mechanical characteristics) of the rotaxanes formed in comparison with the starting compounds. Some authors 48 &plmn; 59 consider crown-ether-based polyrotaxanes as specific copolymers of the cyclic and linear components. The solubilities of poly- urethane- and polyester-based rotaxanes depend on their compo- sition as well as on the nature and size of the macrocycle. For example, the incorporation of 60-crown-20 increases the polarities of polyurethane-based rotaxanes so that these compounds, con- trary to the original polymers, become soluble in polar solvents. In some cases, synthetic polyrotaxanes were water-soluble producing micellar structures.55, 56 Treatment of polyurethane-based rotax- anes with solvents which are selective with respect to the incorpo- rated polymer was accompanied by the aggregation and even crystallisation of the cyclic component which was attributed 55, 56 to the free migration of the crown ethers along the rod molecule.Studies of the thermal characteristics of polyrotaxanes by DSC revealed that phase-transition temperatures strongly depend on the nature of the interacting components and the composition of the supermolecules formed. For example, the polymer based on NCO+ HO(CH2)6O O(CH2)6OH+OCN 47 CH2 48 CH2 O(CH2)6OCNH O(CH2)6O NHCO O =PM-a-CD, PM-b-CD.31 Scheme 8 O O O O OCN NCO + + 46 O O N N HO(CH2)3OH, OH HO O O (4-ButC6H4)2PhC(CH2)3OH 6 2PF¡ O O But O O O O N O Z O (CH2)3 O 6 y O But n poly(butane-1,4-diyl sebaceate) and 60-crown-20 produced two endothermal peaks at 40 and 60 8C, which corresponded to the melting of the cyclic and linear components, respectively. These values are several degrees lower than those for the corresponding individual crown ethers and the polyester, which suggests a decrease in the crystallinity of each of the polyrotaxane compo- nents.53 The glass transition of polyurethane-based rotaxanes is also observed at a lower temperature range in comparison with the glass transition temperatures for the original components.59 According to Gibson et al.,48 ± 59 the properties of polyrot- axanes formed by polymerisation of monomers can be changed directionally by varying their compositions.The feasibility of incorporation of crown ethers into polymers as plasticisers was also considered.56 2. Linear polyrotaxanes based on cyclodextrins The procedure for the preparation of cyclodextrin-containing polyrotaxanes by the method 1 included polycondensation of 1,4-bis(o-hydroxyhexyloxy)benzene (47) and 4,40-methylenedi- phenylisocyanate (48) (Scheme 9) in the presence of permethy- lated a- and b-cyclodextrins (PM-a-CD and PM-b-CD).60 This approach was used to synthesise a series of polyurethane-based pseudopolyrotaxanes in high yields (85% ± 92%) with the starting components taken at different ratios.It was found that the compositions of the synthetic polymers depend on the PM-CD: monomer ratio. The maximum content of the macro- cycles for PM-a-CD and PM-b-CD is one molecule of a cyclo- dextrin per four and five repeating fragments of the polymer, respectively. A 1H NMR spectroscopic study revealed that in the polymers synthesised PM-a-CD fragments are accommodated on the polymethylene groups, whereas PM-b-CD, which has a larger cavity, is predominantly localised on the aromatic groups of the Scheme 9 RuCl2(PPh3)3, H2O NHC O (CH2)6OCNH O(CH2)6O CH2 O n O32 rod macromolecule. As in the case of the polyrotaxanes contain- ing crown ethers, the glass transition temperature of cyclodextrin- based polyurethane pseudopolyrotaxanes was lower than that of the native polymer.This is attributed to partial destruction of polyurethane-specific intramolecular hydrogen bonds as a result of shielding of polar NH-groups of the polymer by the cyclic macromolecule. A similar strategy was used in the polycondensation of monomers which contained either binding centres or blocking groups in the presence of a macrocycle.61 It was shown that catalytic oxidative polycondensation of compounds 49 and 50 in the presence of a-CD resulted in the formation of irregular polyrotaxanes which comprised block copolymers incorporating the structural fragments A and B in a 16 : 84 ratio. H2N 49 H2NRuCl2(PPh3)3 a-CD H2O A= (CH2)11O(CH2)11 B= (CH2)11O(CH2)11 NH C= (CH2)11 N It is of note that the polyrotaxanes synthesised contain no structural fragments of the C type, whereas in the absence of cyclodextrin the polycondensation affords a polymer which con- tains*20% of such blocks.An alternative strategy of the polyrotaxane synthesis con- sisted in preliminary synthesis of inclusion complexes of a series of diamines with b-cyclodextrin and their subsequent polycondensa- tion with isophthaloyl or terephthaloyl chlorides 62 (method 3). The conclusion concerning the formation of the macromolecular cyclodextrin ± polymer complex was made on the basis of the results of elemental and differential thermal analyses. Radical polymerisation was used in the synthesis of cyclodextrin-contain- ing homopolymers and copolymers based on inclusion complexes of b-CD with vinylidene chloride, allyl chloride, styrene and methyl methacrylate.63 In this case, the reaction was accompanied by the chain transfer to cyclodextrin.The attempts to characterise unambiguously the compositions and structures of the resulting complexes failed owing to their poor solubilities and the presence of by-products.62, 63 For this reason, the synthesis of supramolec- ular structures incorporating polymers and cyclodextrin from the inclusion complexes of the corresponding monomers did not acquire popularity. a. Water-insoluble cyclodextrin-containing polyrotaxanes Two independent groups of investigators 64 ± 85 demonstrated the possibility of applying the molecular self-assembly principle (method 4) to the synthesis of polyrotaxanes.This method con- sists in the direct interaction of cyclodextrin and polymers in aqueous solutions. A group of Japanese investigators 64 ± 80 carried out a detailed study of interactions of poly(ethylene oxides) (PEO) with a-cyclo- dextrin. It was shown that mixing of aqueous solutions of the polymer and CD resulted in the precipitation of a weakly soluble product. It was assumed that in this case `self-organisation' of the inclusion complex occurred in which cyclodextrin molecules are NH2+HO(CH2)12OH 50 NH2 (A)l (B)m (C)n (B)m N NH ; N HN N NH ; N NH N . NH I G Panova, I N Topchieva threaded onto the polymeric chain.This type of complexes have acquired the name of `molecular necklaces' (MN). As a matter of fact, these structures represent pseudopolyrotaxanes which can be converted into polyrotaxanes by modification of their terminal groups. Studies of complexation of poly(ethylene oxides) with a-cyclo- dextrin by the nephelometric method revealed that the lowest molecular mass of a polymer necessary for the formation of insoluble complexes is 300. However, in a more recent publication by these authors it was shown that `molecular necklaces' can be prepared from tetra(oxyethylene) dibromide (MM=176).78 The rate of complexation reaches a maximum at the average molecular mass (Mn) of 1000 and shows a tendency to decrease with a further increase in Mn.68 This result is attributed to a decrease in the number of terminal groups with an increase in the molecular mass of the polymer, which in its turn is due to the inclusion nature of the complexes.Evidence for the formation ofMNcan be obtained from the results of elemental and thermogravimetric studies as well as from 1Hand 13C NMRspectroscopy and X-ray diffraction data. Thus 1H NMR spectroscopy was used to determine the compositions of the complexes synthesised. Irrespective of the molecular mass of PEO and the molar ratios of the reagents, the complexes formed had strictly stoichiometric compositions where one molecule of a-cyclodextrin corresponded to two ethylene oxide units. Molecular simulation revealed that the diameter of the PEO chain matches perfectly the width of the inner cavity of a-CD, whereas the length of two ethylene oxide fragments is practically equal to the height of the cyclodextrin cone.Additional evidence in favour of MN formation can be derived from the fact that in the case where PEO molecules contained bulky terminal groups (2,4-dinitrophenyl or 3,5-dinitrobenzoyl groups), the sizes of which exceed that of the inner cavity of a-CD, cyclodextrin loses its ability to be threaded onto the polymeric chain and no inclusion complex is formed. It was suggested that the driving force of self-organisation of the complexes are hydrophobic interactions between the cyclodextrin cavity and the polymer fragments as well as the formation of hydrogen bonds between the OH groups of the neighbouring CD molecules.Further studies showed that similar complexes could be prepared with other cyclodextrin ± polymer pairs (Table 1). These data suggest that hydrophobic polymers can be used for complexation along with hydrophilic ones. Although the forma- tion of complexes based on hydrophobic polymers takes much more time and requires preliminary sonication of the reaction mixture, the pseudopolyrotaxanes produced possess strictly stoi- chiometric compositions and they can be obtained in sufficiently high yields. It should be noted that the dependences of the yields of MN on the molecular mass of the polymer differ substantially for the complexes prepared from hydrophilic or hydrophobic poly- mers and cyclodextrin.Thus for the a-CD ±PEO complex, this dependence is described by a curve which consists of two parts. First, the yield of the polymer increases with an increase in the molecular mass and then is independent of the molecular mass. For hydrophobic polymers, this dependence is bell-shaped;65, 71, 74 in some cases, e.g., for poly(isobutylene),73 the product yield decreases monotonically. The observed regularities can be explained as follows. In aqueous solutions, hydrophobic polymers exist in an aggregated state. Since the tendency for aggregation increases with an increase in the molecular mass, the accessibility of the terminal groups of the polymer for the interaction with cyclodextrin is expected to decrease; therefore, only part of the macromolecules can find their `partners'.Some polymers, e.g., poly(oxytrimethylene), form pseudopolyrotaxanes with both a- and b-cyclodextrins (see Table 1), which was attributed 72 to different conformations of the polymer incorporated. It was shown with the help of 1H NMR spectroscopy and other analytical methods that the stoichiometric compositions of the complexes are usually independent of the molecular masses of the polymers in theMMrange studied and are consistent with the results of molecular simulation studies.64 ± 68 Violations of thisRotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them Table 1. Pseuropolyrotaxanes based on a- and b-cyclodextrins and polymers.Polymer Poly(ethylene oxide) Poly(propylene oxide) Poly(methyl vinyl ether) Poly(oligoethylene) Poly(isobutylene) Poly(oxytrimethylene) Poly(oxytetramethylene) Poly(e-caprolactam) regularity were observed only for the interaction of a- and b-cyclodextrins with poly(oxytrimethylene).72 When polymers with MM42000 were used, the compositions of MN remained constant and corresponded to one molecule of cyclodextrin per 1.5 ± 2 or 2 ± 2.5 monomeric units of the polymer for a- and b-CD, respectively. However, with an increase in the molecular mass of the rod macromolecule, the stoichiometry of the complex formed changed (see Table 1). Presumably, the increase in the hydro- phobicity with an increase in MM prevents the diffusion of the polymer in the aqueous medium and the involvement of all of the macromolecules in the complex formation.72 Probably, the pre- cipitation of the complex is accompanied by co-precipitation of the free polymer; therefore, the composition of the pseudopoly- rotaxane cannot be calculated exactly.It was shown 69 that g-cyclodextrin forms no stable complexes with unmodified PEO, although, like b-cyclodextrin, it forms a 2 : 1 complex with poly(propylene oxide) (PPO) (see Table 1). It was also found that poly(ethylene oxide) which contained bulky terminal substituents, e.g., the 3,5-dinitrobenzoyl substituent, interacted with g-cyclodextrin to form crystalline complexes in very high yields.70 A 1H NMR spectroscopic study revealed that the cavity of g-CD accommodates four oxyethylene fragments, which suggests that g-cyclodextrin is threaded simultaneously onto two polymeric chains.To corroborate this hypothesis, Harada et al.69 obtained a fluorescently labelled polymer, viz., bis(2-naphthylacetyl)poly(ethylene oxide). The MN prepared on the basis of this compound and g-cyclodextrin also had a stoichiometric composition 1 : 4. Fluorescence spectroscopic stud- ies revealed the presence of excimers, which suggests close contacts between the naphthyl residues and corroborates the hypothesis that the g-cyclodextrin molecule incorporates two PEO chains (Fig. 6). Similar crystalline double-stranded inclusion complexes MM300 400 600 1000 1500 2000 5000 400 425 725 1000 2000 3000 4000 20 000 702 100 500 800 1350 2700 700 1200 3100 250 1000 530 Yields of products (%) (number of monomeric units : number of CD molecules) a-CD 22 (2 : 1) 83 89 91 93 94 21 none """"""none 67 (3 : 1) none """"87 (1.5 ± 2.0 : 1.0) 90 (1.5 ± 2.0 : 1.0) 34 (5 : 1) 82 (1.5 : 1.0) 7 7 100 (2.8 : 1.0) 82 (1 : 1) g-CD b-CD none traces 68 " " " " " " " " " " " " 1 (2 : 1) 76 (2 : 1) 71 27 74 84 77 96 80 50 31 32 20 27 15 none 67 (3 : 1) 68 " none 70 67 (3 : 1) " 73 18 64 (3 : 1) 8 90 4 96 5 87 52 (2.0 ± 2.5 : 1.0) 7 72 67 (2.0 ± 2.5 : 1.0) 7 55 (4 : 1) 7 7 7 72 7 7 74 based on g-cyclodextrin and PEO (MM=1500) were obtained in high (*80%) yields;86 in this case the complexation did not necessitate blocking of the chain termini by bulky substituents.Later, a group of Japanese investigators synthesised a poly- rotaxane 51 based on the molecular necklaces by the reaction of terminal amino groups of bisaminopoly(ethylene oxide) incorpo- rated into a-cyclodextrin with fluoro-2,4-dinitrobenzene.66 The yield of the reaction product after isolation and purification by GPC was 60%. Subsequent modifications of the polyrotaxane 51 allowed the authors to synthesise oligomers containing cross- linked cyclodextrins, the so-called `polymeric tubes' (Fig. 7).80 These compounds were synthesised by treatment of the polymer 51 in 10% NaOH with epichlorohydrin.Using GPC, it was shown that epichlorohydrin cross-linked CD molecules along the poly- meric chain with the formation of hydroxypropylene bridges. The blocking groups were removed by hydrolytic cleavage with 25% NaOH which resulted in the release of the polymer enclosed inside the tube. The final product (yield 92%) represented a hollow tube which consisted of about 15 cross-linked cyclodextrin molecules (MM=20 000) (52, see Fig. 7). Probably, such structures can be used for selective separation of substances. Figure 6. A schematic representation of an inclusion complex of g-cyclo- dextrin with bis(2-naphthylacetyl)poly(ethylene oxide).69 33 Ref.34 HN O2N O NO2 HN O2N O NO2 HO HO Figure 7. A scheme of synthesis of polymeric tubes from polyrotaxanes based on bisaminopoly(ethylene oxide) and a-cyclodextrin.85 It was shown 87 that the reaction of cyclodextrin with the conjugated conducting polymer 53 (polyaniline), which contains emeraldine bases, NH NH afforded a pseudopolyrotaxane in which the polymer was incor- porated inside the cavity of the non-conducting cyclic molecules.These structures have been termed as `insulating molecular wires'. This system was used to demonstrate that cyclodextrins prevent chemical oxidation of the rod macromolecule, e.g., on doping of polyaniline with iodine. The use of modified CD (particularly, of methylated macro- cycles) as `hosts' allows one to compare processes of molecular recognition involving native CD and their derivatives.Using 1H NMRspectroscopy, it was shown than none of the methylated cyclodextrins form complexes with PEO as can be evidenced from the fact that no precipitation occurred even after 2-months' storage of their mixture. A different situation is observed in the interaction of these cyclodextrins with hydrophobic polymers. Complexes of PPO and poly(tetrahydrofuran) (PTHF) with heptakis- and hexakis-(2,6-di-O-methyl)cyclodextrins (DM-CD) as well as with heptakis- and hexakis-(2,3,6-tri-O-methyl)cyclo- dextrins (TM-CD) have been described in the literature.79 It was shown that the addition of DM-b-CD first increases significantly the solubility of PPO in water and then a crystalline complex is formed.However, TM-a-CD, TM-b-CD and DM-a-CD neither favour the solubilisation of PPO in water nor form inclusion complexes. The solubility of PTHF in water increases in the presence of low concentrations of DM-b-CD and DM-a-CD. At high concentrations of these cyclodextrins, the solubility of PTHF decreases and inclusion complexes are precipitated. TM-b-CD also forms inclusion complexes with PTHF. The yields of PTHF±DM-b-CD complexes increase with an increase in the weight-average molecular mass (Mw), it is a maximum at Mw=1000. The stoichiometric composition of PTHF± DM-b-CD complexes corresponds to one molecule of the macro- O OHO O O HO HO HO N 0.5 53 O O O 51H2C CHCH2Cl, 10% NaOH HO O O O HO HO HOPolymeric tube 52 N 0.5 n O O O O HO O O O HO 25% NaOH HO HO cycle per 1.0 ± 1.5 monomeric units of the rod macromolecule. Taking into account the number of atoms in the repeating fragment of the polymer per one CD molecule, it appears that the composition of the PTHF±DM-b-CD complex is consistent with the stoichiometric composition of the corresponding MN based on a-CD.The experimental data altogether suggest that hydrophobic interactions between methylated cyclodextrins and hydrophobic polymers make a weighty contribution to the process of molecular recognition. Based on the geometrical correspondence of theCDmolecules to polymeric `guests', one can postulate the existence of ternary complexes which represent MN with low-molecular-weight `guests' incorporated into them.Such complexes were obtained in PEO-b-CD ± aromatic compound systems.88 Benzene, its mono-, di- and tri-substituted derivatives were used as aromatic compounds. After mixing of these three components, a complex precipitated from the aqueous solution. Radiolabelled 3H-PEO was used for quantitative determination of poly(ethylene oxide) content in the complexes. The content of b-CD was determined polarimetrically, while that of the aromatic compound was established by UV spectroscopy. The composition of the com- plexes corresponds to one b-CD molecule per two units of PEO and one molecule of the aromatic compound. The ternary com- plexes precipitate with benzene, benzoic acid and p-nitrophenol but do not precipitate in the presence of o-nitrophenol and 2,4- dinitrophenol. X-Ray diffraction studies have shown that the structures of the ternary complexes are identical with that of MN.Simulation of the ternary complexes demonstrated that the regular orientation of CD in MN is not disturbed upon incorpo- ration of benzene and its monosubstituted derivatives into their cavities. The molecular dynamics of MN based on a-CD ±PEO89 and b-CD ± PPO 90 complexes has been studied. It was shown that the main driving force of molecular recognition are the van der Waals interactions. Hydrogen bonds provide arrangement of the CD rings in a `head-to-head' and `tail-to-tail' fashion. Cyclodextrins in polyrotaxanes exist in a more symmetrical and a less rigid conformation than in the individual state.The formation of polyrotaxanes is accompanied by the transition of the polymers to the stretched conformation due to an increase in the proportion I G Panova, I N Topchieva O O HN NO2 O O2N O HN NO2 O O2N HO HO HO HORotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them of trans-conformers in comparison with the state of the isolated polymeric chains. The structure- and energy-related reasons for the non-statistical distribution ofCDinMNprepared on the basis of PEO± PPO block copolymers were established using the dynamic Monte Carlo method.91 It was found that the stability of the complexes is determined by both hydrophobic interactions between the `host' cavity and the `guest' molecule and the hydro- gen bonds between the cyclodextrin molecules.It should be noted that the interest in MNis generated largely by fundamental problems. According to Tonelli et al.,92 ± 94 the polymeric inclusion complexes are convenient subjects for study- ing the behaviour of ordered and isolated polymeric chains, which simulates the state of oriented polymers in the crystalline phase. It was also shown that macromolecular inclusion complexes can be used for the preparation of high-strength oriented fibres. Removal of cyclic molecules from the complexes was carried out by treatment of the polymers with a solvent which is selective with respect to cyclic compounds.92 The selectivity of formation of crystalline polymeric inclusion complexes incorporating cyclo- dextrins served as a basis for the development of a new procedure for purification of polymeric materials under laboratory condi- tions, the so-called extractive crystallisation.94 b.Pseudopolyrotaxanes based on block copolymers Considerable progress in the synthesis of supramolecular struc- tures based onCDand polymers is associated with the use of block copolymers (BC) of ethylene oxide and propylene oxide (plur- onics) as the `guest' molecules. Pluronics differ in their composi- tions, number of blocks and mutual arrangements, which permits the synthesis ofMNhaving different structures and properties. By varying the length of the free component of the complex based on a BC and cyclodextrin, one can obtain both water-insoluble 95 ± 99 and water-soluble 100 polymeric inclusion complexes.For steric reasons, a-CD cannot interact with a poly(ethylene oxide) com- ponent of BC of the PPO ±PEO± PPO type. A systematic study of the reactions of a-, b- and g-CD with different types of PEO ± PPO block copolymers 95 ± 99 has been carried out. Their characteristics are listed in Table 2. The interaction of a- and b-CD with BC I and BC II built up of poly(ethylene oxide) and poly(propylene oxide) blocks of virtually equal lengths has been studied.95 It was found that the addition of solutions of block copolymers to aqueous solutions of the corresponding macrocycles results in the precipitation of water- insoluble complexes.Using the a-CD ±BC I system as an exam- ple, it was shown that with an increase in the pluronic concen- tration the mass of the isolated complex increases at first and after reaching a certain maximum remains unchanged, which suggests the formation of a stoichiometric complex. Polarimetric and IR spectroscopic studies of these complexes as well as molecular simulation studies revealed that different pluronic blocks become involved in this process depending on the type of the cyclodextrin (a- or b-CD, which differ in the diameter of their inner cavity) used for the complexation. Thus, the interaction with a-CD involves Table 2. Some characteristics of the block copolymers based on poly- (ethylene oxide) (PEO) and poly(propylene oxide) (PPO) used in the synthesis of pseudopolyrotaxanes.95 ± 99 MM Degree of polymerisation Content of PPO (%) Block Type of copolymer copoly- mer PPO PEO 28 20 19 24 10 a 30 18 18 a 52 a 40 50 60 45 23 40 3000 2000 2700 6000 3000 PEO± PPO PEO± PPO PEO± PPO ± PEO PEO± PPO ± PEO PPO ±PEO± PPO III III IV Va The degree of polymerisation of one block.35 PPO block PEO block a-CD PEO block b-CD Figure 8. Aschematic representation of a- and b-cyclodextrin complexes with ethylene oxide and propylene oxide diblock copolymers.95 only the PEO block, while the interaction with b-CD, only the PPO block. The stoichiometric compositions of the complexes are similar to those of MN based on homopolymers, viz., two monomeric units of ethylene oxide or propylene oxide per one a- or b-CD molecule, respectively.Thus the interactions of a- and b-CD with the PEO± PPO diblock copolymers result in the formation of new BC (Fig. 8) which consist of a rigid block, viz., a MN, and a free flexible poly(alkylene oxide). A study of the interactions of cyclodextrins with PEO ± PPO triblock copolymers III ±V (see Table 2) revealed that the com- positions of the crystalline complexes depend on the position of the interacting block and the reaction conditions.96 ± 98 If CD is threaded onto the inner block of the copolymer, the complex formed (54, Fig. 9) has a stoichiometric composition which is characteristic of cyclodextrin complexes with homopolymers and diblock copolymers. In those cases where CD is threaded onto the peripheral blocks, two types of block structures can be formed depending on the reaction conditions, viz., BC with a symmetrical position of MN (Fig.9, complexes 55 and 56) and non-sym- metrical BC which are composed of three different blocks, one of them being MN (Fig. 9, complexes 57 and 58). This depends on the concentration of the reagents in the solution. Thus in saturated solutions where the rate of complexation is comparable with the rate of crystallisation, it is the non-symmetrical complexes with one filled block that are formed. In dilute cyclodextrin solutions, i.e., under conditions where the rate of crystallisation is much lower than the rate of threading of CD onto the polymeric chains, both peripheral blocks of the complexes represent MN.PPO block PEO block b-CD 54 55 PPO block PEO block a-CD 56 57 58 Figure 9. Aschematic representation of a- and b-cyclodextrin complexes with ethylene oxide and propylene oxide triblock copolymers.36 As has been noted above, two types of inclusion complexes of g-cyclodextrin with poly(alkylene oxides) are possible. These comprise either one PPO chain or two PEO chains. The use of PEO ±PPO block copolymers as `guests' makes it possible to elucidate to which of these blocks g-CD manifests higher affinity. To answer this question, the complexation of g-CD with PEO ±PPO diblock copolymers was studied where PEO and PPO blocks are sterically equally accessible for the interaction with cyclodextrin.96 ± 98 An analysis of the compositions of the complexes formed shed some light on the localisation of g-cyclo- dextrins, since the number of g-CD molecules that are threaded onto PEO and PPO blocks differs significantly for the given BC (I or II).It was shown experimentally that the number of g-CD molecules per one copolymer molecule (rexp) represents an inter- mediate value between the rtheor values calculated in the assump- tion that either PEO or PPO blocks take part in the complexation. This finding suggests that the interaction of g-CD with PEO and PPO is nonselective. The use of the g-cyclodextrin ± triblock copolymer couple opens up an opportunity for preparing new non-linear BC.Complexation of g-CD with pluronics of the PEO± PPO ±PEO type which contain peripheral ethylene-oxide blocks affords double-stranded inclusion complexes. It was found 97 that in saturated solutions the composition of the complex formed remains unchanged at any value of the g-CD :BC IV ratio. This suggests that the interaction of g-CD with the above block copolymer results in a stoichiometric complex, namely, a double- stranded inclusion complex in which two strands of PEO which belong to different copolymer molecules appear to be incorpo- rated into the channel formed by the macrocycles. Taking account of different accessibility of the PEO blocks with respect to a-CD, it was demonstrated that the interaction of g-CD with a triblock copolymer of the PEO ±PPO ±PEO type yields compound 59 (Fig. 10) which is characterised by nonsymmetrical distribution of the free PEO blocks.In dilute solutions, the complexation of g-CD with the PEO ±PPO ±PEO copolymer results in pseudopolyro- taxane 60 in which both PEO blocks are coated with the CD molecules (see Fig. 10). Thus, the vast potentials in the design of pluronics and the ability of cyclodextrins to interact selectively with PEO and PPO blocks enable one to use them as a basis for the synthesis of inclusion complexes of different compositions and molecular architecture. PEO block PPO block g-CD 59 60 Figure 10. A schematic representation of g-cyclodextrin complexes with the triblock copolymer IV.c. The complexes of nonionic surfactants with cyclodextrins Poly(ethylene oxide)-containing surfactants can be regarded as particular BC which comprise hydrophilic poly(ethylene oxide) blocks, whereas the hydrocarbon fragments play the role of their hydrophobic `tails'. PEO surfactants of different chemical nature, viz., octylphenyl PEO ethers [Triton X-45 (61a) and Triton X-100 (61b)], polyethylene glycol-1000 monostearate (62) and dodecyl poly(ethylene oxide) ether (63) were used as `guests'.97, 99, 101, 102 I G Panova, I N Topchieva O(CH2CH2O)nH ButCH2CMe2 61a,b n = 5 (a), 10 (b) O n-C12H25O(CH2CH2O)23H n-C17H35CO(CH2CH2O)23H 63 62 Mixing of saturated aqueous solutions of poly(alkylene oxides) and a-CD resulted in the formation of a crystalline precipitate the structure of which is similar to that of MN based on PEO. The determination of the compositions of the complexes showed that one CD molecule corresponds to two monomeric units; thus, the a-CD molecules are selectively threaded onto the PEO fragments of surfactants.Important information about the type of interaction of PEO surfactants with cyclodextrins in dilute solutions can be derived from an analysis of colloidal and chemical properties of the surfactants, primarily, from the effect of CD on the critical micelle concentration (CMC). The depend- ences of CMC on the CD: surfactant molar ratio represent curves with saturation, which allows one to determine the stoichiometric compositions of inclusion complexes in solution.It is worth noting that the compositions of such complexes are identical both in solution and in the solid phase. The complexes formed by the interaction of the same surfactant with a-, b- and g-CD differ drastically both in the structures and their colloidal and chemical properties.101, 102 The chemical nature of the group linking together the hydrophilic and hydrophobic fragments of surfactants was found to affect critically the localisation and possible migration of CD molecules along the surfactant chains. The covalent binding of poly(ethylene oxide) fragments to cyclodextrin molecules results in the formation of PEO±CD conjugates which represent bouquet-like structures endowed with amphiphilic properties (Fig.11).103 ± 105 The conjugates have molecular masses of 3000 ± 5500 and are characterised by narrow molecular mass distributions; the average degree of substitution is 8 to 12 ethylene oxide units per one glucose residue. A study of the complexation of the conjugates with Triton X-100 (61b) revealed that the pseudopolyrotaxanes formed have a stoichiometric composition, i.e., one molecule of the conjugate is threaded onto each hydrophilic fragment of the surfactant. These pseudopolyrotaxanes can form micellar structures in aqueous solutions. The architecture of the spherical molecular assemblies consisting of highly branched structural elements resembles that of dendrimers (Fig. 12). Branched structures of yet another type were obtained 99, 106 as with a result of interactions of star-shaped conjugates of PEO and PEO ±PPO diblock copolymers with proteins, e.g., a-chymotryp- sin (ChT).Such conjugates are formed as a result of one-point covalent attachment of the monofunctional derivatives of the polymers to the amino groups of the protein. Mixing of these compounds cyclodextrin (PEO ± ChT ±CD and Figure 11. The structure of the poly(ethylene oxide) ± cyclodextrin con- jugate.104Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them Figure 12. The hypothetical dendrimer-like structure based on the poly- (ethylene oxide) ± cyclodextrin conjugate and a micelle of Triton X-45.105 BC± ChT ±CD conjugates) results in the formation of precipi- tates.The determination of their compositions revealed that they are similar to those of the complexes based on linear polymers and the corresponding CD. This implies that all the polymeric chains within the conjugates are accessible for the interaction with the CD. The crystalline structures of the resulting complexes are identical to those of MN. A decrease in the solubility of the complexes in water in comparison with the original polymer ± protein conjugates or non-covalent polymer ± protein adducts limits their application in biotechnology. The PEO ±CD conju- gates were used to confer solubility onto the complexes prepared on the basis of polymer ± protein adducts and CD.107, 108 The complexation between PEO chains, which are the components of covalent and non-covalent PEO ±ChT and PEO ±CD adducts, was studied using a kinetic method based on the analysis of enzymic properties of novel supramolecular structures incorpo- rating these components.107 For this purpose, the rate constants of thermoinactivation of ChT (k) in the adducts of PEO ± ChT with PEO ± b-CD were determined.A decrease in k suggests that complexation of the constituents occurs. The stoichiometric compositions of the complexes formed were determined from the dependence of k on the PEO ± b-CD :PEO(ad) molar ratio, where PEO(ad) is the poly(ethylene oxide) that is involved in the adducts. It was shown that each of the polymeric chains of the PEO± ChT conjugates forms an inclusion complex with PEO± b-CD, whereas in the case of non-covalent PEO ±ChT complexes only a half of the polymeric chains of PEO(ad) take part in the formation of the supramolecular structures.The hypothetical structures of supra- molecular dendritic assemblies are depicted in Fig. 13. d. Studies of the structural organisation of crystalline pseudopolyrotaxanes based on cyclodextrins Supramolecular assemblies can be characterised both by the type of the intermolecular interactions which hold together their constituents and by their spatial configuration, viz., their archi- tecture