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Russian Chemical Reviews 69 (6) 461 ± 480 (2000) Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment Yu V Tomilov, I V Kostyuchenko, OMNefedov Contents I. Introduction II. The formation of nitrogen-containing heterocyclic systems from compounds with a cyclopropane fragment III. Formation of a cyclopropane ring spiro-fused with a heterocycle IV. Functionalisation of heterocyclic compounds containing a spirocyclopropane fragment V. Conclusion Abstract. and synthesis of methods the on data published The The published data on the methods of synthesis and chemical transformations of nitrogenous heterocyclic compounds chemical transformations of nitrogenous heterocyclic compounds spiro-fused with a cyclopropane fragment are described system- spiro-fused with a cyclopropane fragment are described system- atically and generalised.The bibliography includes 146 references atically and generalised. The bibliography includes 146 references. I. Introduction Synthesis and studies of the properties of highly strained carbo- cyclic compounds, including those incorporating a cyclopropane ring, is a field of organic chemistry which is developing most intensely. Today, many methods for the synthesis of cyclopro- panes are known; their chemical transformations have been studied, and diverse spheres of practical use of these compounds have been found by now. The introduction of a spiro-fused cyclopropane fragment in a heterocyclic molecule changes the reactivity of the heterocycle.The high strain of the three-carbon ring predetermines is ability to undergo facile opening with a change in the spiro-carbon atom hybridisation from sp3 to sp2. Since heterocyclic compounds (including mono- and polynitro- gen-containing ones) find use as medicines and as chemical means for plant and animal protection, synthesis of their analogues with a spirocyclopropane fragment is interesting both from the theo- retical viewpoint and for the preparation of new biologically active compounds, in particular, potential pharmaceuticals. Synthesis of heterocycles containing a spiro cyclopropane fragment involves either the formation of a heterocyclic structure from compounds that already possess a three-carbon ring or the formation of a cyclopropane ring in structures incorporating the required heterocycle. The first approach is primarily based on various [3+2]- and [4+2]-cycloaddition reactions that can be carried out using either cyclopropane-containing dipolarophiles (dienophiles), e.g., methylidenecyclopropanes, or nitrogen-con- taining 1,3-dipoles or dienes in which one atom of the cyclo- propane ring is involved in the reactive fragment.Diazocyclopropane generated in situ, which readily reacts with Yu V Tomilov,OMNefedovNDZelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky prosp. 47, 117913 Moscow, Russian Federation. Fax (7-095) 135 63 90. E-mail: tom@cacr.ioc.ac.ru (Yu V Tomilov) I V Kostyuchenko Institute for Problems of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow Region, Russian Federation.Fax (7-096) 515 35 88 Received 11 January 2000 Uspekhi Khimii 69 (6) 507 ± 527 (2000); translated by S S Veselyi #2000 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2000v069n06ABEH000571 461 461 471 476 478 certain unsaturated compounds to give spiro[cyclopropanedihy- dropyrazoles], is a promising building block of the latter type. The second approach is based on the addition of aliphatic diazo compounds to the activated exocyclic double bond in a heterocycle followed by dedinitrogenation of the resulting dihy- dropyrazoles, as well as on the addition of carbenes or ylides to methylidene-substituted heterocycles.This review is a first attempt at generalisation of the published data on the synthesis and some chemical transformations of heterocyclic compounds incorporating a spirocyclopropane frag- ment and at least one nitrogen atom in the ring. The presented material is mostly arranged according to the class of the key compounds used for the construction of the spirocyclopropane- containing azaheterocycles. The structures in which the cyclo- propane fragment is not spiro-fused directly with the azahetero- cycle are not considered. II. The formation of nitrogen-containing heterocyclic systems from compounds with a cyclopropane fragment 1. Cycloaddition involving diazocyclopropane Diazocyclopropane (1) is a promising compound for the synthesis of compounds incorporating a spiro-fused cyclopropane fragment which are difficult to access.1± 4 Generally, diazocyclopropane (1) is generated by decomposition of N-cyclopropyl-N-nitrosourea (2a) 1, 4 or N-cyclopropyl-N-nitrosocarbamate (2b) 2, 3 on treat- ment with strong bases, by analogy with the synthesis of aliphatic diazo compounds.5 Unlike the majority of the known aliphatic and cyclic diazo compounds, both diazocyclopropane (1) and all of its derivatives mentioned in the literature 6±9 are quite unstable compounds which have not been detected in individual form.Nevertheless, the formation of diazocyclopropanes in situ follows from the methods used for their generation and chemical trapping. For example, its reactions with unsaturated compounds result in 1,3-dipolar cycloaddition products, viz., the corresponding spi- ro[cyclopropane-4,5-dihydro-3H-pyrazoles]. MeONa NCOY N2 1 2a,b NO Y=NH2 (a), OEt (b).The reaction of diazocyclopropane (1) with oxosteroids 2, 3 should be noted as one of the first examples of the trapping of compound 1 with unsaturated compounds. For example, diazo-462 cyclopropane (1) generated in situ undergoes selective addition to the D16 bond of the diene 3 to give dihydropyrazole 4. The reaction of an excess of the diazo compound 1 with the carbonyl group of the adduct 4 results in oxaspiropentane 5. Thermolysis 2 of the dihydropyrazole 4 isolated in individual form, as in the case of similar dihydropyrazoles obtained by the addition of other diazoalkanes,10 occurs non-selectively: in addition to the usual reaction product, viz., the spiropentane derivative 6, the b-sub- stituted a,b-enone 7 is formed (the ratio 6 : 7 is 3.5 : 1).O 2b, KOH 710 8C 3 AcO ON N + 4 (63%) O O D 4 + 7 6 It should be noted that the reaction of diazocyclopropane (1) with the cyclohexenone fragment of steroids under the same conditions occurs in a different way.3 For example, the reaction of compound 8 gives not only the expected addition product to the D16 bond, i.e., the adduct 9, but also compound 10 due to the six- membered ring expansion, which is similar to homologisation of cyclic ketones on treatment with diazomethane.11 Cyclobutanone 11 formed upon formal addition of cyclopropylidene to the carbonyl group of the cycloheptane fragment of compound 10 3 was identified as a minor product. O 2b, KOH, MeOH 710 8C 8 O O N N +O O 9 (25%) O N N O + 11 (2% ± 7%) Although diazocyclopropane (1) can in principle be trapped by alkenes to give spiro[cyclopropanedihydropyrazoles], this reaction did not find synthetic application for a long time, primarily because the nature of unsaturated substrates which can enter into 1,3-dipolar cycloaddition with compound 1 was not O N N 5 (15%) O N N + 10 (19%) Yu V Tomilov, I V Kostyuchenko, OMNefedov determined with certainty.In fact, there are several examples where generation of diazocyclopropane (1) in the presence of unsaturated compounds, such as cyclohexa-1,4-diene,12 bicyclo- propylidene,13 or cycloalkyl-substituted bicyclopropyl- idenes,14 ± 16 resulted in spirane hydrocarbons rather than dihydropyrazoles which were formed due to [1+2]-cycloaddition of cyclopropylidene to these compounds.Generation of diazo- cyclopropane from compounds 2a,b can produce, in addition to cyclopropylidene, other unstable species. The pathways of trans- formation of cyclopropylnitrosourea 2a and cyclopropylnitro- soureas substituted at the cyclopropane ring on treatment with reagents of different basicity and nucleophilicity were studied in a series of works by Kirmse et al.1, 17 ± 27 It was assumed that their reactions give rise to cyclopropyldiazonium salts, as well as cyclopropyl and allyl cations due to the dedinitrogenation of these salts.