or `suprastructure'. The phase state and the organisation of macromolecular inclusion complexes are studied using TGA, DSC, X-ray diffraction analysis as well as by optical, scanning electron and scanning tunnelling microscopy.An X-ray diffraction analysis showed that the precipitates formed by poly(alkylene oxide) ± cyclodextrin complexes have crystalline structures and differ from one another and from the original components in the type of the crystal lattice. It should be noted that the method which is commonly employed for the description of the structural organisation of `molecular necklaces' is based on comparison of the diffractograms of MN and the 1 2PEO± ChT conjugate 2 1 PEO ± ChT complex Figure 13. The hypothetical dendrimer-like structures of the complexes formed by the covalent (a) and non-covalent (b) adducts of PEO ± ChT and the b-CD ± PEO conjugate; (1) a-chymotrypsin, (2) poly(ethylene oxide), (3) covalent adduct based on PEO and b-cyclodextrin (b-CD ± PEO).107 complexes of the corresponding CD with various low-molecular- weight compounds.According to Saenger's classification,34 the structures of the CD-based complexes can be divided into two main types, viz., cage-type structures in which cyclic molecules form brick network patterns and channel-type structures where the macrocycles are stacked sequentially in a pillar-like fashion. A comparative analysis of the diffractograms revealed 68, 71, 72 that MN belong to channel-like structures. However, this approach discloses only the qualitative differences but cannot provide quantitative evaluation of the parameters of the crystal lattices of macromolecular inclusion complexes. Harada et al.76, 77 have succeeded in growing single crystals of a-CD complexes with tetra- and hexa(ethylene oxide) and b-CD with poly(propylene oxide) (MM=425), which mimic MN, and 37 a + 3 b + 338 the b-CD ± poly(oxytrimethylene) complex (MM=1400) and carried out their detailed X-ray diffraction analysis.It was found that in all these cases the macrocycles are arranged in a `head-to- head' and `tail-to-tail' fashion to form hydrogen bonds between all the secondary hydroxy groups of the large bases of the cyclo- dextrin torus. Water molecules are localised within the structure of a-CD-based [4]-Rt between the minor bases of the macrocycles. The b-CD dimers are shifted relative to one another due to the presence of only one hydrogen bond between the primary OH groups.Rod-like macromolecules are localised inside the narrow channels formed by cyclodextrins and exist in a trans-conforma- tion.The use of single crystals for the disclosure of the structural organisation of rotaxanes allows one to estimate, with a high degree of accuracy, the unit cell parameters, to determine the coordinates of all the atoms within the composition of the complex and to characterise the intermolecular contacts. How- ever, this method has not received wide acceptance in structural studies of high-molecular-weight compounds because of the difficulty and sometimes impossibility of obtaining suitable large-sized single crystals. An approach to the description of the structural organisation of polymeric crystals consists in the use of oriented samples and in the recording and interpretation of X-ray fibre patterns.It was shown 86, 109 that in contrast to ordinary polymers whose orientation demands preliminary treatment, the formation of MN is accompanied by spontaneous formation of oriented structures. An X-ray diffraction analysis which includes a comparison of X-ray fibre patterns and diffractograms enables one to index the observed reflections, to determine the parameters of crystal lattices of the complexes formed and thus to characterise the structure of polymeric inclusion complexes at the molecular level. The results obtained suggest that crystallisation of MN results in the formation of structures in which cyclodextrin molecules are arranged one after another along a common symmetry axis.X-Ray diffraction data suggest the hexagonal, monoclinic and tetragonal packing of MN based on a-, b- and g-cyclodextrins, respectively. In order to obtain the information about the morphology of the crystallites formed by MN and the nature of their mutual packing in the course of precipitation, cyclodextrin complexes with poly(alkylene oxides) were studied by optical microscopy and scanning electron microscopy.86, 109 The crystals of the b-CD ± PPO complexes have the shape of sharply edged parallelo- grams, whereas those of the g-CD ±PEO complexes have the shape of rectangular parallelipipeds with an average facet size of the order of several microns, which is consistent with the results of an X-ray diffraction analysis of the symmetry of the crystal lattices of the complexes. The precipitates of cyclodextrin ± poly(alkylene oxide) complexes represent lamellar structures the MN in which are located at right angles to the planes of the lamellae.Isolated MN were visualised by scanning tunnelling micro- scopy. Japanese investigators 75, 87 have succeeded in photograph- ing a-CD ±PEO and b-CD ± polyaniline complexes containing discernible rod-like structures. Their lengths correspond to the lengths of the extended molecule of the polymeric `guest', while their widths match the diameter of the macrocycle. These results are of fundamental importance for the under- standing of the mechanism of the self-assembly of the supra- molecular structures formed by polymeric inclusion complexes at different levels of their structural organisation.Three main stages in the formation of the nanostructures in such complexes can be distinguished. The first step consists in the threading of the macrocycles onto the polymeric chains. The driving forces of this process are the cooperation of the hydrophobic interactions between the nonpolar cavity of the cyclic molecule and the fragments of the polymeric `guest' and the formation of hydrogen bonds between the hydroxy groups of the cyclodextrins. The second step is the crystallisation of MN and the formation of lamellar crystallites the inclusion complexes in which are located at right angles to the planes of the lamellae.In the third step, I G Panova, I N Topchieva individual crystallites of the complex are aggregated to form an oriented precipitate. In the precipitation, the lamellae are aligned in parallel to the plane of the support to form an axial pattern of the precipitated material. Thus, polymeric cyclodextrin ± poly(al- kylene oxide) inclusion complexes can serve as a basis for the design of well-organised supramolecular assemblies. e. Water-soluble polyrotaxanes Cyclodextrin-containing water-soluble pseudopolyrotaxanes were first synthesised by the interaction of CD with polyelectro- lytes.81 ± 85 Self-assembly method was used to obtain inclusion complexes of the so-called poly(iminooligomethylenes) (64a ± c),81 viz., the polymers containing oligomethylene and quaternary ammonium fragments (65,82 66,83 67a,b84, 85), with a-cyclodextrin.In this case, the threading of CD molecules occurs by virtue of cooperation of hydrophobic and van der Waals interactions between the cyclodextrin cavity and the aliphatic sites of the polymers. H H + + + N +N N (CH2)10 (CH2)m N (CH2)n H H 65 64a ± c m=n = 6 (a); 11 (b); m=10, n = 3 (c). Me Me H + + + N (CH2)m N N (CH2)n (CH2)10 H Me Me 66 67a,b m=n=10 (a); m=6, n=10 (b). Using 1H NMR spectroscopy, it was shown that a-CD molecules are localised on oligomethylene fragments containing no less than 10 units. Therefore, the short-chain polymer 64a does not form any complex with a-CD. In contrast with poorly soluble MN, soluble complexes are formed at a very low rate at room temperature, this takes from several hours to several months and even years (in the case of compound 66).Such a kinetics is attributed to the low rate of migration of CD molecules along the polymeric chain which in turn is due to steric hindrances created by bulky hydrate shells around the charged amino groups. At higher temperatures, slipping of the macrocycles over these `barriers' occurs (method 5, Section III) resulting in a significant increase in the threading rate.85 Polyrotaxanes 68a,b which are also readily soluble in water were prepared on the basis of MN consisting of polymers 64b,c and a-CD, respectively.81 N (CH2)11 0.1 O N 0.3 n 68a N (CH2)3NH(CH2)10 0.67 O N 0.3 *60 68b The binding of a-CD molecules to definite sites of the polymeric chain was achieved by acylation of the imino groups by nicotinyl chloride.Using polymers 64c and 66 as examples, it was demonstrated that b-CD which has a larger cavity does not form any stable inclusion complexes. However, the use of an a- and b-CD mixture made it possible to prepare polyrotaxanes containing 60% b-CD and 7.5% a-CD in which b-CD wasRotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them blocked at the ends by a-CD molecules which slip off the chain at a very low rate.83 The possibility of formation of a water-soluble pseudopolyr- otaxane was also demonstrated for the b-CD ± triblock copolymer PEO ±PPO ± PEO.100 It was found that the interaction of b-CD with block copolymers of the PEOn ± PPOm ±PEOn type gives either a crystalline precipitate (n m) or a water-soluble complex (n m) depending on the composition of the polymer used.The addition of cyclodextrin induces an upfield shift of the methyl and methylene proton signals in the 1H NMR spectra. This suggests the complexation with block copolymers incorporated into the cavity of CD. Amphiphilic DM-b-CD as a macrocycle and an analogous PEO ±PPO ±PEO copolymer with blocks of approximately equal sizes (n&m) were used to study the interactions of cyclodextrin with polymers in a monolayer. This study showed 100, 110 that the polymer passes from the coil to the rod-like conformation during complexation. Hence, one of the approaches to the synthesis of water-soluble MN consists in the introduction, into the starting polymer, of hydrophilic fragments which are not involved in the complexation.Yet another approach to confer water solubility onto poly- meric complexes is based on chemical modification of CD molecules in polyrotaxanes. The synthesis of water-soluble bio- degradable polyrotaxanes was carried out by Ooya et al.111 ± 114 These authors used bis[aminopoly(ethylene oxide)] as the polymer and a-cyclodextrin as the cyclic compound. The terminal groups were blocked by an excess of L-phenylalanine (L-Phe) derivatives. The polyrotaxane formed was treated with propylene oxide which alkylated theOHgroups of CD. The enhanced solubility ofMNin water seems to be due to the destruction of hydrogen bonds.A three-step synthesis including removal of protective groups from the fragment of the stopper is depicted in Scheme 10. The results of light scattering studies 112, 113 suggest that the polyrotaxanes based on hydroxypropylated a-CD and PEO (MM=2000 for 69a and 4000 for 69b) aggregate in aqueous solutions; the degree of aggregation of polyrotaxanes is much lower than that of the H2N O Bn NH BnO NH O Bn NH H2N O MM=2000 (a), 4000 (b). original PEO containing the same terminal fragments and is equal to 16 ± 23 and 2 for the complexes 69a,b, respectively. It was noted also that these polyrotaxanes preserve their rod-like conformation in solutions.It was found 112, 113 that enzymic hydrolysis of peptide bonds with papain which resulted in the cleavage of the stoppers brought about simultaneous supramolecular destruction of polyrotaxanes 69a,b. This leads to complete dissociation of these polyrotaxanes into constituents irrespective of the degree of their aggregation (Fig. 14). Figure 14. The destruction of the polyrotaxanes 69a,b caused by enzymic hydrolysis of terminal L-Phe groups.113 It was shown 116, 117 that polyrotaxanes of the type 69a,b can be used in pharmacology and medicine as drug carriers and drug permeation enhancers. The interaction of these polyrotaxanes with blood cells was studied in detail; it was found that hydroxy- propylated polyrotaxanes increase the fluidity of membranes and control the level of calcium by inhibiting platelet-induced eleva- tion of Ca2+.The same group of investigators proposed to use this principle in the design of drug conjugates on the basis of polyrotaxanes and were the first to attempt to prepare such conjugates with insulin 112 and theophylline 115 which are covalently linked to CD molecules (Fig. 15). O O O O O O Bn BnO NH O O O O O CHMe H2CO H2, Pd/C OH x O O O O OH y Polyrotaxane 69a,b Enzyme `Stoppers' O NH2 O O OO NH O OH x O NH O OH y 69a,b 39 Scheme 10 Bn O OBn NH O BnNH2 O40 Hydroxypropylated a-CD Bn NH CH2CH2O CH2CH2O CH2CH2O CH2CH2O CH2CH2O CH2CH2O H2N O PEO O HN O Biodegradable fragment Figure 15.The drug ± polyrotaxane complex prepared on the basis of poly(ethylene oxide) blocked by L-phenylalanine and hydroxypropylated a-cyclodextrin. 3. Comb-like polyrotaxanes Non-covalent interactions of cyclodextrins with lateral fragments of comb-like polymers is yet another interesting example of molecular recognition. The determination of rate constants for the complexation of cyclodextrin with a series of copolymers of acrylamide with alkyl methacrylates (Table 3) 118 demonstrated the possibility of selective interaction of CD with comb-like polymers resulting in the formation of pseudopolyrotaxanes. In order to design true polyrotaxanes, Ritter et al.119, 120 proposed to use the strategy of covalent attachment of preformed pseudo- rotaxane 70 which is blocked at one end to the activated side fragments of the polymer (Scheme 11).Table 3. The constants of complexation (K) of cyclodextrins and aliphatic fragments of water-soluble copolymers of acrylamide with alkyl meth- acrylates.118 Alkyl in alkyl methacrylate K /litre mol71 a-CD Bun But Bui n-C6H13 iso-C8H17 n-C12H25 55 736 290 303 990 A series of polyrotaxanes incorporating DM-b-CD have been synthesised.119 ± 123 It was found that these polyrotaxanes are less viscous than the starting polymers, apparently due to destruction of the hydrogen bonds between the fragments in the rod macro- molecule. Me Me C C CH2 CH2 C O CO2Me NH (CH2)10 O C (EtO)2OC n =DM-b-CD.g-CD b-CD 3407 757 7 7 110 294 660 751 245 +H2N(CH2)3CNH O m 70 Biodegradable fragment CH2CH2O CH2CH2 O HN HN O The same group of investigators made an attempt to synthe- sise comb-like polyrotaxanes by radical polymerisation in aque- ous solutions of the corresponding pseudorotaxanes based on b-CD, DM-b-CD and N-methacryloyl-11-aminodecanoic acid (method 2). However, this attempt was unsuccessful, since poly- merisation was accompanied by elimination of the macrocycle from the side fragments of the polymer being formed.124 Alkylation of NH groups of poly(benzoimidazoles) with Br(CH2)12OC(O)CH2CPh3 in the presence of TM-b-CD resulted in comb-like polyrotaxane 71a ± d.125 N X N X=p-C6H4 (a), (CH2)8 (b), (CH2)11O(CH2)11 (c), (CH2)11 (d); O O 71a ± d Ph3C It was found that the degree of N-alkylation and the amount of the macrocycles incorporated depend on the lengths of the `spacers' between the benzoimidazole fragments.Me THF CPh3 CH2 CC O NH (CH2)10 C O NH (CH2)3 C O NH CPh3 I G Panova, I N Topchieva Bn NH NH2 OCH2CH2 O O O Drug (theophylline or insulin) =TM-b-CD. Scheme 11 Me C CH2 CO2Me m nRotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them IV. Supramolecular devices based on rotaxanes and polyrotaxanes Characteristic physicochemical properties of rotaxane-like struc- tures are determined by both the unusual topology and the nature of their constituents.In the recent years, rotaxanes as molecular assemblies are considered as promising candidates for the con- struction of supramolecular devices which represent functional, structurally organised systems.126 ± 128 The feasibility of using rotaxanes in this area is due primarily to the ease of control over molecular directionality which determines the specific spatial configuration of their constituents. The introduction of photo-, electro- or ion-active groups into rotaxane molecules will allow the transfer of energy, electrons or ions as well as the transmission of signals and the storage of information.12, 126 ± 128 Rotaxanes [2]-Rt which incorporate two different porphyrins as stoppers can serve as examples.The photophysical properties of [2]-Rt 10 and 72a,b were studied 12, 129 ± 131 and the rates of a photoinduced intramolecular electron transfer from the excited Zn-porphyrin to Au-porphyrin (1, 22 and 34 ps for complexes 10, 72a and 72b, respectively) were compared to that in the dumbbell- shaped bisporphyrin 73 (55 ps). It was found that in the case of rotaxanes, the rate of the electron transfer increases significantly, the maximum increase being observed for complex 10. This finding was attributed to the presence of copper(I) ions which play the role of mediators and to changes in the energy of the orbitals in the supermolecule under effect of the coordination centre.129 ± 131 RN O O O N N M N N O O O N 10, 72a,b R R N+ N Au N N R NN N N Zn N N R73 M=Cu+ (10), Zn2+ (72a), none (72b); R=1,3-But2C6H3.R N+ Au N N R e7 N N ZnN R e7 41 The photosensitive rotaxane 74 was prepared on the basis of the naphthalene derivative of a-cyclodextrin (N-a-CD) and poly(ethylene oxide) with dansyl groups as stoppers.132 O7 O S hn OEnergy transfer Energy transfer CH2O Me2N NMe2 O OS NH (CH2CH2O)nCH2CH2NH SO O 74 O O7 CH2O SO =N-a-CD. The fluorescence spectra of rotaxane 74 displayed a significant decrease in the intensity of signals elicited by the naphthalene fragments in comparison with the original N-a-CD which is due to the transfer of energy from the excited naphthalene groups of modified CD to the terminal dansyl groups of the rod molecule of PEO.The results of these studies are of interest for the construc- tion of photochemical supramolecular devices which are able to effect directed transfer of electrons and energy. Yet another promising line of investigations is the preparation of controlled `molecular switches' (or `shuttles' according to Stoddart). Molecular switch-on/off processes represent reversible transitions of one of the components between the two positions which differ either in structure or in conformation. The recently synthesised [2]-Rt 75 (Scheme 12) can serve as an example of an electrochemical (or chemical) `molecular shuttle'.127, 133 In this case, the migration of the macrocycle 14 occurs as a result of a redox reaction or protonation ± deprotonation.The synthesis of a photoreactive molecular switch prepared on the basis of CD-containing [2]-Rt 76 has been carried out (Fig. 16).134 Here, azobenzene was used as a rod molecule, while 2,4-dinitrophenyl groups were used as stoppers. Irradiation of an aqueous solution of the complex 76 with UV light (l=360 nm) induced trans ± cis-isomerisation of the azobenzene fragment. This reaction is reversible which was confirmed by the reverse reaction occurring upon irradiation of the solution in the visible region of the spectrum (l=430 nm). These changes in the configuration of the rod molecule induce the migration of the cyclodextrin molecule from one binding centre to another. A pH-sensitive `molecular shuttle' was synthesised by self-organisa- tion of aliphatic diamines and a triamine ligand.135, 136 Studies with polyrotaxanes based on b-CD and the PEO ±PPO ±PEO triblock copolymer showed that these poly- mers also manifest the properties of `molecular switches'.137, 138 The transition of polyrotaxanes from the insoluble into the soluble state can occur either upon a rise in the temperature or upon an increase in a pH above 12 due to the destruction of the hydrogen bonds between the CD molecules.As a result, the macrocycles migrate along the rod macromolecule. 1H NMR studies of poly- rotaxane solutions in 0.1 M NaOH showed that at room temper- ature CD molecules are distributed statistically along the whole polymeric chain, whereas upon heating the macrocycles are predominantly localised on PPO fragments (Fig. 17).Apparently, by changing such parameters as temperature and permittivity of the medium, one can govern the solubility of polyrotaxanes and the distribution of the CD molecules. The design of photonic, electroninc and ionic switching devices based on molecular components and their incorporation42 O O Pri3SiO NH O Pri3SiO O Pri3SiOO N + +N NO2 O2N Figure 16. A photosensitive `molecular switch' based on b-cyclodextrin. PEO Figure 17. A mechanical `molecular switch' based on polyrotaxane. into well-organised assemblies is the next step in the development of functional materials on a nanoscale. Further studies in this field will inevitably culminate in the construction on their basis of multifunctional chemical `machines' as the basis for the develop- ment of chemical informatics and an analysis of functioning of these devices in close conjunction with related biological proc- esses.126 + O O O NH +N + N O O NH NH + + N N 14 + + O O O NH2 NH2 O N N N+ + b-CD N O2N NO2 76 PPO b-CD D * * * +N + N O O O OSiPri3 N + N + O O O O O 75 +N + N O O O O +N N + + + trans l=430 nm l=360 nm + + cis Thus, we are witnessing a revival of interest in rotaxane-like structures. New papers are being published and these are devoted to a search for their practical application.The literature data concerning polyrotaxanes consider them as a new type of regu- latory polyfunctional rigid-chain polymers.It is these properties that determine the area of their further applications. New oppor- tunities are emerging for the construction of complex polymeric structures which combine the blocks of `molecular necklaces' with the flexible blocks of free polymers. Therefore, the fundamental problems related to the development of methods of synthesis of new supramolecular assemblies and investigation into their struc- tural organisation and properties still remain in the focus of attention. This review has been written with the financial support of the Russian Foundation for Basic Research (Project No. 00-03- 32770). References 1. D B Amabilino, J F Stoddart Chem.Rev. 95 2725 (1995) 2. I T Harrison, S Harrison J. Am. Chem. Soc. 89 5723 (1967) 3. I T Harrison J. Chem. Soc., Chem. Commun. 231 (1972) 4. G Agam, D Graiver, A Zilkha J. Am. Chem. Soc. 98 5206 (1976) 5. G Agam, A Zilkha J. Am. Chem. Soc. 98 5214 (1976) I G Panova, I N Topchieva Scheme 12 7e7 +e7 TFA OSiPri3 pyridine OSiPri3 + + + +Rotaxanes and polyrotaxanes. Their synthesis and the supramolecular devices based on them 6. C O Dietrich-Buchecker, P A Marnot, J-P Sauvage Tetrahedron Lett. 23 5291 (1982) 7. C O Dietrich-Buchecker, J-P Sauvage Tetrahedron Lett. 24 5091 (1983) 8. CWu, PRLecavalier,YXShen,HGibson Chem. Mater. 3 569 (1991) 9. C Dietrich-Buchecker, J-P Sauvage Tetrahedron 46 503 (1990) 10.J-C Chambron, V Heitz, J-P Sauvage J. Chem. Soc., Chem. Commun. 1131 (1992) 11. J-C Chambron, A Harriman, V Heitz, J-P Sauvage J. Am. Chem. Soc. 115 6109 (1993) 12. J-C Chambron, V Heitz, J-P Sauvage J. Am. Chem. Soc. 115 12 378 (1993) 13. F Diederich, C O Dietrich-Buchecker, J-F Nierengarten, J-P Sauvage J. Chem. Soc., Chem. Commun. 781 (1995) 14. J-C Chambron, C O Dietrich-Buchecker, J-F Nierengarten, J-P Sauvage J. Chem. Soc., Chem. Commun. 801 (1993) 15. B Odell, M V Reddington, A M Z Slawin, N Spenser, J F Stoddart, D J Williams Angew. Chem. 100 1605 (1988) 16. R C Helgeson, T L Tarnowski, J M Timko, D J Cram J. Am. Chem. Soc. 99 6411 (1977) 17. P R Ashton, A M Z Slawin, N Spenser, J F Stoddart, D J Williams J. Chem. Soc., Chem.Commun. 1066 (1987) 18. Y A Shen, P T Engen,M A Berg, J P Merola, K P Parry, A M Slawin, J F Stoddart Macromolecules 25 2768 (1992) 19. P L Aneli, P R Ashton, R Ballardini, V Balzani,M Delgado, M T Gandolfi, T T Goodnow, A E Kaifer, D Philp, M Pietraszkiewicz, L Prodi, M V Reddington, A M Z Slawin, N Spenser, J F Stoddart, C Vicent, D J Williams J. Am. Chem. Soc. 114 193 (1992) 20. P R Ashton,MGrognuz, AM Z Slawin, J F Stoddart, D J Williams Tetrahedron Lett. 32 6235 (1991) 21. P L Aneli, N Spenser, J F Stoddart J. Am. Chem. Soc. 113 5131 (1991) 22. X Sun, D B Amabilino, J W Parsons, J F Stoddart Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 34 104 (1993) 23. D Philp, A M Z Slawin, N Spenser, J F Stoddart, D J Williams J. Chem.Soc., Chem. Commun. 1584 (1991) 24. P R Ashton, R A Bissell, N Spencer, J F Stoddart,M S Tolley Synlett 923 (1992) 25. V Balzani, A Credi, G Mattersteig, O A Matthews, F M Raymo, J F Stoddart, M Venturi, A J P White, D J Williams J. Org. Chem. 65 1924 (2000) 26. E Cordova, R A Bissell, N Spenser, J F Stoddart, A E Kaifer J. Org. Chem. 58 6550 (1993) 27. M Asakawa, G L Brown, S Menzer, F M Raymo, J F Stoddart, D J Williams J. Am. Chem. Soc. 119 2614 (1997) 28. P R Ashton, D Philp, N Spencer, J F Stoddart J. Chem. Soc., Chem. Commun. 1124 (1992) 29. R R Ashton,M Belohradsky, D Philp, J F Stoddart J. Chem. Soc., Chem. Commun. 1269 (1993) 30. M Asakawa P R Ashton, R Ballardini, V Balzani,M Belohradsky, M T Gardolfi, O Kocian, L Prodi, F M Raymo, J F Stoddart, M Venturi J.Am. Chem. Soc. 119 302 (1997) 31. D B Amabilino, P R Ashton,M Belohradsky, F M Raymo, J F Stoddart J. Chem. Soc., Chem. Commun. 751 (1995) 32. A Villers C.R. Hebd. Seances Acad. Sci. 112 536 (1891) 33. J Szejtli Cyclodextrins and Their Inclusion Complexes (Budapest: Academia Kiado, 1982) 34. W Saenger, in Inclusion Compounds (Eds J L Atwood, J E D Davies, D D MacNicols) (London: Academic Press, 1984) 35. J Szejtli, in Topics in Inclusion Science (Ed. J ED Davies) (Dordrecht: Kluwer Academic 1988) p. 26 36. H-J Schneider Angew. Chem., Int. Ed. Engl. 30 1417 (1991) 37. A K Chatjigakis, C Donze, A W Coleman, P Cardot Anal. Chem. 64 1632 (1992) 38. G Wenz Angew. Chem., Int. Ed. Engl. 33 803 (1994) 39.C A Nepogodiev, J F Stoddart Chem. Rev. 98 1969 (1998) 40. H Ogino J. Am. Chem. Soc. 103 1303 (1981) 41. R S Wylie, D H Macartney J. Am. Chem. Soc. 114 3136 (1992) 42. T V S Rao, D S Lawrence J. Am. Chem. Soc. 112 3614 (1990) 43. J S Manka, D S Lawrence J. Am. Chem. Soc. 112 2440 (1990) 44. R Isnin, A E Kaifer J. Am. Chem. Soc. 113 8188 (1991) 45. J F Stoddart Angew. Chem., Int. Ed. Engl. 31 846 (1992) 46. A Harada, M Kamachi Chem. Commun. 1413 (1997) 43 47. S Anderson, T D WClaridge, N L Anderson Angew. Chem., Int. Ed. Engl. 36 1310 (1997) 48. P T Engen, H W Gibson New J. Chem. 17 723 (1993) 49. H Marand, A Prasad, C Wu,M Bheda, H W Gibson Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 639 (1991) 50. H W Gibson, P T Engen, S-H Lee, S Liu, H Marand Polym.Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 64 (1991) 51. H W Gibson, C Wu, Y X Shen, M Bheda, J Sze, P Engen, A Prasad, H Marad, D Loveday, G Wilkes Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 593 (1991) 52. H W Gibson, C Wu, Y X Shen, M Bheda, J Sze, P Engen, A Prasad, H Marad, D Loveday, G Wilkes Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 637 (1991) 53. Y X Shen, H W Gibson Macromolecules 25 2058 (1992) 54. X Shen, P T Engen, M Berg, J S Merola, H W Gibson Macromolecules 25 2786 (1992) 55. Y X Shen, D Xie, H W Gibson J. Am. Chem. Soc. 116 537 (1994) 56. H W Gibson, S Liu, P Lecavalier, C Wu, Y X Shen J. Am. Chem. Soc. 117 852 (1995) 57. H W Gibson, D Nagvekar, N Yamaguchi,W S Bryant, S Battacharjee Polym.Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 38 64 (1997) 58. H W Gibson, D Nagvekar, W S Bryant, J Powell, S S Battacharjee Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 38 115 (1997) 59. P E Mason,WS Bryant, HWGibson Macromolecules 32 1559 (1999) 60. I Yamaguchi, Y Takenaka, K Osakada, T Yamamoto Macromolecules 32 2051 (1999) 61. I Yamaguchi, K Osakada, T Yamamoto J. Am. Chem. Soc. 118 1811 (1996) 62. N Ogata, K Sanui, J Wada J. Polym. Sci., Polym. Lett. 14 459 (1976) 63. MMaciejewski J. Macromol. Sci., Chem. 13A 77 (1979) 64. A Harada, M Kamachi Macromolecules 23 2821 (1990) 65. A Harada, M Kamachi J. Chem. Soc., Chem. Commun. 1322 (1990) 66. A Harada, J Li, M Kamachi Nature (London) 356 325 (1992) 67. A Harada, J Li, M Kamachi Macromolecules 26 5698 (1993) 68.A Harada, J Li, S Suzuki,MKamachi Macromolecules 26 5267 (1993) 69. A Harada, J Li, M Kamachi Nature (London) 370 126 (1994) 70. J Li, A Harada, M Kamachi Bull. Chem. Soc. Jpn. 67 2808 (1994) 71. A Harada, M Okada, J Li,M Kamachi Macromolecules 28 8406 (1995) 72. A Harada, M Okada, J Li Acta Polym. 46 453 (1995) 73. A Harada, S Suzuki,M Okada,M Kamachi Macromolecules 29 5611 (1996) 74. A Harada, Y Kawaguchi, T Nishiyama,M Kamachi Macromol. Rapid. Commun. 18 535 (1997) 75. A Harada, in Abstracts of Reports of the 9th International Symposium on Cyclodextrins, Santiago de Compostela, 1998 2-O-2 76. A Harada, J Li, M Kamachi, M Kitagawa, Y Katsube Carbohydr. Res. 305 127 (1998) 77.S Kamitori, O Matsuzaka, S Kondo, S Muraoka, K Okuyama, K Noguchi,M Okada, A Harada Macromolecules 33 1500 (2000) 78. A Harada, M Okada, Y Kawaguchi, M Kamachi Polym. Adv. Technol. 10 3 (1999) 79. M Okada,M Kamachi, A Harada Macromolecules 32 7202 (1999) 80. A Harada, J Li,MKamachi Nature (London) 364 516 (1993) 81. G Wenz, B Keller Angew. Chem., Int. Ed. Engl. 31 197 (1992) 82. B Keller, G Wenz, in Abstracts of Reports of the 6th International Symposium on Cyclodextrins (Ed. A R Hedges) (Paris: Editions de Sante, 1992) p. 192 83. G Wenz, B Keller Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 34 (1) 62 (1993) 84. G Wenz, F Wolf, M Wagner, S Kubik New J. Chem. 17 729 (1993) 85. W Herrmann, B Keller, G Wenz Macromolecules 30 4966 (1997) 86.I G Panova, V I Gerasimov, F A Kalashnikov, I N Topchieva Vysokomol. Soedin., Ser. B 40 2077 (1998) a 87. K Yoshida, T Shimomura, K Ito, R Hayakawa Langmuir 15 910 (1999) 88. I N Topchieva, E I Popova, F A Kalashnikov, I G Panova, V G Avakyan, A L Ksenofontov, V I Gerasimov Dokl. Akad. Nauk 357 648 (1997) b 89. J Pozuelo, F Mendicuti,WL Mattice Macromolecules 30 3685 (1997) 90. J Pozuelo, F Mendicuti,W Mattice Polym. J. 30 479 (1998) 91. B Mayer, C T Klein, I N Topchieva, G KoÈ hler J. Comput.-Aided Mol. Design 13 373 (1999)I G Panova, I N Topchieva 44 137. H Fujita, T Ooya,M Kurisawa, H Mori, M Terano, N Yui Macromol. Rapid. Commun. 17 509 (1996) 138. H Fujita, T Ooya,M Kurisawa, N Yui. Adv. Polym. Biomater. Sci. 649 (1997) a�Polym. Sci. (Engl. Transl.) b�Dokl. Chem. Technol., Dokl. Chem. (Engl. Transl.) c�Russ. J. Bioorg. Chem. (Engl. Transl.) d�Biol. Membr. (Engl. Transl.) 92. A E Tonelli Polym. Int. 43 7) 93. A E Tonelli, S Nojima Macromolecules 27 7220 (1994) 94. L Huang, A E Tonelli J. Macromol. Sci., Rev. Macromol. Chem. Phys. 38C 781 (1998) 95. I G Panova, V I Gerasimov, T E Grokhovskaya, I N Topchieva Dokl. Akad. Nauk 347 61 (1996) b 96. I N Topchieva, I G Panova, V I Gerasimov in Preprints of the 8th International Cyclodextrin Symposium, Budapest, 1996 p. 31 97. I G Panova, V I Gerasimov, V N Tashlitskii, I N Topchieva, V A Kabanov Vysokomol. Soedin., Ser. A 39 663 (1997) a 98. I N Topchieva, I G Panova, V I Gerasimov, K I Karezin, V A Kabanov Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 38 589 (1997) 99. I N Topchieva, V I Gerasimov, I G Panova, K I Karezin, N V Efremova Vysokomol. Soedin., Ser. A 40 310 (1998) a V A Kabanov Vysokomol. Soedin., Ser. A 36 271 (1994) a Akad. Nauk 355 357 (1997) b 100. I N Topchieva, A L Blyumenfel'd, A A Klyamkin, V A Polyakov, 101. I N Topchieva, K I Karezin, I G Panova, V I Gerasimov Dokl. 102. I N Topchieva, K I Karezin J. Colloid Interface Sci. 213 29 (1999) 103. I N Topchieva, V A Polyakov, S V Elezkaya, G V Bystryzky, K I Karezin Polym. Bull. 38 359 (1997) 104. I N Topchieva, P Mishnik, G Kyun, K I Karezin, S V Eletskaya Dokl Akad. Nauk 360 (1998) b 105. I N Topchieva, PMischnick, G Kuehn, V A Polyakov, S V Elezkaya, G I Bystryzky, K I Karezin Bioconjugate Chem. 9 676 (1998) 106. I N Topchieva, N V Efremova, B I Kurganov Usp. Khim. 64 293 (1995) [Russ. Chem. Rev. 64 277 (1995)] 107. I N Topchieva, E M Sorokina, E M Medvedeva, N V Efremova, B I Kurganov Bioorg. Khim. 25 520 (1999) c 108. I Topchieva, E Sorokina, N Efremova, A Ksenofontov, B Kurganov Bioconjugate Chem. 11 22 (2000) 109. I G Panova, V I Gerasimov, F A Kalashnikov, I N Topchieva Dokl. Akad. Nauk 355 641 (1997) b 110. A A Klyamkin, I N Topchieva, S Yu Zaitsev, V P Zubov Biol. Membr. 13 313 (1996) d 111. T Ooya, H Mori, M Terano, N Yui Macromol. Rapid. Commun. 16 259 (1995) 112. T Ooya, N Yui Adv. Polym. Biomater. Sci. 283 (1997) 113. H Fujita, T Ooya, N Yui Macromol. Chem. Phys. 199 2311 (1998) 114. J Watanabe, T Ooya, N Yui Chem. Lett. 1031 (1998) 115. T Ooya, N Yui J. Control. Rel. 58 251 (1999) 116. W Kamimura, T Ooya, N Yui J. Control. Rel. 44 295 (1997) 117. N Yui, T Ooya, T Kumeno Bioconjugate Chem. 9 118 (1998) 118. M Born, H Ritter Macromol. Chem. Rapid. Commun. 12 471 (1991) 119. H Ritter Makromol. Symp. 77 73 (1994) 120. M Born, T Koch, H Ritter Acta Polym. 45 68 (1994) 121. M Born, T Koch,H Ritter Macromol. Chem. Phys. 196 1761 (1995) 122. M Born, H Ritter Angew. Chem., Int. Ed. Engl. 35 309 (1995) 123. M Born, H Ritter Adv. Mater. 8149 (1996) 124. J Jeromin, H Ritter Macromolecules 32 5236 (1999) 125. I Yamaguchi, K Osakada, T Yamamoto Macromolecules 30 4288 (1997) 126. J-M Lehn Supramolecular Chemistry (Weinheim: VCH, 1995) 127. V Balzani,M Go mez-Lo pez, J F Stoddart Acc. Chem. Res. 31 405 (1998) 128. N Armaroli, V Balzani, J-P Collin, P Gavina, J-P Sauvage, B Ventura J. Am. Chem. Soc. 121 4397 (1999) 129. J-C Chambron, A Harriman, V Heitz, J-P Sauvage J. Am. Chem. Soc. 115 6109 (1993) 130. E David, R Born, E Kaganer, E Joselevich, H DuÈ rr, J Willner J. Am. Chem. Soc. 119 7778 (1997) 131. S S Zhu, P J Carroll, TMSwager J. Am. Chem. Soc. 118 8713 (1996) 132. M Tamura, D Gao, A Uen, in Abstracts of Reports of the 9th International Symposium on Cyclodextrins, Santiago de Compostela, 133. R A Bissell, E Cordova, A E Kaifer, J F Stoddart Nature 134. M-V Martinez-Diaz, N Spenser, J F Stoddart Angew. Chem., 135. D A Leigh, A Murphy, J P Smart, A M Z Slawin Angew. Chem., 136. A S Lane, D A Leigh, A Murphy J. Am. Chem. Soc. 119 11 092 1998 4-P-9 (London) 369 133 (1994) Int. Ed. Engl. 36 1904 (1997) Int. Ed. Engl. 36 728 (1997) (1997)