+ a + + N N 7N2 7H+ H+ 2a,b b N2 H2C C CH2 7N2 1 (a) weak base; (b) strong base. Systematic studies of 1,3-dipolar cycloaddition of diazocyclo- propane (1) to alkenes, first of all a systematic search for efficient traps for compound 1 to give spiro[cyclopropanedihydropyr- azoles], date back to the beginning of the 1990s. It was found that reactions of diazocyclopropane (1), generated in situ on treatment of cyclopropylnitrosourea (2a) with sodium methoxide, with norbornene 4 and other compounds containing the bi- cyclo[2.2.1]heptene fragment 28 mostly result in spiro[cyclopropa- nedihydropyrazoles] of the types 12 and 13, exclusively as exo- isomers.Good yields (50% ± 70%) are achieved if a molar excess as low as 1.5-fold of the unsaturated substrate with respect to cyclopropylnitrosourea (2a) is used. NN 12 (55% ± 60%) 1 NCONH2 MeONa, MeOH, CH2Cl2 710 to730 8C 2a NO NN 13 (45% ± 50%) The asymmetrically substituted hydrocarbon 14 gives a mix- ture of isomeric spiro[cyclopropanedihydropyrazoles] 15a and 15b due to the different approach of diazocyclopropane to the double bond; their ratio was *1 : 1 and the overall yield was 55%± 58%. The polycyclic diene 16 reacts with diazocyclopro- pane (1) in a similar way.28 Despite the steric hindrance created by the spirocyclopropane fragment in the norbornene moiety, dihy- dropyrazoles 17a and 17b (in a ratio *1.4 : 1) are also formed exclusively as exo-isomers, although their overall yield (23%) is markedly lower than that of norbornene unsaturated at position 7.It should be noted that this reaction did not give any addition products of diazocyclopropane (1) (or cyclopropylidene) to the cyclopentene double bond. N Me Me Me N 1 N + N 14 15a 15bSynthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment N N N N 1 + 16 17b 17a The reaction of norbornadiene with diazocyclopropane (1) generated in situ also occurs as 1,3-dipolar cycloaddition, although less selectively, and results in a mixture of isomeric mono- (18) and bisadducts (19) in 32%± 35% and 35% ±38% yields, respectively.4 N N 1 + + N N 710 to720 8C endo-18 exo-18 N N N N + + N+ N N N anti,exo,exo-19 syn,exo,exo-19 N N N N + + N N N N anti,exo,endo-19 syn,exo,endo-19 Unlike the adducts 12, 13, 15 and 17, monospiro[cyclopro- panedihydropyrazoles] 18 are a mixture of exo- and endo-isomers in the ratio*4 : 1, while the bisadducts 19 formed from them are a mixture of four isomers in the ratio *10 : 7 : 1.3 : 1.Although a two-fold excess of norbornadiene is used, bisadducts 19 are formed in an even greater quantity than monoadducts 18; the addition of the second diazocyclopropane molecule to monoad- ducts 18 occurs exclusively at the exo position. Benzvalene and 3,3-disubstituted cyclopropenes are also effi- cient trapping agents for diazocyclopropane (1).4, 28, 29 N 1 N (60%) R N R 1 N R R (62% ± 70%) R=Me; R±R=(CH2)3. The reaction of diazocyclopropane (1) with alkynylcyclopro- pene 20 results in regioisomeric dihydropyrazoles 21a and 21b in the ratio*3 : 1; this reaction does not involve the triple bond.29 Me Me Ph Ph N Me Me 1 N N Me Me + N C Ph C C CPh CPh CPh 21b 21a 20 1,3-Dipolar cycloaddition products are formed in reactions of diazocyclopropane (1) with methyl cyclopropenecarboxylates 22 and 23.28, 29 The regioselectivity is low in the case of the cyclo- propene 23.Me Me COOMe MeOOC 22 COOMe 1 MeOOC 23 Me In the synthesis of dihydropyrazoles from cyclopropenes 20 and 22, alternate addition of cyclopropylnitrosourea (2a) and the corresponding cyclopropene to a suspension of MeONa in a MeOH± ether mixture at 720 to 730 8C was found to be the method of choice.29 It should be noted that the majority of the resulting polycyclic spiro[cyclopropanedihydropyrazoles] possess rather high thermal stability.30 For example, dihydropyrazoles 12 and 13 are stable when heated to 200 8C.In the gas phase at 410 ± 450 8C, they undergo dedinitrogenation to give a mixture of strained hydro- carbons, viz., spiro[tricyclo[3.2.1.02,4]octane-1,30-cyclopropane] (24) or spiro[pentacyclo[4.4.0.02,8.03,5.07,9]decane-4,10-cyclopro- pane] (25), as well as isomeric compounds 26 or 27 containing a fused cyclobutane fragment (overall yield 30% ± 70%). An increase in temperature favours the isomerisation of the spirane hydrocarbons 24 and 25 to the corresponding unsaturated com- pounds 26 and 27. 12 410 ± 455 8C 7N2 24 13 410 ± 450 8C 7N2 25 The unsaturated 4,5-dihydro-3H-pyrazole 18 obtained by the addition of diazocyclopropane (1) to norbornadiene eliminates cyclopentadiene instead of N2 on thermolysis to give 3(5)-vinyl- pyrazole (28).30 340 ± 370 8C 18 NN 7 In addition to strained cyclic unsaturated compounds, con- jugated aliphatic dienes such as buta-1,3-diene can also play the role of trapping agents for diazocyclopropane (1).28 At 725 8C, 6-vinyl-4,5-diazaspiro[2.4]hept-4-ene (29) is formed as the major product; unlike polycyclic dihydropyrazoles, it readily undergoes polymerisation to give a rubber-like substance.The reaction of diazocyclopropane (1) with 2-methylbuta-1,3-diene also occurs as 1,3-dipolar addition, but 6-isopropylidene-4,5-diazaspiro[2.4]- hept-4-ene (31) rather than 5-isopropenyldihydropyrazole 30 is formed in this case as the main reaction product. Apparently, the addition of diazocyclopropane occurs mostly to the unsubstituted 463 Me Me COOMe MeOOC 1 N N (48%) H H N N N +MeOOC N Me Me (*16%) (*30%) + + endo-26 exo-26 + + endo-27 exo-27 N H N 28 (75%)464 double bond, while the resulting dihydropyrazole 30 undergoes isomerisation under the reaction conditions.28 1, CH2Cl2 725 8C N N 29 (42%) Me Me Me 1, CH2Cl2 *H Me H 720 8C N N 31 (32%) N N 30 It is well known that the reactivity of alkenes with respect to diazomethane and other aliphatic diazo compounds in 1,3-dipolar cycloaddition reactions is largely determined by the nature of the double bonds and that the reaction accelerates upon introduction of electron-withdrawing substituents.31 Successful 1,3-dipolar cycloaddition in the case of low-activity alkenes is usually pro- vided by keeping the reaction mixture for a long time.This technique cannot be employed in reactions with diazocyclopro- pane because of its instability, which undoubtedly decreases the number of potential unsaturated partners of this reaction. It has recently been established that styrene 32 and vinyl bromide 33 are rather good trapping agents for diazocyclopropane (1) generated in situ.33 1,3-Dipolar cycloadditions involving these alkenes occur regioselectively to give 5-phenyl- (32a) and 5-bromospiro[cyclo- propane-1,30-dihydropyrazoles] (32b), respectively.However, unlike the majority of spiro[cyclopropanedihydropyrazoles] con- sidered above, including compound 32a, bromodihydropyrazole 32b is unstable and undergoes partial resinification and partial transformation to 3(5)-(2-bromoethyl)pyrazole (33) upon storage in an inert atmosphere at 15 8C for 8 ± 10 days.33 The reaction of the compound 32b with MeONa in MeOH at 25 8C for 2 h results in a mixture of 3(5)-(2-methoxyethyl)- (34) and 3(5)-vinylpyra- zoles (28) [overall yield*80%, ratio (3 ± 4) : 1].33 R R CH2Cl2 N2+ H 720 to730 8C H N N 32a,b R=Ph (a, 67%), Br (b, 60%).8 ± 10 days Br N N 32b H 33 (55% ± 60%) MeONa, MeOH +28 OMe N N 34 H It should be noted that the reaction of diazomethane with vinyl bromide in ether readily results in pyrazole hydrobromide due to the facile dehydrobromination of the bromodihydropyr- azole formed initially.34 Thus, the spirocyclopropane moiety in the compound 32b reduces the ability of the heterocyclic fragment to undergo deprotonation. Acrylic acid derivatives are good substrates for reactions involving diazocyclopropane (1); for example, the addition of cyclopropylnitrosourea (2a) to a mixture of methyl methacrylate and sodium methoxide (ratio 1 : 1.5 : 1.5) affords dihydropyrazole 35 in a yield up to 70%.35 COOMe COOMe 2a, MeONa 725 to730 8C Me Me N N 35 (*70%) Yu V Tomilov, I V Kostyuchenko, OMNefedov Diazocyclopropane (1) reacts with acrylonitrile and methyl acrylate with equal efficiency.However, in this case the composi- tion of the reaction products depends on the conditions and the reagent ratio.36 In particular, generation of diazocyclopropane (1) by the addition of cyclopropylnitrosourea (2a) to a mixture of an unsaturated compound and MeONa in a solvent was found to be unacceptable due to a side reaction of methanol addition to the electron-deficient double bond of acrylonitrile or methyl acrylate. The side reaction can be inhibited almost completely by changing the order of addition of the reagents.36 At the ratio 2a : acrylate *1 : 1, the expected spiro[cyclopropane-1,50-4,5-dihydro-1H- pyrazoles] 36a,b are formed as the main reaction products (yields *70%).36 R R *H 2a, MeONa,MeOH, CH2Cl2 725 to715 8C H N N H R HN N 36a,b R=CN (a, 70%), COOMe (b, 69%).It was shown later 37 that the synthesis of dihydropyrazole 36a can be carried out with equal success with the use of K2CO3 instead of MeONa, but in this case complete decomposition of cyclopropylnitrosourea (2a) at 0±5 8C takes as long as 1 ± 2 h. Dihydropyrazoles 36a,b (especially 36b) are rather labile compounds which undergo partial decomposition even under the conditions of preparative TLC. An increase in the amount of acrylonitrile or methyl acrylate to 2 ± 2.5 equiv. with respect to cyclopropylnitrosourea decreases the fraction of dihydropyrazoles 36a,b to *15% and results in new reaction products, viz., functionally substituted dihydropyr- azoles 37a,b, which, as shown in special experiments,36 ± 38 are formed upon reaction of dihydropyrazoles 36a,b with the excess of unsaturated substrates.The generation of the anions 38a,b is probably the driving force of the observed transformations. This procedure makes it possible to obtain spiro[cyclopropanedihy- dropyrazoles] containing functional substituents in the side chain and in the dihydropyrazole ring (see Section III). R R R 7 H R MeONa, CH2Cl2 725 to715 8C HN N 36a,b R N N 37a,b N N 38a,b R=CN (a, 84%), COOMe (b, 80%). Diazocyclopropane (1) undergoes regioselective addition to trans-b-nitrostyrene (39) to give 3- nitro-4-phenylspiro[cyclopro- pane-1,50-4,5-dihydro-1H-pyrazole] (40).37 Ph H NO2 Ph NO2 2a, K2CO3, CH2Cl2 0± 5 8C 39 HN N 40 (45%) 1,3-Dipolar cycloaddition of diazocyclopropane (1) to phenyl vinyl sulfide,38 divinyl ether 37 and methylidenecyclopropane 4 occurs with low efficiency (the yields of dihydropyrazoles are 5%, 13% and 12%, respectively).The reaction with methylidene- cyclopropane gave a mixture of two regioisomers 41a,b in the ratio *3 : 1; in addition to dihydropyrazoles, the reaction of cyclo- propylidene with methylidenecyclopropane also gave dispi- ro[2.0.2.1]heptane (42). As it could be expected, cyclopropyl methyl ether and allene were the main side products of decom- position of cyclopropylnitrosourea (2a).4Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment 2a, MeONa, MeOH 725 8C + + N N 41b (3%) N N 41a (9%) 42 (10%) 2.Cycloaddition involving substituted diazocyclopropanes Along with the cycloaddition of diazocyclopropane (1) generated in situ to the unsaturated compounds considered above, there are examples of [3+2]-cycloaddition of substituted diazocyclopro- panes to activated C=C bonds. For example, in the beginning of the 1960s, American authors obtained N-(2,2-diphenylcyclo- propyl)-N-nitrosourea (43) and studied its decomposition in the presence of bases or on heating.7, 39, 40 On treatment with lithium ethoxide in saturated hydrocarbons, nitrosourea 43 is decom- posed with evolution of N2 but without the yellow coloration typical of diazo compounds; this reaction gives 1,1-diphenylallene (44) in high yield.In the presence of diethyl fumarate, the corresponding dihydropyrazole 45 is formed upon 1,3-dipolar cycloaddition of 2,2-diphenyldiazocyclopropane (46) to the dou- ble bond.7Ph Ph Ph Ph EtOLi NCONH2 N2 46 43 NO Ph C CH2 7N2 Ph 44 (>90%) COOEt Ph Ph COOEt COOEt EtOOC HN N 45 (47%) Thermal decomposition (60 ± 82 8C) of nitrosourea 43 in heptane or in an excess of diethyl fumarate results in the same compounds 44 and 45 (yields 95% and 44%, respectively);40 this is untypical of other N-alkyl-N-nitrosamides. The reaction of 2,2-dimethyl- and 2,2-dichlorodiazocyclopro- panes, generated in situ from the corresponding N-nitroso-N- cyclopropylureas 47a,b, with a reactive dipolarophile, viz., 3,3- dimethylcyclopropene, was studied.8 In both cases, a mixture of two isomeric dihydropyrazoles was formed in *70% yield; the ratio of the anti and syn isomers was 2.2 : 1 for compound 48a and 1 : 1.3 for compound 48b.R R Me NCONH2+ MeONa, MeOH 710 8C Me 47a,b NO Me Me R Me N R Me N + N N syn-48a,b R R anti-48a,b R=Me (a), Cl (b). Generation of substituted diazocyclopropanes from substi- tutedN-nitroso-N-cyclopropylureas is a promising method for the synthesis of nitrogenous heterocycles containing a polyspiran 465 fragment. It has been shown recently 9, 41, 42 that diazospiropen- tane (49) generated in situ from N-nitroso-N-spiropentylurea (50) reacts with 3,3-dimethylcyclopropene or methyl methacrylate to give 4,5-dihydro-3H-pyrazoles 51a,b or 52a,b fused with the spiropentane fragment (as mixtures of isomers in the ratio*1 : 1).N2 MeONa, MeOH NCONH2 750 8C 49 50 ON Me Me Me Me Me Me + N N N 51b N 51a Me Me CO2Me CO2Me Me CO2Me + N N 52b N N 52a The yields of the 1,3-dipolar cycloaddition products 51 and 52 increase considerably with a decrease in the temperature of the reaction. For example, the yield of dihydropyrazoles 52 is*20% at 720 8C and increases to 72% at 750 8C.9 Evidently, diazo- spiropentane (49) is even less stable than diazocyclopropane (1).Unlike strained cycloalkenes or alkenes with electron-with- drawing substituents, bicyclopropylidene (53) reacts with diazo- cyclopropanes generated in situ to give polyspirocyclopropane- containing hydrocarbons, in particular, triangulans 54 ± 56, instead of dihydropyrazoles ([3+2]-cycloaddition prod- ucts).13 ± 16, 43 Evidently, diazocyclopropanes cannot react with bicyclopropylidene (53) according to 1,3-dipolar cycloaddition due to a specific nature of the double bond in this compound, which manifests itself, in particular, in a noticeable shortening of this bond;44 these compounds undergo dedinitrogenation to give the corresponding cyclopropylidenes 