ISSN:0036-021X    

出版商:RSC    

年代:2001

数据来源: RSC

摘要:

Russian Chemical Reviews 70 (1) 45 ± 63 (2001) Mechanochemical synthesis of intermetallic compounds T F Grigorieva, A P Barinova, N Z Lyakhov Contents I. Introduction II. Mechanochemical synthesis of intermetallic compounds and solid solutions at concentration limits of binary equilibrium diagrams III. Mechanochemical synthesis of non-equilibrium phases in bimetallic systems with negative mixing enthalpies IV. Mechanochemical synthesis of supersaturated solid solutions in systems with positive mixing enthalpies V. Quasicrystals and amorphous alloys VI. Phase and structural transformations in the mechanochemical synthesis of intermetallic compounds Abstract. mechanochemical the on studies of state current The The current state of studies on the mechanochemical synthesis shown is It considered.is systems metallic binary of synthesis of binary metallic systems is considered. It is shown that that this intermetallic of preparation the for suitable is method this method is suitable for the preparation of intermetallic com- com- pounds of limits concentration in solutions solid and pounds and solid solutions in concentration limits of equilibrium equilibrium diagrams The systems. binary many of diagrams of many binary systems. The mechanochemical mechanochemical approach for promise most the exhibit to demonstrated is approach is demonstrated to exhibit the most promise for prepar- prepar- ing by characterised systems in compounds intermetallic ing intermetallic compounds in systems characterised by large large differences the of densities the in and points melting the in differences in the melting points and in the densities of the initial initial components sizes grain nanometer with phases as well as components as well as phases with nanometer grain sizes and and metastable the influence which factors, major The phases.metastable phases. The major factors, which influence the con- con- centration solid non-equilibrium of existence of limits centration limits of existence of non-equilibrium solid solutions solutions prepared revealed. are method, mechanochemical the by prepared by the mechanochemical method, are revealed. Using Using numerous of formation the that demonstrated is it examples, numerous examples, it is demonstrated that the formation of solid solid solutions may involve several stages.At the first stage, nanosized solutions may involve several stages. At the first stage, nanosized layered simultaneous with formed are structures composite layered composite structures are formed with simultaneous dis- dis- persion of the initial components (the formation of a large contact persion of the initial components (the formation of a large contact area). The second stage involves the synthesis of intermetallic area). The second stage involves the synthesis of intermetallic compounds step, third the At composites. layered nanosized in compounds in nanosized layered composites. At the third step, the the intermetallic give to solvent metal a in dissolved are compounds intermetallic compounds are dissolved in a metal solvent to give a solid references 397 includes bibliography The solution. solid solution.The bibliography includes 397 references. I. Introduction Intermetallic compounds can exist only in the crystalline state. Individual molecules cannot be distinguished in these compounds and they cannot be melted or dissolved without the loss of individuality and do not exist in the gaseous phase. In addition, the physicochemical properties of intermetallic compounds differ substantially from those of their components.1±3 Intermetallides with a particular composition differ in the chemical properties not only from the constituent metals, but also from intermetallides, which are characterised by the same elemental composition, and yet contain the components in a different ratio.4, 5 T F Grigorieva, A P Barinova, N Z Lyakhov Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch of the Russian Academy of Sciences, ul.Kutateladze 18, 630128 Novosibirsk, Russian Federation. Fax (7-383) 232 28 47. Tel. (7-383) 217 09 58. E-mail: root@solid.nsk.su (T F Grigorieva). Tel. (7-383) 232 86 83. E-mail: lyakhov@solid.nsk.su (N Z Lyakhov) Received 24 April 2000 Uspekhi Khimii 70 (1) 52 ± 71 (2001); translated by T N Safonova #2001 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2001v070n01ABEH000598 45 46 47 50 52 53 Presently, a general theory, which would allow one to reveal factors stabilising particular intermetallic compounds, is lacking.A search for these factors was performed as follows. A group of systems in which the stability of intermetallic phases can be related to the effect of a particular factor was established after which the effect of this factor in other systems in which it was less evident was analysed. Three factors were revealed, viz., the ratio of the total number of valence electrons (e) to the total number of atoms per unit cell (a), the tendency for the maximum filling of space (i.e., for the formation of closest packing or structures with high coordination numbers) and the difference between the electro- negativities of the components. The latter factor is of minor importance and is clearly manifested only in a small group of Zintl phases,6 viz., in compounds of active metals (alkali metals, alkaline-earth metals, magnesium and aluminium) with germa- nium, tin, lead and bismuth.7, 8 Hume-Rothery demonstrated 9 that phases with the same electron concentration (e/a) have similar crystal structures.In different systems, one of the following three types of structures is characteristic of phases with an electron concentration of 3/2, the so-called b phases: body-centred cubic (BCC) structures (the Cu ± Zn, Cu ±Al and Cu ± Sn systems), structures of the b-Mn type (Cu ± Si, Ag ±Al and Au ± Al) or hexagonal structures (Ag ± Zn, Cu ± Si and Ag ± Sn). Phases with an electron concen- tration of 21/13 have complex cubic structures of g-brass. In the case of e/a=7/4, e phases with hexagonal close-packed (HCP) structures are formed. The b, g and e phases have come to be known as electron compounds.In the case of a favourable dimension factor (more exactly, the number of electrons per unit cell), the electron concentration is of primary importance in the formation and stability of a particular crystal structure. Compounds belonging to the MgZn2 , MgCu2 and MgNi2 structural types (the so-called Laves phases) are the most wide- spread intermetallides. For these compounds, the ratios between the atomic radii of the components (in addition to the above- mentioned stabilising factors) are also of great importance. The characteristic feature of Laves phases is that the smaller atoms (Zn, Cu and Ni) are grouped together to form tetrahedra linked to each other.The MgZn2 , MgCu2 and MgNi2 structures differ in the mode of arrangement of the tetrahedra. The bulkier magne- sium atoms occupy the holes in the network of tetrahedra. As a result, very close packed structures are formed, the coordination number of the bulkier atoms being equal to 16. This value is larger than the coordination number (12) corresponding to the maxi- mum density of packing of spheres of the same size. The46 coordination numbers of the smaller atoms in these structure are equal to 12.6 The above-mentioned factors are responsible for the stability of solid solutions as one of the types of intermetallic compounds.7 In the case of similar electronegativities of the elements and a favourable dimension factor, the electron concentration is the major factor affecting the limiting solubility.The quantitative theory of solubility of polyvalent elements in metals of the copper group is based on the concept of filling of the first Brillouin zone with electrons in the face-centred cubic (FCC) crystal structure.8 Theoretically (taking into account the electron concentration), a solid solution can exist over wide concentration limits. However, the preparation of such solutions in these limits is determined primarily by the dimension factor. It was empirically established that if the atomic diameter of the element dissolved differs from the atomic diameter of the solvent by more than 14%± 15%, the dimension factor is unfavourable and the region of existence of the solid solution is limited.9 No reliable theoretical explanation has been provided for the threshold value of 15%. Quantitative calculations were carried out within the framework of an elastic- sphere model.King 10 calculated the dimension factors for 469 substitution solid solutions and confirmed the above threshold value. Therefore, the major factors influencing the formation and thermodynamic stability of intermetallic phases at equilibrium were revealed empirically. Main procedures for the preparation of equilibrium interme- tallic compounds involve alloying followed by homogenisation and sintering. Intermetallides with high formation enthalpies are generally prepared by the self-propagating high-temperature syn- thesis.Yet another procedure for the synthesis of intermetallic compounds, viz., the mechanochemical method, has been devel- oped intensively in recent years. This method is promising in the synthesis of equilibrium and metastable phases, supersaturated solid solutions and amorphous phases and allows the preparation of intermetallides from components possessing high melting and boiling points (for example, MoSi2) as well as from components characterised by large differences between these points (for example, the boiling point of magnesium in the Mg± Ti system is lower than the melting point of titanium). The mechanochemical procedure can be used for the introduction of the third component into a binary system to impart special properties to intermetal- lides.Compounds prepared by the mechanochemical method are characterised by high dispersity (in most cases, nanosized particles are obtained), which affects the physicochemical properties of these compounds. Currently, one of the major problems with which researchers are faced in dealing with mechanochemical synthesis is to reveal the factors governing the formation and stability of phases prepared by this method. In the present review, the experimental data on the problems of the mechanochemical synthesis in metallic systems published over the last 15 years are systematised. Earlier data, as a rule, are cited in the discussion of the general problems of metal deforma- tion and mass transfer in the solid body. II.Mechanochemical synthesis of intermetallic compounds and solid solutions at concentration limits of binary equilibrium diagrams Analysis of the published data demonstrated that the mechano- chemical method can be used for the synthesis of all major groups of intermetallic compounds, viz., of the following electron com- pounds: e and b phases in the Zn ±Ag 11 and Cu ± Zn 12 systems, g phases in the Cu ± Zn system,13 e and Z phases in the Cu ± Sn system,14 Z (Cu2Sb) and d (Cu4.5Sb) phases in the Cu ± Sb system 15 and the Laves phases Fe2Ti,16 Mg2Ni,17 ± 19 Mg2Cu,19 MgZn2 19 and Fe2Tb.20 The mechanochemical procedure for the synthesis of intermetallic compounds is most promising when the T F Grigorieva, A P Barinova, N Z Lyakhov use of conventional metallurgical methods presents difficulties, in particular, in the synthesis of silicides of refractory metals.For example, the melting point of molybdenum (2620 8C) is virtually equal to the boiling point of silicon (2600 8C), whereas the densities of these elements differ by a factor of more than four (10.2 and 2.308 g cm73, respectively). In the case of silicon and tungsten, the difference between these parameters is even larger [Tmelt (W)&3400 8C; r(W)=19.35 g cm73]. Reactions of these elements can occur only through reactive diffusion at very high temperatures over a long period. However, it is very difficult to prepare monophase systems even under these conditions.4 Silicides of molybdenum,21 ± 27 tungsten 28 and tanta- lum 22, 29, 30 were synthesised by the mechanochemical method.The stoichiometric intermetallide NbSi2 was prepared according to this method after continuous activation for 65 min.31, 32 The use of the mechanochemical method substantially simplified the preparation of iron silicides.26, 27, 33, 34 The boiling points of the first metals in the Mg± Ni, Mg± Ti, Mg± Si, Al ± Nb, Al ± Ru, Sn ±Nb and Te ±Cu binary systems are lower than the melting points of the second metals, but the mechanochemical approach allowed the preparation of the intermetallides Mg2Si,17, 35, 36 Mg2Ni,37 NbAl3 ,38 Nb3Sn, Nb6Sn5 ,39 AlRu 40 and Cu2Te.41 Even more so, the synthesis of intermetallides according to conventional procedures presents technological problems due to a large difference between the melting points of the initial compo- nents.Hence, such intermetallides as FeSn, FeSn2 ,42 ± 44 Ti3Al,38, 45, 46 TiAl,45 ± 51 TiAl3 ,41, 45, 46, 52 AlPd,53 Nb3Ge, Nb5Ge2 , NbGe2 ,39, 54 ZrAl,55 Ni3Sn2 ,56 Ni3Sn,56 Ni2Al3 ,57 NiAl,57 ± 65 VAl3, V5Al8, V4Al2 and VAl10 66 were prepared by the mechanochemical method. The intermetallide Cu7Hg6 , which is of practical importance, was prepared by mechanical alloying of copper with mercury.67, 68 These metals differ substantially in melting points. In addition, the vapour pressure of mercury at elevated temperature is very high. Relushko et al.69 studied the mechanochemical synthesis of iron aluminides in the Fe ±Al system and revealed the sequence of formation of the Fe2Al5 and FeAl phases, i.e., the authors followed the stages of the synthesis of the intermetallides. The formation of the intermetallides in this system was also considered in more recent studies.Thus, Bonetti et al.70 investigated Fe3Al and FeAl and Morris and Morris 71 studied FeAl3. However, attempts to bring the mechanochemical synthesis to completion are not necessarily successful. In some cases, pro- longed (during many hours) mechanochemical activation is required. It was found that mechanochemical treatment can substantially decrease the temperature of the subsequent thermal synthesis. Thus, preliminary mechanochemical activation of molybdenum and silicon powders for 2 h allowed the preparation of the intermetallide MoSi2 at 800 8C.72, 73 After mechanochem- ical treatment of tungsten and silicon powders, the temperature of the synthesis of WSi2 was 950 8C.28 In the synthesis of b-FeSi2, the duration of preliminary activation was decreased (50 h) by using brief mechanochemical treatment followed by annealing at 700 8C.74 Conventional procedures for the synthesis required prolonged annealing at 982 8C;75 however, the desired homoge- neity of b-FeSi2 was not achieved even in this case.Brief annealing of non-equilibrium systems obtained upon mechanochemical activation also afforded intermetallides, for example, Fe3Al, FeAl, FeAl3 ,76 Fe2Al5 ,76, 77 g-TiAl, TiAl3 51, 52 and the corre- sponding compounds in the Co ±Ti system.78 Systems characterised by large heats of formation of interme- tallic compounds are worthy of particular consideration.Prelimi- nary mechanochemical activation of these systems favours the subsequent self-propagating high-temperature synthesis. The new approach involving mechanochemical activation and self-propa- gating high-temperature synthesis extends the range of systems in which the latter can be performed,79, 80 expands the concentration limits of the synthesis and allows one to accelerate substantially the synthesis and to perform it in the solid-phase mode.79, 81 This approach was used for the preparation of the intermetallides NiTi,Mechanochemical synthesis of intermetallic compounds NiAl, Ni3Al, NiGe,79 ± 81 Ni3Si,82 FeSi2 ,75 NbAl3 ,83 FeAl 84 ± 87 and MoSi2 .86, 88, 89 The mechanochemical method was employed for the synthesis of equilibrium solid solutions in systems characterised by contin- uous and very wide solubility ranges.Thus, Pavluykhin et al.90 investigated the conditions of accelerated diffusion in binary metallic systems upon mechanochemical activation in centrifugal planetary mills and obtained solid solutions in the Fe ±Cr system. Davis and Koch 91 were the first to examine the possibility of mechanical alloying of solid solutions consisting of fragile com- ponents. In the cited study, mechanical alloying of germanium with silicon (compositions containing 72 at.% and 50 at.% of Si) was investigated. Silicon and germanium are isomorphous and their unit cell parameters depend almost linearly on the concen- tration of the second element. The measured unit cell parameter of germanium was larger than that expected based on the Vegard rule, but this deviation virtually disappears in the case of speci- mens containing more than 72 at.% of Si.At lower concentrations of silicon, the deviation of the unit cell parameter persists even after annealing. Yurchikov et al.92, 93 studied the formation of intermetallic compounds and solid solutions in the Fe ±Cr and Fe ± Si systems under high pressure on doubled Bridgman anvils with a rotating central part. Neverov et al.94, 95 prepared a large number of solid solutions on Bridgman anvils. In the Fe ±Co system, solid solutions with body-centred cubic structures were formed on mechanical alloying of mixtures con- taining less than 80 at.% of Co, whereas solid solutions with face- centred cubic structures were formed in the case of 90 at.% of Co.96 ± 99 In this system, the sizes of blocks of the body-centred cubic and face-centred cubic phases were 10 ± 30 and 40 ± 70 nm, respectively.Monophase solid solutions were obtained in the Fe ±Ni system with the use of a planetary ball mill.100 All phase compositions in the Fe ±Mn system were obtained in a high-energy ball mill. However, the concentration limits of the regions of solid solutions were substantially extended compared to those observed in the equilibrium diagram. The particle sizes were 20 ± 80 nm.101 The mechanochemical synthesis of nanocrystalline solid sol- utions with body-centred cubic structures using high-energy mills was reported.102 ± 106 It was suggested that a solid solution of aluminium in iron became partially ordered on prolonged activa- tion.Nanocrystalline solid solutions of iron containing 4 mass% (8 at.%) of Al were prepared in a high-energy SPEX 8000 ball mill (USA) during intervals from 10 to 60 min.107 Therefore, analysis of the published data demonstrated that the mechanochemical synthesis of equilibrium intermetallic com- pounds is most efficient in the cases of large differences between the melting points and between the densities of the initial components, high temperatures of the synthesis and, if required, in the preparation of phases with nanosized grains.{ This method is used more widely in preparation for the subsequent thermal synthesis or for the self-propagating high-temperature synthesis.III. Mechanochemical synthesis of non-equilibrium phases in bimetallic systems with negative mixing enthalpies The mechanochemical synthesis of non-equilibrium phases can successfully compete with such methods for their preparation as superfast quenching and precipitation from the gaseous phase. Practical interest in metastable compounds (i.e., in systems with an excessive free energy) arises from their high reactivities. These phases find wide application. It is evident that chemical activity of metastable phases depends substantially on crystal structure imperfection, which, in turn, is determined by the degree to { The term `nanosized grain' used in many modern publications is generally related to the sizes of coherent-scattering regions.47 which the phase is in non-equilibrium. Therefore, the major problem of the preparation of metastable phases is to achieve the maximum concentration deviation from the equilibrium state with retention of the crystal structure of the initial phase. As mentioned above, in equilibrium systems, the maximum concen- tration of an alloying (dissolved) element in solid solutions is determined by the electron concentration and the difference between the atomic radii, which should be no higher than 15%. Analysis of the published data demonstrated that mechano- chemical synthesis leads to changes of priorities and variations in the above parameters.First, the mutual correlation between the crystal structures of the components assumes great importance. Second, the dimension factor is shifted to the region of 15% ± 28% to attain substantial concentration deviations. Binary metallic systems in which the course of mechanochem- ical synthesis of non-equilibrium phases is governed by the differ- ence between the atomic radii are listed in Table 1. It can be seen that metastable solid solutions characterised by a substantial deviation of the concentration form the equilibrium state can be synthesised by the mechanochemical method in systems in which the solubility of one element in another is limited by the dimension factor and in which the difference between the atomic radii is 15%± 25%.The concentrations of such solid solutions are higher than both the low-temperature (in all the cases under consider- ation) and high-temperature (Cu ± Hg, Ni ± Sn and Fe ± Sn) equi- librium limits. For the Cu ± Sn system, these concentrations are also higher than the concentrations of solid solutions prepared by fast quenching, (in the latter case, these values amount to only 8 at.% of Sn; Fig. 1). Tianen and Schwarz 56 prepared super- saturated solid solutions of tin based on a-nickel with the lattice parameter a=0.3699 nm, which is 5% larger than that of pure nickel. Table 1. Differences between the atomic radii (DR) and the concentrations of equilibrium (C) and supersaturated solid solutions (c) prepared by the mechanochemical method in different systems.Ref. System DR(%) C (at.% of the second element) II c (at.% of the second element) I 108 ± 111 111 ± 113 114 ± 116 117 ± 119 117 ± 119 120 ± 124 125, 126 10 17 11 17.7 14.5 323 Cu ± Sn Cu ±Hg Cu ± In Ni ± Sn Ni ± In Fe ± Sn Ni ± Bi 11.25 (8528C) 5 (6578C) 10.8 (5748C) 10.4 (11308C) 14.5 (9088C) 9.8 (9008C) 0.5 (>5008C) *00 >100 >20 19 20 23 21 25 20 30 Note. The following notations are used: I is the concentration at high temperatures and II is the concentration at room temperature. The limiting non-equilibrium concentration decreases as the difference between the atomic radii increases further.In the Ni ± Bi system in which the difference between the atomic radii is 30%, the enthalpy of formation of solid solutions calculated by the Miedema method 127 ± 129 has a small negative value. Accord- ing to the equilibrium diagram,108 this system contained two intermetallic compounds with the bismuth contents of 78.08 mass% (NiBi) and 91.44 mass% (NiBi3), the solubility of bismuth in solid nickel being no higher than 0.5 at.%.125 Solid solutions of bismuth in nickel with bismuth concentrations of up to 3 at.% were synthesised by the mechanochemical method.126 In systems in which the limiting solubility is determined by the electron concentration, the content of the alloying element exceed- ing the value allowed in this crystal structure is very difficult to achieve. In the Cu ±Al system, the difference between the atomic radii is 11%.Taking into account the electron concentration under equilibrium conditions at room temperature, the limiting48 T /8C 700 500 300 100 Figure 1. Equilibrium diagram of the Cu ± Sn system (a) and the limiting concentrations of the solid solution prepared by fast quenching (b) and the mechanochemical method (c). aluminium content in copper can be as high as 20 at.%. Solid solutions with a maximum aluminium content of up to 23 at.% were also prepared by the mechanochemical method.111, 130, 131 If there is structural compatibility between the metal serving as the solvent and the closest intermetallide and there is a favourable dimension factor, the resulting solid solutions are characterised by a very broad concentration range of supersaturation. In the Ni ±Al system, the intermetallic compound Ni3Al is structurally similar to nickel serving as the solvent.132 According to the equilibrium diagram, the limiting solubility of aluminium in nickel is 13.5 at.% and 3.85 at.% at 1100 and 500 8C, respectively.At room temperature, the solubility is insignificant. The homogene- ity region of the intermetallic compound Ni3Al varies from 23 at.% to 27.5 at.% of Al.108 Solid solutions of aluminium in nickel containing up to 28 at.% of Al were synthesised by the mechanochemical method.111, 133 The Ni ±Ga system is characterised by an electron concen- tration identical to that observed in the Ni ±Al system and by the favourable dimension factor (DR^10%).134 The maximum gal- lium content in the equilibrium solid solution of gallium in nickel is 24.3 at.%.At the peritectic temperature of 1210 8C, the a 0 phase (Ni3Ga) was formed. The solubility of gallium in nickel depends substantially on the temperature. For example, the solubility at 700 8C decreases to 15 at.% of Ga.135 The system contained the b phase, viz., the solid solution based on the intermetallide NiGa. The homogeneity region of the b phase falls in the concentration ranges of gallium from 36 at.% to 60 at.% and from 48.3 at.% to 53.3 at.% at high and low temperatures, respectively. At 1204 8C and a concentration of gallium of 29.4 at.%, the a 0 and b phases formed an eutectic.At 940 and 685 8C , two peritectoid reactions proceeded giving rise to new phases, viz., g and d, respectively. The low-temperature g 0 a 10 20 30 40 50 60 70 b g z aor e (Cu) d ZZ0 bc 60 40 20 0Cu 90 c (mass%) 80 80 c (at.%) Sn T F Grigorieva, A P Barinova, N Z Lyakhov phase formed from the g phases below 685 8C has the Ni3Ga2 composition and is characterised by a narrow homogeneity region. The Ni3Ga phase (the Cu3Au structural type) is structur- ally similar to b-nickel (the face-centred cubic structure). The succeeding Ni3Ga2 phase crystallises in the g-Mn structural type, which can be described as a deformed structure of b-nickel, whereas the NiGa phase crystallises in the CsCl structural type (the body-centred cubic structure).132 The mechanochemical method was used for the preparation of solid solutions of gallium in nickel with a Ga concentration of up to 50 at.%,117, 133 i.e., including the concentration range of existence of both structurally similar phases. In the Ni ±Ge system, the difference between the atomic radii of the metals is small,134 but the region of existence of the solid solution, which is determined by the electron concentration, is noticeably narrower than that in the Ni ±Ga system.According to the equilibrium diagram, the limiting solubility of germanium in nickel is 13.8 at.% at 1161 8C.125 The solid solution is followed by the b phase, which is a solid solution based on the intermetallide Ni3Ge.The b phase is homogeneous in the concentration range from 22.9 at.% to 24.8 at.% of Ge and has the cubic structure of the Cu3Au type similar to that of b-nickel. The following e phase is a solid solution based on Ni2Ge with the hexagonal structure of the nickel-arsenide type, which differs substantially from the structure of the preceding phase. The mechanochemical method was used for the synthesis of non-equilibrium solid solutions whose homogeneity region extends to a concentration of 25 at.% of Ge.133 It is known that a solid solution of aluminium in a-iron was formed in the Fe ±Al system at concentrations of aluminium varying from 0 at.% to 25 at.% (quenched alloys).132 The further addition of aluminium led to a gradual ordering of the solid solution.Under favourable conditions, for example, upon anneal- ing, ordering started even at 18 at.% of Al. At 25 at.% and 50 at.% of Al, the intermetallides Fe3Al and FeAl, respectively, were formed. Solid solutions of aluminium in iron with an aluminium content of up to 50 at.% were prepared by the mechanochemical method.136 ± 138 Therefore, the mechanochemical method enables one to extend substantially the concentration range of existence of solid solutions toward the non-equilibrium region if the intermetallic compounds closest to the metal, which serves as the solvent, are structurally similar. Metastable solid solutions can be prepared by the mechano- chemical method from powders of metals in different systems among which are systems characterised by large differences between the melting points and between the densities of the initial components, by high melting points of the resulting intermetallic compounds and by narrow homogeneity regions of the equili- brium chemical compound.In the synthesis of supersaturated solid solutions, as in the synthesis of intermetallides, systems with very large differences between the melting points of the initial components attract particular attention. Among these are systems containing tungsten (Tmelt&3400 8C) and tantalum (Tmelt= 3015 8C) whose melting points are higher than boiling points of many metals. In the Ni ±W system, the boiling point of nickel (2900 8C) is lower than the melting point of tungsten and hence compounds are difficult to prepare from these elements by conventional procedures. According to the equilibrium diagram, this system contained (a) the a phase, viz., a solid solution of tungsten in nickel with a homogeneity regions from 0 at.% to 35 at.% of W at 900 8C and from 0 at.% to 41.5 at.% of W at temperatures from 1000 8C to the melting point, (b) the b phase, viz., the intermetallic compound Ni4W, and (c) the g phase, viz., a solid solution of nickel in tungsten containing*4 at.% of Ni.125 Solid solutions of tungsten in nickel were synthesised from a mixture of these metals by the mechanochemical method.139 An analogous ratio between the melting points of the initial components is observed in the Fe ±W system.According to theMechanochemical synthesis of intermetallic compounds equilibrium diagram, the system contained two intermetallides, viz., Fe2W and Fe3W2 . At 1520 8C and at room temperature, the solubility of tungsten in iron is 33 mass% (13 at.%) and 8 mass% (3 at.%), respectively. At 1640 8C, the solubility of iron in tungsten in the solid state is only 0.8 mass%(2.6 at.%).125 The solid-phase synthesis in this system was carried out by the mechanochemical method to produce solid solutions.140 In the Cu ± Ta system, the mixing enthalpy is close to zero, the difference between the atomic radii is large (*25%), the initial components belong to different structural types, and the boiling point of copper is almost 600 8C lower than the melting point of tantalum.According to the published data,108, 141 the solid-phase solubility of tantalum in copper is virtually absent. At 1200 8C, only 0.009 at.% of Ta was dissolved in copper and no other metallic compounds were formed. Supersaturated solid solutions of tantalum in copper were prepared by the mechanochemical method.142 In the Cu ±Nb system, the difference between the melting points of the initial components is also large. According to the equilibrium diagram, the system contained only two phases, viz., solid solutions based on copper (a) and niobium (b). The solubility of niobium in copper at 1100 and 20 8C is 1.66 mass% (1.14 at.%) and 0.2 mass% (0.13 at.%), respectively. The solubility of copper in niobium at high temperatures and at 700 8C amounts to *2 at.% and 0.07 at.%, respectively.141 Solid solutions with concentrations of each component up to 10 mass% (7.05 at.%) were prepared by the mechanochemical method.143, 144 The limiting solubilities (*10 at.%) both of niobium in a solid solution of nickel (a face-centred cubic structure) and of nickel in a solid solution of niobium (a body-centred cubic structure) were achieved in the Ni ±Nb system by the mechano- chemical method.145 For comparison, is should be noted that the equilibrium solubilities are 4.2 at.% of Nb (at 987 8C) and 3.5 at.% of Ni (at 1000 8C).146 Solid solutions of aluminium based on different metals are of particular interest in materials technology. These compounds differ sharply from the starting compounds in chemical proper- ties.The concentration of aluminium introduced has a pro- nounced effect on the properties. Gerasimov et al.147 observed the formation of supersaturated solid solutions based on a-tita- nium for the compositions Ti1007xAlx (x<60 at.%). The solu- tions were formed even if the equilibrium phases Ti3Al and TiAl were used as the starting components. The authors believed that the intermetallides can decompose and tribochemical equilibrium was established in the course of mechanical alloying giving rise to metastable phases. Solid solutions in the Ti ±Al system were prepared in a planetary ball mill using the TixAl1007x composi- tions (x=75 at.%, 50 at.% and 35 at.%). In none of the compo- sitions examined did amorphisation occur.In all cases, the formation of solid solutions was observed, viz., the hexagonal Ti(Al) solid solution in the cases of Ti75Al25 and Ti50Al50 and a mixture of hexagonal Ti(Al) and cubic Al(Ti) solid solutions in the case of Ti35Al65. Variations in the conditions of activation led to a change in the quantitative ratio between the hexagonal and cubic phases.148 It is known that the equilibrium concentration of aluminium in niobium is less than 10 at.% at 1000 8C.149 The use of the mechanochemical method allowed an increase in the concentra- tion to 30 at.%.150 Supersaturated solutions were formed in the Zr ±Al system containing up to 15 at.% of Al, the lattice parameters a and c of zirconium being decreased from 0.3235 to 0.3200 and from 0.5196 to 0.5148 nm, respectively.{ After mechanochemical activation for 12 h, the particle size was*12 nm.55 { Here, the first and second values correspond to the lattice parameters of zirconium and of the solid solution of aluminium in zirconium, respec- tively.49 Solid solutions with an Al content of up to 50 at.% were formed in the Al ± Pd system in which the equilibrium solubility of aluminium in palladium is 15 at.%.53 The mechanochemical method was used for the synthesis of solid solutions Al ± 10 at.% ofX(X=Ti, Zr or Hf) from powders of the metals.151 Supersaturated solid solutions containing up to 13 at.% of Sb with a grain size of 10 nm were obtained in the Cu ± Sb system.152 The maximum concentration of 2.1 at.% of Sb was achieved in the Fe ± Sb system.153 In the Fe ± Tb system, the mechanochemical method made it possible to attain a solubility of 36 at.% of Tb.20 Metastable solid solutions W± 25 mass% (25 at.%) of Re with nanosized grains were also prepared by this method.154 Systems in which the absence of solubility of one element in another one is associated neither with the difference between the atomic radii nor with the difference in the structural type, but is most probably determined by the electron concentration are a special case.For example, the difference between the atomic radii in the Ge ± Sn system is *12%.134 The face-centred cubic structure of germanium is similar to the tetragonal structure of b-Sn.125 However, the equilibrium concentration of germanium in solid tin falls in the concentration range of 0.001% ± 0.1% (see Ref.125) and the formation of intermetallides was not observed. Solid solutions with a substantial deviation from the equilibrium state containing 12 at.% ± 24 at.% of Sn were synthesised by the mechanochemical method.155 These concentrations of tin are substantially higher than its concentrations in solid solutions prepared by fast quenching.156 The non-equilibrium solubility of germanium in tin is achieved if the particle sizes of germanium are no larger than 10 nm. In the Ge ±Al system in which the initial elements belong to the same structural type and the difference between the atomic radii is very small (only*3%), no intermetallides are formed.At 424 8C and 54 mass% (30.3 at.%) of Ge, the eutectic consisting of two solid solutions appeared. The germanium content in a solid solution based on aluminium decreased from 5.1 mass% (*2 at.%) at the eutectic temperature to 0.3 mass% (>0.1 at.%) at 20 8C.125 Metastable intermetallic compounds were obtained by quenching from the liquid state.42, 157 Structur- ally similar metastable intermetallides were also synthesised by the mechanochemical method.158, 159 Analysis of the experimental data demonstrated that systems in which the atomic radius of the alloying element is larger than that of the metal serving as the solvent are characterised by higher equilibrium solubilities than those observed in systems with other ratios between the atomic radii.For example, the solubilities of aluminium (R=0.143 nm) in nickel (R=0.124 nm), iron (R=0.126 nm) and copper (R=0.128 nm) amount to tens of atomic percent, whereas the solubilities of iron, nickel and copper in aluminium are close to zero. The use of the mechanochemical method allowed a substantial extension of the region of existence of such solid solutions. Thus, metastable solid solutions based on aluminium with Cu and Fe contents of up to 33 at.% (see Ref. 160) and 10 at.%, respectively, were prepared.161 ± 163 Pekala and Oleszak 164 prepared a solid solution with composition Fe10Al90 in a horizontal low-energy ball mill after activation for 200 h. The average size of crystallites of the solid solution was *7 nm.It was found that the mechanochemical formation of the solid solution in the course of activation was preceded by the short-duration formation of the intermetallide FeAl3 from pow- ders of iron and aluminium. Dunlap et al.165 compared the microstructures of supersaturated solid solutions of iron in aluminium synthesised by the mechanochemical method and fast quenching and demonstrated that alloys with composition Al98Fe2 prepared by fast quenching occurred as monophase supersaturated solid solutions. In the initial stage of the mecha- nochemical synthesis, a supersaturated solid solution whose microstructural properties are similar to those of quenched alloys was formed. Further activation led to a decrease in the grain size and gave rise to an amorphous phase.50 Supersaturated solutions with a magnesium content of up to 45 at.% were synthesised in the Al ±Mg system by the mechano- chemical method.The particle sizes were in the range of 2 ± 10 nm.166 In the case of intermetallides with low enthalpies of formation or with enthalpies close to mixing enthalpies, supersaturated solid solutions can be prepared not only by mechanochemical synthesis from powders of the initial elements, but also on mechanochem- ical activation of intermetallides resulting in disordering of the equilibrium intermetallic phases synthesised by other methods. For example, the intermetallides Nb3Al,167 V3Ga,168 Nb3Au,169 ± 171 Ni3V,172, 173 Cr53Fe 174 and Fe3Ge 176 were trans- formed into solid solutions with body-centred cubic structures, whereas NbAl2 (see Ref.172) and TiAl3 (see Ref. 175) were transformed into solid solutions with face-centred cubic structures upon mechanochemical activation. As a result of disordering of equilibrium intermetallides, solid solutions also formed in the Ni ±Al system.177 Supersaturated solid solutions of tin in iron characterised by a substantial deviation from the equilibrium state can be prepared using mechanochemical activation both of a monophase interme- tallide and a mixture of intermetallic compounds.178 ± 180 Therefore, the mechanochemical method allows the prepara- tion of supersaturated solutions in systems with negative enthal- pies of mixing of the components.For most systems, the degree of supersaturation depends on the difference between the atomic radii of the initial elements, their structural compatibility and the electron concentration. IV. Mechanochemical synthesis of supersaturated solid solutions in systems with positive mixing enthalpies Of systems with positive mixing enthalpies, the Fe ±Cu system has received the most study. If the concentrations of the components are equal to 50 at.% each, the mixing enthalpy calculated by the Miedema method 127 ± 129 is 22 kJ mol71. It is believed that one of the reasons for the immiscibility of these metals in the solid state is the difference in their structural types. Thus, copper has the face- centred cubic (FCC) lattice and a-iron has the body-centred cubic (BCC) lattice.However, it is known that the structural type of iron changes as the temperature is increased: a-Fe (BCC)?b-Fe (BCC) at 770 8C?g-Fe (FCC) at 920 8C. Hence, the possibility of dissolution is higher at high temperatures. At 1094 8C, the equilibrium solubilities of iron in copper and copper in g-iron are 3.8 mass% (4.2 at.%) and *8 mass% (*7.1 at.%), respec- tively.108, 125 Solid solutions, which are non-equilibrium at room temperature, can be prepared by quenching from vapour or liquid phases. For example, solid solutions based on iron (BCC lattice) in the concentration range of up to 15 mass% (13.5 at.%) of Cu and based on copper (FCC lattice) in the concentration range of up to 20 mass% (22 at.%) of Fe were obtained from melts by quenching.181 Supersaturated solid solutions in a wider concen- tration range were prepared by precipitation from the vapour phase in vacuo on a support at room temperature.It was demonstrated 182 that solutions had BCC structures if the copper content was lower than 50 mass%(47 at.%) and FCC structures if the copper content was higher than 70 mass% (68 at.%). Solutions with concentrations of copper in the range of 50 mass%± 70 mass% were not prepared. Supersaturated solid solutions in a wide concentration range were also synthesised by quenching from the vapour phase. Solid solutions based on iron existed up to 40 mass%(37 at.%) of Cu. Solid solutions based on copper with a FCC structure occurred up to 60 mass%(57 at.%) of Cu.183 Benjamin 184 was the first to report the results of mechano- chemical alloying of the components in the Fe ±Cu system.He obtained the homogeneous mixtures 80 mass% (82 at.%) of Fe ± 20 mass% (18 at.%) of Cu and 50 mass% (24 at.%) of T F Grigorieva, A P Barinova, N Z Lyakhov Pb ± 50 mass% (76 at.%) of Cu in a high-energy laboratory mill. Metallographic studies of a specimen of the Cu ± Fe system confirmed its homogeneity. It was also noted that the colour changed from red (the colour of copper) to grey (the colour of steel). Neverov et al.94, 185 obtained solid solutions on a Bridgman anvil. The concentrations of copper in iron and iron in copper reached 40 mass% and 10 mass %, respectively. Gusev 186 dem- onstrated that solid solutions based on copper (FCC lattice) with compositions up to Cu40Fe60 and solid solutions based on iron (BCC lattice) with compositions up to Cu30Fe70 can be obtained in a centrifugal planetary ball mill. Kaloshkin et al.187, 188 prepared supersaturated solid solutions Fe1007xCux (x=20 ± 80) from powders of iron and copper in a planetary ball mill.The mechanochemical formation of solid solutions was completed in 30 min. It was also established that the FCC phase of the solid solution, the BCC phase of the solid solution and a mixture of these phases were formed at x=40 at.% ± 80 at.% of Cu, x=20 at.% of Cu and x=30 at.% of Cu, respectively. In studies of structural changes occurring in the course of mechanical alloying, Barro et al.189 observed the formation of solid solutions in the FexCu1007x system (x=5, 10 and 20).Uenishi et al.190 performed mechanical alloying of the solid solution Fe17xCux and prepared also monophase compositions with BCC (if x<40 at.%) and FCC (if x>40 at.%) structures. Yavari et al.191 confirmed that the lattice parameters in these compositions were increased. Eckert et al.192, 193 prepared solid solutions FexCu1007x in a SPEX 8000 ball mill. It was demonstrated that monophases with FCC and BCC structures exist at x460 and x580, respectively, whereas solid solutions with FCC and BCC structures coexist in the range of 604x480. The formation of solid solutions starts when grains reach nanometer sizes. Jiang et al.194, 195 also observed the formation of solid sol- utions in the Cu ± Fe system and detected small amounts of g-Fe (a FCC structure) in all specimens subjected to mechanochemical treatment for more than 10 h.Supersaturated solid solutions in the Cu ± Fe system were also prepared in SPEX 8000 ball mills in more recent studies (see, for example, Refs 196 ± 206). It was established by different methods that monophase supersaturated solid solutions were formed in mixtures containing more than 80 mass%or less than 60 mass%of copper, whereas two phases coexisted in the region with a copper content from 50 mass%± 60 mass%to 80 mass %. Therefore, the mechanochemical method allows the prepara- tion of supersaturated solid solutions throughout the concentra- tion range of existence of a binary system with a high positive heat of mixing of the initial components (Fig.2). The Cu ±Co system also has a positive mixing enthalpy (*20 kJ mol71 for the equiatomic composition). According to the data reported by different researchers, the concentration of cobalt in a solid solution based on copper (b phase) at 1100 8C changes from 5.2 mass% to 8 mass% (from 5.6 at.% to 8.5 at.%) and the concentration of copper in a solid solution based on cobalt at the same temperature changes from 12 mass% to 14 mass% (from 11.2 at.% to 13.1 at.%). At temperatures below 500 8C, the mutual solubility of one element in another is no higher than 0.1%.108 The low mutual solubility is attributable to the difference in the structural types of these elements.However, it is known that a-Co (the hexagonal close-packed structure) is transformed into b-Co at 350 ± 470 8C. The latter, like copper, has a FCC structure. The high mutual solubility of these elements is quite possible due to the insignificant difference between their atomic radii. Fast quenching made it possible to dissolve up to 20 mass% of Co and less than 25 mass% of Cu in cobalt. The mechanochemical method was used for the preparation of solid solutions with FCC structures throughout the concentration range of existence of this binary system.197, 199, 207 ± 213 In a number of studies, it was found that phase transformations of cobalt occurred upon mechanochemical activation in ball mills.214 ± 216 The Cu ±Cr system is also characterised by a positive mixing enthalpy (*20 kJ mol71 for the equiatomic composition).In thisMechanochemical synthesis of intermetallic compounds 40 20 T /8C d-Fe 1400 g-Fe 1200 1000 Tc a-Fe 800 600 BCC BCC BCC BCC 40 20 0 Fe Figure 2. Equilibrium diagram of the Fe ±Cu system (a) and the regions of existence of solid solutions synthesised by quenching from a melt (b), quenching from the vapour phase (c), precipitation from the vapour phase (d ) and the mechanochemical method (e). system, as in the above-considered one, the difference between the atomic radii of the initial metals is insignificant, but their structural types differ substantially (BCC and FCC structures, respectively).The solubility of chromium in copper varies from 1.25 mass% to 0.5 mass% (from 1.5 at.% to 0.6 at.%) at 1050 8C and it is less than 0.03 mass% at 400 8C. The solubility of copper in chromium is 0.16 at.% and 0.085 at.% at 1300 8C and 1150 8C, respectively.141 Chromium has several crystal mod- ifications, viz., a-Cr (BCC structure), b-Cr and g-Cr. Supersatu- rated solid solutions characterised by substantial deviations from the equilibrium state were prepared by the mechanochemical method.217 ± 220 In the Cu ±V system, the atomic radii of the initial metals have close values, whereas their structural types are different (FCC and BCC structures, respectively). According to the equilibrium dia- gram, solid solutions based on copper (a) and vanadium (b) are formed in the system. The maximum solubility of vanadium in copper is 0.8 at.% at 1120 8C (0.1 at.% at 20 8C) and the maximum solubility of copper in vanadium is 8 at.% at 1530 8C.141 A wide range was found in which the components in the liquid state were immiscible (the range from 4.0 at.% to 84.6 at.% of V).Solid solutions both with BCC and FCC structures were prepared on mechanochemical activation.218, 221 It was demonstrated 221 that the particle sizes of the components should be no larger than 30 nm for solid solutions to be prepared. a 80 c (mass%) 60 L Cu b FCC c FCC d FCC e FCC BCC+FCC80 60 c (at.%) Cu 51 In the Cu ±Ag system, both components have FCC lattices, the difference between the atomic radii is *11% and the melting points of the components have close values.However, according to the equilibrium diagram of this system, the components have limited solubilities in the solid state at the eutectic temperature (*780 8C). At this temperature, the solubility of silver in copper is 8.0 mass% (4.9 at.%) and the solubility of copper in silver is 8.8 mass% (14.1 at.%). Quenching at a rate of cooling of 107 deg s71 afforded a continuous series of solid solutions. On cooling at lower rates, a continuous series of solid solutions was not detected. Depending on the conditions, solid solutions with different contents of the second element can be synthesised by the mechanochemical method throughout the concentration range of this system.42, 186, 222 ± 225 In the Pb ±Al system, both elements also have FCCstructures, the difference between their atomic radii is*18% and both metals are rather low-melting.However, the system is characterised by a positive mixing enthalpy. The metals do not form intermetallides and mutual solubility is absent. Supersaturated solid solutions were prepared in this system by the mechanochemical method.226 The Fe ±Ag system is characterised by a very high positive mixing enthalpy, the initial elements have different structural types (BCC and FCC, respectively) and the mutual solubility of the components is limited even in the liquid state. The solubility of silver in solid iron is no higher than 0.01% and the solubility of iron in solid silver is 0.0006%.125 Solid solutions are difficult to synthesise by the mechanochemical method.227 ± 230 Only very thin dispersions of iron in a silver matrix were obtained; the average radius of iron particles was equal to several nanometers.230 In systems with positive mixing enthalpies, a low mutual solubility of one component in another may be associated with a large difference between the atomic radii of the initial elements.For example, this difference in the Cu ± Bi system is *30% and the solubility of bismuth in copper in the solid state is only 0.003 at.% at 800 8C, the solubility of copper in bismuth being insignificant.231 The formation of the metastable intermetallide with composition Cu5Bi2 was observed in this system.232 The mechanochemical method was used for the preparation of super- saturated solid solutions of bismuth in copper with a concen- tration of bismuth of up to 4 at.%; the average grain size was *10 nm.233 The Fe ± In system is also characterised by a positive mixing enthalpy and the difference between the atomic radii of*23%.In the equilibrium state mutual solubility is completely absent. Solid solutions of indium in iron with rather low concentrations of indium were prepared by the mechanochemical method.234 In solid solutions prepared by the mechanochemical method in systems characterised by positive mixing enthalpies and large differences between the atomic radii, the maximum solubilities of one element in another are rather low compared to those in systems in which the differences between the atomic radii of the initial elements are smaller and the elements can adopt similar structures due to phase transitions on mechanochemical activa- tion.The use of the mechanochemical synthesis for the preparation of intermetallides and solid solutions in immiscible systems with a large difference between the melting points of the initial compo- nents, in particular, in systems in which the melting point of one component is higher than the boiling point of another one, is of most practical interest.For example, the Mg±Ti system is characterised by a positive mixing enthalpy (12 kJ mol71). In this system, the difference between the atomic radii is *9%, the components belong to the same structural type and the melting point of titanium is *500 8C higher than the boiling point of magnesium.Hence, solid solutions are difficult to prepare by conventional methods (probably, they can be synthesised by precipitation from the vapour phase). Solid solutions of titanium in magnesium with concentrations of up to 20 mass% of Ti were synthesised by the mechanochemical method.235 Moritaka et al.236 examined the Ti ± xMg system (x=10 at.%, 20 at.%,52 30 at.%, 40 at.%, 50 at.%, 60 at.%, 70 at.%, 80 at.% and 95 at.%). Mechanical alloying was carried out in a Frich ball mill (P-7 type). Supersaturated solid solutions were detected at a magnesium content of 560 at.%. In the range from 70 at.% to 80 at.% of Mg, the coexistence of solid solutions based both on titanium and magnesium was observed.The sizes of crystallites were larger and nonuniform distortions of the lattices of solid solutions based on magnesium were more substantial than those observed in the case of nanocrystalline solid solutions based on titanium. The Cu ±W system is characterised by a very high positive mixing enthalpy (35 kJ mol71). In this system, the difference between the atomic radii is *8%, the structural types of the initial metals are different (FCC and BCC, respectively) and the boiling point of copper is lower than the melting point of tungsten. Solid solutions were synthesised in this system by the mechano- chemical method.237, 238 Raghu et al. 239 performed mechanical alloying in the systems Cu ± 5 mass% (1.9 at.%) of W and Cu ± 15 mass% (5.2 at.%) of W and demonstrated that non- equilibrium solubilities both of copper in tungsten and tungsten in copper occurred.Therefore, the use of mechanochemical synthesis in systems which are immiscible in the equilibrium state allows the prepara- tion both of metastable intermetallic compounds and non-equili- brium solid solutions. In systems in which the atomic radii of the initial components have close values and their structural types become similar due to phase transitions, the concentration ranges of existence of supersaturated solid solutions prepared by the mechanochemical method are extended most significantly com- pared to those of analogous solutions prepared by quenching.If the immiscibility in the equilibrium state is dictated by the differ- ence between the atomic radii of the initial components, a substantially lower solubility is attained. In the latter case, rarely, if ever, can supersaturated solid solutions be prepared by quench- ing, whereas a particular solubility is achieved using the mecha- nochemical method, but this solubility is substantially lower than that in systems in which the difference between the atomic radii is small. V. Quasicrystals and amorphous alloys Follstaedt and Knapp 240 were the first to use solid-phase diffu- sion for the synthesis of icosahedral phases in the Al ±Ru and Al ±Mn systems. The melting point of ruthenium is substantially higher than that of aluminium and an alloy of these elements is difficult to prepare by quenching.Hence, the search for new procedures for the synthesis of these alloys is a topical problem. The formation of an icosahedral phase in experiments on hetero- phase diffusion signifies that nuclei of this phase are formed and grow more rapidly than the crystalline phase with the correspond- ing composition and a lower free energy in the solid state. This may be due to the fact that the fragments characterised by the short-range icosahedral order are more ordered in the crystal structure. Taking into account the results of experimental inves- tigation of heterodiffusion and assuming that the mechanism of formation of amorphous alloys and supersaturated solid solutions on mechanical alloying is also associated with the process of heterodiffusion, Follstaedt and Knapp suggested that an icosahe- dral phase can also be prepared by mechanochemical alloying.Independently, Ivanov et al.241 were the first to synthesise the icosahedral phases Mg32(Zn, Al)49 and Mg32(Cu, Al)49 from ele- ments by the mechanochemical method and performed structural transformations of the corresponding Frank ± Casper cubic phases into icosahedral phases by mechanochemical activation. The synthesis of the icosahedral phase Mg32(Zn, Al)49 from the elements involved an intermediate step giving rise to an amor- phous phase. Apparently, clusters possessing short-range icosa- hedarl order were formed in this step. Then an icosahedral phase arose. This phase appeared to be rather stable and remained unchanged in the course of further treatment in a ball mill.The T F Grigorieva, A P Barinova, N Z Lyakhov authors demonstrated that the synthesis of the icosahedral phase on mechanical alloying of metallic powders was accompanied by intermediate formation of an amorphous phase. Mechanochem- ical treatment of the cubic phase led to gradual broadening and then disappearance of a series of X-ray diffraction reflections belonging to this phase, whereas the remaining reflections were shifted so that they corresponded to the icosahedral phase. The X-ray diffraction reflections of the final product are broadened compared to those of quenched specimens. The metastable icosahedral phase was transformed into the cubic phase upon heating.According to the data of differential scanning calorim- etry, this transformation was accompanied by three exothermic effects. The first of these effects most probably corresponds to annealing of defects in the icosahedral phase, which is confirmed by the fact that the X-ray diffraction reflections corresponding to this phase were narrowed after annealing of a specimen at the temperature of the first exothermic peak. Eckert et al.242 synthesised quasicrystals of Al65Cu20Mn15 from the elements by mechanochemical activation in a planetary ball mill for 90 h. This phase also appeared to be stable to mechanochemical treatment. Thus, the X-ray diffraction pattern remained virtually unchanged in the course of grinding during 160 h.Unlike the authors of the above-considered study, Eckert et al. did not observe the formation of an intermediate amorphous phase and suggested that the formation of the icosahedral phase proceeded by a mechanism of heterodiffusion at the expense of heat, which was released upon dissipation of the kinetic energy of colliding balls. More recently (see, for example, Ref. 243), the icosahedral phase Al70Cu20Fe10 has been synthesised from a mixture of metallic powders by the mechanochemical method. Local icosahedral symmetry was observed in alloys of aluminium with molybdenum after their mechanical grinding.244 The investigation performed by Schwarz and Johnson,245 who demonstrated that amorphous alloys can be formed through heterodiffusion in a layered composite, has stimulated increased interest in the preparation of amorphous alloys in solid-phase processes. More recently, Schultz 246 has prepared a voluminous amorphous nickel ± zirconium alloy by the annealing of a repeat- edly rolled layered specimen. These facts suggested that the preparation of amorphous alloys by mechanical alloying occurred as a solid-phase process.During the last decade, a rich variety of amorphous alloys both in binary and multicomponent metallic systems, including systems characterised by large differences in the melting points and in the densities of the initial components, have been synthesised by mechanical alloying of powders of elements. For example, it was demonstrated that amorphous alloys can be prepared in the Ni ±Mg system by the mechano- chemical method (this process depends substantially on the blend composition). In addition, the formation of an amorphous alloy in magnesium-rich compositions was preceded by the formation of the intermetallic compound Mg2Ni, whereas amorphous alloys were formed immediately from metallic powders in compositions with high nickel contents in spite of the fact that, according to the equilibrium diagram, the intermetallide Ni2Mg existed in this concentration range.247 Nanosized amorphous alloys were also prepared in the Cu ± Zr system.248 The amorphous alloys Alx±Zr1007x ,249 Fe50±Ta50 ,250 NixTa1007x ,251 Cu ± Ti,252 Fe75Zr25 253 and Fe66.7Zr33.3 254 were synthesised. In the Ti ±Fe system, the for- mation of amorphous alloys was preceded by the formation of the supersaturated solid solutions b-Ti(Fe) and a-Fe(Ti) and the intermetallides FeTi and Fe2Ti.255 Amorphous phases were pre- pared in the systems Fe ± 6 mass%(11.3 at.%) of Si (see Ref.256) and Se ± As.257 In the Fe ±Cr system, amorphous alloys contain- ing only 28 mass% (26.5 at.%) and 45 mass% (43 at.%) of Fe were prepared.258 Multicomponent systems containing boron, phosphorus, silicon, carbon and other elements, for example, Ni50Pd40Si10 (see Ref. 259) and YNi2B2C,260 have received much consideration. In the latter system, the formation of nanocrystal- line or amorphous phases is determined to a large extent by theMechanochemical synthesis of intermetallic compounds activation parameters (an amorphous phase appeared only after prolonged activation).Amorphous phases with composition Cu867xSnxP14 (x=2 ± 15) can be prepared from powders of the initial elements, the time of the preparation of the amorphous phase depending on the tin content in the mixture. Thus, the duration of activation was 28, 20, 12 and 32 h at x=4, 5, 8 and 10, respectively.261 The alloy Fe39Ni39Si10B12 can be prepared both in the amorphous and nanocrystalline states.262 An amorphous alloy with composition (Zr0.65Al0.075Cu0.175Ni0.1)1007xFex (x420) was synthesised from powders of the initial elements.263 Ermakov et al.264 ± 267 were the first to perform amorphisation of intermetallic compounds by the mechanochemical method.They carried out the structural transformation of the intermetallic compounds X± M, where X=Y, Gd or Tb and M=Fe or Co, from the crystalline to amorphous state in a wide concentration range by mechanical grinding. In the late 1980s, investigations of this process have been started by many researchers.268 ± 272 Amorphisation of intermetallides was examined in the Sn ± Nb, Ge ± Nb,39, 269 Cr ± Ti, Cu ± Ti, Fe ± Ti, Mn± Ti, Co ± Ti, Ni ± Ti, Cu ± Cr, Ni ± Zr, Mn± Si 270 and Ni ±Al 271, 272 systems. Koch 13 was the first to initiate the process of amorphisation of interme- tallides and called it `mechanical grinding' rather than `mechanical alloying' from the initial elements. In the last decade, this process has been studied intensively. Amorphisation of the Laves phases Fe2Sc and Fe2Y was investigated.273, 274 It was demonstrated that vigorous mechanical grinding of the intermetallide Fe2Sc led initially to partial chemical disordering followed by amorphisa- tion, whereas Fe2Y was transformed into the amorphous state without preliminary disordering.Amorphisation of the interme- tallides Ni10Zr7 and NiZr2 was also studied.275 ± 277 Skakov et al.278 investigated the process of amorphisation in the Ni ±Nb system. An amorphous phase with composition Fe78P22 was prepared by mechanical grinding. 279 Poon et al.280 succeeded in transforming supersaturated solid solutions based on titanium into amorphous phases. For some systems, amorphisation upon mechanical grinding occurred as a cyclic process.For example, investigations of the structural evolution of powders of elements upon mechanical grinding of the Co75Ti25 and Co50Ti50 mixtures 281 ± 283 demon- strated that the formation of amorphous alloys with these compositions occurred rather rapidly, but these alloys were trans- formed into Co3Ti and CoTi (both compounds have BCC structures) on further mechanical treatment. These intermetallides were thermally stable and were not transformed into other phases upon heating to 1300 K. However, further grinding again afforded the amorphous compositions Co75Ti25 and Co50Ti50 . Surinach et al. 284 observed the transformation of an amorphous phase into a nanocrystalline phase in the Fe77.5Cu1Nb3Si9.5B9 system and determined the activation energy of the nanocrystal- line transformation.Amorphous structures can also be prepared according to the mechanochemical method by grinding intermetallides together with metallic powders. Thus, an amorphous phase in the Cu ±Cd system was prepared by grinding the equilibrium d phase together with a copper powder.285 It should be noted that attempts to obtain an amorphous structure in this system either by mechanical alloying of powders of copper and cadmium or by grinding of the single d phase failed. Amorphous phases in the Mg±Ni and Mg±Ni ±V systems were synthesised upon mechanical grinding of the Mg2Ni alloy with powders of nickel and vanadium, respectively.286 An amor- phous phase was formed by mechanical grinding of the interme- tallide EuFe2 as well as by its grinding with powders of europium and iron.287 More complex amorphous phases were also synthes- ised in such a manner.The amorphous compositions Mg2Ni1M0.1 (where M=Ni, Ca, La, Y, Al, Si, Cu or Mn) can be prepared by mechanochemical grinding of the binary system of the interme- tallide Mg2Ni0.9M0.1 and a powder of nickel.288 The regions of existence of amorphous alloys synthesised by the mechanochemical method were calculated and determined 53 experimentally in a large number of studies (see, for example, Refs 289 ± 295). VI. Phase and structural transformations in the mechanochemical synthesis of intermetallic compounds Benjamin 184, 296, 297 considered mechanical alloying of metallic powders in attritors as a repeated process of cold welding under pressure and grinding.He believed that a metal particle is flattened upon its initial collision with balls, i.e., the ratio of the surface area of the particle to its volume increases, surface films of adsorbed impurities being disrupted. Flattened metal particles contact with each other through the freshly formed surfaces giving rise to a layered composite of powdered particles (Fig. 3). The layers in this composite become thinner as welding and grinding are continued. The formation of layered composites was detected in many systems.13, 230, 247, 298, 299 There are five typical stages of evolution of a mixture of powders of two plastic metals (Fig. 4).The formation of layered composites from mixtures of metal- lic powders is accompanied by their intensive dispersion as evidenced by the results of investigations on deformation of metals. Initially, the so-called elementary structure of slip bands appears upon deformation of pure metals even without the use of activators and mills.300 This band consists of thin slip lines, which 50 mm Figure 3. Microphotograph of a cross-cut cleavage of the layered com- posite (the system Ni ± 14 at.% of Al, mechanochemical activation for 30 s).80 2 1 Initial components 5 4 3 Figure 4. Typical stages of evolution of plastic powders in the course of mechanochemical activation;84 (1) plastic deformation of the initial particles (flattening), (2) the forma- tion of new contacts between the initial elements, (3) accumulation of dislocations and breakage of layers into blocks, (4) and (5) subsequent stages of mixing and diffusion giving rise to the product.54 cover the crystal surface uniformly.As plastic deformation is developed, packets of slip bands arise and deformation is dis- tributed less uniformly throughout the bulk of the crystal. More in-depth investigation demonstrated that crystals were broken up into blocks, which were slightly disordered with respect to each other, even in the initial stage of deformation. At this stage, the appearance of dislocation networks was observed in studies of a thin foil by electron microscopy. Further development of plastic deformation led to roughening of the dislocation network to form an irregular cellular structure, the density of dislocations at the interface of the cells being substantially higher than the average density throughout the bulk.At this stage, the growth of disor- dered blocks was observed.300 The mechanism of formation of the cellular structure is not entirely known. However, it is assumed that processes of polygonisation associated with dislocation climb and rearrangement are of great importance in this mechanism. Since dislocation climb can occur only under the action of very large stresses or through diffusion inflow of point defects,301 the formation of the cellular structure is estimated taking into account these factors. At rather high temperatures (close to the temper- ature of recrystallisation), the formation of a cellular structure is promoted by a high rate of migration of vacancies.The concen- tration of vacancies in plastically deformed metal is also high. Thus, it is believed that this concentration and the equilibrium concentration of point defects at temperatures close to the melting point are of the same order of magnitude. According to van Bueren,302 after low-temperature deformation, which leads to a change in the linear dimensions of the specimen by only 10%, the concentration of point defects reaches 1019± 1020 cm73. Appa- rently, the high concentration of point defects upon low-temper- ature deformation is responsible for the formation of a cellular structure. In addition, low-temperature deformation is favourable for a decrease in the cell dimensions.303 Rapid deformation also influences the cell dimensions, viz., it causes the formation of extremely small cells.303, 304 The formation of cellular structures characterised by the disordered arrangement of the adjacent cells and substantial deformations were observed for chromium,303 iron,305 copper,306 tantalum,307 molybdenum and its alloys 308 ± 312 and for a number of other metals and alloys.313 ± 316 Therefore, domains of the crystal lattice are rearranged in the course of plastic deformation.This effect was revealed both for metals and their alloys in wide ranges of temperature, stresses and rates of deformation. The fragment-boundary angles depend on the degree of deformation and can be as large as several tens of degrees.The boundaries are either small-angle walls and networks or grain boundaries of a deformation nature. Plastic deformation arising under the joint action of high pressure and shear on mixtures of metals leads to a decrease in the dimensions of coherent-scattering regions compared to the anal- ogous regions for individual compounds treated analo- gously.317 ± 321 Positron studies of structural defects in metals subjected to high pressure and shear deformations demonstrated that vacancy clusters with sizes of up to 0.5 nm were formed in these specimens. In addition, specimens were intensively saturated with dislocations as the degree of deformation increased.319 Therefore, plastic deformation leads to the formation of non- equilibrium point defects and their clusters and to a high density of dislocations.As the degree of deformation increases, a cellular structure is developed followed by fragmentation. In the case of plastic deformation of heterogeneous mixtures, blocks become smaller and interactions at the boundaries of dissimilar blocks occur. Processes of grinding and formation of layered composites occur more vigorously in planetary ball mills because rapid shear deformations are realised on collisions in such mills. The dynamics of grinding, the microstructure and the sizes of the particles formed depend both on the conditions of mechanical treatment and on the properties of metals as exemplified by copper, nickel, iron and germanium.320 ± 326 T F Grigorieva, A P Barinova, N Z Lyakhov The process leading to a decrease in the grain size in ball mills involves three steps.326 1.Initially, deformation is localised in slip bands consisting of a series of high-density dislocations. 2. When a particular degree of deformation is achieved, annihilation and recombination of these dislocations take place within small-angle grain boundaries separating individual grains. The grain sizes thus obtained are 20 ± 30 nm. 3. The orientation of individual crystalline grains with respect to the adjacent grains becomes totally random. These stages are typical of deformation processes, which involve metals with BCC lattices and intermetallic compounds and which occur at high rates of deformation.Eckert et al.327 found that the minimum grain size of nano- crystalline metals (generally, 6 ± 22 nm) is achieved if two com- petitive process take place, viz., substantial plastic deformation caused by mechanical treatment in a ball mill and relaxation of the material. Moreover, it was found that the minimum grain size of metals with FCC lattices is in inverse proportion to the melting point.328, 329 Fecht et al.328 demonstrated that the average grain sizes of metals with BCC lattices and hexagonal close-packed lattices are decreased to 9 and 13 nm, respectively. The initial step of the mechanical synthesis in metallic systems involves the formation of layered composite structures accompa- nied by simultaneous dispersion of the initial components to nanosized grains.The formation of such layered composites results in an increase in the contact area between the initial components. It is known that heterogeneous solid-phase reactions can proceed only at the regions of tight contacts of the reacting phases. At these regions, a layer of the product arises and the further course of the reaction depends on the mechanism of diffusion of the reacting compounds through this layer. Solid- phase compounds are transferred primarily through diffusion whose rate depends on the mobility of lattice defects (their mobility is particularly high at the crystal surface even at low temperature).330 Pavlyukhin et al.90 studied the formation of solid solutions in the Fe ±Cr system and demonstrated that accelerated diffusion can proceed in binary metallic mixtures upon their mechanical activation in centrifugal planetary mills.Based on the results of MoÈ ssbauer spectroscopy, the authors estimated the diffusion coefficient (D) for the system containing spherical particles of radius R under conditions of activation. The determined value D^1075± 1077 cm2 s71 is seven orders of magnitude larger than the diffusion coefficient of chromium in iron at 1600 K (10712± 10714 cm2 s71). A change in the microstructure of the alloy, which is generally observed in the initial step of mechanical alloying, was ignored in calculations. However, since the thickness of layers changes substantially in the course of mechanical alloying, the radius of the initial species is not the only factor determining the diffusion path. In the case of plastic deformation of metals, diffusion can be substantially accelerated due to destruction and generation of dislocations 331 along which the rate of diffusion in metals is several orders of magnitude larger than along other direc- tions.332 ± 339 In addition, it was demonstrated 340 ± 345 that the diffusion coefficient is linearly proportional to the rate of defor- mation.Therefore, solid-phase dissolution of elements can be substantially accelerated on rapid plastic deformation. If this process is accompanied by the formation of layered composites, mass transfer can be promoted, on the one hand, due to short diffusion distances, and, on the other hand, due to acceleration of diffusion upon rapid plastic deformation.Clemens 346 found parallels between mechanochemical syn- thesis and solid-phase transformations in layered film systems. He believed that the role of mechanical activation consists in the formation of a composite from disperse particles of the initial components and promotion of diffuse mixing due to generation of non-equilibrium defects.Mechanochemical synthesis of intermetallic compounds Hellstern and Schultz 347 considered phase formation taking into account solid-phase diffusion. In the cited study, mechanical mixing of pure powders of iron and chromium was performed in a ball mill under argon. The authors believed that mechanical treatment afforded a layered microstructure consisting of two elements and the layers became thinner in the course of treatment.Since this system possesses a substantial chemical driving force, which favours diffusion between layers, the process occurs through the mechanism of a solid-phase diffusion reaction. An analogous viewpoint was also followed in a more recent study.348 In the latter study, it was demonstrated that particles with a typical layered structure were formed in Ni ±Zr and Fe ± Zr systems at the initial stage of mechanical treatment of initially crystalline powders in a mill. Further mechanical treatment afforded composites consisting of ultrathin layers in which solid- phase diffusion proceeded. Samwer suggested 349, 350 that amor- phous alloys are formed in the course of solid-phase diffusion and this process occurs at low temperature due to rapid diffusion of one component into another one.As a result of mechanical treatment, particles of the components adopt a `multilayer-sand- wich' form and a negative heat of mixing is the driving force for the process. Koch et al.271 also believed that mechanochemical reactions are accompanied by the formation of ultradisperse composite particles, solid-phase diffusion occurs in these particles and a negative mixing enthalpy is the driving force for diffusion. Most researchers attributed fast mass transfer in mechano- chemical reactions characterised by negative mixing enthalpies to a large contact area and a high rate of solid-phase diffusion at high rates of plastic deformation of metals.A large number of experimental studies of spontaneous diffusion arising when particles of the initial components (which are in intimate contact) become nanosized, have been carried out in recent years. In many systems, non-equilibrium solid-phase solubility of one element in another one is readily realised when grains become nanosized. It was found that extremely high diffusion rates are characteristic of highly disperse nanosized particles.351 ± 353 It was found that copper immediately dissolved in nanosized gold particles at room and lower temperatures.354 Fast spontaneous alloying afforded the intermetallides AuSb2 , InSb and AlSb.355 ± 357 It was demonstrated that every pair of elements is characterised by its own critical grain (particle) size at which spontaneous alloying starts at room temperature. The critical size of the initial particles increases as the heat of alloy formation increases.In the Au ± Cu,358 Au ± Zn 353 and Au ±Al 359 systems, the mixing enthalpies are negative and spontaneous alloying takes place even in the case of a rather large critical particle size. In the Au ±Ni system, the enthalpy is positive and spontaneous alloying at room temperature occurs only if grains are very small. In the In ±Al system, the mixing enthalpy is substantially larger than zero and hence, spontaneous alloying was not achieved (Fig. 5). Phase diagrams for systems consisting of nanosized particles differ substantially from standard diagrams and the solid-phase solu- bility of one element in another increases essentially (reaches several tens of percent) even if the elements virtually do not form solid solutions.361 It was assumed that relaxation of lattice distortions, which may be caused by a dissolved atom, proceeds much more readily in nanosized particles than in bulkier particles because the lattice becomes more mobile (Fig.6).362, 363 Therefore, mass transfer in layered composite structures containing nanosized grains, which are formed in the first step in metallic systems with negative mixing enthalpies, proceeds through spontaneous diffusion. This diffusion can take place at room temperature because the critical grain size at which it starts depends on the mixing enthalpy, viz., the larger the (negative) mixing enthalpy the larger the appropriate grain size.In systems in which intermetallides with high heats of formation (or, at least, in which the heats of formation of intermetallic compounds are substantially larger than the heats of mixing of solid solutions), these intermetallic compounds are formed first. Examination of 50 40 30 20 In+AlAu+Ni 100740 Heat of formation of alloys /kJ mol71 Figure 5. Dependence of the critical sizes of the initial particles on the heat of formation of alloys in different systems at 300 K;360 (1) complete spontaneous alloying at 300 K, (2) partial spontaneous alloying, (3) alloying does not occur.Au cluster Particle size /nm 96 K Au cluster 200 ± 250 K 250 ± 290 K Figure 6. Scheme of spontaneous alloying of gold and antimony par- ticles. the mechanochemical synthesis of solid solutions demonstrated that in layered composites, intermetallides are actually formed first. In the second step of the mechanochemical synthesis, intermetallides characterised by a high heat of formation and a high content of the alloying element arise in the Ni ± Ge, Ni ± Al, Ni ± Si, Ni ± Bi, Ni ± Sn, Ni ± In, Ni ± Ga, Cu ± Sn, Cu ± In, Cu ±Ga and Fe ± Sn systems.111, 113, 115 ± 119, 121 ± 124, 126, 132, 364 X-Ray dif- fraction data corresponding to the phase formation in the course of the mechanochemical synthesis of solid solutions of bismuth in nickel are shown in Fig.7. In this system, two intermetallic compounds, viz., NiBi (78.8 mass% Bi) and NiBi3 123 Au+Cu Au+Zn 40 0 Au cluster a-Sb cluster Au cluster a-Sb cluster AuSb2 cluster 55 Au+Al 8056 Intensity Ni 4321 30 35 Figure 7. X-Ray diffraction patterns of the products of mechanical alloying of nickel with 10 mass% of bismuth. The activation time (min): (1) 1, (2) 3, (3) 10, (4) 90.126 (91.44 mass% Bi), exist.108 The enthalpies of formation of these compounds calculated by the Miedema method 127 ± 129 are approximately 74 kJ mol71 for NiBi and 72 kJ mol71 for NiBi3 . In the course of the mechanochemical synthesis of solid solutions in this system, the formation of layered composites is followed by the formation of the intermetallide NiBi (see Fig.7). It is worthy of note that the above-mentioned phase can be formed under equilibrium conditions only if the bismuth content is 78 mass% and the mixture subjected to mechanical activation contains only 10 mass% of Bi. As the time of activation was increased, the intensities of reflections of the NiBi phase increased (see Fig. 7, curves 2 and 3), the lattice parameter of nickel remaining the same. The growth of the NiBi phase proceeded until the bismuth was completely consumed. Only further activa- tion of the resulting intermetallide with unconsumed nickel led to a decrease in the intensities of reflections of the intermetallide NiBi, broadening of the diffraction peaks of nickel and their shift to the small-angle region (see Fig.7, curve 4), which is indicative of the formation of a solid solution. Analogous changes in the diffraction patterns were observed for other systems. The dynam- ics of changes in the phase composition of the mixture can be followed using the Fe ± Sn system as an example (Fig. 8). Thus, the amount of the intermetallic compound FeSn2 increased and then decreased upon mechanochemical dissolution of FeSn2 in iron to form a solid a-solution of tin in iron. Mechanochemical activation led to a decrease in the grain size of a-Fe to 10 ± 20 nm and the resulting intermetallide FeSn2 also contained nanosized particles (Fig. 8 b). It should be noted that the intensive formation of the solid solution a-Fe(Sn) was observed only if the grain sizes of the phases a-Fe and FeSn2 reached 3 ± 8 nm.These values agree well with other data on the mechanochemical synthesis of solid solutions in this system.122 Investigations demonstrated that the dynamics of formation of intermediate intermetallic compounds in the second step of the mechanochemical synthesis of solid solutions in metallic systems characterised by negative enthalpies of formation correlates with the enthalpies of formation of equilibrium intermetallic com- pounds.365 ± 368 Comparative studies of mechanochemical synthesis from a mixture of metallic powders and from a mixture of a metal serving as the solvent and intermetallic compounds, whose phase compo- sitions are identical to those of substances which are formed in the intermediate stage of the mechanochemical reaction of the metal- lic powders, demonstrated that the dynamics of formation of the solid solution is virtually the same in both cases.369 Ni Ni NiBi NiBi Bi 20 25 y /deg T F Grigorieva, A P Barinova, N Z Lyakhov a c (at.%) 100 2 50 3 4 0 b r /nm 20 2 10 3 0 c a /nm 0.300 0.290 1 2 5 10 20 30 40 60 70 0 Time of grinding /h Figure 8.Dependences of the phase composition (a), the average size of crystallites (b), the lattice parameter of the resulting BCC phase and the concentration of tin (c) on the time of grinding in a Pulverizette-5 mill;123 (1) a-Fe(Sn), (2) a-Fe, (3) FeSn2, (4) b-Sn. Therefore, the synthesis of solid solutions in metallic systems characterised by negative mixing enthalpies may involve the following stages.1. The formation of layered composite structures with simul- taneous dispersion of the initial components to nanosized par- ticles (a sharp increase in the contact area between the initial components). 2. The formation of intermetallic compounds in nanosized layered composites. 3. Dissolution of intermetallic compounds in the metal acting as the solvent to form a solid solution. Most of researchers assumed that the process of formation of amorphous alloys from metallic powders involves two steps. In the first step, layered composites containing nanosized grains are formed. The formation of an amorphous alloy in the second step proceeds through diffusion in a heated specimen. It is believed that the specimen is heated at the expense of the energy of collision of balls and the temperature increases to hundreds of degrees, but it does remain inadequate to attain crystallisation of an amorphous alloy. This point of view was confirmed by Petzoldt et al.370 The authors observed amorphous interlayers between layers of nickel and niobium by electron microscopy. These interlayers are analogous to those between layers of nickel and zirconium observed by Meng et al.371 in experiments on annealing of sputtered films.In a number of studies, the formation of intermetallic phases before amorphisation was detected. This fact seems to be quite reliable because amorphous alloys in many systems were prepared by mechanical grinding of intermetallides.The formation of intermetallic compounds involves, most probably, two steps 1 1 cSn (at.