57 ± 59, which are mostly isomerised into allenes. The reaction of cyclopropylidenes 57 ± 59 with the original bicyclopropylidene (53) occurs as [1+2]-cyclo- addition to give triangulans 54 ± 56.53 MeONa NCONH2 57 2a NO 54 (30%) 53 MeONa NCONH2 NO 58 + C 55 (23%) 53 MeONa NCONH2 NO 59466 C + (27%) 56 (14%) Diazocyclopropane and cyclopropylidene do not react with alkynes, such as PhC:CH, MeO2CC:CCO2Me and HC:CC(Me)=CH2.29, 37 3. Cycloaddition to methylidenecyclopropane and its derivatives Syntheses of spirocyclopropane-containing azaheterocycles make use of cycloaddition of nitrogen-containing 1,3-dipoles to methylidenecyclopropane and its derivatives with substituents both in the cyclopropane ring and at the double bond. For example, the reaction of diazomethane with methylidene- cyclopropane at 3 8C for two weeks results in a mixture of two regioisomeric dihydropyrazoles 60a,b (overall yield 90%, ratio 55 : 45).45 The addition of diazomethane and 3-diazoprop-1-ene to 2,2-difluoromethylidenecyclopropane also occurs non-selectively; a mixture of three regioisomeric 4,5-dihydro-1H-pyrazoles 61a ± c (*3.7 : 1 : 1) is formed in the latter case.46 + +CH2N2 N N 60b N N 60a F F + CHN2 F F F F F F N NH + + NH N HN N 61a 61b 61c Phenyl azide slowly adds to methylidene- (62a), benzylidene- (62b) or (diphenylmethylidene)cyclopropane (62c) to give the thermally stable spiro[dihydrotriazolecyclopropanes] 63a ± c.It is assumed 47, 48 that the reaction occurs through a concerted mech- anism with the addition of the terminal nitrogen atom of phenyl azide to the tetrasubstituted carbon atom of the cyclopropane ring.Photolytic dedinitrogenation of 4,5-dihydro-1H-1,2,3-tri- azoles 63a ± c (Pyrex, high-pressure mercury lamp) affords new azaheterocycles 64a ± c, which are derivatives of 1-phenylaza- spiropentane (yields 90%, 99% and 90%, respectively).47, 48 R2 R1 R2 R1 R1 PhN3 NPh hn 7N2 NPh R2 N N 63a ± c 64a ± c 62a ± c R2 Compound R1 T t Yield of 63 (%) /days /8C a H H 70 ± 80 70 ± 80 38 51 6011 ± 2 1 ± 2 20 50 100 100 bc Ph Ph HPh Apparently, the azaspiropentane fragment can also be formed upon direct addition of nitrenes to the double bond of methyl- idenecyclopropanes. At least, this is how the photochemical reaction of methyl azidoformate with methylidenecyclopropane Yu V Tomilov, I V Kostyuchenko, OMNefedov to give 1-(methoxycarbonyl)azaspiropentane (65) is believed to occur.48 N3COOMe NCOOMe hn, 3 h 7N2 NCOOMe 65 (35%) Unlike phenyl azide, cyanogen azide and p-nitrobenzenesul- fonyl azide do not give any stable dihydrotriazoles in reactions with cyclopropylidenecycloalkanes: they readily undergo dedi- nitrogenation. The addition of cyanogen azide to cyclopropyl- idenecyclohexane (*20 8C, 7 days) probably occurs non- regioselectively, since hydrolysis of the reaction mixture gives spiro[2.6]nonan-4-one and spiro[3.5]-nonan-1-one (yields 46% and 30%, respectively).49 The reactions of p-nitrobenzenesulfonyl azide with cyclopropylidenepolyspiroalkanes 66 occur regioselec- tively via dihydrotriazoles 67 which readily undergo dedinitro- genation with simultaneous ring expansion to give imides 68.50 ± 52 N NNSO2C6H4NO2-p p-NO2C6H4SO2N3 7N2 60 8C, 2 ± 6 days m m 67a ± c 66a ± c NSO2C6H4NO2-p m+1 68a ± c (73% ± 87%) m = 0 (a), 1 (b), 2 (c).Similarly, diazocyclopropane (1) probably adds to the imide 68a via an unstable dihydrotriazole, which is transformed into the imide 68b.52 Diverse heterocyclic compounds containing a spirocyclopro- pane fragment are obtained by treatment of methylidenecyclo- propanes with dihydrotriazoledione 69; the reaction pathway depends considerably on the nature of the substituents at the cyclopropane ring. In particular, [2+2]-cycloaddition of trans- 2,3-dimethyl-1-methylidenecyclopropane to dihydrotriazoledione 69 at room temperature to give the adduct 70 occurs slowly.53 Me O Me N 25 8C, 36 h N O NPh + N N Me Me O NPh 70 69 O With benzylidenecyclopropane, dihydrotriazoledione 69 reacts much faster.However, in this case compound 71 formed in the first step, i.e., a product of formal [4+2]-cycloaddition involving the benzene ring of the substituent, contains a cyclo- hexadiene fragment and readily adds the second molecule of dihydrotriazoledione 69 to give the bisadduct 72.53 O PhN N N O N 69 69 O N N N NPh O O O NPh 71 72Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment The cycloaddition of dihydrotriazoledione 69 to bicyclopro- pylidene (53) occurs in an unexpected way; simple closure of the four-membered heterocycle in the resulting zwitter-ion 73 does not occur in this case.After an alkyl shift, the carbon atom in the cyclopropane fragment that was involved in the formation of the first C7N bond is attacked by the nucleophilic nitrogen atom. Diaziridine 74 is the only reaction product that was isolated.54 O O N 69, 0 8C NPh N NPh N 53 + N7O O 73 74 (83%) Unlike the methylidenecyclopropanes considered above, con- jugated alkenylidenecyclopropanes react with dihydrotriazole- dione 69 as true dienes to give [4+2]-cycloadducts. For example, the reaction with bis(cyclopropylidene)ethane occurs almost instantaneously and gives high yield of the cycloadduct 75 where both cyclopropane fragments are retained in the molecule.55 ONPh 69, PhH 20 8C NN O 75 (90%) 1-Methyl-2-silyloxyprop-2-enylidenecyclopropane (76) can act as a 1,3-diene in the reaction with the dihydrotriazoledione 69, giving a heterocyclic compound 77 in 55% yield.56 O Me Me N NPh 69, 0 8C, 30 min CH2Cl2 N ButMe2SiO ButMe2SiO 76 77 (55%) O Synthesis of polycyclic heterocycles with a spirocyclopropane fragment in the molecule is carried out using the reaction of the dihydrotriazoledione 69 with cyclic dienes 78a,b or with their derivatives.The [4+2]-cycloadducts 79a,b are formed in high yields under mild conditions.57 ± 61 Subsequent transformations of the heterocyclic adduct 79b afforded highly strained dispi- ro[2.0.2.4]decane 80.59, 60 n O N NPh N 69 0 ±50 8C n 78a,b O 79a,b (50% ± 60%) n = 1 (a), 2 (b).a, b, c, d hn 79b N + N 80 (29%) (a) H2, Pd/C, MeOH; (b) ButOK, DMSO, H2O; (c) CuCl2, H2O, EtOH; (d ) KOH. Both linear and cyclic nitrones can act as 1,3-dipolar com- pounds in reactions with methylidenecyclopropanes.62 ± 66 The reaction of methylidenecyclopropane with nitrones 81a ± c occurs as [3+2]-cycloaddition with retention of the cyclopropane frag- ment; in this case, mixtures of regioisomers 82a ± c and 83a ± c are 467 formed in the ratio (2 ± 9) : 1 in 69% ±86% yield,62 which are difficult to separate. Spiro[cyclopropane-1,40-isoxazolidines] 83a ± c are more thermally stable than their regioisomers 82a ± c.The latter undergo rearrangement (400 8C, 0.2 mmHg) to deriv- atives of 4-piperidones 84a ± c and enaminones, which allows one to isolate the isoxazolidines 83a ± c from the reaction mixture. R1 R1 O 60 8C + R2N R2N R1HC NR2+ 81a ± c O 83a ± c O 82a ± c R1 R2NH O D R2N O + 82a ± c R1 84a ± c R1=Ph, R2=Me (a); R1±R2=CH2CH2C(Me)2 (b), (CH2)4 (c). The use of alkyl- and aryl-substituted methylidenecyclopro- panes and derivatives of cyclopropylideneacetic acid in these transformations makes it possible to obtain various fused spiro- [cyclopropaneisoxazolidines] which are of interest as starting compounds in the syntheses of isoquinoline, quinolizidine, indo- lizidine and some other heterocyclic structures.63 ± 72 Electron- donating substituents at the double bond favour the formation of spiro[cyclopropane-1,40-isoxazolidines], whereas the 1,50-regio- isomers are formed in the presence of electron-withdrawing substituents.For example, the addition of cyclic nitrone 81b to substituted methylidenecyclopropane 85 results exclusively in isoxazolidine 86, whereas the reaction of the same nitrone 81b with the methyl ester 87a or cyclopropylideneacetonitrile (87b) affords stereoisomeric spiro[cyclopropane-1,50-isoxazolidines] 88a,b and 89a,b.63, 72 Me (CH2)2Ph (CH2)2Ph Me 81b, PhMe 13 h N O 85 Me Me 86 (90%) H H R R R + 81b 50 8C, 40 h Me Me 87a,b O O N Me 89a,b N Me 88a,b Yield of 88 (%) Yield of 89 (%) R Compound 21 70 CO2Me CN ab 42 17 The nitrones 81a ± c react with bicyclopropylidene (53) at 20 ± 60 8C to give high yields of isoxazolidines 90a ± c, in which both spirocyclopropane fragments are retained.However, heating of the reaction mixture in aromatic hydrocarbons as solvents at 80 ± 130 8C results in isomerisation of the isoxazolidines obtained to the corresponding spiro[cyclopropane-1,30-piperidin]-4-ones 91a ± c; only the cyclopropane ring adjacent to the labile N7O bond is involved in the rearrangement.73, 74 R1 80 ± 130 8C 81a ± c+ PhH 20 ± 60 8C N 53 O R2 90a ± c O R1 N R2 91a ± c468 Yield of 90 (%) Yield of 91 (%) R2 R1 Compound Ph abc 63 80 65 Me (CH2)2CMe2 (CH2)4 93 80 60 Isomerisation of isoxazolidines 90a ± c to piperidones 91a ± c probably occurs by homolytic cleavage of the N7O bond in the heterocycle followed by fast rearrangement of the radicals and ring closure.Only reactions with nitrones with symmetrically substituted bicyclopropylidenes, where isoxazolidines incorporating a spiro- cyclopropane fragment are formed selectively, are of preparative value. Otherwise, a complex mixture of isomeric compounds is formed, as is the case, e.g., of the cycloaddition of the nitrone 81b to monosubstituted bicyclopropylidenes 92a,b. Mixtures of iso- mers 93 and 94 (overall yield 65%± 85%) could not be separated chromatographically or after their thermal rearrangement to the corresponding piperidones.74 R H H R + 81b, PhH 25 8C, 18 days N N O O Me Me Me Me R 94a,b 93a,b 92a,b R=CO2Me (a), SPh (b).The cycloaddition of nitrones to the double bond of the methylidenecyclopropane fragment can occur in an intramolecu- lar manner as well. The reaction with nitrone 95a containing a trisubstituted double bond (25 8C, 24 h, yield 87%) occurs regioselectively to give the cycloadduct 96a. The presence of an additional methyl group in the nitrone 95b decreases the polarity of the double bond and the reactivity of the nitrone. At 80 8C (2 h), a mixture of two isomers 96b and 97 in the ratio *2 : 1 is formed.75 R + R 4 Me + 1) Pr4NRuO¡ 2) MeNHOH N (CH2)3 HO(CH2)4 95a,b O7 R Me O O MeN MeN 97 96a,b R = H (a), Me (b). Unsaturated analogues of isoxazolidines, viz., spiro[cyclopro- panedihydroisoxazoles], can be obtained by 1,3-dipolar cyclo- addition of nitrile oxides to methylidenecyclopropanes.The reaction of nitrile oxides 98a ± c with non-substituted methylide- necyclopropane occurs regioselectively to give spiro[cyclopro- pane-1,50-dihydroisoxazoles] 99a ± c.76 Only in the case of acetonitrile oxide (98c) was the formation of a different regio- isomer (*3%) observed. RN RCNO + 98a ± c O 99a ± c R=Ph (a, 65%), Bn (b, 35%), Me (c, 60%). R 5 160 ± 163 8C N NH O 20 O RCNO 98a,d 100a,d 101a,d R R=Ph (100a, 64%), 2,4,6-Me3C6H2 (100d, 100%). Yu V Tomilov, I V Kostyuchenko, OMNefedov Spiro[cyclopropane-1,50-dihydroisoxazoles] substituted in the cyclopropane ring are obtained in a similar way from nitrile oxides 98a ± d and substituted methylidenecyclopropanes.77 Reactions of methylidenespiropentane with nitrile oxides 98a (20 8C, 16 h) and 98d (60 8C, 4 h) in benzene results in dihydroisoxazoles 100a,d, thermal rearrangement of which to ketones 101a,d occurs regio- selectively, exclusively with opening of the inner cyclopropane ring at the C(5)7C(20) bond.78 The cycloaddition of nitrile oxides 98a ± c to bicyclopropyli- dene (53) occurs less efficiently than to methylidenecyclopro- pane.73, 74 Because of this, partial dimerisation of nitrile oxides to furoxans occurs.The yields of dispirano dihydroisoxazoles 102 can be increased by performing slow generation of nitrile oxide in situ (e.g., in the synthesis of nitrile oxide 98a by treatment of benzohydroxymoyl chloride with NaHCO3) or by using spatially hindered nitrile oxides, e.g., 98d.However, the presence of extremely bulky substituents in the nitrile oxide molecule, e.g., in compound 98e, again decreases the yield of the target product. It should be noted that in the case of the nitrile oxide 98a the resulting dihydroisoxazole 102a partially reacts with it to give compound 103.74 Ph R O O RCNO + N N N 53 98a,c ± e Ph O 102a,c ± e 103 t /days Yield of 102 (%) R Compound T /8C 40 10 67 17 66 20 110 110 Ph Me 2,4,6-Me3C6H2 Ph3C acde 7727 Bicyclopropylidene (53) undergoes [2+2]-cycloaddition to chlorosulfonyl isocyanate to give the b-lactam 104, but this is not the main product.Evidently, the reaction can occur as a two-step process to give the 1,4-zwitter ion 105. The main reaction product is methylidene-g-lactam 106 formed by opening of one cyclo- propane ring in the intermediate 105.54 O +O C NSO2Cl 7 NSO2Cl + 53 105 O O + NSO2Cl NSO2Cl 104 (15%) 106 (85%) Bicyclopropylidene (53) readily undergoes [4+2]-cycloaddi- tion to heterodienes such as 1,2,4,5-tetrazine and its derivatives. The primary cycloaddition product readily undergoes dedinitro- genation, while the resulting 8,9-diazadispiro[2.0.2.4]deca-7,9- diene (107) undergoes trimerisation to the fused heterocyclic N N N N N 53 1.5 h, 20 8C N N N N N 107 N N N N NN 108 (86%)Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment compound 108 with six spiro-fused cyclopropane fragments in the molecule (a mixture of two stereoisomers).79 Attempts to trap the heterodiene 107 failed.Synthesis of fused azaheterocycles with a spirocyclopropane fragment can be carried out by the reactions of cyclopropylide- neacetates with imines. For example, the ester 87a undergoes formal [4+2]-cycloaddition to imine 109a to give spiro[cyclopro- pane-1,30-dihydroisoquinoline] 110. The reaction of chloro-sub- stituted methylidenecyclopropane 87c with imines 109b,c in methanol gives the Michael adducts 111b,c in almost quantitative yields.These adducts are thermally stable, but in the presence of lithium diisopropylamide or potassium tert-butoxide, carbenes are generated; the latter are transformed to compounds 112b,c with a dihydro-2-azaazulene skeleton due to intramolecular cyclo- addition to the benzene ring followed by isomerisation.80, 81 This bicyclic system has been studied much less than the 1-azaazulene derivatives. H COOMe NH 87a, D, CCl4 R1=Ph N R1 109a ± c 110 (32%) Ph COOMe COOMe Cl LDA or ButOK 87c 109b,c Cl N MeOH R2 111b,c (40% ± 72%) MeOOC COOMe N NR2 R2 112b,c (48% ± 70%) R2 [R2=H(b), Me (c)]. R1 =Ph (a), The cyclopropyl substituent at position 1 of azaazulenes 112b,c can be opened on treatment with electrophilic reagents, which enables intramolecular cyclisation of the salts 113b,c to give derivatives 114b,c.81 MeOOC + HCl, Et2O 112b,c NH Cl7 NaI, MeCN 90 8C, 15 h R2 113b,c MeOOC MeOOC + NaBH4, MeOH I7 N N H R2 R2 114b,c (51% ± 75%) R2=H(b), Me (c).Unlike 1-alkenylidenecyclopropanes which react with di- hydrotriazoledione 69 or with chlorosulfonyl isocyanate with opening of the cyclopropane ring,82 N-mesitylcyclopropylidene- azomethine (115) reacts with N-(dicyanomethylidene)aniline or phenyl isocyanate to give spiro[azetidinecyclopropanes] 116 and 