%) 30 15 0Mechanochemical synthesis of intermetallic compounds because intermetallides can arise immediately in layered compo- site structures. In layered composite structures, which are formed in metallic systems, spontaneous diffusion of the initial compounds can proceed at room temperature due to the thermodynamic driving force for the process. In analogous layered composites formed in systems characterised by a positive mixing enthalpy, this driving force is absent. It can be suggested that the formation of solid solutions under conditions of mechanochemical activation pro- ceeds, most probably, through quenching from the liquid state because, first, the temperatures of phase transitions, including the solid phase?liquid phase transition, sharply decrease compared to those in a bulky material as the sizes of the initial particles decrease to several nanometers,372 ± 376 and, second, sharp local increases in temperature and pressure can take place in activators.Bowden et al.377 ± 379 gained experimental evidence for the existence of local heating and revealed their sites, which arise at the contacts between particles of solid compounds on their mechanical treatment. The authors established that the area of heating sites is, on the average, 1072 cm2, the time of their existence is 1075± 1073 s and the temperature jumps at the sites of heating can be as large as 800 ± 1000 K and sometimes even larger.According to the hypothesis proposed by Dubnov, Sukhikh and Tomashevich,380 individual dislocation pairs with antiparallel Burgers vectors in the regions of intensive shear can annihilate with restoration of a perfect structure and liberation of the dislocation energy, which, according to estimates made by Cottrell,381 is *1 eV. Since the atomic forces act only through very short distances, the region of energy liberation is limited to a radius of about one interatomic distance. In this case, local heating is*103 K. Avvakumov 321 also concluded that local sites of heating limited by the melting point of particles being treated can arise in the mechanochemical processes.Urakaev and Avvakumov 382 calculated the thickness of the molten zone. They believed that this value can reach 561077 cm if the size of rubbing particles is *1074 cm and the sites of local heating (taking into account the possibility of melting of particles treated) are limited by their melting points. Kopylov et al.383 suggested that intermetallic compounds can be synthesised in a planetary mill due to short-period local heating on friction of the particles. Based on the results of calculations, it was con- cluded 384 ± 387 that high local temperatures and pressures can arise in the course of mechanochemical activation. Dannik 388 solved the problem of collision of two particles taking into account frictional forces on interaction of rigid bodies.Based on Dannik's equations, Urakaev 389 calculated the temper- atures at the contacts between inorganic particles rubbed in drums of centrifugal planetary mills. The maximum local temperature at the rubbing surface of the particles is*1030 Kand the lifetime of this temperature is 1079 s. Ermakov, Yurchikov and Barinov 390 also considered the problem of the effect of the temperature on processes occurring in mechanochemical activators. They believed that substantially heated and rapidly cooled local regions (hot spots) can appear at the surface of the particles. The lifetime of hot regions of sizes 1 ± 10 nm `heated' almost to the melting point is 1073± 1076 s. The authors also estimated the rate of cooling of these regions at 106 ± 109 deg s71.The appearance of hot sites has also been observed in more recent studies. For example, the intermetallide SnTe was synthesised at room temperature by repeated cold pressing of granulated tin and powdered tellurium.391 The system consisted of the initial elements until the pressing action provided an adequate mechanical energy. Hot regions of diameter 1 ± 2 nm were observed at the metal surface with particle sizes of 10 ± 15 nm. In these regions, 0.25% ± 0.35% of the total deforma- tion energy was accumulated after 30-fold pressing (1.25 g of a mixture of Sn and Te, 343 MPa). Eckert et al.392 also calculated the high local temperatures arising at contact sites.The experiments were carried out using a 57 `Pulverizette-5' planetary ball mill (Frich, Germany) at the ball rates of 2.5, 3.6 and 4.7 m s71. The temperatures at the contact sites, which are shifted with respect to each other due to deforma- tion caused by colliding balls, were calculated as described by Schwarz and Koch.393 The following values were obtained: at the rate of 2.5 m s71, DT=80 deg; at the rate of 3.6 m s71, DT=167 deg; at the rate of 4.7 m s71, DT=287 deg. The authors believed that the average temperature of the drum, which was 50, 80 and 120 8C, respectively, in the case of the above-mentioned rates, should be added to the temperature developed due to collisions. Zalkin 394 concluded that molten zones can arise at temper- atures, which are substantially lower than the melting point of a low-melting element; in this case, diffusion has virtually no effect on the onset of melting.Experimental investigations aimed at direct measurement of local temperatures are many fewer in number compared to studies in which local temperatures were calculated. Changes in the temperature are sometimes determined on vibrating mills with the use of thermocouples. A thermocouple is attached to the outer wall of the drum and the temperature can be monitored through- out the process. In this case, it is assumed that the temperatures of the drum, balls and the material under treatment are equal or differ insignificantly. Kimura et al.395 used this procedure for the measurements of the temperature of the drum wall depending on the rate of the stirrer of the attritor and demonstrated that the temperature of powders reached 573 K.The AGO planetary ball mills are characterised by very high energies and the input power of *1 W per cm3 of the drum volume.396 The temperature of balls can amount to 500 8C increasing very rapidly.397 Hence, not only dispersion of the initial components, but also substantial temperature jumps, which arise upon contact of the material treated with balls, should be taken into account in mechanochemical synthesis in high-energy mills. Analysis of the published data demonstrated that mechano- chemical synthesis of non-equilibrium solid solutions in metallic systems characterised by a positive mixing enthalpy involves two steps.In the first step, layered composite structures containing nanosized grains of the initial components are formed. In the second step, solid solutions arise. The second step can proceed through quenching of the liquid phase in which, apparently, mixing of the components occurs. The liquid phase is formed both due to a sharp decrease in the temperature of phase transition to the liquid state when grains become nanosized and due to local temperature jumps in the contact region at the instant grinding particles collide. In the case of metallic systems with a positive mixing enthalpy, it seems reasonable to speak about mechanical alloying rather than about the mechanochemical synthesis of non-equilibrium solid solutions.Unfortunately, the term `mechanical alloying' is assigned in the literature both to systems in which chemical reactions proceed and to systems in which components are only mixed. The formation of intermetallic compounds upon liquid-phase contact interaction in metallic systems, which are characterised by a negative mixing enthalpy and which contain a low-melting component, should also be taken into account. The presence of layered composites in metallic systems containing nanosized grains in which the melting temperature is sharply decreased with simultaneous existence of rather high temperature jumps at sites of contacts with grinding particles can ensure contact melting of the components and their chemical reaction in the liquid phase.Presently, there is no agreement regarding the nature of mechanochemical synthesis, viz., the question of whether it is a solid-phase process or it proceeds in the liquid phase remains open. A large number of calculations and experimental studies available in the literature indicate that substantial temperature jumps can occur in activators. However, the direct mechanochem- ical synthesis from components with high melting temperatures and the fact that mechanochemical synthesis can be performed on58 Bridgman anvils and in low-energy ball mills in which high temperatures are difficult to attain provide evidence in favour of the solid-phase nature of the processes. In the present review, various opinions as to the mechanisms of processes occurring in mechanochemical synthesis in metallic systems are surveyed. It should be noted that most researchers consider the preparation of amorphous alloys and supersaturated solid solutions by the mechanochemical method as the process of disordering of equilibrium phases.References 1. S P Yatsenko Indii. Svoistva i Primenenie (Indium. Properties and Applications) (Moscow: Nauka, 1987) 2. G V Samsonov, V N Bondarev Germanidy (Germanides) (Moscow: Metallurgiya, 1968) 3. E I Gil'debrand, A B Fasman Skeletnye Katalizatory v Organi- cheskoi Khimii (Skeletal Catalysts in Organic Chemistry) (Alma-Ata: Nauka, 1982) 4. G V Samsonov, L A Dvorina, B M Rud' Silitsidy (Silicides) (Moscow: Metallurgiya, 1979) 5. A E Vol, Stroenie i Svoistva Dvoinykh Metallicheskikh Sistem (Structure and Properties of Binary Metallic Systems) (Moscow: Fizmatgiz, 1959) Vol.1 6. E M Sokolovskaya, L S Guzei Metallokhimiya (Metallochemistry) (Moscow: Moscow State University, 1986) 7. C S Barrett, T B Massalski Structure of Metals (Oxford: Pergamon Press, 1980) 8. Ya S Umanskii, Yu A Skakov Fizika Metallov (The Physics of Metals) (Moscow: Atomizdat, 1978) 9. W Hume-Rothery Elements of Structural Metallurgy (London: Institute of Metals, 1961) 10. H W King J. Mater. Sci. 1 79 (1964) 11. V V Neverov, P P Zhitnikov Fiz. Met. Metalloved. (11) 143 (1990) a 12. B T McDermott, C C Koch Scr. Metall. 20 669 (1986) 13. C C Koch Annu. Rev. Mater. Sci. 19 121 (1989) 14. Y Z Yang, Y L Zhu, Q S Li, X M Ma, Y D Dong, Y Z Chuang Mater.Sci. Technol. 14 551 (1998) 15. M Kis-Varga, D L Beke Mater. Sci. Forum 225 ± 227 465 (1996) 16. S Enzo, P Macri, P Rose, N Cowlam, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 101 17. Z T Liu, O N C Uwakweh J. Mater. Synth. Proc. 5 (2) 135 (1997) 18. S Ordonez,G Garcia,D Serafini,A San MartinUMater. Sci. Forum 299 ± 300 478 (1999) 19. H Enoki, D Sun, E Akiba, F Gindl J. Alloys Compd. 285 279 (1999) 20. P Ruuskanen Mater. Sci. Forum 269 ± 272 139 (1998) 21. B B Bokhonov, I G Konstanchuk, V V Boldyrev J. Alloys Compd. 218 190 (1995) 22. E Belyaev, O Lomovsky, G Golubkova Mater. Sci. Forum 179 ± 181 403 (1995) 23. E Yu Belyaev, O I Lomovsky, A I Ancharov, B P Tolochko Nucl.Instrum. Methods Phys. Res., A 405 435 (1998) 24. B K Yen, T Aizawa, J Kihara Mater. Sci. Eng., A 220 8 (1996) 25. S N Patankar, S-Q Xiao, J J Lewandovski, A H Heuer J. Mater. Res. 8 1311 (1993) 26. E Yu Belyaev, O I Lomovskii, in Khimiya Tverdogo Tela i Novye Materialy (Sb. Dokl. Vseros. Konf.), Ekaterinburg, 1996 [The Chem- istry of Solids and New Materials (Collection of Reports of All- Russian Conference), Ekaterinburg, 1996] Vol. 1, p. 212 27. N Iwamoto, S Uesaka Mater. Sci. Forum 88 ± 90 763 (1992) 28. E Ivanov, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 415 29. A A Popovich, V N Vasilenko, in Mekhanokhimicheskii Sintez v Neorganicheskoi Khimii (Mechanochemical Synthesis in Inorganic Chemistry) (Novosibirsk: Nauka, 1991) p.168 30. A A Popovich, V N Vasilenko, V P Reva Poroshk. Metall. (11) 22 (1992) 31. L Liu, F Padella, WGuo,MMagini Acta Metall. Mater. 43 3755 (1995) 32. T Lou, G Fan, B Ding, Z Hu J. Mater. Res. 12 1172 (1997) T F Grigorieva, A P Barinova, N Z Lyakhov 33. D Oleszak, M Jachimovich, H Matyja Mater. Sci. Forum 179 ± 181 215 (1995) 34. M Umemoto, S Shiga, K Raviprasad, I Okane Mater. Sci. Forum 179 ± 181 165 (1995) 35. L Lu, M O Lai, M L Hoe Nanostruct. Mater. 10 551 (1998) 36. M Riffel, J Schilz J. Mater. Sci. 33 3427 (1998) 37. L Zaluski, A Zaluska, J O Strom-Olsen J. Alloys Compd. 217 245 (1995) 38. D Oleszak,MBurzynska-Szyszko, H Matyja J.Mater. Sci. Lett. 12 3 (1995) 39. C C Koch, M S Kim J. Phys. 46 5731 (1985) 40. E Hellsten, H J Fecht, C C Garland,W L Johnson Proc. MRS Symp. 132 137 (1989) 41. K Chattopadhaya, K Sridhar J. Alloys Compd. 264 293 (1998) 42. K B Gerasimov, V V Boldyrev Mater. Res. Bull. 31 1297 (1996) 43. G Le GaeÈ r, P Mattezzi, B Fultz J. Mater. Res. 7 1387 (1992) 44. V A Varnek, L A Strugova, E G Avvakumov Fiz. Tv. Tela 16 (6) 1816 (1974) b 45. D K Nukhopadhaya, S Suryanarayana, F H Froes, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 131 46. S Ghosh, D Linch, E C Baburaj, F H Froes, in Proceedings of Sym- posium on Synthesis of Lightweight Metals.III, San-Diego, 1999 p. 43 47. J H Ahn,K R Lee,H K Cho Mater. Sci. Forum 179 ± 181 153 (1995) 48. J S C Jang, C C Koch J. Mater. Res. 5 498 (1990) 49. M Qi,M Zhu, G B Li, D Z Yang J. Mater. Sci. Lett. 11 1147 (1992) 50. P S Goodwin, T M T Hinder, A Wisbey, C M Ward-Close Mater. Sci. Forum 269 ± 272 53 (1998) 51. St Lauer, Z Guan, H Wolf, Th Wichert Mater. Sci. Forum 269 ± 272 485 (1998) 52. R C Benn, P K Mirchandani,A S Watwe, in Modern Development in Powder Metallurgy No. 4 (Princton: Metal Powder Industries Federation, 1988) p. 479 53. A Calka, A P Radlinski Scr. Metall. 23 1497 (1989) 54. E A Kenik, R J Bayuzick,M S Kim, C C Koch Scr. Metall. 21 1137 (1987) 55. H J Fecht,G Han, Z Fu,W L Johnson J. Appl. Phys. 67 1744 (1990) 56.T J Tianen, R B Schwarz J. Less-Common Met. 140 99 (1988) 57. E Ivanov, T Grigorieva, V Boldyrev, A Fasman, S Mihkailenko, O Kalinina Mater. Lett. 7 51 (1988) 58. E Ivanov, S Makhlouf, K Sumiyama, K Suzuki, H Yamauchi, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 177 59. C Kuhrth, H Schropf, L Schultz, E Arztz, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 269 60. E Hellsten, H J Fecht, Z Fu,WL Johnson J. Mater. Res. 5 498 (1990) 61. B L Huang, J Vallone,M J Luton Nanostruct. Mater. 5 411 (1995) 62. I Borner, J Eckert Mater. Sci. Forum 225 ± 227 377 (1996) 63. E Ivanov, S Makhlouf, K Sumiyama, H Yamauchi, K Suzuki, G Golubkova J.Alloys Compd. 185 28 (1992) 64. S Makhlouf, K Sumiyama, K Suzuki J. Alloys Compd. 199 119 (1992) 65. T Chen, J M Hampikian, N N Thadhani Acta Mater. 47 2567 (1990) 66. F Cardellini, V Contini, G Mazzone Philos. Mag., A 78 1021 (1998) 67. T F Grigorieva, E Yu Ivanov, G V Golubkova, E I Petrachkov, T G Marenina, in Mekhanokhimicheskii Sintez v Neorganicheskoi Khimii (Mechanochemical Synthesis in Inorganic Chemistry) (Novosibirsk: Nauka, 1991) p. 214 68. T F Grigorieva, E Yu Ivanov, V V Boldyrev, E I Petrachkov, T I Samsonova, V P Chuev Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 3 73 (1989) 69. P F Relushko, I P Berestnitskaya, V V Moskvin, L I Trusov, V I Novikov, P Yu Butyagin, in X Vsesoyuz.Soveshch. po Kinetike i Mekhanizmu Khimicheskikh Reaktsii v Tverdom Tele (Tez. Dokl.), Chernogolovka, 1989 [The Xth All-Union Meeting on Kinetics and Mechanism of Chemical Reactions in Solids (Abstracts of Reports), Chernogolovka, 1989] p. 187 70. E Bonetti, G Scipione, S Enzo, R Frattini, L Schiffini Nanostruct. Mater. 6 397 (1995) 71. M A Morris, D G Morris Mater. Sci. Forum 88 ± 90 529 (1992) 72. E Gaffet, N Malhouroux-Gaffet J. Alloys Compd. 205 27 (1994) 73. N Malhouroux-Gaffet, E Gaffet J. Alloys Compd. 198 143 (1993) 74. M Umemoto, S Shiga, K Raviprasad Mater. Sci. Forum 225 ± 227 841 (1996)Mechanochemical synthesis of intermetallic compounds 75. C Gras, E Gaffet, F Bernard, J C Niepce Mater. Sci. Eng., A 264 94 (1999) 76. F Cardellini, V Contini, R Gupta, G Mazzone, A Montone, A Perin, G Principi J.Mater. Sci. 33 2519 (1998) 77. M Meyer, L Mendoza-Zelis, F H Sanchez Mater. Sci. Forum 225 ± 227 441 (1996) 78. R Martinez-Sanchez, J G Cabanas-Moreno, H A Calderon, M Umemoto Mater. Sci. Forum 225 ± 227 435 (1996) 79. M A Korchagin, T F Grigorieva, A P Barinova, N Z Lyakhov Int. J. SHS (3) (2000) 80. T F Grigorieva, M A Korchagin, A P Barinova, N Z Lyakhov Dokl. Akad. Nauk 369 345 (1999) c 81. M A Korchagin, T F Grigorieva, A P Barinova, N Z Lyakhov Dokl. Akad. Nauk 372 40 (2000) c 82. J Lagerbom, T Tianen,M Lehtonen, P Lintula J. Mater. Sci. 34 657 (1999) 83. V Gauthier, C Josse, F Bernard, E Gaffet, J P Larpin Mater. Sci. Eng., A 265 117 (1999) 84. F Charlot, E Gaffet, B Zeghmati, F Bernard, J C Niepce Mater.Sci. Eng., A 262 279 (1999) 85. D Klein, J C Niepce, F Charlot, E Gaffet F Bernard Acta Mater. 47 619 (1990) 86. F Charlot, C Gras,M Gramond, E Gaffet, F Bernard, J C Niepce J. Phys. IV, Colloq. 8 (P5) 497 (1998) 87. E Gaffet, F Charlot, D Klein, F Bernard, J-C Niepce Mater. Sci. Forum 269 ± 272 379 (1998) 88. F Charlot, C Gras, F Bernard, J C Niepce, E Gaffet Acta Mater. 47 2113 (1999) 89. C Gras, E Gaffet, F Bernard, D Vrel, J C Niepce in Book of Abstracts of the Vth International Symposium on SHS, Moscow, 1999 p. 38 90. Yu T Pavlyukhin, Yu E Manzanov, EGAvvakumov, V V Boldyrev Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 6 84 (1981) 91. R M Davis, C C Koch Scr. Metall. 21 305 (1987) 92. E E Yurchikov, V P Pilyugin, R I Kuznetsov, in IV Vsesoyuz.Seminar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p. 80 93. E E Yurchikov, V P Pilyugin, V A Barinov, in IV Vsesoyuz. Semi- nar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p. 185 94. V V Neverov, Doctoral Thesis in Physicomathematical Sciences, Novokuznetsk Pedagogical Institute, Novokuznetsk, 1995 95.V V Neverov, V N Burov Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 9 3 (1979) 96. R BruÈ ning, K Samwer, C Kuhrt, L Schultz J. Appl. Phys. 72 2978 (1992) 100. V V Cherdyntsev, S D Kaloshkin, I A Tomilin, E V Shelekhov, 101. V V Tcherdyntsev, S D Kaloshkin, I A Tomilin, E V Shelekhov, 97. C Kuhrt, L Schultz J. Appl. Phys. 71 1896 (1992) 98. C Kuhrt, L Schultz J. Appl. Phys. 73 6588 (1993) 99. V V Cherdyntsev, S D Kaloshkin, Yu V Baldokhin, I A Tomilin, E V Shelekhov Fiz. Met. Metalloved. 84 (4) 154 (1997) a Yu V Baldokhin Nanostruct. Mater. 12 139 (1999) Yu V Baldokhin Mater. Sci. Forum 269 ± 272 145 (1998) 102. V I Fadeeva, A V Leonov, L N Khodina Mater. Sci. Forum 179 ± 181 397 (1994) 103. K Wolski, G Le Caer, P Delcroix, R Fillit, F Thevenot, J Le Core Mater.Sci. Eng., A 207 97 (1996) 104. E Bonetti, G Scipione, G Valdre, G Cocco, R Frattini, P P Marci J. Appl. Phys. 74 2053 (1993) 105. S Surinach, X Amils, S Gialanella, L Lutterotti,M D Baro Mater. Sci. Forum 235 ± 238 415 (1997) 106. V I Fadeeva, V K Portnoy, Yu V Baldokhin, G A Kochetov, H Matyja Nanostruct. Mater. 12 625 (1998) 107. H G Jiang, R J Perez,M L Lau, E J Lavernia J. Mater. Res. 12 1429 (1997) 108. M Hansen, K Anderko Constitution of Binary Alloys) (New York: McGraw-Hill, 1961) 109. V V Chervyakova, A A Presnyakov Slozhnye Latuni i Bronzy (Complex Brasses and Bronzes) (Alma-Ata: Nauka, 1974) 59 110. I S Miroshnichenko Zakalka iz Zhidkogo Sostoyaniya (Hardening from the Liquid State) (Moscow: Metallurgiya, 1982) 111.T F Grigorieva, Candidate Thesis in Chemical Sciences, Institute of Solid State Chemistry and Mechanosynthesis, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1988 112. E Lugscheider, G Yang Z. Met.kd. 62 548 (1971) 113. E Ivanov Mater. Sci. Forum 88 ± 90 475 (1992) 114. A E Vol, I Kagan, Stroenie i Svoistva Dvoinykh Metallicheskikh Sistem (Structure and Properties of Binary Metallic Systems) (Moscow: Fizmatgiz, 1976) Vol. 3 115. T F Grigorieva, V V Boldyrev Dokl. Akad. Nauk 340 329 (1995) c 116. T F Grigorieva, A P Barinova, V V Boldyrev Neorg. Mater. 32 41 (1996) d 117. T F Grigorieva, A P Barinova, V V Boldyrev Neorg. Mater. 31 1551 (1995) d 118. T F Grigorieva, A P Barinova, V D Belykh, E Yu Ivanov, V V Boldyrev, in Proceedings of the 5th European Conference on Advanced Materials, Processes and Applications (EUROMAT'97), Maastricht, 1997 V.1, p. 447 119. T F Grigorieva, V V Boldyrev Dokl. Akad. Nauk 340 195 (1995) c 120. O Kubashewski Iron Binary Diagrams (Berlin: Springer, 1982) 121. A F Cabrera, F H Sanchez, L Mendoza-Zelis Mater. Sci. Forum 179 ± 181 231 (1995) 122. G Le Caer, P Delcroix, M O Kientz, B Malaman Mater. Sci. Forum 179 ± 181 469 (1995) 123. E P Elsukov, G A Dorofeev, G N Konygin, A L Ul'yanov, V A Barinov, T F Grigorieva, V V Boldyrev Khim. Interes. 126. T F Grigorieva, V V Boldyrev, T I Samsonova Dokl. Akad. Nauk Ustoich. Razvit. 6 131 (1998) e 124. E P Yelsukov, G A Dorofeev, V A Barinov, T F Grigorieva, V V Boldyrev Mater.Sci., Forum. 269 ± 272 151 (1998) 125. A E Vol, I Kagan, Stroenie i Svoistva Dvoinykh Metallicheskikh Sistem (Structure and Properties of Binary Metallic Systems) (Moscow: Fizmatgiz, 1962) Vol. 2 340 495 (1995) c 127. A R Miedema,R Boom, F R de Boer J. Less-Common Met. 41 283 (1975) 128. A R Miedema J. Less-Common Met. 46 67 (1976) 129. A R Miedema, P F de Chatel, F R de Boer Physica B 100 1 (1980) 130. T F Grigorieva, E Yu Ivanov, V V Boldyrev, S V Vos'merikov, T I Samsonova Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Kkhim. Nauk (5) 91 (1989) 131. T F Grigorieva, E Yu Ivanov, in XVI Vsesoyuzn. Nauchn.-Tekh- nich. Konf. `Poroshkovaya Metallurgiya' (Tez. Dokl.), Sverdlovsk, 1989 [The XVIth All-Union Scientific and Technical Conference `Powder Metallurgy' (Abstracts of Reports), Sverdlovsk, 1989] Part 1, p.61 132. G B Bokii Vvedenie v Kristallokhimiyu (Introduction in Crystal Chemistry) (Moscow: Moscow State University, 1954) 133. T F Grigorieva, A P Barinova, V V Boldyrev, E Yu Ivanov Solid State Ion. 101 ± 103 17 (1997) 134. M P Shaskol'skaya Kristallografiya (Crystallography) (Moscow: Vysshaya Shkola, 1984) 135. S P Yatsenko Gallii. Vzaimodeistvie s Metallami (Gallium. Interaction with Metals) (Moscow: Nauka, 1974) 136. T F Grigorieva, G V Golubkova, E Yu Ivanov, in XVI Vsesoyuz. Nauch.-Tekhnich. Konf. `Poroshkovaya metallurgiya' (Tez. Dokl.), Sverdlovsk, 1989 [The XVIth All-Union Scientific and Technical Conference `Powder Metallurgy' (Abstracts of Reports), Sverdlovsk, 1989] Part 1, p.108 137. S Enzo, G Mulas, R Frattini Mater. Sci. Forum 269 ± 272 385 (1998) 138. D Oleszak, P H Shingu Mater. Sci. Eng., A 181/182 1217 (1994) 139. T G Popova, P Y Butyagin, A N Streletski, V K Portnoy Colloid J. 59 737 (1997) 140. X S Huang, T Mashimo J. Mater. Process. Technol. 85 135 (1999) 141. Dvoinye i Mnogokomponentnye Sistemy na Osnove Medi. Spravoch- nik (Binary and Multi-Component System Based on Copper. Handbook) (Moscow: Nauka, 1979) 142. J H He, E Ma Proc. MRS Symp. 481 637 (1998) 143. A H Advani,N N Thadhani Metall. Mater. Trans. A, Phys. Metall. Mater. Sci. 30 1367 (1999)60 144. D G Morris, M A Morris, A Benghalem, C Bisell, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p.353 145. P Y Lee, C C Koch J. Non-Cryst. Solids 94 88 (1987) 146. I J Duerden,WHume-Rothery J. Less-Common Met. 11 381 (1966) 147. K B Gerasimov, V V Kolpakov, A A Gusev, E Yu Ivanov, in Proceedings of the 2nd International Symposium on the Solid State Chemistry, Pardubice, 1989 p. 9 148. A V Leonov, E Szewczak, O E Gladilina, H Matya, V I Fadeeva Mater. Sci. Forum 225 ± 227 277 (1996) 149. C E Lundin, A S Yamamoto Trans. AIME 236 863 (1966) 150. E Hellstern, L Schultz, R Bormann, D Lee Appl. Phys. Lett. 53 1399 (1988) 151. R B Schwarz, P B Desch, S R Srinivasan, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p.227 152. M Kis-Varga, D L Beke Mater. Sci. Forum 225 ± 227 465 (1996) 153. M Kis-Varga, D L Beke, S Meszaros, K Vad, Gy Kerekes, L Daroczi Mater. Sci. Forum 269 ± 272 961 (1998) 154. E Yu Ivanov, B D Bryskin Mater. Sci. Forum 269 ± 272 111 (1998) 155. P Boolchand, C C Koch J. Mater. Res. 7 2876 (1992) 156. R N Kuzmin, S V Nikitina Sov. Phys.-Solid State 13 3151 (1972) 157. H Jones Rep. Prog. Phys. 36 1425 (1973) 158. P Ramachandrarao,M G Scott,G A Chadwick Philos. Mag., B 25 961 (1972) 159. P J Yvon, R B Schwarz, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 393 160. F Li, K N Ishihara, P H Shingu Metall. Trans. A, Phys. Metall.Mater. Sci. 22 2849 (1991) 161. P H Shingu, B Huang, S R Nishitani, S Nasu J. Jpn. Inst. Met., Suppl. 29 3 (1988) 162. P H Shingu, B Huang, J Kuyama, K N Ishihara, S Nasu, in New Materials by Mechanical Alloying Technique (Eds E Artz, L Schultz) (Oberursel, Germany: DGM Informationgeselschaft, 1989) p. 319 163. B Huang, N Tokizane, K N Ishihara, P H Shingu, S Nasu J. Non-Cryst. Solids 117/118 688 (1990) 164. M Pekala, D Oleszak Mater. Sci. Forum 235 ± 238 547 (1997) 165. R A Dunlap, J R Dahn, D A Eelman, G R Mackay Hyperfine Interact. 116 117 (1998) 166. A Calka,W Kaczmarek, J S Williams J. Mater. Sci. 28 15 (1993) 167. M Oering, R Bormann J. Phys. Colloq. 51 C4-169 (1990) 168. L M Di, H Bakker J. Phys., Condens. Matter 3 3427 (1991) 169.L M Di, H Bakker J. Appl. Phys. 71 5650 (1992) 170. L M Di, H Bakker J. Phys., Condens. Matter 3 9319 (1991) 171. L M Di, H Bakker, P Barczy, Z Gacsi Acta Metall. Mater. 41 2923 (1993) 172. H Bakker, L M Di Mater. Sci. Forum 88 ± 90 27 (1992) 173. H Yang, H Bakker, in Proceedings of the 2nd International Conference on Structural Applications of Mechanical Alloying, Vancouver, 1993 p. 401 174. H Yang, L M Di, H Bakker Intermetallics 1 29 (1993) 175. G F Zhou, H Bakker Europhys. Lett. 30 433 (1995) 176. M Oering, Z H Yan, T Klassen, R Bormann Phys. Status Solidi, A 131 671 (1992) 177. T F Grigorieva, M A Korchagin, A P Barinova, N Z Lyakhov Metally (4) 64 (2000) 178. E P Elsukov, V V Yakovlev, V A Barinov Fiz. Met. Metalloved.77 (4) 131 (1994) a 179. E P Elsukov, V V Yakovlev, E V Voronina, V A Barinov, in Dokl. Mezhdunar. Nauch. Seminara `Mekhanokhimiya i Mekhani- cheskaya Aktivatsiya', Sankt-Peterburg, 1995 (Proceedings of International Scientific Seminar `Mechanochemistry and Mechanical Activation', St-Petersburg, 1995) p. 67 180. E P Yelsukov, E V Voronina, G N Konygin, V A Barinov, S K Gogovnikov, G A Dorofeev, A V Zagainov J. Magn. Magn. Mater. 166 334 (1997) 181. PHDuwerRHWillens,WKlement Jr J. Appl. Phys. 31 1136 (1960) 182. E F Kneller J. Appl. Phys. 35 2210 (1965) 183. K Sumiyama, T Yoshitake, Y Nakamura Acta Metall. 33 1791 (1985) 184. J S Benjamin Sci. Am. 234 40 (1976) 185. V V Neverov, V N Burov, P P Zhitnikov Izv. Sib. Otd. Akad.Nauk, Ser. Khim. Nauk (5) 54 (1983) T F Grigorieva, A P Barinova, N Z Lyakhov 186. A A Gusev, Candidate Thesis in Chemical Sciences, Institute of Solid State Chemistry and Mechanosynthesis, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1993 187. S D Kaloshkin, I A Tomilin, G Andrianov, Yu V Baldokhin, E V Shelehkov Mater. Sci. Forum 225 ± 227 331 (1996) 188. S D Kaloshkin, I A Tomilin, E V Shelekhov, V V Cherdyntsev, G A Andrianov, Yu V Baldokhin Fiz. Met. Metalloved. 84 (3) 68 (1997) a 189. M J Barro, E Navarro, P Agudo, A Hernando, P Crespo, A Garsia Escorial Mater. Sci. Forum 235 ± 238 553 (1997) 190. K Uenishi, K F Kobayashi, S Nasu, H Hatano, K N Ishihara, P H Shingu Z. Met.kd. 83 132 (1992) 191. A R Yavari, P J Desre, T Benameur Phys.Rev. Lett. 68 2235 (1992) 192. J Eckert, J C Holzer,W L Johnson J. Appl. Phys. 73 131 (1993) 193. J Eckert, J C Holzer, C E Krill, W L Johnson J. Appl. Phys. 73 2794 (1993) 194. J Z Jiang, U Gonser, C Gente, R Bormann Appl. Phys. Lett. 63 2768 (1993) 195. J Z Jiang, U Gonser, C Gente, R Bormann Appl. Phys. Lett. 63 1056 (1993) 196. P P Macri, P Rose, R Frattini, S Enzo, G Principi, W X Hu, N Cowlam J. Appl. Phys. 76 4061 (1994) 197. P P Macri, S Enzo, N Cowlam, R Frattini, G Principi, W X Hu Philos. Mag., B 71 249 (1995) 198. P P Macri, P Rose, D E Banda, N Cowlam, G Principi, S Enzo Mater. Sci. Forum 179 ± 181 249 (1995) 199. R Elkalkouli, P Chartier, J -F Dinhut Mater. Sci. Forum 179 ± 181 267 (1995) 200.K Tokumitsu Mater. Sci. Forum 269 ± 272 467 (1998) 201. F Cardellini, V Contini, G D'Agostino, A Filipponi Mater. Sci. Forum 269 ± 272 473 (1998) 202. P Gorria, P Crespo, J M Barandiaran, A Hernando, J S Garitaonandia, J L Hodeau, E Dooryhee Mater. Sci. Forum 269 ± 272 479 (1998) 203. S Q Wei, H Oyanadi, C Wen, Y Z Yang,W H Lui J. Phys. Condens. Matter 9 11077 (1997) 204. T Mashimo, X S Huang J. Alloys Compd. 288 299 (1999) 205. P J Schilling, JHHe,RCTittsworth, EMa Acta Mater. 47 25 (1999) 206. R A Dunlap, D A Felman, G R Mackay J. Mater. Sci. Lett. 17 437 (1998) 207. J G Cabanas-Moreno, V M Lopez-Hirata, H A Calderon, J C Rendon-Angeles Scr. Metall. Mater. 28 645 (1993) 208. J G Cabanas-Moreno, H Dorantes, V M Lopez-Hirata, H A Calderon, J M Hallen-Lopez Mater.Sci. Forum 179 ± 181 243 (1995) 209. F W Gayle, F S Biancaniello Nanostruct. Mater. 6 429 (1995) 210. A Ye Yermakov,M A Uimin, A V Shangurov, A V Zarubin, Y V Chechetkin, A K Shtolz, V V Kondratyev, G N Konygin, E P Yelsukov, S Enzo, P P Macri, R Frattini, N Cowlam Mater. Sci. Forum 225 ± 227 147 (1996) 211. S W Mahon, X Song,M A Howson, B J Hickey, R F Cochrane Mater. Sci. Forum 225 ± 227 157 (1996) 212. C Gente, M Oering, R Bormann Phys. Rev. B, Condens. Matter 48 13 244 (1993) 213. J X Huang, Y K Wu, A Q He, H Q He Nanostruct. Mater. 4 293 (1994) 214. F Cardellini, G Mazzone Philos. Mag., A 67 1289 (1993) 215. J Y Huang, Y K Wu, H Q He Appl. Phys. Lett. 66 308 (1995) 216. J Y Huang, Y K Wu, H Q He Acta Mater.44 120 (1996) 217. Y Ogino, T Yamasaki, S Myrayama, R Sakai J. Non-Cryst. Solids 117/118 737 (1990) 218. D G Morris, M A Morris Scr. Metall. Mater. 24 1701 (1990) 219. M A Morris, D G Morris Mater. Sci. Eng., A 111 115 (1989) 220. D G Morris, M A Morris Mater. Sci. Eng., A 104 201 (1989) 221. M Baricco, L Battezzati, S Enzo, I Soletta, G Cocco Spectrochim. Acta, Part A 49 1331 (1993) 222. K Uenishi,K F Kobayashi,K N Ishihara, P H Shingu Mater. Sci. Eng., A 134 1342 (1991) 223. S D De la Torre, A Yamamoto, K N Ishihara, P H Shingu, T Hirano, Y Awakura Mater. Sci. Forum 179 ± 181 237 (1995) 224. T G Richards, G P Johari Philos. Mag., B 58 445 (1998) 225. R Najafabadi, D J Srolovitz, E Ma,M Atzmon J. Appl. Phys. 74 3144 (1993)Mechanochemical synthesis of intermetallic compounds 226. M Zhu, X Z Che, Z X Li, J K L Lai, M Qi J.Mater. Sci. 33 5873 (1998) 227. Q A Pankhurst, N S Cohen, M Odlyha J. Phys., Condens. Matter 10 1665 (1998) 228. N S Cohen, Q A Pankhurst, L F Bardin J. Phys., Condens. Matter 11 8839 (1999) 229. P H Shingu, K N Ishihara, K Uenishi, J Kuyama, S Nasu in Solid State Powder Processing (Eds A H Clauer, J J de Barbadillo) (Cincinnatti: The Minerals Metals and Materials Society, 1990) p. 21 230. M Angiolini, A Deriu, F Malizia, G Mazzone, A Montone, F Roncone, M Vittori-Antisari, J S Pedersen Mater. Sci. Forum 269 ± 272 397 (1998) 231. D J Chakrabarti, D E Laughloh Binary Alloy Phase Diagr. 5 732 (1984) 232. A K Covington, K Groenwolt, BW Howlett J.Inst. Met. 89 291 (1961) 233. R Birringer, H Hahn, H Hofler, J Karch, H Gleiter Defects Diffus. Forum 59 17 (1988) 234. P A I Smith, J M D Coey J. Magn. Magn. Mater. 197 199 (1999) 235. S B Dodd, S Morris, M Wardclose, in Symposium of Synthesis of Lightweight Metals. III, San Diego, 1999 p.177 236. H Moritaka, K Asai, Y Takemoto, A Sakakibara Mater. Sci. Forum 235 ± 238 187 (1997) 237. E Gaffet, C Louison, M Harmelin, F Faudot Mater. Sci. Eng., A 134 1380 (1991) 238. T Aboud, B-Z Weiss, R Chaim Nanostruct. Mater. 6 405 (1995) 239. T Raghu, R Sundaresan, T R R Mohan, P Ramakrishnan Mater. Sci. Forum 225 ± 227 397 (1996) 240. D M Follstaedt, J A Knapp J. Less-Common Met. 140 375 (1988) 241. E Ivanov, I Konstanchuk, B Bokhonov, V Boldyrev React.Solids 7 167 (1989) 242. J Eckert, L Schultz, K Urban Appl. Phys. Lett. 55 117 (1989) 243. P Barua, V Srinivas, B C Murty Philos. Mag., A 80 1207 (2000) 244. M Monagheddu, F Delogu, L Schiffini, R Frattini, S Enzo Nanostruct. Mater. 11 1253 (1999) 245. R B Schwarz,W L Johnson Phys. Rev. Lett. 51 415 (1983) 246. L Schultz, in Proceedings of WRS European Meeting on Amorphous Metals and Non-Eequilibrium Processing, Strasbourg, 1984 p. 135 247. S J Ji, J C Sun, Z W Yu, Z K Hei, L Yan Int. J. Hydrog. Energy 24 (1) 59 (1999) 248. N Q Wu, L Z Su,M Y Yuan, J M Wu, Z Z Li Mater. Sci. Eng., A 257 357 (1998) 249. H W Sheng, K Lu, E Ma Proc. MRS Symp. 481 433 (1998) 250. C K Lin, P Y Lee, J L Yang, C Y Tung, N F Cheng, Y K Hwu J.Non-Cryst. Solids 234 520 (1998) 251. P Y Lee, J L Yang, H M Lin J. Mater. Sci. 33 235 (1998) 252. A A Savin, V A Chaika Poroshk. Metall. (7 ± 8) 118 (1998) 253. R Pizarro, J M Barandiaran, F Plazaola, A Gutierrez J. Magn. Magn. Mater. 203 143 (1999) 254. M Bionducci, G Navarra, R Bellisent, G Concas, F Congiu J. Non-Cryst. Solids 252 605 (1999) 255. A A Novakova, O V Agladze, B P Tarasov, G V Sidorova, R A Andrievsky Mater. Sci. Forum 269 ± 272 127 (1998) 256. YXu,CS Kiminami,AF Filho,CBolfarini Scr.Mater. 42 213 (1999) 257. T Fukunaga, S Kajikawa J. Non-Cryst. Solids 250 384 (1999) 258. S K Xia, F C Rizzo Assuncao, E Baggio-Saitovich Mater. Sci. Forum 225 ± 227 459 (1996) 259. H F Zhang, J Li, Q H Song, Z Q Hu J. Mater. Res. 13 2779 (1998) 260.L Ledig, D Hough, C G Oertel, J Eckert,W Skrotzki J. Alloys Compd. 285 27 (1999) 261. BWZhang, HWXie, S Z Liao J. Mater. Process. Technol. 90 378 (1999) 262. J J Sunol Mater. Sci. Forum 269 ± 272 503 (1998) 263. R Lin, M Seidel, J Z Jiang, J Eckert Mater. Sci. Forum 269 ± 272 461 (1998) 264. A E Ermakov, V V Serikov, V A Barinov, Ya S Shchur Fiz. Met. Metalloved. 42 (2) 408 (1976) a 265. A E Ermakov, E E Yurchikov, V A Barinov, in Fizicheskie Svoistva Magnitnykh Materialov (Physical Properties of Magnetic Materials) (Sverdlovsk: Urals Scientific Centre, Academy of Sciences of the USSR, 1982) p. 82 266. A E Ermakov, E E Yurchikov, V A Barinov Fiz. Met. Metalloved. 53 (2) 302 (1982) a 61 267. A E Ermakov, V A Barinov, E E Yurchikov Fiz.Met. Metalloved. 54 (5) 935 (1982) a 268. V A Barinov, Candidate Thesis in Chemical Sciences, Institute of Physics of Metals, Urals Branch of Academy of Sciences of the USSR, Sverdlovsk, 1986 269. M S Kim, Ph.D Thesis, North Caroline State University, North Caroline, 1987 270. P Y Lee, J Jang, C C Koch J. Less-Common Met. 140 73 (1988) 271. C C Koch, J Jang, P Y Lee, in Proceedings of DGM Conference on New Materials by Mechanical Alloying Technique, Calw-Hirsau, 1988 p. 101 272. E Ivanov, T Grigorieva, G Golubkova, in Proceedings of the 2nd Japan-Soviet Symposium on Mechanochemistry, Tokyo, 1988 p. 219 273. C Larica, K M B Alves, E Baggio-Saitovich, A P Guimaraes J. Magn. Magn. Mater. 145 306 (1995) 274. S K Xia, C Larica, V A Rodriguez, F C Rizzo Assuncao, E Baggio-Saitovich Mater.Sci. Forum 225 ± 227 389 (1996) 275. M Abdellaoui, E Gaffet J. Alloys Compd. 209 351 (1994) 276. Y Chen,M Bibole, R Hazif, G Martin Phys. Rev. B, Condens. Matter 48 14 (1993) 277. L Chaffron, S Poissonet Mater. Sci. Forum 225 ± 227 217 (1996) 278. Yu A Skakov, N P Djakonova, T A Sviridova, E V Shelekhov Mater. Sci. Forum 269 ± 272 595 (1998) 279. E P Yelsukov, G N Konygin, A V Zagainov, V A Barinov J. Magn. Magn. Mater. 195 601 (1999) 280. S J Poon, K J Doherty, A J Akerman, G J Shiffet, D J Li Scr. Mater. 38 603 (1998) 281. K Aoki, M S El-Eskandarany, K Sumiyama, K Suzuki Mater. Sci. Forum 269 ± 272 119 (1998) 282. M Sherif El-Eskandarany, K Aoki, K Sumiyama, K Suzuki Appl.Phys. Lett. 70 1679 (1997) 283. M Sherif El-Eskandarany, K Aoki, K Sumiyama, K Suzuki Scr. Mater. 36 1001 (1997) 284. S Surinach,M Enrech, A Khalladi, J S Munoz, M D Baro Mater. Sci. Forum 225 ± 227 347 (1996) 285. D L Zhang, T B Massalski Metall. Mater. Trans. A, Phys. Metall. Mater. Sci. 29 2425 (1998) 286. L Sun, G X Wang, H K Liu, D H Bradhurst, S N Don Electrochem. Solid State Lett. 3 (3) 121 (2000) 287. E Passamani, C Larica,W R Santos, K M B Alves, A Boindo, E Nunes J. Phys., Condens. Matter 11 1147 (1999) 288. N Terashita, M Takahasi, K Kobayashi, T Sasai, E Akiba J. Alloys Compd. 295 541 (1999) 289. C J Van der Kolk, A R Miedema, A K Nilssen J. Less-Common Met. 145 1 (1988) 290. AWWeeber, P I Loeff, H Bakker J.Less-Common Met. 145 293 (1988) 291. A W Weeber, H Bakker Physica B 135 93 (1988) 292. R Bormann, F Gartner, K Zoltzer J. Less-Common Met. 145 19 (1988) 293. E Hellstern, L Schultz, J Eckert J. Less-Common Met. 140 93 (1988) 294. J Eckert, L Schultz, K Urban J. Less-Common Met. 145 283 (1988) 295. L Schultz, E Helstern, in Glass Formation by Mechanical Alloying in Science and Technology of Rapidly Quenched Alloys (EdsMTenhover, L E Tanner, WL Johnson) (Boston: Material Research Society 1989) Pap. G 1.1, p. 4 296. P S Gilman, J S Benjamin Annu. Rev. Mater. Sci. 13 279 (1983) 297. J S Benjamin Metall. Trans. A 1 2943 (1970) 298. E Ivanov, I Konstanchuk, A Stepanov, V V Boldyrev J. Less-Common Met. 131 25 (1987) 299. E Yu Ivanov, Doctoral Thesis in Chemical Sciences, Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1990 300.V A Pavlov Fizicheskie Osnovy Plasticheskoi Deformatsii Metallov (Physical Foundations of Plastic Deformation of Metals) (Moscow: Academy of Sciences of the USSR, 1962) 301. J Friedel Dislocations (Oxford: Pergamon Press, 1964) 302. H G Van Bueren Imperfections in Crystals (Amsterdam: North- Holland, 1960) 303. Yu E Zubets, V A Manilov, G F Sazhin Fiz. Met. Metalloved. 28 (6) 1055 (1969) a 304. O A Kaibyshev, G A Kaibysheva, Ya S Umanskii, G M Epshtein Fiz. Met. Metalloved. 24 (3) 505 (1967) a62 305. A S Ke, in Pryamoe Nablyudenie Nesovershenstv v Kristallakh (Direct Study of Imperfections in Crystals) (Moscow: Metallurgizdat, 1964) p.160 306. NAKoneva, EVKozlov,NAPonova,Yu F Ivanov, LNIgnatenko, in International Symposiums on Metastable Mechanically Alloyed and Nanocrystalline Materials, Rome, 1966 p. D21 307. W Spitzig, T E Mitchell Acta Metall. 14 1311 (1966) 308. E V Belik, S N Kaverina, V N Minakov, V I Trefilov Fiz. Met. Metalloved. 24 (3) 535 (1967) a 309. V A Wilox, A Gillbert Acta Metall. 15 601 (1967) 310. S V Konetskii, G I Kulesko, N N Nasikhanova Fiz. Khim. Obrab. Mater. (3) 73 (1971) 311. Z V Vrublevskaya, G A Ivanova, L G Orlov Fiz. Met. Metalloved. 20 (3) 448 (1965) a 312. E D Martynov, V I Trofimov, S A Firstov Dokl. Akad. Nauk SSSR 176 1276 (1967) c 313. V A Likhachev, M M Myshlyaev, O N Sen'kov, in IV Vsesoyuz.Seminar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p. 168 314. N D Zemtsova, in IV Vsesoyuz. Seminar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p. 61 315. L G Chernykh, V A Starenchenko, in IV Vsesoyuz. Seminar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p.63 316. L A Kornienko, G L Balach, B F Dudarev, in IV Vsesoyuz. Semi- nar `Struktura Dislokatsii i Mekhanicheskie Svoistva Metallov i Splavov' (Tez. Dokl.), Sverdlovsk, 1987 [The IVth All-Union Meeting `Structure of Dislocation and Mechanical Properties of Metals and Alloys' (Abstracts of Reports), Sverdlovsk, 1987] p. 65 317. V A Zhorin, D P Shashkin, N S Enikolopyan Dokl. Akad. Nauk SSSR 278 144 (1984) b 318. V A Zhorin, V B Fedorov, V D Khakimova Dokl. Akad. Nauk SSSR 275 1447 (1984) c 319. I B Kevdina, V A Zhorin, V P Shantarovich Dokl. Akad. Nauk SSSR 280 394 (1985) c 320. P Le Brun, E Gaffet, L Froyen, L Delaey Scr.Metall. Mater. 26 1743 (1992) 321. E G Avvakumov Mekhanicheskie Metody Aktivatsii Khimicheskikh Protsessov (Mechanical Methods for the Activation of Chemical Processes) (Novosibirsk: Nauka, 1986) 322. I Barker, B Ralph, N Hansen, in Proceedings of the 8th Interna- tional Conference on Strength in Metals and Alloys (ICSMA-8), Tampere, 1988 Vol. 1, p. 277 323. A L Windgrove J. Inst. Met. 100 313 (1972) 324. H H Hausner,M Kumar Mal, in Handbook of Powder Metallurgy (New York: Chemical Publishing Company, 1982) p. 542 325. T F Grigorieva, M A Korchagin, A P Barinova, N Z Lyakhov Khim. Inter. Ustoich. Razvit. 8 685 (2000) e 326. H-J Fecht Nanostruct. Mater. 6 33 (1995) 327. J Eckert, J C Holzer, C E Krill, W L Johnson J.Mater. Res. 7 1751 (1992) 328. H-J Fecht, E Hellstern, Z Fu,W L Johnson Adv. Powder Metall. 1 111 (1989) 329. T G Nich, J Wadsworth Scr. Metall. 25 955 (1991) 330. WE Garner Chemistry of the Solid State (London:Butterworth, 1955) 331. MYa Bernshtein, V A Zaimovskii Mekhanicheskie Svoistva Metallov (Mechanical Properties of Metals) (Moscow: Metallurgiya, 1979) 332. R WBalluffi, in Termicheski Aktivirovannye Protsessy v Kristallakh (Thermally Activated Processes in Crystals) (Translation into Russian; Moscow: Mir, 1973) p. 42 333. R W Balluffi, A L Ruoff J. Appl. Phys. 34 1634 (1963) 334. A L Ruoff, R W Balluffi J. Appl. Phys. 34 1848 (1963) 335. R W Balluffi Phys. Status Solidi 42 11 (1970) 336. S M Klotsman, A N Timofeev, I Sh Trakhtenberg Fiz. Met. Metalloved. 23 (2) 257 (1967) a T F Grigorieva, A P Barinova, N Z Lyakhov 337. P V Pavlov, L V Maiorov, V V Panteleev Fiz. Tv. Tela 6 (2) 382 (1964) b 338. C H Lee, R Maddin J. Appl. Phys. 32 1848 (1961) 339. E W Hart Acta Metall. 5 597 (1957) 340. LMShestopalov, Yu P Romashkin Fiz. Tv. Tela 2 (12) 2998 (1960) b 341. Yu P Romashkin Fiz. Tv. Tela 2 (12) 3050 (1960) b 342. S V Zemskii,N E Fomin,G K Mal'tseva Fiz. Khim. Obrab. Mater. (4) 91 (1974) 343. S V Zemskii, P L Gruzin, A S Tikhonov Fiz. Khim. Obrab. Mater. (5) 83 (1971) 344. M A Krishtan, R I Dubrovskii, O V Stepanova Fiz. Khim. Obrab. Mater. (6) 88 (1973) 345. L N Larikov, A M Makara, A T Nazarchuk, V M Fal'chenko Fiz. Khim. Obrab. Mater. (4) 113 (1971) 346. B M Clemens Phys. Rev. B, Condens. Matter 33 (11) 7615 (1986) 347. E Hellstern, L Schultz Appl. Phys. Lett. 49 1163 (1986) 348. L Schultz J. Less-Common Met. 145 233 (1988) 349. K Samwer, in Hydrogen in Disordered and Amorphous Solids (New York: Plenum, 1986) p. 173 350. K Samwer J. Less-Common Met. 140 25 (1988) 351. Y Huang, J Z Jiang, H Yasuda, H Mori Phys. Rev. B, Condens. Matter 58 R 11817 (1998) 352. H Mori,M Komatsu, K Takeda, H Fujita Philos. Mag. Lett. 63 173 (1991) 353. H Yasuda, H Mori Phys. Rev. Lett. 69 3747 (1992) 354. H Yasuda, H Mori, M Komatsu, K Takeda Appl. Phys. Lett. 61 2173 (1992) 355. H Mori, H Yasuda Intermetallics 1 35 (1993) 356. H Yasuda, H Mori, T Muraki, T Sakata Z. Phys. D, At. Mol. Clusters 31 209 (1994) 357. H Yasuda, H Mori Mater. Sci. Eng., A 217/218 249 (1996) 358. H Yasuda, H Mori Z. Phys. D, At. Mol. Clusters 31 131 (1994) 359. H Mori, H Yasuda J. Microsc. 180 33 (1995) 360. H Mori, H Yasuda Mater. Sci. Forum 269 ± 272 327 (1998) 361. H Yasuda, H Mori Mater. Sci. Forum 269 ± 272 333 (1998) 362. J Harada, K Ohshima Surf. Sci. 106 51 (1981) 363. T Matsubara, Y Iwase, A Momokita Prog. Theor. Phys. 58 1102 (1977) 364. T F Grigorieva, A P Barinova, V V Boldyrev, E Yu Ivanov Dokl. Akad. Nauk 345 343 (1995) c 365. T F Grigorieva, A P Barinova, E Yu Ivanov, V V Boldyrev Dokl. Akad. Nauk 350 59 (1996) c 366. T F Grigorieva, A P Barinova, E Yu Ivanov, V V Boldyrev Mater. Sci. Forum 235 ± 238 577 (1997) 367. V V Boldyrev, S V Tsybulya, S V Cherepanova, G N Kryukova, T F Grigorieva, E Yu Ivanov Dokl. Akad. Nauk 361 784 (1998) c 368. T F Grigorieva, S V Tsybulya, S V Cherepanova,G N Kryukova, A P Barinova, V D Belykh, V V Boldyrev Neorg. Mater. 36 194 (2000) d 369. T F Grigorieva, M A Korchagin, A P Barinova, V V Boldyrev Khim. Inter. Ustoich. Razvit. 7 505 (1999) e 370. F Petzoldt, B Scholz, H-D Kunze Mater. Lett. 5 280 (1987) 371. WL Meng,CWNieh,WL Johnson Appl. Phys. Lett. 51 1693 (1987) 372. M Takagi J. Phys. Soc. Jpn. 9 359 (1951) 373. J Sambles Proc. R. Soc. London A, Math. Phys. Sci. 324 339 (1971) 374. G L Allen, R A Bayles,W W Gile, W A Jesser Thin Solid Films 144 297 (1986) 375. T Castro, R Reinfenberger, E Choi, R P Andres Phys. Rev. B, Condens. Matter 42 8548 (1990) 376. H Yasuda, H Mori Z. Phys. D, At. Mol. Clustors 37 181 (1996) 377. F P Bowden, D Tabor The Friction and Lubrication of Solids (Oxford: Clarendon Press, 1958) 378. F P Bowden, F P S Thomas Proc. R. Soc. London, A, Math. Phys. Sci. 223 29 (1954) 379. F P Bowden, P A Persson Proc. R. Soc. London, A, Math. Phys. Sci. 260 433 (1961) 380. A V Dubnov, V A Sukhikh, I I Tomashevich Fiz. Goren. Vzryv. 7 (1) 147 (1972) 381. A H Cottrell Dislocations and Plastic Flow in Crystals (Oxford: Clarendon Press, 1953) 382. F Kh Urakaev, E G Avvakumov Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 7 10 (1978) 383. A V Kopylov, E G Avvakumov, F Kh Urakaev Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 4 8 (1979)63 Mechanochemical synthesis of intermetallic compounds 384. F Kh Urakaev, in Trenie i Iznos (Friction and Wear) (Minsk: Nauka i Tekhnika, 1980) Vol. 1, No. 6, p. 1078 385. F Kh Urakaev, E G Avvakumov, Kh Iost Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Khim. Nauk 3 9 (1982) 386. F Kh Urakaev, I L Zhogin, E L Gol'dberg Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 3 124 (1985) 387. FKh Urakaev Izv. Sib. Otd. Akad. Nauk, Ser. Khim. Nauk 7 5 (1978) 388. A N Dannik Izbrannye Trudy (Selected Proceedings) (Kiev: Academy of Sciences of Ukr. SSR, 1952) Vol. 1 389. F Kh Urakaev, Candidate Thesis in Chemical Sciences, Institute of Solid State Chemistry and Mechanosynthesis, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1978 390. A E Ermakov, E E Yurchikov, V A Barinov Fiz. Met. Metalloved. 52 (6) 1184 (1981) a 391. S D De La Torre, K N Tshihara, P H Shingu Mater. Sci. Eng. A 266 37 (1999) 392. J Eckert, L Schultz, E Hellstern, K Urban J. Appl. Phys. 64 3224 (1988) 393. R B Schwarz, C C Koch J. Appl. Phys. Lett. 49 146 (1986) 394. V M Zalkin Priroda Evtekticheskikh Splavov i Effekt Kontaktnogo Plavleniya (Nature of Eutectic Alloys and Contact Melting Effect) (Moscow: Metallurgiya, 1987) 395. H Kimura,M Y Kimura, F Takada J. Less-Common Met. 140 113 (1988) 396. USSR P. 975 068; Byull. Izobret. (43) 23 (1982) 397. K B Gerasimov, A A Gusev, V V Kolpakov, E Yu Ivanov Sib. Khim. Zh. (3) 140 (1990) a�Phys. Met. Metall. (Engl. Transl.) b�Phys. Solid. State (Engl. Transl.) c�Dokl. Chem. Technol., Dokl. Chem. (Engl. Transl.) d�Inorg. Mater. (Engl. Transl.) e�Chem. Sustain. Dev. (Engl

ISSN:0036-021X    

出版商:RSC    

年代:2001

数据来源: RSC

摘要:

Russian Chemical Reviews 70 (1) 65 ± 79 (2001) Chemical modification and blending of polymers in an extruder reactor E V Prut, A N Zelenetskii Contents I. Introduction II. Characteristic features of reactive blending processes III. Grafting of low-molecular-mass compounds onto polymers IV. Reactions between terminal groups of polymers V. Transesterification reactions and interchange processes VI. Preparation of thermoplastic elastomers by dynamic vulcanisation VII. Solid-phase reactions in an extruder reactor Abstract. an in polymers of blending and modification Chemical Chemical modification and blending of polymers in an extruder the between Relationships discussed. are reactor extruder reactor are discussed. Relationships between the param- param- eters a of duration time, mixing reaction the affecting eters affecting the reaction kinetics, kinetics, viz., ., mixing time, duration of a chemical in system the of time residence the and reaction chemical reaction and the residence time of the system in the the extruder produced materials the of structure the and reactor, extruder reactor, and the structure of the materials produced are are analysed.of grafting (i) of mechanisms The analysed. The mechanisms of (i) grafting of low-molecular-mass low-molecular-mass compounds terminal between reactions (ii) polymers; onto compounds onto polymers; (ii) reactions between terminal groups groups of and transesterification (iii) and polymers different of different polymers and (iii) transesterification and interchange interchange reactions mechanism the affecting factors The considered. are reactions are considered.The factors affecting the mechanism of of dynamic thermoplastic of properties the and vulcanisation dynamic vulcanisation and the properties of thermoplastic elas- elas- tomers polysaccharides of reactions Solid-phase identified. are tomers are identified. Solid-phase reactions of polysaccharides in in an extruder are discussed. The priority aspects of studies on the an extruder are discussed. The priority aspects of studies on the chemical noted. are polymers of blending and modification chemical modification and blending of polymers are noted. The The bibliography includes 90 references bibliography includes 90 references. I. Introduction Polymeric composites are currently widely used and actively studied.Particular interest has been shown in multicomponent polymer blends and alloys. The creation of such polymeric materials entails the possibility of combining attractive qualities of each component of the polymer blend in the end product.1 ±3 Useful properties of polymer blends are affected by such charac- teristics as the nature of the dispersed and dispersion phases, the volume ratio of the phases, the sizes and size distributions of the particles of the dispersed phase, and interfacial adhesion. Much attention is paid by investigators to the processes of preparation of materials by blending components in which chemical reactions proceed.4, 5 Such processes are called `reactive blending' or `reactive extrusion'.Only a few polymers are thermo- dynamically compatible and form blends with homogeneous morphology at a molecular level. The majority of polymers exhibit E V Prut N N Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, 117977 Moscow, Russian Federation. Fax (7-095) 938 21 56. Tel. (7-095) 939 71 55. E-mail: evprut@center.chph.ras.ru A N Zelenetskii N S Enikolopov Institute of Synthetic Polymer Materials, Russian Academy of Sciences, ul. Profsoyuznaya 70, 117393 Moscow, Russian Federation. Fax (7-095) 420 22 29. Tel. (7-095) 332 58 45. E-mail: anzel@icpm.ru Received 4 September 2000 Uspekhi Khimii 70 (1) 72 ± 87 (2001); translated by AMRaevsky #2001 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2001v070n01ABEH000624 65 65 67 70 71 71 75 limited compatibility or are incompatible and their blends possess heterogeneous morphologies.Reactive blending extends the possibilities of controlling the phase structures of multicomponent polymeric materials. Not only does the technology for reactive blending of polymers open new ways for the employment of polymeric products already available but also permits the creation of blends, the preparation of which by other methods has been economically unfavourable. Application of methods of organic chemistry and reactive blend- ing allows preparation of diverse modified polymers and polymer blends based on a a small number of industrially produced polymers.4 II. Characteristic features of reactive blending processes 1.Blending condition Blending of polymers is an intricate physicochemical process, which proceeds under the action of mechanical and temperature fields. If blending of polymers is accompanied by chemical reactions, their rates are determined by the character of blending, temperature gradients and by diffusion of the reagents and products. These characteristics can be controlled if reactive blending is carried out in extruder reactors. Currently, continuous extruder reactors (Fig. 1) are available. Extrusion is used for the preparation of products or semifinished items of desired shape by forcing polymer melts through an exit (a shape-forming orifice).6± 8 Extrusion processing of plastics is effected by using mainly single-screw and twin-screw extruders.Technologies with employment of extruder reactors combine the processes that are usually separated, e.g., blending, chemical reactions and moulding. Here, new problems arise associated with, e.g., changes in the viscosity during the reaction or heat removal. Some lines of attacking such problems, as applied to polymerisation reactions, have been considered.5, 9 It was found that in the case of chemically reacting systems twin-screw extruders are preferable to single-screw extruders owing to more efficient mixing and heat removal. However, the complexity of chemical and physical processes proceeding in an extruder reactor hampers the choice of the moulding parameters and equipment. This requires experimental and theoretical studies on the evolution of the structure and properties of polymers during the preparation of materials using extruder reactors.10 ± 13 However, experimental investigation of the polymer structure is a compli- cated multiparameter problem.On the other hand, only a few66 Reagents Volatile products Initial components C A B Product Figure 1. A scheme of an extruder reactor. theories which allow qualitative description of the changes in the polymer structures after completion of the chemical reactions in the system have been developed.14 ± 16 This can be illustrated as follows. If a reaction proceeds in the melt, the reaction rate can be strongly affected by diffusion.Changes in the blend composition during the reaction can in turn affect the diffusion processes. Therefore, a theory is required which describes the evolution of the structure of a polymer blend taking into account the mutual influence of the chemical reaction and diffusion.17 Changes in the structure of a model heterogeneous blend, in which the copolymer AB is an intermediate of a polymerana- logous reaction A?B have been considered.18 It was shown that diffusional mixing has a pronounced effect on the reaction kinetics. This effect manifests itself if the characteristic time of the chemical reaction, tr=1k , (k is the rate constant of the chemical reaction) is shorter than, or comparable with, the mixing time tm.The mixing can be consid- ered efficient if (1) tm<tr . This condition holds well for the alcoholysis of poly(ethylene- co-vinyl acetate) with aliphatic alcohols (octan-1-ol, 2-ethylhexan- 1-ol, 3-phenylpropan-1-ol) in the bulk and in solution (dodecan-1- ol) with dibutyltin dilaurate as catalyst.19 The bulk reaction was carried out in a Haake Rheochord mixer (Germany). It was shown 19 that the reaction in solution and in the bulk follows the same mechanism, which is independent of the nature of the alcohol. The equilibrium constants of the reactions in solution and in the bulk were equal. The reaction rates were of the second order with respect to the concentrations of reagents. The viscosities of the systems in solution and in the bulk differed by five orders of magnitude.Based on the results of analysis of the kinetic data, it was suggested that (i) the reaction rate is substan- tially lower than the diffusion rate and (ii) mechanical mixing is necessary only for the homogenisation of the reaction system in the initial stage of the reaction (once this is achieved, mixing is of no significance during the reaction). However, the differences between the limiting degrees of conversion have not been discussed.19 From the plots reported in this study it follows that the limiting degree of conversion in the bulk at 180 8C is *65% while that in solution at 170 8C is *90%. This is most likely due to the change in the viscosity of the reaction system. Usually, the viscosity of the medium increases during the reaction, thus hampering homogenisation of the reaction system and leading to the formation of structurally inhomogeneous material.Changes in the viscosity during the ionic and radical polymerisation reactions have been analysed 9, 20 and a theoretical approach to quantitative estimation of these changes has been considered. During the reaction, the system can become heterogeneous and the reaction kinetics can in turn change. The kinetics of the E V Prut, A N Zelenetskii chemical reactions in homogeneous and heterogeneous polymer melts have been analysed taking the esterification reaction between 1-naphthylacetic acid (NAA) and a random ethylene/ ethyl acrylate/glycidyl methacrylate (E ± EA±GMA) terpolymer as an example.21 Being initially homogeneous, the system NAA± E ± EA±GMA became heterogeneous upon addition of an inert polymer, viz., polystyrene (PS).Polystyrene and E ±EA±GMA are immiscible, whereas NAA can be mixed with both polymers in the concentration and temperature ranges studied. It was shown that the mechanisms of these reactions are identical and that the rate of NAA diffusion is much higher than the reaction rates in both systems. Thus, preparation of materials with homogeneous distribu- tion of submicroscopic particles of the dispersed phase requires that the condition (1) be met. 2. Effect of the residence time of a system in an extruder reactor (2) The reaction in an extruder reactor goes to completion if tr tf , where tf is the mean residence time of the reaction system in the extruder reactor (hereafter, the residence time).This time depends on the ratio of the extruder length, l, to the longitudinal compo- nent of the flow rate, V, (3) tf= l V . Generally, the residence time is determined by some distribution function.22 The distribution functions, f(t), for a ZSK-30 co- rotating twin-screw extruder (Werner and Pfleiderer, Germany; screw length-to-diameter ratio, l/d=42) are shown in Fig. 2a. Proceeding to the dimensionless time y= t , tf where t is the current residence time of the reaction system in the extruder reactor, gives the residence time distribution function, f(y), shown in Fig. 2 b.As can be seen, the f(y) curves are shifted to a short-time domain when the feed rate Q and screw speed N increase, i.e., tf shortens and the f(y) curves match one another.It is believed that the mechanical mixing intensity does not vary much upon varying Q and N at a constant Q/N ratio. On the other hand, the residence time distribution function, which characterises macromixing, changes. The ratio between the convection mass transfer in a flow and free molecule diffusion is characterised by the Peclet number (criterion), Pe (Ref. 24) b a 103 f(t) f(y) 2 12 123 8 1 4 0 0 2 1 400 200 y 600 t /s Figure 2. Residence time distribution function in dimensional (a) and dimensionless form (b) as a function of the feed rate Q and screw speed N at a constant Q/N value of 1/43 kg min h71 rev71; (1) Q=5.6 kg h71, N=240 rev min71; (2) Q=3.5 kg h71, N=150 rev min71; (3) Q=2.1 kg h71, N=90 rev min71.24Chemical modification and blending of polymers in an extruder reactor Pe 26 24 22 300 200 tf /s Figure 3.Dependence of the Peclet number on the residence time. Pe=Vl D , where D is the diffusion coefficient. The dependence of the Peclet number on tf is shown in Fig. 3. As can be seen, the Pe number increases as tf increases. This plot was constructed using the results obtained by Sun et al.23 Unfortunately, they reported no numerical data for the calculation of the Peclet numbers. At small Pe values, free molecule diffusion predominates, while convection mass transfer is predominant at large Pe values. Hence, the contribution of the convection mass transfer increases with lengthening of the residence time tf, (i.e., with a decrease in the feed rate Q and screw speed N).The residence time was found to be the main parameter which controls the degree of grafting (q) of, e.g., GMA onto polypropy- lene (PP). As Q and N decrease, tf and q (Fig. 4) increase. On the other hand, the degree of grafting decreases with increase in the energy supplied per unit mass of the reacting system U (Fig. 5). Thus, the degree of grafting is mainly determined by the mixing mechanism rather than energy expenditure. q 0.5 0.3 300 200 tf /s Figure 4. Dependence of the degree of grafting of GMA onto PP (q) on the residence time at l/d=42, Q/N=1/43 kg min h71 rev71.q 4.5 3.5 700 600 U /kJ kg71 500 Figure 5. Dependence of the degree of grafting on the energy supplied per unit mass of the reaction system atQ/N=1/43 kg min h71 rev71 (see Ref. 24). 67 III. Grafting of low-molecular-mass compounds onto polymers 1. Grafting onto polypropylene Modification of polymers is carried out for compatibilisation of polymer blends. This is achieved by using block and graft copolymers.25 Preparation of diverse polymer blends by reactive blending has been reported.4 The synthesis of graft copolymers of polyalkenes by reactive extrusion has been reviewed 26 and the mechanisms of grafting and structures of graft copolymers depending on the reaction conditions have been analysed.Polypropylene is one of the intensively studied polymers. Grafting of GMA onto PP proceeds by a radical mechanism. The limiting degree of grafting increases with increase in the peroxide concentration 23 as well as upon introduction of styrene as the second monomer. In the latter case,Mw increases from 220 000 in the absence of styrene to 350 000 in the presence of styrene. The stage that follows grafting is blending of polymers. Here, reactions of graft polymers with other blend components take place. These reactions result in improvement of interfacial adhe- sion. Problems arising where two processes, viz., functionalisation and chemical mixing, are carried out in one extrusion step have been considered.27, 28 In situ compatibilisation of PP and poly(butylene terephtha- late) (PBT) blends (PP : PBT=70 : 30) was carried out by one- step reactive extrusion in a ZSK-30 co-rotating twin-screw extruder (Werner and Pfleiderer, Germany) (d=30 mm, l/d=42).27 Possible screw configurations are schematically rep- resented in Fig.6.28 The extruder is divided into two functional zones: grafting of GMA onto PP is carried out in the first part of the extruder and the reaction between the GMA-g-PP and the carboxy group of the PBT is carried out in the second part of the extruder. It was found that changes in the compatibility of the PP ± PBT blend are accompanied by changes in its morphology. In the mechanical blend of the initial components, the particle size of the dispersed phase (PBT) was larger than in the blend of grafted PP and PBT.In the latter case, the interfacial adhesion was also improved. The plot of the residence time distribution function in the reaction of PP with PBT 27 is similar to that considered above (see Fig. 2 a). As the feed rate Q and screw speed N increase, the residence time distribution function curve is shifted to the short- a PP+monomers+ peroxide PBT Gas removal N2 240 8C 230 8C 200 8C b PP+monomers+ peroxide PBT Gas removal N2 N2 240 8C 200 8C Figure 6. Examples of screw configurations for combining the modifi- cation of PP and its blending with PBT.2868 b a I /J m71 eb (%) 1 20 140 2 100 80 150 N /revmin71 50 150 N /rev min71 50 Figure 7.Dependence of the elongation at break (a) and impact strength (b) on the screw speed at Q/N=1/30 kg min h71 rev71 (see Ref. 27). Temperature: (1) 0 and (2) 720 8C. time domain. In dimensionless coordinates, the plots of these functions match one another (see Fig. 2b).24 The elongation at break and the impact strength depend on the residence time of the system in the extruder. With a decrease in Q and N, the residence time lengthens and, correspondingly, the elongation at break (eb) and the impact strength (I) increase (Fig. 7). The effects of the chemical nature and concentration of compounds subject to grafting onto PP, the concentration of the initiator (peroxide) and some other parameters on PP modifica- tion have been studied.28 Among the three compounds studied, namely, acrylic acid (AA), maleic anhydride (MA) and GMA, the last-named compound was found to be the most efficient for the modification of PP ± PBT blends.After optimisation of the reaction conditions, the elongation at break and impact strength of the modified PP ± PBT blend (PP : PBT=70 : 30) increased 15- to 20-fold as compared with the corresponding parameters for the mechanical blend. Further increase in the PBT concentration leads to a decrease in the elongation at break and impact strength of the modified PP ± PBT blend. This is probably due to cross- linking reactions. Comparison of the properties of the polymer blends prepared by one-step reactive extrusion 27 and by conventional two-step technique showed that the elongations at break and impact strengths of the blends prepared by the former method are higher.8 Numerous studies have been concerned with grafting of MA onto PP.29 ± 34 It was shown 29 that if the reaction was carried out with 2,5-dimethyl-2,5-bis(tert-butylperoxy)hexane as the initia- tor, the dependence of the degree of grafting on the MA concen- tration passes through a maximum.This is due to the fact that the PP ±MA system becomes a two-phase system with an increase in the MA concentration and, hence, the effective concentrations of the MA and peroxide decrease. In this case, the grafting reaction was carried out in a batch mixer at 215 ± 220 8C at a rotor speed of 64 rev min71 over a period of 15 min. If grafting is carried out in a twin-screw extruder (200 8C, tf=3 min, screw speed= 75 rev min71), the degree of grafting increases; however, intense degradation of the extrudate is observed.Modification of PP is accompanied by its degradation. An important problem is to reduce the degree of polymer degradation during the grafting. It was found 23 that introduction of an electron-donor monomer (e.g., styrene) causes an increase in the degree of grafting of MA onto PP and substantially inhibits degradation. Similar results were obtained by Bettini and Agnelli 30, 31 who studied the effect of content of MA and a 46.5% concentrate of 2,5-dimethyl-2,5-bis(tert-butylperoxy)hexane in CaCO3, the rotor speed and duration of the reaction on the degree of grafting ofMA onto PP and on changes in the molecular mass (MM).Blending was carried out in a System 90 torque rheometer (Haake, Germany) equipped with a Rheomix 600 mixer. It was found that an increase in the peroxide concentration leads to an increase in the degree of grafting and to a decrease in the MM. The dependence of the degree of grafting on the MA concentration E V Prut, A N Zelenetskii passes through a maximum, the position of which is determined by the rotor speed and duration of the reaction. Degradation of PP is a complex function of the MA concentration: at high MA concentration, the melt flow index (MFI) decreases, i.e., the degradation of PP is retarded. Grafting of MA onto PP of different stereoregularity in melt and in solution in the presence of dicumyl peroxide has been compared.32 ± 34 Similarly to the reactions discussed above, the dependence of the degree of grafting on the MA and peroxide concentrations was also found to pass through an extremum.The degree of grafting in the melt was higher than that in solution (with xylene and decalin as solvents). The maximum degree of grafting onto atactic PP was found to be higher than onto isotactic PP. However, the modified atactic PP was more compositionally heterogeneous. Different types of peroxides were used as radical initiators of the grafting reactions. Naturally, the question arises: how does the chemical nature of the peroxide affect the grafting kinetics? A number of functional peroxides (peroxy esters) has been studied.35 The structures of functional nonsymmetric peroxides and the corresponding trade names are shown below.CH3 O C OO CH CH C CH3 OH Luperox PMA CH3 CH3 O C CH2 CH3 C OO CH2 OH Luperco 212-P75 CH3CH3 O C OO CH CH C CH3CH2 OH CH3 Luperox TA-PMA CH3 O C CH3CH2 CH2 C OO CH2 OH CH3 Lupersol 512 Blending of PP and peroxides was carried out in a Rheochord 90 counter-rotating, twin-screw extruder (Haake, Germany). The screw speed was 15 rev min71, which corresponded to a residence time of *7 min. The reactions were carried out in a N2 atmo- sphere. It was assumed that the residence time is sufficient for the peroxides to decompose completely. The degree of grafting of a carboxylic acid onto PP and degradation of PP has been studied.35 Grafting reactions carried out in the presence of peroxides which decompose to give methyl radicals were found to be more efficient than those in the presence of peroxides which decompose to give ethyl radicals.The increase in the concentration of polymeric radicals leads to an increase in the degree of grafting and to greater degradation of PP. A similar effect was also observed upon the formation of radicals with double bonds. Thus, varying the molecular structure of the peroxide allows the degree of grafting of functional groups onto PP to be changed. Grafting ofMAonto PP can also be carried out using not only radical reactions accompanied by intense degradation of PP but also other types of reactions.The degradation upon radical modification of PP can be reduced and the process becomes controllable if a `specific' functionalisation, viz., the reaction of the terminal vinylidene groups with various compounds, is carried out. Among possible reactions, the Alder ene addition seems to be the most convenient to be performed in an extruder reactor.36 The reaction rate depends on the acidity and basicity of the ene moiety and enophilic fragments and on the reaction conditions; it increases in the presence of Lewis acids. Grafting ofMAonto PP in the presence of Lewis acids (SnCl2, RuCl2) in an LSM 30.34 co-rotating twin-screw extruder (Leis- tritz, Germany; d=34 mm; l/d=42) has been studied.36Chemical modification and blending of polymers in an extruder reactor Grafting of MA onto PP using the Alder ene reaction was shown 36 to proceed without considerable degradation of PP.An increase in the reaction temperature and the MA concentration leads to an increase in the degree of grafting, which also increases with improved mixing. For this reaction, RuCl2 was found to be a more efficient catalyst than SnCl2. 2. Grafting onto polyethylene Polyethylene (PE) is yet another polymer which is widely used in polymer blends. The number of different types of PE is larger than that of PP. Therefore, it is of interest to analyse the effect of grafting onto PE as function of its structure. Grafting of diethyl maleate (DEM) onto high-density polyethylene (HDPE) and linear low-density polyethylene (LLDPE) in two co-rotating twin-screw extruders, namely, a ZSK-30 extruder (Werner and Pfleiderer, Germany) and a ECS-2E25 extruder (Berstorff, Ger- many) has been studied.37 Screw configurations, extrusion con- ditions and the order of introduction of the components into the extruder were varied.The effects of different parameters on the residence time distribution function were analysed. As for PP, the efficiency of grafting was determined by the residence time. When the transport delay time and the mean residence time exceeded certain critical values, the concentration of free radicals decreased owing to secondary reactions (e.g., thermal oxidation, mechano- chemical degradation and/or chain branching, i.e., the formation of long branches for LLDPE), which resulted in a decrease in the degree of grafting.An increase in the degree of grafting with increase in the initiator concentration was independent of the screw configura- tion and extruder type. The molecular mass distribution (MMD) of the DEM graft LLDPE was virtually the same as that of the initial sample. However, Mw ± of the DEM graft HDPE decreased and the MMD became narrower. Hence, the degree of grafting onto PE is determined by the residence time of the system in the extruder while the MMD is determined by the type of the PE. Rosales et al.37 also studied the influence of chemical nature of the peroxide by comparing the effects of a 90% solution of 2,5- dimethyl-2,5-bis(tert-butylperoxy)hexane and dicumyl peroxide.The second initiator was found to be less efficient. A study of the effect of the degree of grafting on the rheological and thermal properties has been reported.38 It was shown that the rheological properties are more sensitive to the changes due to grafting than the structural parameters determined from the measurements of thermal behaviour. An increase in the dynamic viscosity with increase in the degree of grafting was observed at low frequencies of strain sweep. Mention was made that the blends obtained possess enhanced compatibility with polyamides and polyesters. Compared to the molecular structure characteristics, the rheological properties of the modified LLDPE are also more sensitive to the changes due to reactions at low peroxide concen- trations.39, 40 LLDPE was extruded in the presence of the initiator, 2,5-dimethyl-2,5-bis(tert-butylperoxy)hexane, in a co-rotating twin-screw extruder (Leistritz, Germany; d=34 mm, l/d=35). The screw configuration was varied.The peroxide concentration was low in order to prevent cross-linking. In this case, the MMD broadened owing to an increase in the percentage of the high- molecular-mass fraction, which increased with increase in the peroxide concentration. The proportion and lengths of the side groups were deter- mined by different methods (size-exclusion liquid chromatogra- phy, nuclear magnetic resonance, differential scanning calorimetry). It was found that the proportion of unsaturated terminal units in the modified LLDPE diminished.Based on the results obtained, a reaction mechanism was proposed. The authors established that an increase in the complex viscosity at low frequencies of strain sweep is due to the formation of a small number of long-chain branches. Changes in the molecular parameters of the modified LLDPE affected not only the shear characteristics of the flow but also the flow character- 69 istics in the longitudinal direction. The modified LLDPE had higher viscosity in the longitudinal direction. However, this was accompanied by a decrease in the tensile deformability. Swelling of the extrudate decreased with increase in the peroxide concen- tration. The efficiency of the LLDPE modification in the extru- sion strongly depended on the temperature and quality of mixing.The influence of extrusion on the cross-linking and degrada- tion of PE has been studied.41 Cross-linking of HDPE in the presence of a peroxide, 1,3-bis(tert-butylperoxyisopropyl)benzene (system 1), and mixtures of this peroxide with coagents, viz., trimethylolpropane triacrylate (TMPTA) (system 2) and para- benzoquinone (PBQ) (system 3), in the extrusion in a twin-screw extruder (d=25 mm; l/d=30) at 230 8C has been studied. It was shown that the MFI decreased rapidly as the peroxide concentration increased in system 1, more smoothly in system 2 and showed a slight increase in system 3. The last-named effect was probably due to degradation of HDPE. Thermal properties of the modified HDPE depend on the peroxide concentration in a complex manner.The melting temper- ature, Tm, and the crystallisation temperature, Tcr, increase with increase in the peroxide concentration. On the other hand, Tm decreases while Tcr increases as the concentration of the perox- ide ±TMPTA initiator increases. Initially, the heat of melting increases and then decreases with increase in the concentration of the initiator. The effect of the peroxide and TMPTA concentrations on the mechanical properties can be followed from the data listed in Table 1. As can be seen, the impact strength increases by*7-fold as compared to that of the initial HDPE. Table 1. The effect of the peroxide and TMPTA concentrations on the mechanical properties of cross-linked HDPE.eb D I E sy [Peroxide] a [TMPTA] a MFI /g/10 min 61 62 62 1084 1400 37.5 64 62 63 1032 1410 39.0 62 1016 1420 38.5 0.2 148 1290 27.5 600 576 1290 30.0 20 30 770 1440 42.0 30 908 1340 35.0 30 20 61 1011 1340 35.5 20 20 7 7 4.74 0.05 7 1.62 7 0.3 0.95 0.05 0.3 0.037 0.01 0.1 1.78 0.01 0.2 0.98 0.02 0.1 0.49 0.02 0.13 Note. The following notations are used here and in Tables 2 ± 5: D is the hardness (arbitrary units), I is the notched Izod impact strength (J m71), E is the flexural modulus (MPa), sy is the yield stress (MPa) and eb is the elongation at break (%). a The concentrations of peroxide and TMPTA are given in mass parts per 100 mass parts of HDPE. 3. Grafting onto an ethylene/propylene terpolymer and polylactide Grafting of MA onto ethylene/propylene/ethylidenenorbornene terpolymer (EPDM, with ethylene and ethylidenenorbornene concentrations of 56 mass% and 5.7 mass %, respectively) in a Rheomix 750 mixer (Haake-Buchler, Germany) at*160 8C with dicumyl peroxide as the initiator has been studied.42 It was shown that the amount of the gel fraction initially increases up to 4 mass% with an increase in the MA concentration and then decreases.On the other hand, the amount of the gel fraction increases monotonically with increase in the peroxide concentra- tion.As in the case of polyalkenes, the dependence of the degree of grafting onto EPDM on the MA concentration increases as the MA concentration increases up to 3 mass% and then decreases, thus passing through an extremum.The degree of grafting70 increases with increase in the peroxide concentration. The reac- tion is accompanied by cross-linking and degradation of the terpolymer. Introduction of an electron donor (e.g., stearamide) into the reaction system inhibits side reactions, viz., cross-linking and degradation. The optimum content of stearamide was found to be*20 mass %. Grafting of MA onto other types of polymers has also been studied. In particular, a study on the grafting of MA onto polylactide in a co-rotating twin-screw extruder (Baker Perkins, United Kingdom) with 2,5-dimethyl-2,5-bis(tert-butylperoxy)- hexane as the initiator has been reported.43 Polylactide is a biodegradable polymer widely used in medicine.It was shown that the degree of grafting increases with increase in the initiator concentration, whileMMdecreases (the MFI increases). The ratio of the weight-average molecular mass to the number-average molecular mass, Mw=Mn, remained virtually constant. It was found that even a small amount of the MA graft onto polylactide essentially improves the interfacial adhesion in the polylactide- based blends and composites. IV. Reactions between terminal groups of polymers Chain extension in PBT owing to the reactions of the epoxy groups of diglycidyl tetrahydrophthalate with the terminal hydroxy and carboxy groups of PBT has been studied.44 The synthesis of high-molecular-mass PBT is a rather compli- cated problem.Industrially, PBT with an MFI greater than 20 g/10 min can be produced, while the PBT with relatively low MM possesses poor mechanical properties. Therefore, the prob- lem of chain extension is topical. One of the possible ways of solving this problem is to carry out reactions of bifunctional compounds with terminal groups of PBT. Guo and Chan 44 carried out the reaction of epoxy groups with the carboxy and hydroxy groups of PBT in a Rheomix 600 mixer (Haake, Germany). The rotor speed was varied from 30 to 120 rev min71 and the temperature was varied from 230 to 280 8C. As the temperature was raised and the rate of shear increased, the duration of the reaction of the terminal groups of PBT with the epoxy groups decreased owing to an increase in the rate of diffusion of the epoxy groups.The duration of the reaction was found to be *3 min at 260 8C. Therefore, this reaction can be performed in both single-screw and twin-screw extruders. The results of mechanical and rheological tests of the PBT thus obtained are listed in Table 2. As can be seen, the MFI value decreases rapidly with increase in the concentration of epoxy groups, while the notched Izod impact strength and the elongation Table 2. The effect of the concentration of epoxy groups [E] on the mechanical properties of PBT.41 sbn /MPA sb /MPa e (%) I/J m71 MFI /g/10 min [E] (mass %) 35.4 29.8 23.5 17.8 15.4 13.1 10.3 8.4 5.0 3.6 2.6 19.9 20.2 22.9 23.2 24.1 25.7 26.3 34.4 39.2 51.9 49.5 88.6 91.2 91.7 93.2 89.3 93.3 92.1 92.5 93.0 92.4 92.2 50.2 62.3 76.9 101.8 130.4 267.7 262.5 278.5 329.2 360.1 360.0 53.7 54.4 53.9 52.3 52.6 52.3 53.5 53.0 53.0 52.9 52.1 00.4 0.5 0.7 0.8 0.9 1.0 1.2 1.3 1.4 1.6 Note.The following notations are used: sb is the tensile strength and sbn is the bending strength. E V Prut, A N Zelenetskii at break increase. The PBT thus obtained was found to be more thermally stable. On the other hand, the reaction considered above can be accompanied by cross-linking; the longer the chain the higher the degree of cross-linking. Cross-linking begins as the concentration of epoxy groups exceeds 1.2 mass %; the amount of the gel fraction was 7.97 mass% at an epoxy group concentration of 1.4 mass %.Compatibilisation of PP and a liquid-crystal copolyester Vectra A900 (LCC) following the reactions between the epoxy groups of poly(ethylene-co-GMA) (EGMA) containing 12% GMA with the hydroxy and/or carboxy groups has been studied.45 It was found that theEGMAgraft LCC is formed at the PP ±LCC interface and the surface tension decreases. Blending was carried out in a co-rotating twin-screw extruder (d=30 mm) in the temperature range 265 ± 290 8C. The PP ±LCC blends thus obtained possessed higher elongations at break and impact strengths. The LCC domains were found to be of smaller size and the crystallinity of the modified PP was lower than that of the blends prepared by conventional (mechanical) technique.The use of ethyltriphenylphosphonium bromide as a catalyst improves the blend compatibility owing to grafting. A broad class of polymer blends based on polyamides (PA) was obtained.1 Compatibilisation by the strengthening of the interaction between the blend components is a major way of modification of toughened materials. Kudva et al.46 studied blends of Nylon-6 with acrylonitrile/ butadiene/styrene terpolymer (ABS) and poly(styrene-co-acrylo- nitrile) (SAN) using copolymers of GMA with methyl methacry- late (MMA) as compatibilisators. The GMA molecules contain epoxy groups which can react with the terminal groups of PA, while poly(methyl methacrylate) (PMMA) can be mixed with the SAN phase of ABS at any concentration of acrylonitrile.Blends were prepared in a Killion single-screw extruder (Germany) (d=25.4 mm; l/d=30) at 240 8C and a screw speed of 40 rev min71 or in a Baker-Perkins co-rotating twin-screw extruder at 240 8C and a screw speed of 170 rev min71. The dependence of the mass-average size of the SAN particles (dw ± ) on the GMA concentration in poly(GMA-co-MMA) is shown in Fig. 8. The complex shape of the curve describing the variation of dw ± is due to chemical reactions between the epoxy groups and the amino and carboxy terminal groups of Nylon-6 at the interface (Fig. 9). Owing to the nature of the PA, the inter- domain space is filled with loop-like and bridging structures. dw /mm 0.75 0.50 0.25 [GMA] (mass%) 8 4 0 Figure 8.Dependence of the mass-average size of SAN particles on the GMA content in poly(GMA-co-MMA). The blend ratio was Nylon-6 :SAN: poly(GMA-co-MMA)=75 : 20 : 5. The SAN copolymer contained 25% of acrylonitrile. In the absence of poly(GMA-co-MMA), a blend with the ratio Nylon-6 :SAN=75 : 25 was studied.43 It was found that the notched Izod impact strength decreases upon introduction of the copolymer containing 3 mass% of GMA (Fig. 10). When the GMA content was 5 mass% and 10 mass %, the impact strength increased. More intense mixing using a twin-screw extruder resulted in a substantial decrease inChemical modification and blending of polymers in an extruder reactor HC O H2C COOH COOH H2N NH2 H2C H2C H2C O O O HC HC HC Elastomer particle SAN matrixpoly(GMA-co-MMA) Figure 9.A scheme of the reaction between Nylon-6 and poly(GMA-co- MMA) in the Nylon-6 ± ABS ± poly(GMA-co-MMA) blend.43 b a 1072 I /J m71 1072 I /J m71 1 3 8 8 4 1 4 3 2 2 4 40 60 20 40 20 0720 t /8C 60 t /8C Figure 10. Temperature dependences of the notched Izod impact strength for Nylon-6 ±ABS blend (1) and ternary blends Nylon-6 : ABS :(GMA± MMA)=47.5 : 47.5 : 5.0 at aGMAcontent of3%(2),5%(3) and 10% (4) in single-screw (a) and twin-screw (b) extruders.43 the domains of the dispersed phase and in an increase in the impact strength. V. Transesterification reactions and interchange processes The kinetics of the transesterification reaction between poly- (ethylene terephthalate) (PETP) and co[poly(PETP ± p-hydroxy- benzoate)] copolyesters (PHB ± PETP) at blend ratios of 85 : 15, 70 : 30 and 50 : 50 in a Brabender Plasticorder mixer (Germany) at 275, 285 and 293 8C has been studied taking two types of the PHB± PETP copolyesters, with a PHB: PETP ratio of 40 : 60 (P46) and 60 : 40 (P64), as examples.47 It was shown that the reaction is described by a second-order kinetic equation and the effective rate constant of the reaction depends on the blend ratio and temperature. Yet another type of reaction, namely, interchange processes between a polyhydroxyether of bisphenol A and a segmented copolyetherester Hytrel, has been studied.48 The copolyester is a thermoplastic elastomer comprising rigid crystallisable tetra- methylene terephthalate blocks and flexible polytetramethyle- ne ± ether glycol ± terephthalate blocks.Mixing of the components was carried out in a Brabender Plasticorder mixer. The kinetics of the interchange reactions was studied by tracing the torque variations. After mixing for 15 min, the interchange processes are completed to yield mainly branched and cross- linked products. The induction period was independent of the blend ratio and always exceeded 15 min at 240 8C. 71 Owing to specific interactions, the components of this blend are miscible at any ratios. Because of this, only one glass transition temperature is observed. VI. Preparation of thermoplastic elastomers by dynamic vulcanisation Among reactive blending processes in an extruder reactor, dynamic vulcanisation is the most promising for industrial use.49 Thermoplastic elastomers (TPE), prepared from polymer blends by dynamic vulcanisation, are a specific class of materials which, on the one hand, can be processed in the molten state as thermo- plastic polymers and, on the other hand, possess the properties of vulcanised elastomers at operating temperatures.Since they are quite competitive with conventional rubbers in the market, interest in these materials is currently increasing.50 The merit of TPE is their ability to be reprocessed. The properties of TPE do not change essentially upon reprocessing. This allows complete recycling and waste utilisation.Creation of polymer blends which can be non-waste processed is an important ecological problem due to the increasing accumulation of plastics waste and environmental protection demands.51 The history of the creation of different types of TPE up to the year 1987 has been considered in a comprehensive review by Legge.52 Technological fundamentals of the preparation of mod- ern types of TPE have been developed by Coran.49 An in situ dynamic vulcanisation technique has been proposed, where vul- canisation of an elastomer proceeds simultaneously with its mixing with a thermoplastic polymer. This allows the preparation of blends with unique morphology characterised by `dispersion' of the particles of the vulcanised elastomer in a continuous thermo- plastic matrix.This technique permits the production of materials with excellent operating characteristics and these materials can be readily non-waste reprocessed.53 Polymeric compositions based on 11 different elastomers and 9 thermoplastic polymers have been considered.49 Combining these elastomers and plastics allowed the preparation of more than 75 types of TPE. 1. The mechanism of dynamic vulcanisation The properties of TPE depend on many parameters such as blend composition, the nature of vulcanising agents, blending condi- tions, temperature ± time superposition during the formation of network structure of the elastomer, etc. The preparation of TPE with improved mechanical properties requires mixing of dispersions of submicron sizes.49, 50, 53 In particular, the tensile strength and elongation at break of the PP ± EPDM-based blends (PP :EPDM=40 : 60) increase with the decrease in the domain size (Fig.11). In this case, mixing is superimposed on the cross-linking reaction which causes changes sb /MPa 5 4 20 3 2 1 100 400 200 eb (%) Figure 11. `Stress ± strain' diagrams for PP ±EPDM blends (PP :EPDM=40 : 60) with different domain size of the elastomer phase (6denotes a break).49 Number-average domain size /mm: (1) 72, (2) 39, (3) 17, (4) 5.4, (5) 1 ± 1.5.72 I in the morphology of the elastomer phase, thus resulting in an increase in the viscosity of the medium and hampering the blend homogenisation. Therefore, efficient blending leading to a mate- rial with homogeneous submicroscopic distribution of the par- ticles of the dispersed phase requires that the condition (1) be met.The plots shown in Fig. 12 illustrate the effect of the density of cross-links, ne, on the tensile strength sb and tension set e?of TPE. As can be seen, sb monotonically increases with increasing ne, whereas e decreases rapidly even at small ne values. It is note- worthy that the rigidity of the material varies only slightly in this case.sb /MPa e? (%) 25 I 25 1 60 15 2 20 5 3 15 5 1075 ne /mol ml71 26 Figure 12. The effect of the density of cross-links ne on the tensile strength sb (1) and tension set e? (2).47 Polypropylene-based TPE are usually prepared at temper- atures above 180 8C.Degradation of TPE, which occurs at this temperature, detracts from the properties of the PP and elastomer phase.54 If peroxides are used as vulcanising agents, degradation is accompanied by cross-linking. Therefore, the preparation of TPE with optimum properties requires knowledge of the parameters of temperature ± time superposition during the formation of a net- work structure of the elastomer in the blend. Additionally, if the process is performed in the presence of peroxides, one should know the kinetics of (i) degradation and cross-linking of PP and (ii) the formation of interfacial polymer ± elastomer links. 