117. In the latter case, a considerable amount of the cycloadduct 118 is formed.83 469 C NMes 115 NMes PhN C(CN)2 N NC 25 8C, 48 h Ph CN 116 (75%) NMes HN O + PhN C O 25 8C, 24 h N O Ph NMes 118 (45%) 117 (40%) 4.Other methods for the synthesis of azaheterocycles incorporating a spirocyclopropane fragment Heterocyclic compounds incorporating a spirocyclopropane frag- ment in the molecule can be obtained by typical cyclocondensa- tions involving cyclopropane derivatives. However, certain conditions have to be observed in order to keep the cyclopropane fragment unchanged in the course of the reaction. For example, the reaction of pyrazolidine-3,5-dione 119 with 1,1-cyclopropane- dicarbonyl dichloride in the presence of an equimolar amount of triethylamine results in compound 120 containing a three-carbon ring. On the other hand, this reaction carried out with heating in THF in the absence of a base is accompanied by the three-carbon ring opening and results in the chloroethyl derivative 121.84 R O O O Et3N 20 8C N O NH O COCl NH R 120 (51%) + NH COCl O O O 119 N THF, D R Cl(CH2)2 N HO O 121 (54%) R=cyclo-C6H11.Intramolecular cyclisation of 1,1-disubstituted cyclopropane 122 on treatment with Ba(OH)2 results in lactam 123 containing a spirocyclopropane fragment. The latter undergoes heterocycle opening to give 1-(2-aminoethyl)cyclopropanecarboxylic acid on refluxing in aqueous dioxane in the presence of Ba(OH)2.85 (CH2)2NHCO2Et EtO2C Ba(OH)2, MeOH 65 8C, 14 h 122 7OOC (CH2)2NHá3Ba(OH)2 O (86%) O O, D NH 123 (34%) The cyclocondensation method with the use of 1-aminocyclo- propanecarboxylic acid or its derivatives as structural blocks was used for a directed synthesis of a series of spiro compounds, e.g.124 ± 126, which may be interesting as potential medicines.86 ± 88 For example, benzodiazepine 125 was obtained in 48% yield by cyclocondensation of methyl 1-aminocyclopropanecarboxylate with o-nitrobenzaldehyde.88470 O O HN N CH2OH HN NH H2N NH N 124 125 O cyclo-C6H11N(Me)CO(CH2)3O N O NH 126 N The 1-methylamino-2-methylcyclopropanecarboxylic acid moiety spiro-fused with the macrocycle is a constituent of cyclic octadepsipeptides, which are bifunctional antibiotics of the qui- nomycin series that can be intercalated into DNA.89, 90 OH Me O Me O O Me N O HN N N HN O O Me SR S Me O O N HN NH N O N Me O Me O O Me HO R=Bui, Pri, Me.The incorporation of the spirocyclopropane fragment in the benzoxazine heterocycle of ofloxacin (a well-known antibacterial compound belonging to the fluoroquinolone series) was carried out according to the following scheme: condensation of b-oxoester 127 with triethyl orthoformate to give unsaturated ester 128; formation of the 1,4-oxazine ring containing a spiro- cyclopropane fragment by treating compound 128 with 1-(hydroxymethyl)cyclopropylamine hydrochloride followed by heating of the reaction product 129 with anhydrous potassium fluoride in DMSO. Acid hydrolysis of the ester group followed by selective replacement of a fluorine atom by cyclic amines afforded the target compounds 130.91 O O COOMe F COOMe F b a OEt F F F F 128 127 F F O O COOH F COOMe F c, d, e N N R1R2N F F O130a ± c 129 (51%) OH NMe2 NH NR1R2=N (130b, 56%), (130a, 81%), N NHEt N (130c, 86%); (a) HC(OEt)3, (AcO)2O, D, 2.5 h; CH2OH (b) , ButOK, 45 8C; (c) KF, DMSO; (d ) HCl; (e) HNR1R2. NHá3 Cl7 In the reaction of ninhydrin (indan-1,2,3-trione hydrate) (131) with 1-aminocyclopropanecarboxylic acid (132) (molar ratio 1 : 2) in boiling benzene, decarboxylation of the acid 132 occurs to give spiro[cyclopropane-1,20-oxazolidine] 133.The reaction of equi- molar amounts of the acid 132, ninhydrin (131) and N-phenyl- Yu V Tomilov, I V Kostyuchenko, OMNefedov maleimide in acetonitrile under reflux results in spiro[cyclopropane-1,50-pyrrolidine] 134.92 It is assumed 92 that these reactions involve the intermediate 1,3-dipole 135.O NHá OH + COO7 7CO2,7H2O OH 132 131 O O H N + 7 135 O ONPh, MeCN, D, 4 h. (a) 132, PhH, D, 2 h; (b) O In certain cases, the corresponding cyclopropane derivatives were deliberately obtained for the directed syntheses of biolog- ically active compounds containing a spirocyclopropane fragment. For example, (1-benzyloxycarbonyl-1-bromomethyl- idene)cyclopropane (137) was obtained for the synthesis of the cyclopropane analogue of norpenicillin 136.93 The reaction of compound 137 with 4-mercaptoazetidin-2-one 138 in the presence of K2CO3 results in epimeric 2-bisnorpenicillanates 136 (ratio *4 : 1, yield*25%).94 Although the yields of the adducts are low, this method is considered to be convenient 94 because it does not give rise to side transformations of the cyclopropane ring. PhOCH2CONH SH+ NH O 138 PhOCH2CONH NH O PhOCH2CONH O 136 HMPT is hexamethylphosphorous triamide.It is well known 95 that 1-azirines are widely used in the synthesis of heterocyclic systems containing a nitrogen atom in the ring. Highly strained 2-phenyl-1-azaspiropent-1-ene (139) is a useful starting compound for the synthesis of azaheterocycles containing a spirocyclopropane fragment. This compound is obtained by pyrolysis of the addition product of benzonitrile oxide 98a to cyclopropylidenephosphorane.96 The reaction of the spirane 139 with benzonitrile-4-nitrobenzylide (140) generated in situ from N-(4-nitrobenzyl)benzimidoyl chloride occurs regiose- lectively to give the spiro{cyclopropane-1,60-1,3-diazabi- cyclo[3.1.0]hex-3-ene} derivative 141, the structure of which was 3 O O a O HN O O 133 (>90%) Ph N OO O b NH O 134 (30%) Br K2CO3, DMF 20 8C, 30 min CO2CH2Ph 137 S K2CO3, HMPT 20 8C, 8 h Br CO2CH2Ph S N CO2CH2PhSynthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment established from spectroscopic data and by its hydrolysis into 3,4-dihydro-5,6-diphenyl-2-pyridone.97 N Ph O + D 7 PPh3 PhCNO+ 98a PPh3 (61%) + 7 Ph Ph N H3O+ H PhC N CHAr 140 20 8C Ph Ar N 139 (84%) N 141 Ph O Ph HN Ar=4-NO2C6H4. It is well known 98 that nitrones undergo 1,3-dipolar cyclo- addition to compounds containing C=N bonds.Aziridine 139 also reacts with nitrones 142a,b; however, the resulting cyclo- adducts 143a,b are unstable under the reaction conditions (ben- zene, D) and are transformed into cyclopropylamides 144a or 144b.97 Ph O Ph N H O N +RCH NPh 142a,b R 139 NPh 143 N(Ph)COPh R=Ph NH2 144a (51%) N(Ph)COPh R=4-NO2C6H4 N CHC6H4NO2 144b (16%) R=Ph (a), 4-NO2C6H4 (b). III. Formation of a cyclopropane ring spiro-fused with a heterocycle Cycloaddition of various reagents to methylidene derivatives of the corresponding heterocycles is one of the general ways to form a spiro-fused cyclopropane ring in heterocyclic compounds. Cyclo- propanation of the double bond, which is usually activated by electron-withdrawing substituents, is mostly carried out by reac- tions with diazo compounds and ylides.In some cases, an opposite approach is used, where the required azaheterocycle contains a diazo group capable of reacting with an unsaturated substrate. In any case, the originally formed dihydropyrazoles, i.e., 1,3-dipolar cycloadducts, are then transformed into cyclopropane derivatives upon elimination of a nitrogen molecule; depending on the nature of the substituents, this either occurs spontaneously at room temperature or requires elevated temperatures. In a number of cases, the choice of the target heterocyclic compounds, e.g., indolinones or cephalosporins, is dictated by the search for new biologically active compounds.99 ± 104 1. Construction of a cyclopropane ring based on the formation and dedinitrogenation