110 8C is longer than that for the oxidation of the initial PP and can even be longer than the induction period for the oxidation of EPDM at a particular blend ratio.Upon introduction of vulcan- ising agents the oxidation resistance of the material increases and depends on the type of the vulcanising system of the rubber. Degradation products changes the blend morphology, thus changing the properties of TPE. This effect was particularly pronounced in the case of dynamic vulcanisation of ternary PE ± PP ±EPDM blends in the presence of peroxide as the vulcan- ising agent.57, 58 It was found that the tensile strength sb and modulus of elasticity E decrease with increase in the peroxide concentration in the blends with high PP content, whereas in the blends with high EPDM content these parameters increase under the same conditions. George et al.59 showed that the cross-linking reaction dominates over degradation in the PP ± nitrile elastomer blend in the presence of dicumyl peroxide.The effect of the chemical nature and concentration of the vulcanising system on the properties of an EPDM±HDPE blend was studied.60 The vulcanising systems investigated exhibited different induction periods and rates of EPDM vulcanisation. The sulfur-containing vulcanising system exhibited the shortest induction period and the highest rate of vulcanisation, whereas the resin-based system exhibited the longest induction period and the lowest rate of vulcanisation. Studies on the kinetics of vulcanisation of systems with different concentrations of vulcanising agents showed that the rates of vulcanisation remain virtually constant irrespective of the chemical nature of the vulcanising system as the concentrations of these agents is doubled or halved.On the other hand, the induction period lengthens as the concentration of the sulfur- based vulcanising system decreases and remains the same if the resin-based system is used. It was shown 61 that the dependence of the density of cross- links in the ethylene/propylene/vinylnorbornene terpolymer on the peroxide concentration passes through an extremum. Regularities in the cross-linking and degradation of a poly- isoprene elastomer SKI-32 at 190 8C have been reported.55 The content of the sol fraction and itsMMDwas studied as function of the duration of vulcanisation at different concentrations of tetramethylthiuram disulfide (TMTD) and sulfenamide C (SA) used as vulcanising agents.Figure 13 presents typical gel chroma- tograms of the sol fractions of the SKI-32 elastomer cross-linked at different TMTD: SA ratios. After heating the main peak on the chromatogram of the elastomer is shifted towards the low MM region due to the depletion of the rubber fractions with the highest molecular masses. As can be seen, the rates of vulcanisation and degradation depend on the ratio of the components of the vulcan- ising system. For instance, for the same vulcanisation time of 3.5 min the system with the ratio TMTD: SA=2 : 0 exhibits a bimodal distribution (Fig. 13 a), the system with the ratio TMTD: SA=1 : 1 exhibits a shoulder (Fig. 13 b) while the system with the ratio TMTD: SA=0 : 2 exhibits a broad unimodal distribution, which also covers the region of the initial molecular masses (Fig.13 c). The existence of the limiting MM value of the sol fraction of the cross-linked elastomer was established 55 and it was found that this value remains virtually the same at any ratio of the vulcanising agents in the system. A similar picture was also observed in the case of prolonged vulcanisation carried out for 14 min (see Fig. 13, curves 3). Vulcanised EPDM samples exhibited the greatest tensile strength in the presence of the sulfur-containing system, while the largest elongation at break and tension set were attained if the resin-based system was used as the vulcanising agent.The tensile strength increased to some extent with increasing concentration of activators (the sulfur-containing system). A decrease in the con- The kinetics and mechanism of degradation of an elastomer ± polymer blend can be significantly different. It was shown 56 that the induction period for the oxidation of PP ±EPDM blends at a I 1 2 3 4 17 V /ml 21c 4 1 2 Figure 13. Gel chromatograms of the sol fractions of the SKI-32 elastomer cross-linked at 190 8C for (1) 3.5, (2) 7 and (3) 14 min at TMTD: SA ratios of 2 : 0 (a), 1 : 1 (b) and 0 : 2 (c); (4) a gel chromato- gram of the initial elastomer. V /ml 18 22 E V Prut, A N Zelenetskii b 2 3 4 1 16 V /ml 20 24Chemical modification and blending of polymers in an extruder reactor K 4 3 0.8 0.40 20 centration of the vulcanising agents caused some deterioration of the stress ± strain properties and an increase in the elongation at break and tension set.Mechanical properties of the vulcanisates remained virtually unchanged in the presence of the resin-based system. For TPE samples, the concentration of vulcanising agents had almost no effect on the rebound elasticity and hardness. The strain ± strength properties of TPE improved with the increase in the concentration of the sulfur-containing system and deterio- rated as the concentration of the resin-based system increased. A decrease in the concentration of the vulcanising agents caused a decrease in the tensile strength, while the elongation at break and tension set at break increased. K 4 3 0.8 0.4 The effect of the chemical nature of the vulcanising system on the physical properties of the TPE based on the EPDM± PP blends can be followed from the data listed in Table 3.62 As can be seen, TPE prepared with the use of the phenolic system exhibit better characteristics (especially, swelling in oil and tension set at compression).0 60 Table 3. The effect of the chemical nature of the vulcanising system on the properties of TPE based on SKEPT2± PP blends [EPDM : PP=60 : 40 (mass %)].62 Property Vulcanising agent Degree of cross-linking peroxide dimethylol- alkylphenol sulfur-con- taining system 44 25.6 9.72 350 109 43 24.3 8.00 530 194 39 15.9 8.07 450 225 24 43 32 D (arbitrary units) sb /MPA se=100% /MPa eb (%) H (%) e 01 (%) Note. The following notations are used: D is the Shore hardness; se=100% is the stress at 100% elongation; H is the swelling in oil and e 01 is the tension set upon compression (22 h, 100 8C).Figure 15. A schematic representation of the vulcanisation curve. The time taken to reach the limiting degree of cross-linking (t?) can be determined from the relation (4) t?=t Does the thermoplastic polymer affect the kinetics of vulcan- isation of the elastomer? Sengupta and Konar 63 studied this problem taking the vulcanisation of EPDM± PP blends in the presence of a sulfur-containing vulcanisation accelerator in the temperature range from 120 to 190 8C as an example.The blend ratio was varied from EPDM: PP=100 : 0 to EPDM: PP= 100 : 100. Analysis of the vulcanisation curves revealed three time intervals corresponding to the main stages of vulcanisation (Fig. 14), viz., the induction period of the vulcanisation, the network formation period and the reversion period, respectively. The effective activation energy of vulcanisation varies only slightly, being equal to 8.85 kcal mol71 for the initial elastomer and lying between 7.11 and 11.17 kcal mol71 for the EPDM± PP blends. On the other hand, the induction period and the rate constant of the vulcanisation change. Figure 15 presents a general pattern of a vulcanisation curve. In the second stage of vulcanisation, the degree of cross-linking, q, can be to a first approximation written as the following linear relation:64 (4) q=wmax(t7ti), where q? is the limiting degree of cross-linking.As to degradation, it has no pronounced effect on the material structure if tf<td , where td is the induction period of degradation. The limiting degree of cross-linking should be reached during the time tf, therefore t? tf . Based on the inequalities (5) ± (8), a criterion for the choice of optimum temperature ± time superposition during dynamic vul- canisation can be written as follows: tm4ti4t? tf<td . The vulcanising agents and temperature-time superposition during the formation of TPE are chosen taking into account relations (9) and the criteria (10a) ± (10c) where wmax is the maximum vulcanising rate, t is the vulcanising time and ti is the induction period.Preparation of a material with homogeneous submicroscopic distribution of the particles of the dispersed phase requires that the following condition [see the inequality (1) above] be met ti5 R2 6D , (5) tm<ti . 73 b a K 2 4 3 0.8 2 1 0.4 1 0 20 160 60 180 200 t /min t /min c 2 1 120 t /min Figure 14. Dependence of the rel- ative modulus (K) characterising viscoelastic properties of the system on the vulcanisation time t: initial EPDM (a) and EPDM± PP blends with the blend ratio (EPDM: PP) 100 : 42.86 (b) and 100 : 100 (c). Vulcanisation temperature /8C: (1) 120, (2) 150, (3) 170 and (4) 190.wmax t? ti Vulcanisation time (6) i á q1 , wmax (7) (8) (9) (10a)74 (10b) wmax5l=V ¡ ti 1 or 1 , (10c) wmax5td ¡ ti where R is the radius of the extruder and D is the effective diffusion coefficient.64 These conditions hold if the vulcanising agents are introduced into the initial elastomer prior to blending. The problem of the order in which the blend components are fed into the extruder reactor is also topical. For instance, by varying the order of the introduction of carbon black in TPE one can change the resistivity of the end product from 3.761013 to 2.5 O cm. The knowledge of the order in which the components are fed into the extruder reactor and employment of the criteria (10a) ± (10c) allowed the development of one-step dynamic vul- canisation.65 2.Structure and properties of thermoplastic elastomers Thermoplastic elastomers represent two-phase systems in which cross-linked elastomer particles of size*1 to 2 mm are uniformly distributed in the polymer matrix.49, 50, 53 Dynamic vulcanisation has been carried out in either a Brabender mixer or a Berstorff twin-screw extruder.65 The tem- perature-time superposition as well as the type and order of feeding the blend components into the extruder were chosen with account taken of the criteria for the formation of TPE [relation- ships (10a) ± (10c)]. Table 4 lists the results of mechanical and rheological tests of the TPE obtained upon varying the blend ratio. As can be seen, the rigidity and tension set of the TPE increase with the increase in the PP content, i.e., the elastomeric properties of the TPE diminish.On the other hand, the rheological properties of the TPE are improved (the MFI increases). As the oil content increases, the rheological characteristics are also improved, while the strength characteristics deteriorate. Similar results have also been reported by Coran.49 Table 4. Effect of the TPE composition on their mechanical and rheo- E100 eb sb E0 /MPa /MPa /MPa (%) MFIa D e? (%) logical properties. TPE composition [PP] [EPDM] M (vol.%) (vol.%) 270 20.2 86 20 345 17.5 80 15 380 11.1 69 7 2.3 65 5 0.8 80 16 4.3 72 9 6.2 69 7 5.7 5.9 6.2 7.8 12.8 9.7 8.2 4.5 3.8 3.6 3.4 4.4 4.2 3.9 100 67 100 55 100 42 100 36 20 58 30 52 40 47 60 65 70 75 70 70 70 40 35 30 25 30 30 30 452 685 500 446 Note.The following notations are used:Mis the oil content (in mass parts per 100 mass parts of the elastomer), E0 is the initial modulus of elasticity, E100 is the modulus of elasticity at 100% elongation, D is the Shore hardness (in arbitrary units) and e? is the tension set. a In g/10 min. 3. Deformation of thermoplastic elastomers Deformation mechanisms of TPE have been poorly studied as yet.66 It is unclear so far why the mechanical properties of TPE at room temperature are determined by the properties of the dispersed phase rather than of the matrix.67, 68 Figure 16 presents the stress ± tensile strain diagrams of TPE in the coordinates s ± e at a tensile strain rate of 2.461074 s71 and different temperatures.66 Similar patterns of the stress ± ten- E V Prut, A N Zelenetskii b a s /MPa s /MPa 10 1 1 6 2 23 5 4 34 5 5 2 400 200 4 2 e (%) l7l72 Figure 16. Stress ± tensile strain diagrams s ± e (a) and s ± (l7l72) (b).The l values at a tensile strain rate of 2.461074 s71 are given for 20 (1), 50 (2), 75 (3), 100 (4) and 125 8C (5). sile strain diagrams were also observed for other tensile strain rates. No `neck' formation was observed in all cases. At e>3%, the s ± e diagrams are well linearised in the coordinates s ± (l7l72), where l=1+e (Fig. 16 b). At small elongations (e<3%), a rapid increase in s (a jump) was observed.The results obtained can be described by the following equation (11) s=s0+G(l7l72), where s0 is the jump magnitude and G is the modulus determined from the slope of the straight line. Thus, the overall stress is determined by the sum of two contributions, viz., the stress which rapidly increases with the tensile strain and reaches the s0 value and the stress which linearly depends on l7l72. It was found that the jump magnitude, s0, decreases linearly with the increase in the temperature and is independent of the tensile strain rate (Fig. 17). At T?145 8C, s0?0. This temperature corresponds to the onset of the melting of PP. Therefore, it was assumed that s0 is determined by the tensile strain of PP.The modulus G increases as the tensile strain rate increases and decreases with the increase in temperature.{ s0 /MPa 0.8 1234 0.40 100 90 80 T /8C Figure 17. Temperature dependences of the s0 jump at tensile strain rates of 2.461074 (1), 2.461073 (2), 2.461072 (3) and 9.561072 s71 (4). The dependences of the tensile strength sb and elongation at break eb on the tensile strain rate eand temperature are shown in Fig. 18. As can be seen, eb is temperature independent. As e increases, the elongation at break decreases rapidly and then varies only slightly. The tensile strength, sb, is a linear function of loge. The straight lines obtained for different temperatures are parallel to one another.The slope of the straight lines sb ± loge is very small, which means that sb depends only slightly on the tensile strain rate. Based on the results obtained, a structural model and a deformation mechanism were proposed for TPE.66 At high PP { Similar results for other types of TPE were recently obtained by S I Volfson, R R Grabdrashitov and K S Minsker Russ. Polym. News 5 (3) 1 (2000).Chemical modification and blending of polymers in an extruder reactor b a sb /MPa eb (%) 10 800 12345 5 400 73.3 72.3 73.3 72.3 loge (s71) loge (s71) Figure 18. Dependences of the tensile strain (a) and elongation at break (b) on loge at 20 (1), 50 (2), 75 (3), 100 (4) and 125 8C (5). content in the blend, the cross-linked EPDM domains are linked by the PP chains; at high EPDM content, they are linked by the elastomer chains.The space between the EPDM domains and the links is filled with oil and PP spherolites (Fig. 19). Initially, only the PP matrix undergoes deformation, thus being responsible for the initial jump, s0. In further stages, deformation of the PP matrix occurs simultaneously with that of the dispersed EPDM phase. PP macromolecules EPDM domains Oil layer PP matrix Figure 19. A scheme of the TPE structure. 4. Processing of thermoplastic elastomers The processability of TPE depends on their rheological properties. Chung et al. showed 69 that in the molten state thermoplastic elastomers behave like the melts of filled polymers or rubber- modified plastics.The properties of TPE allow their processing in the same manner as thermoplastic polymers, i.e., by compression mould- ing, blow moulding, extrusion welding, calendering and thermo- forming. Comparison of the production processes designed for rubbers and TPE (Scheme 1) reveals the major advantages of TPE, namely, easy processing, the possibility of re-moulding, multiple waste recycling, etc. In the case of TPE, the process parameters are determined by the composition of the TPE and preparation conditions. The structure of the TPE specimens obtained by injection moulding has been studied 70 as a function of the radii of the specimens. It was found that the surface layers are highly oriented.Adecrease in the process temperature leads to the formation of a disordered smectic structure in several TPE specimens and to a change in the EPDM: PP ratio in the layers owing to the orientation of the PP phase.Yet another advantage of TPE as compared to the initial component (PP) is an increase in the highest operating temper- ature. It was shown 71 that at 280 8C the thermo-oxidative stabilities of the blends of PP with rubbers of different nature are higher and the mass losses are *5 to 20 times smaller than those Processing of rubbers Preparation of initial components Mixing Waste Welding Vulcanisation Product of the virgin PP (Fig. 20). Thermal stability of the polymer blends is independent of the blend ratio and is not determined by the thermal stability of the initial rubber (polyisoprene rubber SKI-32, butadiene ± nitrile rubber SKN-402 or EPDM).It was also found that the thermal stability increases in the order PP ± SKN-402<PP ± SKI-32<PP ±EPDMand is independent of the degree of vulcanisation of the elastomer. Mass loss (%) 1 60 40 20 4 0 180 120 60 Figure 20. Isothermal TGA curves obtained at 280 8C in air for PP (1), EPDM (4) and PP ±EPDM blends of compositions (PP :EPDM) (mass %) 95 : 5 (2), 20 : 80 (3), 50 : 50 (5) and 80 : 20 (6). Replacement of traditionally used rubbers by TPE will make it possible to reduce the environmental pollution during their processing. These materials seem to be among the most promising materials to be used in the XXIst century and the areas of application of TPE are intensively expanded.VII. Solid-phase reactions in an extruder reactor Investigations into the solid-phase reactions in extruder reactors date back to the studies carried out by Academician N S Yeniko- lopyan at the N N Semenov Institute of Chemical Physics.72 Solid-phase modification of polymers has an advantage over conventional modification techniques because it is more efficient and ecologically safe and permits substantial reduction of the cost of the end product. 75 Scheme 1 Processing of TPE Preparation of initial components Welding Product Reprocessing 2 3 5 6 240 t /min76 1. Modification of polyalkenes In studies on the solid-phase modification of isotactic PP and low- density polyethylene (LDPE) in the presence of maleic acid and its derivatives (maleic anhydride and sodium maleate) in an extruder reactor it was found that grafting depended only slightly on the presence of a radical initiator, viz., azoisobutyronitrile (AIBN).73 ± 77 The amount of the graft compound was found to be dependent on the intensity of mechanical treatment and the total mechanical energy supplied.The best result (*1.5 mass%) was obtained using the extruder reactor equipped with a set of cams which permitted the highest compression and shear stress of the materials. During processing, the particles of the PP phase undergo plastic deformation and breakdown.78 Mechanical properties of the solid-phase modified polyal- kenes are much the same as those of the initial polymers.The modified polyalkenes exhibit adhesion to aluminium foil, which is more than an order of magnitude higher even at low degree of grafting (0.1 mass% to 0.2 mass %).79, 80 Degradation of the solid-phase modified polyalkenes is reduced as compared to the melt modified polyalkenes. 2. Modification of polysaccharides The interest in natural polymers (in particular, polysaccharides) is due to the need for rational use of these materials and to the design of new ecologically safe processes. The most abundant natural polysaccharides are cellulose and chitin containing in the shells of crustacean and insects and in mushrooms. Natural cellulose is widely used in the production of artificial fibres and films and in the textile industry. Chitin and its deacetylated derivative, chitosan, are of consid- erable interest because they possess film-forming and fibre-form- ing properties and are biologically active compounds.Chitin and its derivatives are thought to be promising materials for biotech- nological processes that use immobilised enzymes, for the creation of ion-exchange membranes for ultrafiltration and dialysis and for use as sorbents and ion-exchange resins. The complex-forming abilities of these polymers and their derivatives containing iono- genic groups can be used for selective extraction of metals from sea water. Systematic studies on the solid-phase modification of natural polysaccharides under the joint action of high pressure and shear strain using different types of equipment 81 showed that under such conditions the polymers pass to the plastic flow state, which is accompanied by changes in their morphologies. This leads to a substantial enhancement of the reactivities of the polymers. These conditions have been employed to prepare three most abundant cellulose derivatives (alkali cellulose, carboxymethyl cellulose and cellulose acetate), chitosan (from chitin) and a number of its derivatives.3. Modification of cellulose The formation of alkali cellulose under the action of concentrated NaOH solutions on cellulose (mercerisation of cellulose) is one of the main stages of the process of viscose fibre production. Industrially, cellulose sheets are treated with a large excess of 18% aqueous NaOH (usually, the ratio of the volume of the liquid to the mass of cellulose varies from 20 to 40).This ratio is dictated by the necessity of complete and uniform swelling of cellulose. The large amount of waste water substantially detracts from the ecological characteristics of this process. If mercerisation of cellulose is carried out in an extruder reactor, cellulose sheets are preliminarily milled and then the milled cellulose is treated with alkali solutions at a minimum volume of water. Depending on the initial concentration of alkali, the alkali cellulose thus formed differs in the degree of substitution of hydroxy groups, degree of polymerisation and some other characteristics. Using the joint effect of shear strain and pressure on a mixture of cellulose with alkali allows the preparation of alkali cellulose with preset characteristics and improved properties, which is due E V Prut, A N Zelenetskii to higher homogeneity of the product.Since in this case the amount of liquid is minimal, the process does not include the stage of removal of excess alkali solution. Here, water consump- tion reduces by an order of magnitude while alkali consumption reduces threefold as compared to the corresponding parameters of conventional procedures for the modification of cellulose. This to a great extent improves the ecological characteristics of the process. Carboxymethyl cellulose (CMC) is one of numerous and valuable cellulose derivatives.Water-soluble CMC is widely used in the food, cosmetic and petroleum refining industry and in pharmacy. Usually, CMC is obtained by treatment of cellulose with monochloroacetic acid (MCAA) in the presence of NaOH in an aqueous or aqueous-organic medium. However, this is accompa- nied by a side reaction (alkaline hydrolysis of MCAA) which nearly halves the efficiency of the procedure employed. The ratio of the contributions of these reactions to the overall process can be changed by excluding water or any other dispersion medium from the reaction volume, i.e., by carrying out a solid- phase reaction under the conditions of shear strain.82 The yield of CMC increases with increase in the initial concentrations of MCAA and alkali in the blend.The degree of substitution varies in parallel and can be as high as 0.94. The efficiency of MCAA increases (up to 60% to 70%, cf. 50% for the conventional process); however, it decreases with increase in the MCAAconcentration in the initial blend. Finely milled cellulose is much more reactive than coarsely milled cellulose and the CMC obtained from the former possesses a higher degree of substitution and solubility. Cellulose acetates are used in the manufacture of artificial fibres, film, lacquers and plastics, so production quantities of cellulose acetates are rather large. Usually, acetylation of cellulose is carried out with acetic anhydride as the acetylating agent and with an acid (e.g., sulfuric acid) as the catalyst at 35 ± 40 8C over a period of 4 to 6 h.It is known that cellulose acetates with a high degree of substitution cannot be obtained by treatment of cellu- lose with acetic acid. Strong intermolecular interaction in solid cellulose due to the formation of hydrogen bonds is the main factor precluding the esterification of the hydroxy groups of cellulose by acetic acid. Figure 21 presents the dependences of the degree of substitu- tion of hydroxy groups on the concentration ofH2SO4 in the blend in the acetylation of cellulose by different acetylating agents under normal conditions and under the conditions of joint action of high pressure and shear strain. Acetylation by acetic acid under normal conditions results in the formation of cellulose acetates with a low Degree of substitution 7 1.0 6 0.5 5 4 3 21 5 10 [H2SO4] (%) Figure 21.Effect of the concentration of H2SO4 on the degree of sub- stitution of the hydroxy groups of cellulose in acetylation under normal conditions (the duration of the acetylation reaction was 4 h, at 20 8C) (1 ± 3) and under plastic flow conditions (p=1 GPa) (4 ± 7). (1, 5) Cellulose :CH3COOH=1 : 3, (2, 7) cellulose :CH3COOH (gla- cial)=1 : 3, (3, 6) cellulose : (CH3CO)2O=1 : 1.5, (4) cellulose : : CH3COOH (glacial)=1 : 1.5.Chemical modification and blending of polymers in an extruder reactor degree of substitution. Treatment of cellulose with acetic anhy- dride yields cellulose acetates with higher degrees of substitu- tion.83 If the process is performed under the conditions of plastic flow and high pressure, the degrees of substitution for all acetylating agents are higher than those observed under normal conditions.4. Delignification of wood Wood is a multicomponent polymeric system. The existing technologies for chemical processing of wood with the aim of cellulose production have some drawbacks. The loss of the wood content in the course of processing is nearly 50% and the amounts of toxic wastes and waste gases are large. Purification of these wastes presents severe difficulties. Modification of the technolo- gies for wood processing to obtain wood pulp in such a way that the yield of the end product be 90% to 95% would allow substantial reduction of toxic waste and waste gases.84 A study on the model processes of delignification of wood and mercerisation of cellulose using Bridgman anvils has been reported.85 The specimens were exposed to the joint action of high pressure and shear strain.It was found that under these conditions the above-mentioned processes proceed without an activation barrier. The activation energy for the delignification of wood by means of alkali cooking was found to be 32 kcal mol71.86 Delignification of wood in an extruder reactor resulted in products with fibrous structures. The reason is that the plastic flow of wood under the joint action of pressure and shear strain occurs mainly along the boundaries of strong, rigid fibres. This results in cleavage of the inter-fibre links and, correspondingly, in degradation of the wood.The fibrous products obtained in the extruder reactor exhibited improved mechanical properties as compared to those of the products prepared by conventional methods. 5. Preparation of chitosan and its derivatives Chitin is less reactive than cellulose. This is due to specific features of its molecular and supramolecular structure, strong hydrogen bonding and a less active surface. Chitosan is usually obtained by long-term treatment of chitin with concentrated NaOH solution at elevated temperatures. The existing technology for the production of chitosan is rather inefficient and requires high energy expenditures, the use of a large excess of aqueous alkali solutions and subsequent utilisation of alkali waste and waste water.It was shown 87 that the grinding of chitin and chitosan in a solvent in an extruder reactor leads to partial breakdown of the crystal structure. This appreciably enhances their reactivities towards etherification and leads to some decrease in MM. Deacetylation of chitin in the temperature range 25 ± 200 8C has been studied.88 An increase in the excess of NaOH favours an increase in both the degree of deacetylation and solubility of the products obtained. The preparation of nearly completely deacety- lated product with a solubility of 90% requires only a fivefold molar excess of NaOH, whereas conventional procedures for the preparation of chitosan require at least 10 moles of NaOH per 1 mole of chitin.Both the degree of deacetylation and solubility of the product can be increased by lengthening the residence time of the reaction system in the extruder reactor. Experimental studies showed that raising the temperature from 25 to 200 8C at the mole ratio chitosan : alkali=1 : 5 results in an increase in the degree of deacetylation from 0.33 to 0.98 and in a substantial decrease in MM. Conventional procedures for the preparation of chitin and chitosan carboxymethyl ethers are inconvenient since they are time-consuming, proceed as multistage reactions and require large consumption of reagents.89 A recently developed solid-phase method 90 for the prepara- tion of these compounds allows improvement of ecological characteristics of the process owing to the absence of solvents 77 and shortening of the reaction time from several hours to several minutes. The reaction was carried out in a Berstorff twin-screw extruder reactor. In the first stage, a mixture of chitin and solid NaOH was extruded at different ratios of the components.Alkali chitosan thus obtained was mixed with an alkylating agent (e.g., MCAA dissolved in isopropyl alcohol or solid sodium mono- chloroacetate) and again fed into the extruder reactor (stage 2). The residence time in the extruder reactor was 3 to 5 min. The effect of the reaction conditions on the properties of the reaction products can be followed from the data listed in Table 5. As can be seen, an increase in the concentration of MCAA and alkali leads to an increase in the degree of substitution, which reaches a maximum value of 1.4.Table 5. Effect of the reaction conditions on the properties of the reaction products. P z A Treact /8C Speci- men number 1073M x1+x2 (see note a) stage 2 stage 1 30 68 0.10 0.62 0.32 0.35 0.29 0.25 0.20 0.45 0.27 0.90 0.40 0.51 0.70 0.68 1.02 1.40 0.65 0.87 80 80 120 100 100 120 60 100 100 absent absent 180 100 200 120 80 100 100 1 : 4.25 : 2.0 1 : 2.60 : 2.3 1 : 4.80 : 2.3 1 : 5.25 : 2.5 1 : 5.25 : 2.5 1 : 8.40 : 2.9 1 : 8.40 : 4.0 1 : 2.60 : 2.3 1 : 4.40 : 4.0 48 7 20 475 70 826 65 70 70 90 46 62 58 45 123456789Note. The following notations are used: A denotes the chitin :NaOH: MCAA mole ratio; P is the solubility in water (in mass %); x1, x2 and z are the degrees of substitution as regards the O-carboxymethyl, N-carboxy- methyl and N-acetyl groups, respectively.Specimen 1 was obtained from chitosan and specimens 2 ± 9 were obtained from chitin. Specimens 4 ± 7 were obtained using a 40% solution of MCAA in isopropyl alcohol and specimens 8 and 9 were obtained using solid sodium monochloroacetate as the alkylating agent. a The molecular mass of the soluble fraction of the end product. The specimen prepared from chitosan in one extrusion step (see Table 5, specimen 1) exhibited a relatively high degree of carboxymethylation (0.9) at smaller consumption of MCAA.The molecular mass decreased dramatically as the temperature increased. This feature is common to solid-phase extrusion- modified polymers. Solid-phase reactions of chitosan with a higher fatty acid (stearic acid) and with dicarboxylic acids (oxalic, malonic and succinic acids) in a twin-screw extruder have been studied.82 The residence time of the reaction system in the extruder was 3 to 5 min. Reaction products of chitosan with higher fatty acids combine the properties of polymeric substances (film-forming, fibre-form- ing, thickening properties, etc.) and surfactants. They can be of interest as amphiphilic materials for the preparation of solid and hydrogel membranes. Modification of chitosan by lipophilic compounds with the aim of enhancement of both the surfactant properties and the ability not only to thicken but also stabilise the food and cosmetic compositions containing oils and lipids is also topical.The addition of stearic acid to chitosan proceeds mainly by an ionic mechanism. Reactions of chitosan with dicarboxylic acids occur as both the ionic and covalent linking. Studies on the reactions of chitosan with phthalic, succinic and maleic anhy- drides showed 89 that these compounds react mainly with the amino groups of chitosan and that the degree of conversion increases with increase in temperature.78 This work has been written with the financial support by the Russian Foundation for Basic Research (Project No. 00-03- 33099). References 1. D R Paul, S Newman (Eds) Polymer Blends (New York: Academic Press, 1978) 2.V N Kuleznev Smesi Polimerov (Polymer Blends) (Moscow: Khimiya, 1980) 3. L A Utracki Polymer Alloys and Blends: Thermodynamics and Rheology (Munich, Vienna, New York: Hanser Publishers, 1989) 4. A O Baranov, A V Kotova, A N Zelenetskii, E V Prut Usp. Khim. 66 972 (1997) [Russ. Chem. Rev. 66 877 (1997)] 5. MXanthos (Ed.) Reactive Extrusion: Principles and Practice (Munich: Hanser Publishers, 1992) 6. V E Gul',M S Akutin Osnovy Pererabotki Plastmass (The Founda- tions of Plastic Processing) (Moscow: Khimiya, 1985) 7. R V Torner Teoreticheskie Osnovy Pererabotki Polimerov (Theoret- ical Foundations of Polymer Processing) (Moscow: Khimiya, 1977) 8. Z Tadmor, C G Gogos Principles of Polymer Processing (New York: Wiley, 1979) 9.A Ya Malkin, V P Begishev Khimicheskoe Formovanie Polimerov (Chemical Moulding of Polymers) (Moscow: Khimiya, 1991) 10. N A Plate, A D Litmanovich, V V Yashin, I V Ermakov, Ya V Kudryavtsev, E N Govorun Vysokomol. Soedin., Ser A. 39 8 (1997) a 11. N A Plate, A D Litmanovich, O V Noa Makromolekulyarnye Reaktsii (Macromolecular Reactions) (Moscow: Khimiya, 1977) 12. A D Litmanovich Dokl. Akad. Nauk SSSR 240 111 (1978) b 13. A D Litmanovich Eur. Polym. J. 16 269 (1980) 14. A D Litmanovich, V O Cherkezyan Eur. Polym. J. 20 1041 (1984) 15. A D Litmanovich, V O Cherkezyan Vysokomol. Soedin., Ser. A 27 1865 (1985) a 16. V O Cherkezyan, A D Litmanovich Vysokomol. Soedin., Ser. A 28 820 (1986) a 17. E N Govorun, Candidate Thesis in Physicomathematical Sciences, Moscow State University, Moscow, 1997 18.L V Kudryavtsev, Candidate Thesis in Physicomathematical Sciences, Moscow State University, Moscow, 1997 19. G-H Hu, J T Lindt,M Lambla J. Appl. Polym. Sci. 46 1039 (1992) 20. A Ya Malkin Polym. Eng. Sci. 20 1035 (1980) 21. G-H Hu, S Triouleyre,M Lambla Polymer 38 545 (1997) 22. H Kramers, K Westerterp Elements of Chemical Reactor�Design and Operation (Amsterdam: Netherlands University Press, 1963) 23. Y-J Sun, G-H Hu,M Lambla J. Appl. Polym. Sci. 57 1043 (1995) 24. D A Frank-Kamenetskii Diffuziya i Teploperedacha v Khimicheskoi Kinetike (Diffusion and Heat Transfer in Chemical Kinetics) (Moscow: Nauka, 1967) 25. J A Manson, L H Sperling Polymer Blends and Composites (Moscow: Khimiya, 1979) 26.G Moad Prog. Polym. Sci. 24 81 (1999) 27. G-H Hu, Y-J Sun,M Lambla J. Appl. Polym. Sci. 61 1039 (1996) 28. Y-J Sun, G-H Hu,M Lambla, H K Kotlar Polymer 37 4119 (1996) 29. G-H Hu, J-J Flat, M Lambla Makromol. Chem., Macromol. Symp. 75 135 (1993) 30. S H P Bettini, J A M Agnelli J. Appl. Polym. Sci. 74 247 (1999) 31. S H P Bettini, J A M Agnelli J. Appl. Polym. Sci. 74 256 (1999) 32. J Garcia-Martinez, O Laguna, E Collar J. Appl. Polym. Sci. 68 483 (1998) 33. J Garcia-Martinez, A Cofrades, S Areso, O Laguna, O Collar J. Appl. Polym. Sci. 69 931 (1998) 34. J Garcia-Martinez,O Laguna, S Areso,O Collar J. Appl. Polym. Sci. 73 2837 (1999) 35. L Assoun, S C Manning, R B Moore Polymer 39 2571 (1998) 36.M R Thompson, C Tzoganakis, G L Rempel J. Appl. Polym. Sci. 71 503 (1999) 37. C Rosales, R Perera, M Ichazo, J Conzalez, H Rojas, A Sanchez, A Diaz Barrios J. Appl. Polym. Sci. 70 161 (1998) 38. C Rosales, R Perera, J Conzalez,M Ichazo, H Rojas, A Sanchez J. Appl. Polym. Sci. 73 2549 (1999) 39. M G Lachtermacher, A Rudin J. Appl. Polym. Sci. 58 2077 (1995) 40. M G Lachtermacher, A Rudin J. Appl. Polym. Sci. 58 2433 (1995) E V Prut, A N Zelenetskii 41. K J Kim, B K Kim J. Appl. Polym. Sci. 48 981 (1993) 42. MMehrabzadeh, S Kasali, MKhosravi J. Appl. Polym. Sci. 70 1 (1998) 43. D Carlson, L Nie, R Narayan, P Dybois J. Appl. Polym. Sci. 72 477 (1999) 44. B Guo, C-M Chan J. Appl. Polym. Sci. 77 1827 (1999) 45.J-P Chiou, K-C Chiou, F-C Chang Polymer 37 4099 (1996) 46. R A Kudva, H Keskkula, D R Paul Polymer 39 2447 (1998) 47. C F Ou,M S Chao, S L Huang J. Appl. Polym. Sci. 73 2727 (1999) 48. M Gaztelumendi, J Nazabal J. Appl. Polym. Sci. 70 185 (1998) 49. A Y Coran, in Thermoplastic Elastomers: A Comprehensive Review (Eds N R Legge, G Holden, H G Schroeder) (Munich, Vienna, New York: Hanser Publishers, 1987) p. 133 50. J Karger-Kocsis, in Polymer Blends and Alloys (Eds G O Shonaike, G P Simon) (New York: Marcel Dekker, 1999) p. 125 51. E V Prut Vysokomol. Soedin., Ser. A 36 601 (1994) a 52. N R Legge Rubber Chem. Technol. 62 529 (1989) 53. E V Prut, in IV Sessiya Mezhdunarodnoi Shkoly Povysheniya Kvali- fikatsii `Inzhenerno-Khimicheskaya Nauka dlya Peredovykh Tekhno- logii' (The IVth Session of International Training Sool `Engineering and Chemical Science for Progressive Technologies') (Moscow: L Ya Karpov Institute of Physical Chemistry, 1998) p.94 54. N Grassie, G Scott Polymer Degradation and Stabilisation (London: Cambridge University Press, 1985) 55. O P Kuznetsova, L M Chepel', G M Trofimova, D D Novikov, A N Zelenetskii, E V Prut Vysokomol. Soedin., Ser. B 39 1706 (1997) a 56. L S Shibryaeva, A A Veretennikova, A A Popov, T A Gugueva, A A Kanauzova Vysokomol. Soedin., Ser. A 41 695 (1999) a 57. C S Ha, S C Kim J. Appl. Polym. Sci. 35 2211 (1988) 58. C S Ha, S C Kim J. Appl. Polym. Sci. 37 317 (1989) 59. S George, N R Neelakantan, K T Varughese, S Thomas J. Polym. Sci., Part B, Polym.-Phys. 35 2309 (1997) 60. T A Gugueva, A A Kanauzova, S V Reznichenko Kauchuk Rezina (4) 7 (1998) 61. MDEllul, P S Ravishankar PMSE Symp., ACS Meeting 79 90 (1998) 62. S Abdou-Sabet PMSE Symp., ACS Meeting 79 86 (1998) 63. A Sengupta, B B Konar J. Appl. Polym. Sci. 66 1231 (1997) 64. E V Prut Khim. Fiz. 17 (9) 67 (1998) c 65. Russ. P. 2 069 217; Byull. Isobr. (32) 168 (1996) 66. L V Kompaniets, N A Erina, L M Chepel', A N Zelenetskii, E V Prut Vysokomol. Soedin., Ser. A 39 1219 (1997) a 67. S Kawabata, S Kitawaki, H Arisawa, Y Yamashita, X Guo J. Appl. Polym. Sci., Appl. Polym. Symp. 50 245 (1992) 68. Y Kikuchi, T Fukui, T Okada, T Inoue J. Appl. Polym. Sci., Appl. Polym. Symp. 50 261 (1992) 69. O Chung, A J Coran, J L White SPE ANTEC Tech. Pap. 43 3455 (1997) 70. M Cakmak, S Cronin PMSE Symp., ACS Meeting 79 113 (1998) 71. V K Skachkova, N A Erina, E V Prut Vysokomol. Soedin., Ser. A 42 1563 (2000) a 72. N S Enikolopyan Dokl. Akad. Nauk SSSR 283 897 (1985) b 73. N S Enikolopov,MD Sizova, L O Bunina, S N Zelenetskii, V P Volkov, N Yu Artem'eva Vysokomol. Soedin., Ser. A 36 608 (1994) a 74. V P Volkov, L O Bunina, MD Sizova, S N Zelenetskii, N Yu Artem'eva, N A Egorova, V P Nikol'skaya, E S Obolonkova, A B Gil'man, S L Kotova Plast. Massy (3) 25 (1997) 75. A N Zelenetskii, L O Bunina, E S Obolonkova, V P Volkov Plast. Massy (7) 19 (1999) 76. L O Bunina, V P Volkov, E S Obolonkova Plast. Massy (7) 13 (1999) 77. L O Bunina, V P Volkov, E S Obolonkova Plast. Massy (7) 22 (1999) 78. A N Zelenetskii,M D Sizova, V P Volkov, N Yu Artem'eva, N A Egorova, V P Nikol'skaya Vysokomol. Soedin., Ser. A 41 798 (1999) a 79. V P Volkov, A N Zelenetskii, M D Sizova, N Yu Artem'eva, N A Egorova, V P Nikol'skaya, in The 1st International Conference `Polymer Modification, Degradation and Stabilisation' (Palermo, Italy: University Palermo, 2000) p. 7 80. V P Volkov, A N Zelenetskii, M D Sizova, L O Bunina, L V Vladimirov, N A Egorova, in Vtoroi Vserossiiskii Karginskii Simpozium `Khimiya i Fizika Polimerov v Nachale XXI Veka' (The Second All-Russian Kargin Symposium `Chemistry and Physics in the Beginning of the XXIth Century') (Chernogolovka: Institute of Problems of Chemical Physics, 2000) p. Ts479 Chemical modification and blending of polymers in an extruder reactor 81. S Z Rogovina, T A Akopova Vysokomol. Soedin., Ser. A 36 593 (1994) a 82. T A Akopova, G A Vikhoreva, S Z Rogovina, V A Zhorin, L S Gal'braikh, N S Enikolopyan Vysokomol. Soedin., Ser. B 32 182 (1990) a 83. S Z Rogovina, L S Sakhonenko, V A Zhorin,M A Trunova Vysokomol. Soedin., Ser. B 31 127 (1989) a 84. S Z Rogovina, T A Akopova, G A Vikhoreva, I N Gorbacheva, S N Zelenetskii Vysokomol. Soedin., Ser. B 40 1389 (1998) a 85. E A Balashova, Candidate Thesis in Chemical Sciences, Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow, 1988 86. E A Balashova, L S Sakhonenko, S Z Rogovina, N S Enikolopyan Dokl. Akad. Nauk SSSR 302 1134 (1988) b 87. S Z Rogovina, V A Zhorin, D P Shashkin Vysokomol. Soedin., Ser. A 31 1255 (1989) a 88. T A Akopova, S Z Rogovina, G A Vikhoreva, S N Zelenetskii, L S Gal'braikh, N S Enikolopyan Vysokomol. Soedin., Ser. B 33 735 89. S Z Rogovina, G A Vikhoreva, T A Akopova, I N Gorbacheva, (1991) a S N Zelenetskii Vysokomol. Soedin., Ser. A 39 941 (1997) a 90. T A Akopova, S Z Rogovina, G A Vikhoreva, S N Zelenetskii Vysokomol. Soedin., Ser. B 37 1797 (1995) a a�Polym. Sci. (Engl. Transl.) b�Dokl. Chem. Technol., Dokl. Chem. (Engl. Transl.) c�Chem. Phys. Rep. (Engl. Tr