of dihydropyrazoles The addition of diazomethane to methylideneindolin-2-one deriv- atives 145a ± d results in spiro[indoline-3,30-dihydropyrazoles] 146a ± d with high regioselectivity.102, 103 Their thermolysis in boiling dioxane or treatment with HCl in MeOH at room temper- 471 ature involves elimination of nitrogen to give spiro[cyclopropane- 1,30-indolin]-2-ones 147a ± d.Chromatography of dihydropyra- zoles 146a,b on Al2O3 is accompanied by their transformation to conjugated enones 148a,b (yields 57% and 74%, respectively) rather than to compounds 147a,b.103 N N CHCOR2 CH2N2 20 8C, 6 h COR2 O O NR1 145a ± d N 146a ± d R1 COR2 120 8C, 2 h or HCl, MeOH, 20 8C O RN1 147a ± d (60% ± 80%) MeCOR2 Al2O3 O RN1 148a,b R1=H,R2=Ph (146a, 92%), Me (146b, 90%), OEt (146c, 62%); O, R2=OEt (146d, 74%).R1=CH2N Unlike methylideneindolin-2-ones 145a ± d, fluoro-substi- tuted 3-(aroylmethylidene)indolin-2-ones 149 react with an ethereal solution of CH2N2 at 20 8C to give directly spiro[cyclo- propaneindolin]ones 150.104 R2 CHCO CH2N2 20 8C X R3 O 149 RN1 R2 CO X O RN1 R3 150 (60% ± 70%) ; R2=2-F, 4-F; X=H, 5-F, 6-F; R1=H, COMe, CH2N R3=H, 2-Me, 3-Me, 5-Me, 3-Cl, 3-F.As in the example considered above, 1,3-dipolar cycloaddition of diphenyldiazomethane to methylideneindolin-2-ones 145c,d in DMF at 20 8C involves nitrogen elimination from the dihydro- pyrazoles formed originally to give spiro[cyclopropanein- dolin]ones 147e,f.102 Ph Ph COOEt 145c,d Ph2CN2, DMF 20 8C O 147e,f RN O (147f, 76%). R = H (147e, 53%), CH2N A similar approach to the construction of a spiro-fused cyclo- propane fragment is also applicable to other heterocyclic systems; depending on the nature of the azaheterocycle and the substituents in the ring, the reaction of diazo compounds with the exocyclic double bond can involve both the formation of the intermediate dihydropyrazoles and their spontaneous dedinitrogenation.The methods (including enantioselective ones) for the syn- thesis of 1-aminocyclopropanecarboxylic acid derivatives were472 developed using 1,3-dipolar cycloaddition of diazomethane to 4-alkylidene(arylidene)-5(4H)oxazolones,105 ± 108 thiazolones 109 and piperazinediones.110±112 The reaction with oxazolones 151 occurs at 20 ± 45 8C with nitrogen elimination and formation of spiro[cyclopropaneoxazolines] 152. On the other hand, the reaction of CH2N2 with piperazinediones 153a,b gives spiro- fused azaheterocycles 154 in high yields and with high diastereo- selectivity (>95%). Photolysis of the latter results in azahetero- cycles 155 in >90% yields. Acid splitting of the six-membered heterocycle in the resulting compounds on treatment with 6M HCl in AcOH at 100 8C results in 1-aminocyclopropanecarboxylic acid derivatives.110, 111 O RHC O R O O N N +CH2N2 PhH, Et2O 20 ± 45 8C 152 Ph 151 Ph R=Ph, 4-ClC6H4, 4-MeC6H4, 4-MeOC6H4 (45% ± 60%), Me (25%), Cl (75%), Br.O O N N CH2N2, PhH N N R2 hn, PhH 7 h 20 8C, 3 ± 8 days N N R2R1 R1 154 153 O H O H O N R2 N R1 155 O H R1=Ac, R2=Ph (a); R1=ButOCO (Boc), R2=Et (b). If the oxazolone ring contains both substituted methylidene and vinyl fragments (cf. compounds 156a,b), the addition of diazomethane occurs mainly to the methylidene fragment and the corresponding cyclopropane derivatives 157a,b are formed as the reaction products even at room temperature.113 The addition of diazomethane to the vinyl group occurs only in compound 156b and only to a minor extent to give the dihydropyrazole 158b, which is stable under these conditions.O O Ar Ar CH2N2 O O N N 20 8C, 15 h Me Me Ph Ph 157a,b (39% ± 45%) 156a,b O 3,4-(MeO)2C6H3 O N Me NN Ph 158b (1.6%) Ar=Ph (a), 3,4-(MeO)2C6H3 (b). The formation of a cyclopropane fragment spiro-fused with the heterocyclic system of cephalosporins is documented.114 For example, diphenyldiazomethane adds to the exocyclic double bond of 2-methylidenecephemes 159 (30 8C, 30 min) to give two isomeric spiro derivatives 160a and 160b in the ratio *3 : 1. It is believed 114 that the reaction occurs through regioselective for- mation of the dihydropyrazole 161. Yu V Tomilov, I V Kostyuchenko, OMNefedov Ph O O H H H Ph S S CH2 Ph2CN2 N R1CH2CN CH2Cl2, 308C N O CH2OAc O NCH2OAc 161 159 CO2R2 CO2R2 O O Ph H H Ph H H H H S S Ph R1CH2CN Ph N N O O CH2OAc R1CH2CN + CH2OAc CO2R2 O 160b (17%) O 160a (47%) CO2R2 R1= , R2=CHPh2.S 1,3-Dipolar cycloaddition of diazomethane to 3-methylidene- cephames 162 occurs at 5 8C in 1 week and only with a great excess of diazomethane.115 1,3-Dipolar cycloaddition products 163 containing a spiro-fused dihydropyrazole fragment is formed in the first stage. H H H H (O)n S (O)n S R1NH R1NH D, DMF N N CH2N2, CH2Cl2 5 8C, 7 days CH2 COOR2 H N N COOR2 H O 163a,b O 162a,b H H H H (O)n S (O)n S R1NH R1NH + N N CH2 H COOR2 H H COOR2 O 165a,b O 164a,b n = 0 (a), 1 (b); R1=PhOCH2CO; R2=4-NO2C6H4CH2.Subsequent thermolysis of the resulting 1-dihydropyrazoles 163a,b occurs non-selectively and results in both products with a cyclopropane fragment, i.e., spiro[cephame-1,30-cyclopropanes] 164a,b (yields 60% and 64%, respectively), and their isomers, i.e., 3-vinylcephames 165a,b (20% and 15% yields, respectively).115 Pure E- and Z-isomers of 2,2,2-trichloroethyl penicillanates 166 containing an exocyclic double bond react with diphenyldi- azomethane to give stable 4,5-dihydro-3H-pyrazoles 167a or 167b, pyrolysis of which occurs stereospecifically and results in penicillanates 168 with a spirocyclopropane fragment.116 Ph N R2 N Ph R1 H H R1 110 ± 130 8C S S Me Me Ph2CN2 25 8C, 6 h N R2O N O Me Me 167a,b CO2CH2CCl3 166a,b CO2CH2CCl3 Ph Ph R1 H R2 S Me N O Me 168a,b CO2CH2CCl3 Yield of 167 (%) Yield of 168 (%) R2 R1 Compound ab 89 15 CO2Bn H 72 H CO2 Bn 87 The cyclopropane fragment spiro-fused with a heterocycle also results from the addition of the corresponding diazo hetero-Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment cycles to activated alkenes followed by dedinitrogenation of the resulting dihydropyrazole.For example, the reaction of 3-diazo- indoles 169 with methyl acrylate or acrylonitrile in boiling benzene results in nitrogen elimination to give substituted spiro[cyclopro- pane-1,30-indoles] 170 with the preferential formation of anti- isomers.117 It should be noted that diazo compounds 169 are rather stable under the same conditions in the absence of unsatu- rated substrates.It is therefore assumed that their reactions with methyl acrylate and acrylonitrile occur as 1,3-dipolar cycloaddi- tion; the intermediate dihydropyrazoles undergo spontaneous dedinitrogenation. Z H H Z N2 R R R+ Z PhH, 80 8C N N 169 syn-170 N anti-170 Yield of R Z Yield of syn-170 (%) anti-170 (%) 11 1753 21 36 43 26 COOMe CN COOMe CN Ph Ph 2-Pyridyl 2-Pyridyl Exhaustive 1,3-dipolar cycloaddition of aliphatic diazo com- pound to allenes followed by partial dedinitrogenation of the resulting spiro-fused bis(dihydropyrazoles) makes it possible to form fragments of an azaheterocycle and a spirocyclopropane simultaneously.118, 119 For example, bis(dihydropyrazole) 171 synthesised by the addition of 2-diazopropane to allene is trans- formed into spiro[cyclopropanedihydropyrazole] 172 on heating to 100 8C.The loss of the second nitrogen molecule to give tetramethylspiropentane (173) occurs only at 200 8C.118 N N Me Me2CN2 Me 100 8C H2C C CH2 Me Me N N 171 N N Me Me Me 200 8C Me Me Me Me Me173 (*100%) 172 (*100%) 2. Cyclopropanation of unsaturated compounds with sulfur carbenes and sulfur ylides Although the cyclopropanation of unsaturated compounds