ISSN:0036-021X    

出版商:RSC    

年代:2001

数据来源: RSC

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Russian Chemical Reviews 70 (1) 81 ± 90 (2001) Rigid-rod poly(benzobisazoles) and molecular composites based on them L G Komarova, A L Rusanov Contents I. Introduction II. Rigid-rod poly(benzazoles) III. Molecular composites IV. Conclusion Abstract. poly(ben- rigid-rod of field the in studies of results The The results of studies in the field of rigid-rod poly(ben- zobisazoles) are them on based composites molecular and zobisazoles) and molecular composites based on them are ana- ana- lysed most are Poly(benzobisazoles) generalised. and lysed and generalised. Poly(benzobisazoles) are most promising promising candidates for high-strength and high-modulus polymeric materi- candidates for high-strength and high-modulus polymeric materi- als, can them on based composites molecular the while als, while the molecular composites based on them can be be employed a with materials polymeric of synthesis the in employed in the synthesis of polymeric materials with a broad broad spectrum of mechanical properties.The bibliography includes 101 spectrum of mechanical properties. The bibliography includes 101 references. I. Introduction Rigid-rod polymers began to attract the keen attention of inves- tigators after two main hypotheses had been put forward,1 namely: 1. Those materials which possess high rigidity manifest the highest deformation strengths. In terms of their moduli of elasticity (E ) the polymers, all the macromolecules in which are straightened in the same direction, can be equivalent to steel. 2.The polymers with relatively low densities possess high mechanical characteristics. This suggests that the values of specific moduli of rupture and deformation strengths of the straightened macromolecules can be very high.2 These statements have predetermined the increased interest of synthetic chemists in the construction of macromolecules which display maximum thermodynamic rigidities.3 High deformation strengths and rigidities of polymers are provided by covalent bonds between the macromolecules which should manifest high levels of straightness and contain predom- inantly aromatic rings. These properties also determine the thermal stabilities of the polymers.3, 4 High levels of molecular straightness are more effectively achieved in fibres than in bulk products; therefore, special attention to the design of high-strength fibres for composite materials was given.3 ±5 The first steps in these investigations were aimed predom- inantly at the preparation of fibres based on aromatic polyamides devoid of non-symmetrical fragments and `hinge' groups, e.g., poly(p-benzamide) and poly(p-phenyleneterephthalamide).6± 12 LGKomarova,AL RusanovANNesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, ul.Vavilova 28, 117813 Moscow, Russian Federation. Fax (7-095) 135 50 85. Tel. (7-095) 135 93 27. E-mail: komarova@ineos.ac.ru (LGKomarova). Tel. (7-095) 135 63 72. E-mail: alrus@ineos.ac.ru (A L Rusanov) Received 2 February 2000 Uspekhi Khimii 70 (1) 88 ± 98 (2001); translated by R L Birnova #2001 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2001v070n01ABEH000578 81 81 86 88 C HN n O O O C HN HNC n The latter polymer, which is commonly known under the commercial name Kevlar, and its different modifications are used as the basis for the preparation of high-modulus and high-strength polymeric materials. In addition to aromatic polyamides synthesised from carbo- cyclic diamines and dicarboxylic acids, polyamides based on heterocyclic monomers, e.g., poly[(2-phenylbenzoimidazole-5,40- diyl)terephthalamide], are of considerable interest.10 O O N HN HN C C NH n It should be noted however that the presence of amide groups in the macromolecules of these polymers limits their thermal and thermohydrolytic stabilities.Hence, in the second step of inves- tigations in this field, the main attention was focused on rigid-rod polymers which contain only aromatic carbo- and hetero- cycles,13 ± 18 the so-called rigid-rod poly(heteroarylenes). II. Rigid-rod poly(benzazoles) In the series of rigid-rod polyheteroarylenes, the poly(benzo- azoles) (PBAz) 1 and 2 and, particularly, poly(benzobisazoles) (PBBAz) 3a ± c or isomeric structures have been studied in especially great detail.17 ± 23 X n m N1 N X X N n m 2 X=NH, NPh, O; n=1, 2.82 N X X N n 3a ± c X=NH (a), O (b), S (c). High-temperature polycyclocondensation of 1,2,4,5-tetraami- nobenzene-,26 4,6-diaminodihydroxybenzene- 27 and 2,5-diami- nobenzene-1,4-dithiol hydrochlorides 28, 29 with terephthalic acid in polyphosphoric acid (PPA) 23 ± 25 is the most popular procedure for the synthesis of the polymers 3a ± c.XH H2N .mHCl+ n HX NH2 4a ± c PPA 3a ± c CO2H +nHO2C 7H2O m=4, X=NH(a); m=2: X=O(b), S (c). If the synthesis is performed at polymer concentrations which are high enough for the formation of anisotropic solutions, the resulting polymeric solutions can be used directly for the prepa- ration of high-modulus fibres 29, 30 and films.31 Because of high oxidisability of the tetrafunctional nucleo- philic monomers 4a ± c, these are used in the form of hydro- chlorides or other salts rather than as free bases. The process is performed in two steps.In the first step which is carried out at 60 ± 80 8C, the nucleophilic monomers are subjected to dehydro- chlorination; in the second step, terephthalic acid is added, the mixture is slowly heated to 190 ± 200 8C and stirred at this temperature for 8 ± 10 h. In the course of polycyclocondensation, the content of P2O5 in PPA decreases, and its properties as the solvent, catalyst and cyclodehydrating agent deteriorate. The addition of P2O5 to the solutions results in both acceleration of the polycyclodehydration reaction and an increase in the molecular mass of the target polymers.32 ± 35 In addition to dicarboxylic acids, the respective acid chlorides are also used for the synthesis of PBBAz in a PPA medium.36 Since the glass transition temperatures of PBBAz often exceed their decomposition temperatures,14 the fibres and films are usually prepared directly from the solutions of these polymers.Poly(benzobisazoles) are soluble in strong acids, e.g., PPA, methanesulfonic acid, chlorosulfonic acid, 100% H2SO4 and Lewis acids (e.g., BiCl3 or SbCl3). Recently,37 it was shown that poly(benzobisthiazole) (PBBT 3c) forms liquid-crystalline solu- tions in nitromethane containing AlCl3 or GaCl3. Liquid-crystal- line solutions of PBBAz yield high-strength and high-modulus films and fibres. Very often, the deformation strength character- 1076 lnu 11 12 10 6 7 8 5 8 9 1 4 4 3 2 0 3 5 7 9 1078 lnE 1 Figure 1. The specific moduli of elasticity (E) and the specific strains (u) of some materials;45 (1) organic compounds, (2) aluminium, (3) steel, (4) `E'-glass, (5) `S'-glass, (6) Kevlar 29, (7) Kevlar 49, (8) freshly formed poly(benzobisoxazole) (PBBO 3b) fibre, (9) boron fibre, (10) freshly formed poly(benzobisthia- zole) (PBBT 3c) fibre, (11) heat-treated PBBT 3c fibre, (12) heat-treated PBBO 3b fibre.L G Komarova, A L Rusanov Table 1. The ultimate rupture strength (s), the modulus of elasticity (E), the elongation at rupture (e) and values of the Kuhn segment (A) of fibres based on rigid-rod polymers. Polymer e (%) A/A Ref. s /GPa E/GPa O O HN HN C C 47 22 17.3 0.70 9 n (Nomex) O HN C 300 38 4 58.9 2.64 C O n NH (Kevlar 29) O HN C 300 39 2.4 127.5 2.64 C O n NH (Kevlar 49) a N S 1060 40, 41 4.5 0.5 ± 2.2 50 ± 76 N n S (PBBT 3c) b N SN n 0.8 ± 2.5 76 ± 265 (<300) 1.0 ± 1060 42 1.5 (4.2) S (PBBT 3c) a N O 34, 44 2.8 ± 3.4 467 7 N n O (PBBO 3b) a a Heat-treated; b freshly formed.istics of PBBAz fibres even surpass those of Kevlar polyamide fibres which is attributed, in particular, to the greater values of the Kuhn segments in PBBAz (see Table 1 and Fig. 1).38 ± 45 The films with controlled planar orientation based on PBBT and PBBO have specific strengths of 2 GPa and moduli of elasticity of 270 GPa. Poly(benzobisazoles) are distinguished by extremely high thermal stabilities, viz., under conditions of a dynamic thermog- ravimetric analysis in air (DT=10 deg min71), they begin to lose weight at temperatures above 600 8C (Fig.2).18 Under conditions of an isothermal analysis in circulating air at 371 8C, their thermal characteristics markedly exceed those of poly(p-benzamide), PBBT 3c being much more resistant to heating than PBBO 3b (Fig. 3).46 Residual weight (%) 2 100 1 80 3 60 40 200 700 500 300 100 T /8C Figure 2. Thermogravimetric analysis of PBBAz in air (the rate of heating is 10 deg min71);18 (1) PBBT, (2) PBBO, (3) poly(benzobisimida- zole) (PBBI 3a).Rigid-rod poly(benzobisazoles) and molecular composites based on them Weight loss (%) 1 2 3 100 80 60 40 200 t /h 140 100 60 20 Figure 3. Isothermal ageing in circulating air at 371 8C; (1) PBBT 3c, (2) PBBO 3b, (3) poly(benzamide).A significant disadvantage of all PBBAz is their low compres- sion strength. Modification of the basic chains of their macro- molecules and the introduction of bulky substituents into macromolecules were undertaken in order to enhance this param- eter, to improve the solubility of PBBAz and to impart specific properties to these systems. Thus the p-phenylene residues of terephthalic acid in the basic chains of PBBAz were replaced by thiophene-2,5-diyl,47 ± 49 fluo- rene-2,7-diyl,50 adamantanediyl,51 bicyclo[2.2.2]octanediyl 52, 53 and 2,20-bipyridinediyl 54 fragments. In particular, the reaction of the 2,5-diaminobenzene-1,4-dithiol dihydrochloride (4c) with thiophene- (5a), bithiophene- (5b) and terthiophenedicarbonyl (5c) dichlorides afforded PBBT 6 soluble in methanesulfonic and sulfuric acids.47 SH H2N 2 HCl+ n HS NH2 4c PPA +n ClOC COCl m 74nHCl, 72nH2O S 5a ± c N S S S m n N6 m=1 (5a), 2 (5b), 3 (5c).A similar approach was used for the synthesis of a thiophene- containing PBBO.49 Although PBBT and PBBO are characterised by much lower values of the Kuhn segment than those of the analogous polymers based on terephthalic acid, the majority of their solutions in various acids manifest liquid-crystalline proper- ties.A certain deviation from a strictly straightened chain was also observed in the case of PBBT 7 prepared from the dihydrochloride 4c in PPA after partial substitution of fluorene-2,7-dicarbonyl dichloride for the terephthaloyl dichloride (Scheme 1).50 Polycyclocondensation at 165 8C results in the formation of high-molecular-weight polymers which are completely soluble in methanesulfonic and sulfuric acids.At higher temperatures, this HS NH2 COCl +m (m+n) 2HCl+n ClOC SH H2N 4c S N S N N S N S n 7 83 reaction is accompanied by the formation of insoluble polymers which can be due to the five-membered ring opening in the fluorene fragment. The colourless PBBT 8 was obtained by the reaction of the dihydrochloride 4c with bicyclo[2.2.2]octane-1,4-dicarboxylic acid (9a), its dimethyl ester (9b) or the dichloride (9c) in PPA.52, 53 SH H2N PPA COX 2HCl+nXOC n 165 8C, 24 h HS NH2 9a7c 4c S N N S n 8 X=OH (9a), OMe (9b), Cl (9c).The resulting polymer is soluble in methanesulfonic and sulfuric acids. In terms of thermal stability, the rupture strength and modulus of elasticity, the polymer 8 ranks below PBBT 3 based on terephthalic acid but considerably surpasses it in compression strength. Poly(benzobisoxazoles) and poly(benzobisthiazoles) contain- ing 2,20-bipyridinediyl residues were obtained by the reaction of 2,20-bipyridine-4,40- or -5,50-dicarboxylic acids with various mononuclear diaminodiols and diaminodithiols (Scheme 2).54 The 4,40-substituted PBBAz 11 and 12 are soluble in methane- sulfonic, sulfuric, trifluoroacetic and formic acids as well as in a mixture of nitromethane with AlCl3. They form strong films.The 5,50-substituted polybenzazoles 13 and 14 are soluble only in methanesulfonic acid and in a mixture of nitromethane with AlCl3. The solutions of PBBAz 14 form lyotropic mesophases in methanesulfonic acid. The poly(benzobisazoles) 12a,b and 13a,b manifest extremely high thermal stabilities in inert media and in air (Table 2). Table 2. Some characteristics of the PBBAz 12 and 13.54 Yield (%) Compound Tdestr /8C Zlog (see a) in air in N2 atmosphere 82 83 86 87 668 585 648 597 591 537 586 569 3.1 3.7 1.7 2.1 13b 13c 12b 12c aMeSO3H, 30 8C, c=0.25 g dl71. The synthesis of the phenyl-substituted poly[benzo(N-phe- nyl)bisimidazole] 15 55, 56 was carried out in two steps. In the first step, 4,6-dianilinobenzene-1,3-diamine 16 reacted with terephtha- loyl dichloride inN-methylpyrrolidone (NMP); in the second step, the poly(dianilino)amide 17 formed is cyclodehydrated in PPA to PBBAz 15.Poly[benzo(N-phenyl)bisimidazole] 15 is one of the first rigid- rod PBBAz. It is soluble in methanesulfonic, sulfuric and formic Scheme 1 PPA 165 8C COCl ClOC m84 HOOC N N HOOC N X=N(a), O (b), S (c). acids as well as in a tetrachloroethane ± phenol mixture (3 : 1). This corroborates the hypothesis 57 that the phenyl substituents in the heterocyclic fragment improve the solubility of polyheteroary- lenes.57 The polymer 15 has a specific viscosity of 9.9 dl g71 and a glass transition temperature (Tg) at 380 8C; at 450 8C, it loses 5% of its mass.Casting of the polymeric solutions was used to obtain films with a rupture strength of 135 MPa. It should be noted that in contrast to other PBBAz, poly- [benzo(N-phenyl)bisimidazole] 15 is not formed by direct reaction of 4,6-dianilinobenzene-1,3-diamine 16 with terephthalic acid or its dichloride in PPA. NHPh PhHN n NH2 H2N 16PhHN C NH O Ph NN Much attention has been given to the synthesis of PBBAz with bulky substituents in the carbocyclic fragments of the macro- molecules. Such structures are usually synthesised by polycyclo- condensation of dicarboxylic acids or their derivatives containing the corresponding substituents. Wolfe and Arnold 27 were among the first who have synthes- ised PBBO 18a ± c based on di-, tri- and tetraphenyl-p-terphenyl- dicarboxylic acids.The solubilities of the phenyl-substituted polymers 18a ± c exceeds markedly that of the unsubstituted PBBO. In addition to methanesulfonic and chlorosulfonic acids, they are soluble in benzenesulfonic acid and a 7 : 3 mixture of m-cresol with dichloro- acetic acid as well as in a 9 : 1 mixture of dichloroacetic acid with methanesulfonic acid. NH2 H2N HO OH 10 COOH N HX NH2 XH H2N 4a ± c N 4a ± c N COOH N 10 N NMP +n ClOC COCl 72nHCl NHPh PPA, 300 ± 310 8C 72nH2O C NH O n 17 Ph N n N 15 N N O O N n 11 X N N X N n 12a ± c N X X N N 13a ± c N N O O N 14 OH HO n NH2 . HCl HCl .H2N R1 +nHO2C Ph ON R1=R2=H(a), R1=H, R2=Ph (b), R1=R2=Ph (c).An analysis of the thermal stabilities of PBBO 3b and the polymer 18b containing a triphenyl-substituted central fragment revealed that the latter is more resistant to isothermal ageing at 316 8C than PBBO 3b, but is decomposed more rapidly at 371 8C (Fig. 4) due to the splitting of the phenyl groups. The poly(benzobisoxazoles), poly(benzobisthiazoles) and poly(benzobisimidazoles) 19a ± f containing benzooxazol-2-yl or benzothiazol-2-yl substituents in the phenyl fragment were obtained using the corresponding substituted terephthalic acids 20.58 ± 61 Weight loss (%) 100 80 60 40 4 200 100 50 Figure 4. Isothermal ageing of PBBO 3b and the polymer 18b powders in circulating air;27 (1) polymer 18b at 316 8C, (2) PBBO 3b at 316 8C, (3) PBBO 3b at 371 8C, (4) polymer 18b at 371 8C.L G Komarova, A L Rusanov Scheme 2 n n + R2 CO2H Ph R1 R2 ON Ph n Ph 18a ± c 1 2 3 t /h 150Rigid-rod poly(benzobisazoles) and molecular composites based on them XH H2N . 2HCl+ n HX NH2 nHO2C X N N X 19a ± f X=Y=O(19a); X=O, Y=S (19b);X=Y=S (19c); X=S,Y=O(19d); X=NH, Y=O (19e); X=NH, Y=S (19f). The PBBAz 19a ± f thus formed were soluble in sulfuric and methanesulfonic acids; the specific viscosities of their solutions in methanesulfonic acid varied from 4 to 19 dl g71. The anisotropic polymeric solutions (10%, w/w) were used to obtain fibres. The fibres from PBBT 19c manifested the most valuable properties, viz., stability of 2.4 GPa and specific modulus of elasticity of 172 ± 207 GPa.Their compression strengths (380 MPa) exceed that of the unsubstituted PBBT 3c. 2,5-Di(benzothiazolyl)terephthalic acid was used together with 2-benzoazolylterephthalic acids 20 in the synthesis of PBBAz, which afforded PBBAz 21.61 XH H2N 2HCl+n n HX NH2 X N N X Y N PPA 72nHCl, 72nH2O CO2H 20 Y N nHO2C R N Y S 22a ± d S N R Y N S n 23a ± d N S N X X N S N 21 Dicarboxylic acids 22a ± d were used as acid components in the synthesis of PBBT and PBBO in order to achieve an even greater disturbance of the close packing of PBBAz and to increase the compression strength.62, 63 It should be noted that high-molecular-weight PBBAz 23a ± d were obtained only in those cases where polycyclocondensation was carried out at very low concentrations of the monomers in PPA (41%), whereas with an increase in their concentration to 10% only low-molecular-weight oligomers could be isolated from their solutions (Scheme 3).62 The poly(benzobisazoles) 23a ± d are soluble in sulfuric, meth- anesulfonic and trifluoromethanesulfonic acids.The intrinsic viscosities, [Z], of the polymers 23a ± d measured in methanesul- fonic acid at 30 8C were equal to 12.0, 7.7, 11.4 and 8.7 dl g71, respectively. The presence of extended side groups in the PBBAz synthes- ised prevents the straightening of the basic chains of the macro- molecules and the formation of anisotropic solutions as a result of which the attempt to prepare high-quality fibres based on them failed.The introduction of insignificant amounts (1 mol.% ± 2 mol.%) of benzothiazolylphenyl-substituted p-terphenyldicar- S PPA 74nH2O,72nHCl N CO2H X Compo- und 23 ab S Ph absent O Ph " c S H O d O H O 85 n Scheme 3 Y R86 boxylic acid as a co-monomer to terephthalic acid results in the copolymers 24.64 R S N S N S N S N m k Ph n R 24 S R= N The polycyclocondensation at the concentrations of 10% (w/w) yielded copolymers with intrinsic viscosities of 20 to 28 dl g71. The fibres prepared from the copolymers 24 manifested a specific strength of 2.5 GPa, a modulus of elasticity of 193 ± 283 GPa and compression strengths of 344 to 482 MPa.The poly(benzobisazoles), e.g., 25 and 26, with aryloxide and arylthio substituents were obtained 65 by the reactions of 4,6- diaminoresorcinol, 2,5-diaminohydroquinone-, 4,6-diaminoben- zene-1,3-dithiol and 2,5-diaminobenzene-1,4-dithiol hydrochlor- ides with 4,8-diaryloxy(arylthio)naphthalene-2,6-dicarboxylic acids in PPA.65 YAr CO2H XH H2N PPA 2HCl+ n 74nH2O HX NH2 HO2C 4a ± c 27 YAr YAr X N N X YAr n 25 NH2 XH PPA 2HCl+27 n 74nH2O H2N XH YAr N N X X YAr n 26 R, R, X=O, S, NH; Ar= R; N R=H, Me, Et, Prn, Pri; Y=O, S. In addition to a single-step synthesis of PBBAz in PPA, two- step synthetic procedures have been developed which yield pre- polymers in the first stage under mild conditions.Their subse- quent solid-phase cyclisation yields poly(benzobisazoles). Thus the polymers 28 which are soluble in mixtures of dichloromethane chloride with methanesulfonic and trifluoro- acetic acids have been synthesised from the silyl derivatives 29 and aryloxy-substituted terephthaloyl dichlorides by Kricheldorf et al.66 ± 70 HNSiMe3 Me3SiX +n ClOC n XSiMe3 Me3SiNH 29 CO NH Me3SiX XSiMe3 CONH N X X N 28 X=O, S; R=Ph, OPh, But, Cl, Br. The use of silylated monomers makes it possible to increase the nucleophilicity of the nitrogen atom, as a result of which the reaction with acid chlorides proceeds more selectively and does not affect the trimethylsilyloxy(thio) groups.71 ± 74 Kimura et al.75 used a stepwise procedure for the synthesis of the alkoxy-substituted PBBT 30.SH H2N n +n ClOC HS NH2 SH HN HN HS S N N S 30 R=Bun, n-C6H13 , n-C8H17 , n-C10H21 , n-C12H25 ; m=1, 2. Nearly all the PBBT 30 were able to form anisotropic melts in the temperature range from 280 to 450 8C. On the whole, it should be noted that most PBBAz can successfully be used for the preparation of high-quality fibres and films; however, bulk products can hardly be obtained, since their glass transition temperatures exceed their decomposition temperatures. This problem was solved, to a large extent, within the framework of a new concept in materials technology, namely, the construction of molecular composites.76 III.Molecular composites The term molecular composites is usually applied to describe systems which consist of rigid-rod molecules dispersed in matrices of flexible-rod molecules at the molecular level; in this case, rigid- rod molecules play the role of reinforcing elements. Molecular composites can be prepared both by mixing rigid- and flexible-rod polymers at the molecular level and by synthesis- ing block and graft copolymers containing rigid- and flexible-rod fragments. Among the first molecular composites were those based on PBBT 3c as a rigid-rod component and polybenzoimidazole (31, ABPBI) as a flexible-rod component.77 ± 79 L G Komarova, A L Rusanov COCl 72nMe3SiCl OC6H4R-4 OC6H4R-4 D 7n (Me3Si)2O, 72nH2O n OC6H4R-4 nMeN COCl (OR)m O O 250 8C, 5 h C C 5 Torr (OR)m n (OR)m nRigid-rod poly(benzobisazoles) and molecular composites based on them NHN n 31 Poly(benzoimidazole) (31) was obtained by homocondensa- tion of 3,4-diaminobenzoic acid in PPA.80, 81 Mixtures of these polymers at the molecular level were prepared from solutions with concentrations below those required for precipitation.78, 79 The mechanical properties of PBBT ± ABPBI molecular composites (both as fibres and as films) are listed in Table 3.As can be seen from the Table 3, the introduction of 30% PBBT into the matrices of ABPBI enhances significantly the deformation strength characteristics of the mate- rial. The results of morphological studies of these mixtures, viz., low- and wide-angle X-ray scattering, optical microscopy and scanning electron microscopy suggest the absence of phase separation.77, 82, 83 Table 3.Mechanical characteristics of fibres and films based on the PBBT ± ABPBI molecular composites. Ref. Product Composite e (%) E/GPa s /MPa 1.1 295.2 3000 675 1110 300 16.8 36.0 82 77 82 fibre "" 7.2 2.5 1.8 1161 1215 1283 16.8 71.7 109.7 77 77 77 """ 552.4 690 918 30.4 88.2 83 83 film " PBBT ABPBI a ABPBI b PBBT ± ABPBI (30 : 70) a see c see d PBBT ± ABPBI (30 : 70) a see e a Freshly formed; b heat-treated; c heat-treated at 427 8C; d heat-treated at 525 8C; e heat-treated at 540 8C.The processability of molecular composites could be improved using thermoplastic polymers, e.g., amorphous and partially crystalline polyamides,84, 85 poly(phenylquinoxalines) 86 and poly(ether ether ketones) 87 as flexible-rod matrices. The mechanical characteristics of the molecular composites based on thermoplastic polymers and PBBT are listed in Table 4. Thus the mechanical properties of the PBBT ± Nylon system exceed those of a monoaxially oriented fibrous composite with identical composition by 50%± 300%. As well as the construction of composites at the molecular level, the design of molecular composites by the synthesis of block and graft copolymers has become a very popular approach. Whereas in the molecular composites prepared by mechanical mixing of flexible- and rigid-rod components the reinforcing HS NH2 PPA n CO2H 2HCl+HO2C SH H2N Excess 1.1% 4c N S CO2H HO2C S N n 33 N N S S N NH n B A 32 87 Table 4.Mechanical characteristics of PBBT ± thermoplastic molecular composites. Product Ref. E/GPa s /MPa Thermoplastics Composi- tion (w/w) 355 17.5 fibre 30 : 70 86 30 : 70 50 : 50 Poly(phenyl- quinoxaline) Nylon Poly(ether ether ketone) Nylon-6,6 345 248 105 183 36.0 11.0 15.8 20.8 "film block " 50 : 50 86 87 87 85 macromolecules are bound to the matrices exclusively due to physical interactions, in block copolymer-based molecular com- posites the flexible- and rigid-rod fragments are linked by covalent bonds.As a result, the transfer of strains from the rigid-rod fragments to the flexible-rod matrices occurs more effectively, hence, the block copolymer-based molecular composites manifest higher deformation strengths and dimensional stabilities. The block copolymers 32 of the ABA type 88 which contain rigid-rod blocks B and flexible-rod blocks A88 were synthesised as model systems. Macromolecules of PBBT 33 with carboxy termi- nal groups ([Z]=10±24 dl g71) used as rigid-rod blocks were introduced into co-polycondensation with 3,4-diaminobenzoic acid hydrochloride, which resulted in the formation of benzoimi- dazole rings and simultaneous binding of the individual blocks (Scheme 4). The compositions of the blocks were varied by changing the content of 3,4-diaminobenzoic acid used for co-polycondensa- tion.As can be seen from Table 5, the moduli of elasticity of the block-copolymeric molecular composites are comparable with those of the dynamic mixtures; their magnitudes depend on the ratios of the rigid- and flexible-rod components. The values of the moduli suggest that the reinforcement does not necessarily require highly extended macromolecules of PBBT 32. Comparison of the breaking strengths (see Table 5) points to a much higher (up to Table 5. Some characteristics of the block copolymers and mixed molec- ular composites.88 E/GPa Ratios a s /MPa e (%) [Z] /dl g71 copolymer PBBT 32 1696 1566 1600 1268 102.7 94.5 115.8 116.5 8.5 10.7 7.3 see b 10.7 12.9 17.7 see b 30 : 70 25 : 75 30 : 70 30 : 70 2.3 2.5 1.4 1.4 a The PBBT 32 :ABPBI 31 ratios for the copolymer; b a physical mixture comprising 30% (w/w) PBBT 32 ([Z]=31 dl g71) and 70% (w/w) ABPBI 31 ([Z]=17.6 dl g71).Scheme 4 NH2 HO2C 2HCl NH2 NNHn n A88 33%) deformation strength of the block-copolymeric molecular composites compared with the materials prepared from mechan- ical mixtures. The polybenzobisthiazoles carrying terminal carboxy groups were introduced into the Friedel ± Crafts polycondensation reac- tion with m-phenoxybenzoic acid in a P2O5 ±MeSO3H mixture.89 This reaction yielded block copolymers of the ABA type which contained flexible-rod polyether ketone blocks and rigid-rod PBBT blocks.In addition to block-copolymeric molecular composites, much attention has been given to the synthesis of molecular composites based on graft copolymers containing rigid- and flexible-rod macromolecules. In particular, benzothiazol-2-yl- substituted PBBI 34 was metallated using NaH in DMSO with subsequent treatment with acrylamide 90 or, which is especially important, with propylene oxide.90 ± 92 The grafted copolymer 35 is soluble in methanesulfonic, 97% formic and trifluoroacetic acids much more easily than PBBI 34. Although the softening of these polymers could not be detected by differential scanning calorimetry, their solid melts could be obtained by compaction at 190 ± 232 8C.The introduc- tion of polypropylene oxide side chains is accompanied by a significant decrease in their thermal stabilities in comparison with that of the starting compound, viz., PBBI 34. N NHN NH34 CH2CH(Me) x N N N N O(Me)CHCH2 x (a) NaH, DMSO, (b) Me CH CH2 . O Of special interest is the synthesis of molecular composites based on grafted copolymers with heat-resistant side chains. Since rigid-rod PBBAz are soluble only in acidic solvents, the set of S N N S S N N S x=(0.02 ± 0.5)y. N a, b S n N S n 35 N O O S x 36O OCO O 37 reactions used for the grafting is rather limited. Evers et al.93,94 used the Friedel ± Crafts reaction of m-phenoxybenzoic acid with poly(benzobisthiazole) in MeSO3H±P2O5 (10 : 1, w/w) for the synthesis of grafted copolymers of the AB type.Thus the reaction of the polybenzobisthiazole copolymer 36 containing 4,40-(o- diphenoxyphenylene) groups which are distributed statistically among the fragments of the rigid-rod PBBT with m-phenoxyben- zoic acid afforded the copolymer 37 (Scheme 5).95 Compaction at high temperatures and pressures (285 8C, 6.9 MPa) is employed for the preparation of bulk products possessing isotropic properties. The main disadvantage of this approach is the low elasticity of the grafted fragments. An alternative approach is based on the use of polybenzobis- thiazole copolymers containing 2,6-dimethylphenoxide side groups as the basic macromolecular chains.96, 97 Treatment of these systems withm-phenoxybenzoic acid in P2O5 ±MeSO3Hwas accompanied by the formation of the grafted copolymers 38 (Scheme 6).According to the dynamic mechanical analysis data, the soft- ening of the grafted copolymers 38 occurs at 180 ± 265 8C depend- ing on the value of y.98 Their secondary processing into bulk products is carried out at pressures up to 40 MPa and at temper- atures which are 40 to 50 8C higher than the softening temper- ature. A specimen containing 46% (w/w) of PBBT 3c and 54% (w/w) of the copolymer 38 manifests a rupture strength of 40 MPa and modulus of elasticity of 9.7 GPa. IV. Conclusion Rigid-rod PBBAz are the most promising materials in those fields where small weight, high deformation strength, rigidity, thermal and chemical stability as well as radiotransparency are the critical factors.The latter property is especially important, and in this respect PBBAz fibres have an indisputable advantage over graph- ite fibres. PBBAz fibres manifest greater elongation at rupture in comparison with graphite fibres and possess higher thermal and thermooxidative stabilities in comparison with Kevlar fibres. This altogether demonstrates their usefulness for aeronautical, aero- space and electronic engineering. Yet another field of application in which PBBAz have obvious advantages over glass, Kevlar fibres and coal plastics are thermostable membranes and filters. Further progress in this area will largely depend on the cost of the monomers and the `cost ± property' ratios of these systems.The main drawback of the materials based on PBBAz is their low compression stability. This review considers the individual approaches to the solution of this problem which are based on structural modifications of these polymers. In recent years, increasing attention has been given to the construction of HO2C SN y S N N S y x n L G Komarova, A L Rusanov Scheme 5 OPhRigid-rod poly(benzobisazoles) and molecular composites based on them N S S N SN y=(0.02 ± 0.3)x . PBBAz that can be cross-linked to form three-dimensional structures.99 ± 101 Further developments in this field will obviously be aimed at the construction of systems whose solidification is not accompanied by the evolution of volatile by-products.References 1. F C Frank Proc. R. Soc. London, A Math. Phys. Sci. 319 127 (1970) 2. A J Kinlock, P R Young Fracture Behaviour of Polymers (London: Applied Science Publishers, 1983) 3. R T Read Polym. Paint Colour J. 178 664 (1988) 4. R T Read Spec. Chem. 9 30 (1989); Ref. Zh. Khim. 13 4 (1989) 5. D Hall Introduction to Composite Materials (Cambridge: Cambridge University Press, 1981) 6. A Ciferri, I Ward (Eds) Ultra-High Modulus Polymers (London: Interscience, 1979) 7. A J Owen, in Developments in Orient Polymers Vol. 2 (London; New York: Applied Science Publishers, 1987) p. 237 8. A A Konkin (Ed.) Termo-Zharostoikie i Negoryuchie Volokna (Thermostable, Heat-Resistant and Non-Combustible Fibres) (Moscow: Khimiya, 1978) p.422 9. M G Dobb, J E McIntyre Adv. Polym. Sci. 60/61 61 (1984) 10. A V Volokhina,G I Kudryavtsev, in Zhidkokristallicheskie Polimery (Mesomorphic Polymers) (Ed. N A Plate) (Moscow: Khimiya, 1988) p. 37 11. BRD P. 1 929 713A; Chem. Abstr. 72 122 796 (1970) 12. J Preston, in Encyclopedia of Polymer Science and Engineering Vol. 11 (Eds H F Mark, NMBikales, C G Overberger, G Menges) (New York: Wiley, 1988) p. 381 13. J P Critchley Angew. Makromol. Chem. B109/110 41 (1982) 14. J F Wolfe, in International Symposium on Materials. Approaches to Property Limits in Polymers, Princeton, 1986 p. 12 15. V N Odnoralova, in Itogi Nauki i Tekhniki. Khimiya i Tekhnologiya Vysokomolekulyarnykh Soedinenii [The Chemistry and Technology of High-Molecular Compounds (Advances in Sciences and Engineering Series)] (Moscow: Izd.VINITI, 1988) Vol. 25, p. 85 16. Y Imai Bull. Jpn. Inst. Met. 25 772 (1986) 17. J P Critchley Prog. Polym. Sci. 2 51 (1970) 18. F E Arnold Jr , F E Arnold Adv. Polym. Sci. 117 257 (1994) 19. A A Izyneev, M M Teplyakov, V G Samsonova, A D Maksimov Usp. Khim. 36 2090 (1967) [Russ. Chem. Rev. 36 912 (1967)] 20. V V Korshak, M M Teplyakov J. Macromol. Sci., Rev. Macromol. Chem. 5 409 (1971) 21. C S Marvel J. Macromol. Sci., Rev. Macromol. Chem. 13C 219 (1975) 22. V V Korshak, G V Kazakova, A L Rusanov Vysokomol. Soedin., Ser. A 31 5 (1989) a 23. E S Krongauz, A L Rusanov, T L Renard Usp. Khim. 39 1591 (1970) [Russ. Chem. Rev. 39 747 (1970)] N S S N x Me O Me N S N S N S x Me 38 HO2C OPh y Me O y CO O 24.N Yoda,M Kurihara J. Polym. Sci., Part D, Macromol. Rev. 5 109 (1971) 25. N Yoda,M Kurihara, M Dokoshi Prog. Polym. Sci. Jpn. 4 1 (1972) 26. R F Kovar, F E Arnold J. Polym. Sci., Polym. Chem. Ed. 14 2807 (1976) 27. J F Wolfe, F E Arnold Macromolecules 14 909 (1981) 28. J F Wolfe, B H Loo, F E Arnold Macromolecules 14 915 (1981) 29. S R Allen, A G Filippov, R J Farris, E L Thomas, C-P Wong, G C Berry, E C Chenevey Macromolecules 14 1135 (1981) 30. US P. 4 606 875; Chem. Abstr. 106 6348 (1987) 31. L Feldman, R J Farris, E L Thomas J. Mater. Sci. 20 2719 (1985) 32. A W Chow, J F Somdell, J F Wolfe Polymer 29 1307 (1987) 33. J F Wolf, in Encyclopedia of Polymer Science and Engineering Vol.11 (Eds H F Mark, NMBikales, C G Overberger, G Menges) (New York: Wiley, 1988) p. 601 34. WO PCT 8 401 160; Chem. Abstr. 101 56 435 (1984) 35. US P. 4 533 724; Chem. Abstr. 101 131 731 (1984) 36. E W Choe, S N Kim Macromolecules 14 920 (1981) 37. S A Jenekhe, P O Johnson Macromolecules 23 4419 (1990) 38. V N Tsvetkov Zhestkotsepnye Polimernye Molekuly (Rigid-Rod Polymer Molecules) (Leningrad: Nauka 1986) 39. A E Zachariadis, R E Porter (Eds) High Modulus Polymers � Approaches to Design and Development (New York: Marcel Dekker, 1987) p. 523 40. A Feldblum, Y W Park, A J Heeger, A G MacDiarmid, G Wnek, F E Karasz, J C W Chien J. Polym. Sci., Polym. Phys. Ed. 19 173 (1981) 41. S-G Chu, S Venkatraman, G C Berry, Y Einaga Macromolecules 14 939 (1981) 42.M Lipovics Chem. Eng. 91 147 (1984) 43. Mater. Eng. 103 39 (1986) 44. S J Krause, T B Haddock, D L Vezie, P G Lenhert, W F Hwang, G E Price, T E Helminiak, J F O'Brien,W W Adams Polymer 29 1354 (1988) 45. Y-H So, J P Heeschen, B Bell, P Bonk, M Briggs, R De Caire Macromolecules 31 5229 (1998) 46. US P. 4 225 700; Chem. Abstr. 94 4410 (1980) 47. M Dotrong, R C Tomlinson, M Sinsky, R C Evers Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 (1) 85 (1991) 48. J H Promislov, E T Samulski, J Preston Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 (2) 211 (1991) 49. JHPromislov, J Preston,E T Samulski Macromolecules 26 1793 (1993) 50. M Dotrong, R C Evers J. Polym. Sci., Part A, Polym.Chem. 28 3241 (1990) 51. TDDong, TGArchibald,AAMalik, FOBonsu,KBaum, L S Tan, F E Arnold Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 (1) 199 (1991) 52. M Dotrong, M H Dotrong, G J Moore, R C Evers Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 32 (1) 201 (1991) 89 Scheme 6 nL G Komarova, A L Rusanov 90 53. M Dotrong, M H Dotrong, C S Wang, H Song, G J Moore, R C Evers J. Polym. Sci., Part A, Polym. Chem. 32 2953 (1994) 54. Sze Chit Yu, Xiong Gong, Wai Kin Chan Macromolecules 31 5639 (1998) 55. D S Tugushi, V V Korshak, A L Rusanov, V G Danilov, G M Cherkasova, G M Tseitlin Vysokomol. Soedin., Ser. A 15 969 95. M Dotrong, M H Dotrong, R C Evers Polymer 34 726 (1993) 96. M Dotrong, M H Dotrong, R C Evers Polym.Mater. Sci. Eng. 65 38 (1991) 97. M Dotrong, M H Dotrong, R C Evers Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 33 477 (1992) 98. U M Vakil, C S Wang, C Y-C Lee,M H Dotrong,M Dotrong, R C Evers Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 33 (1) 479 (1992) 99. T-t Tsai, F E Arnold Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 29 (2) 324 (1988) 100. H H Chuah, T-t Tsai, K H Wei, C S Wang, F E Arnold Polym. Mater. Sci. Eng. 60 517 (1989) 101. W Sweeny J. Polym. Sci., Part A, Polym. Chem. 30 1111 (1992) (1973) a 56. V V Korshak, A L Rusanov, D S Tugushi, G M Cherkasova Macromolecules 5 807 (1972) 57. V V Korshak, A L Rusanov Usp. Khim. 52 812 (1983) [Russ. Chem. Rev. 52 459 (1983)] 58. T-t Tsai, F E Arnold Polym.Prepr. Am. Chem. Soc., Div. Polym. Chem. 27 (2) 221 (1986) 59. US Appl. 84 784; Chem. Abstr. 109 171 065 (1988) a�Polym. Sci. (Engl. Transl.) 60. US Appl. 85 094; Chem. Abstr. 109 171 120 (1988) 61. T-t Tsai, F E Arnold High Perform. Polym. 3 179 (1989) 62. J Burkett, F E Arnold Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 28 (2) 278 (1987) 63. F E Arnold Mater. Res. Soc. Symp. Proc. 134 117 (1989) 64. C S Wang, J Burkett, S Bhattacharya, H-H Chuah, F E Arnold Polym. Mater. Sci. Eng. 60 767 (1989) 65. US P. 4 762 908; Chem. Abstr. 106 85 274 (1987) 66. H R Kricheldorf, J Engelhardt Makromol. Chem. B, Makromol. Chem. Phys. 190 2939 (1989) 67. BRD P. 3 940 792; Chem. Abstr. 115 208 889 (1991) 68. H R Kricheldorf, in Silicon in Polymer Chemistry (Ed.H R Kricheldorf) (Berlin: Springer, 1996) p. 321 69. H R Kricheldorf, J Engelhardt Makromol. Chem. B, Makromol. Chem. Phys. 191 2017 (1990) 70. H R Kricheldorf, A Domschke Polymer 35 198 (1994) 71. Y Imai, Y Oishi Prog. Polym. Sci. 14 173 (1989) 72. A L Rusanov Usp. Khim. 59 1492 (1990) [Russ. Chem. Rev. 59 868 (1990)] 73. R D Katsarava, Ya S Vygodskii Usp. Khim. 61 1142 (1992) [Russ. Chem. Rev. 61 629 (1992)] 74. H R Kricheldorf, in Silicon in Polymer Chemistry (Ed. H R Kricheldorf) (Berlin: Springer, 1996) p. 288 75. K Kimura, D L Meurer, R F Hutzler, P E Cassidy, J W Fitch Macromolecules 27 1303 (1994) 76. S Jenkins, K I Jacob,M B Polk, S Kumar, T D Dang, F E Arnold Macromolecules 33 8731 (2000) 77. W F Hwang, C L Benner, D R Wiff, T E Helminiak J. Macromol. Sci. Phys. B22 231 (1983) 78. W F Hwang, C L Benner, D R Wiff, T E Helminiak, in Proceedings of the 28th IUPAC Macromolecular Symposium, Dayton, 1982 B27 79. W F Hwang,D R Wiff, C Verschoore Polym. Eng. Sci. 23 789 (1983) 80. Y Imai, I Taoka, K Uno, Y Iwakura Makromol. Chem. B, Makromol. Chem. Phys. 83 167 (1965) 81. A W Chow, S P Bitler, P E Penwell, D J Osborn, J F Wolfe Macromolecules 22 3514 (1989) 82. S J Krause, T B Haddock, G E Price, P G Lenhert, J F O'Brien, T E Helminiak,W W Adams J. Polym. Sci., Part B, Polym. Phys. 24 1991 (1986) 83. MWellman, GHusman, AKKulshreshta, T E Helminiak,DR Wiff, C L Benner,W F Hwang Org. Coat. Plast. Chem. 43 783 (1980) 84. T Kyu, T E Helminiak Polymer 28 2810 (1987) 85. C S Wang, I J Goldfarb, T E Helminiak Polymer 29 825 (1988) 86. W F Hwang, D R Wiff, C Verschoore, G E Price, T E Helminiak, W W Adams Polym. Eng. Sci. 23 784 (1983) 87. C A Gabriel, R J Farris,M F Malone, in Nonwavence Conference, New York, 1986 p. 255 88. T-t Tsai, F E Arnold, W F Hwang J. Polym. Sci., Part A, Polym. Chem. 27 2839 (1989) 89. K L Cooper, F E Arnold Polym. Prepr. Am. Chem. Soc., Div. Polym. Chem. 33 (1) 1006 (1992) 90. US P. 5 008 346; Chem. Abstr. 115 115 354 (1991) 91. R C Evers, T D Dang D Moore Polym. Prepr. (Am. Chem. Soc., 92. R C Evers, T D Dang, D R Moore J. Polym. Sci., Part A, Polym. 93. S J Bai, M Dotrong, E J Soloski, R C Evers J. Polym. Sci., Part B, 94. M Dotrong, M H Dotrong, S J Bai, R C Evers Sci. Adv. Mater. Div. Polym. Chem.) 29 (1) 244 (1988) Chem. 29 121 (1991) Polym. Phys. 29 119 (1991) Proc. Eng. Tech. Symp. Ser. 37 1004 (1

ISSN:0036-021X    

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年代:2001

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