with carbenes and their synthetic equivalents is a popular modern method for the construction of three-carbon rings, there are but a few examples of such reactions resulting in azaheterocycles fused with a spirocyclopropane fragment.Cyclopropanation of alkenes with heterocyclic diazo com- pounds in the presence of catalysts is an example. Diazopenicilla- nates and diazocephemes have been reported as cyclopropanating reagents.116 This method is an alternative to the reaction of aliphatic diazo compounds with methylidenepenicillanates or methylidenecephemes in the construction of the same structural fragments. Cyclopropanation of unsaturated compounds acti- vated by electron-donating substituents occurs successfully. For example, the reaction of benzyl 6-diazopenicillanate (174) or 7-diazoceph-3-eme (175) with ethyl vinyl ether in the presence of copper acetylacetonate results in ethoxycyclopropanes 176 or 177 (each as a mixture of four isomers).120 EtO N2 S S Me Me H2C CHOEt N N Me Me Cu(acac)2 O CO2CH2Ph CO2CH2Ph O176 (73%) 174 473 EtO N2 S S H2C CHOEt N N Cu(acac)2 Me Me O O CO2But CO2But 175 177 (53%) The reaction of diazo compounds 174 and 175 with vinyl acetate in the presence of Cu(acac)2 occurs similarly, but the yields of the products do not exceed 10% due to the low stability of the resulting spiro-fused acetoxycyclopropanes.120 The reaction of diazo compounds 174 and 175 with alkenes containing electron- withdrawing groups, both in the presence and in the absence of Cu(acac)2, occurs as 1,3-dipolar cycloaddition and results only in the corresponding spiro-fused 4,5-dihydro-1H-pyrazoles.120 Refluxing of trichloromethyl derivatives of imidazolidines 178 in xylene is presumably accompanied by the abstraction of CHCl3 and generation of a nucleophilic heterocyclic carbene which can add to activated double bonds.For example, the reaction with N-phenylmaleimide affords spirocyclopropane-containing adducts 179.121 O Ar Ar Ar NPh O N N N H 140 8C O NPh 7CHCl3 CCl3 N N N O 179 Ar Ar 178 Ar Ar=Ph (85%), 4-MeC6H4 (57%), 4-MeOC6H4 (77%). The reaction of dihydropyrazine 180 with butyllithium and tosyl azide at770 8C in the presence of cyclohexene results in the spirane adduct 181 (overall yield >70% with respect to the starting dihydropyrazine 180) due to generation and [1+2]- cycloaddition of the heterocyclic carbene 182.122 OMe OMe N N Pri Pri a, b a Li N NNTs MeO N MeO N 180 OMe N OMe Pri N Pri c N MeO N MeO 181 182 .(a) BuLi; (b) TsN3,770 8C; (c) Dichlorocyclopropanation of 2-methylquinoline at 25 8C (CHCl3, 50% NaOH, Et3N+BnCl7) occurs in rather high yields to give compounds 183 and 184 with a spiro[cyclopropane-1,20- quinoline] structure. Probably, dichlorocarbene first adds to the nitrogen atom to give an ylide, which generates 1-formyl-2- methylidenedihydroquinoline (185) in alkaline medium; the latter undergoes the usual dichlorocyclopropanation.123 CCl2 CCl2 Me N N CH2 185 CHO Cl Cl Cl Cl + Cl N Cl N 184 183 CHO CHO474 The method for building the cyclopropane ring by addition of reactive sulfur ylides to double bonds is commonly used in synthetic organic chemistry.124 Unlike the reactions with electro- philic carbenes, alkenes activated with electron-withdrawing groups (Michael acceptors) are used in these processes.Back in 1973, Spry 125 demonstrated the possibility of using sulfur ylides for the cyclopropanation of 2-methylidenecephalo- sporins. For example, the reaction of sulfonylmethylide 186 with functionally substituted methylidenecephemes 187 occurs exclu- sively at the exocyclic double bond to give spiro[cephalosporin- cyclopropanes] 188 in high yields.125 H R1CON H H O 7 + Ph S CH2 + N O NMe2 186 187 H O R1CON H H S N O 188 CO2CH2CCl3 Yield (%) R2 R1 H 80 OAc OAc PhOCH2 PhOCH2 Me 85 64 72 ± 88 OAc S CH2 The reaction of 3-methylidene-2,3-dihydrothiazin-4-one derivatives 189 containing an enone system with ylides 190 results in spiro[cyclopropanedihydrothiazines] 191.126 If ylide 190 con- tains a benzoyl substituent, a mixture (*1 : 2) of spirocyclopro- pane and dihydrofuran derivatives 191b,c and 192b,c is formed. Unsaturated ylide 190 (R2=H) reacts with the enone 189 (R1=Ph) to give only spiro[cyclopropanedihydro-1,2-benzothia- zine] 191a.It is believed 126 that the process starts with nucleo- philic attack of ylides 190 on the b-carbon atom of theC=Cbond in the enones 189; this results in resonance-stabilised betaines, which then undergo cyclisation at the carbon or oxygen atoms to give three- or five-membered rings.The direction of betaine cyclisation is determined by both electronic and steric factors.126 O CHR1 7 + NMe S +R2CHSMe2 190a,b O O189 H R2 O R1 + H NMe S O O 191a ± c R1=Ph, Me; R2=H, COPh. R2 R1 Compound abc Ph Me Ph HCOPh COPh OS CH2 DMF 0 8C, 1 h CH2R2 CO2CH2CCl3 CH2R2 Me2S + O CHR2 7 CHR1 25 8C, 16 h NMe S O O R2 O HR1 H NMe S O O 192a ± c Yield of 191 (%) Yield of 192 (%) 80 22 24 752 55 Yu V Tomilov, I V Kostyuchenko, OMNefedov A common method for the introduction of the spirocyclopro- pane fragment in a morpholinone structure is the reaction of their methylidene derivatives 193, which are obtained from the phos- phonate 194 using the Wittig reaction, with sulfur ylides.127 It should be noted that the diastereoselectivity of methylenation of the double bond by the ylide 195 is higher than that by the ylide 190a; diastereomers of spirane derivatives 196a ± f are formed preferentially (or exclusively) in yields higher than 82% (with the exception for compound 196e).It should be noted that the addition of diazomethane to ethylidenemorpholinone 193b fol- lowed by photolysis of the resulting dihydropyrazole affords a diastereomeric mixture of spirane 196b (ratio 1 : 1.6, overall yield 91%).127 Ph Ph Ph Ph Ph Ph a b O O O BocN BocN BocN O O O O P(OMe)2 H R R 193a ± f 194 196a ± f R = H (a), Me (b), Et (c), Prn (d), Pri (e), Ph (f ); + (a) RCHO, NaH, THF; (b) PhS(O)(NEt2)CH¡2 (195).3. Decarboxylation and g-elimination leading to cyclopropane ring formation The formation of a spiro-fused cyclopropane fragment is carried out by decarboxylation of g-lactones 197 spiro-fused with a heterocyclic system, besides elimination of an N2 molecule from dihydropyrazoles. This method was used for the synthesis of spiro[cyclopropane-1,20-indolin]-3-ones 198 with substituents both in the benzene ring and at the nitrogen atom aimed at the search for novel compounds with antiinflammatory and analgesic effects.99, 100, 128 Spiro-fused g-lactones 197a ± f are obtained in two steps by condensation of the corresponding anthranilic acids with a-bromo-g-butyrolactone.Decarboxylation of the lactones 197a ± f is carried out by heating (150 ± 160 8C) in the presence of an alkali metal chloride to give the heterocycles 198 in 75% ± 94% yields.100, 128 Functionalisation of the benzene ring in the spiro- lactone 197a is carried out before the decarboxylation step. Br CO2H CO2H O O R R Et3N Ac2O Na2CO3 O NH2 HN O O O O O R R NaCl, DMSO 150 ± 160 8C NAc NAc 198a ± f 197a ± f R = H (a), Me (b), OMe (c), Cl (d), Br (e), I (f). 1,3-Elimination from the corresponding functional deriva- tives is a useful method for the formation of a spiro-fused cyclo- propane fragment applicable to various azaheterocyclic structures. In particular, this type of reaction includes cyclo- alkylation of compounds containing reactive hydrogen atoms with 1,2-dibromoethane.For example, the reaction of indolin-2- one with 2 equiv. of dibromoethane in the presence of sodium hydride results in compound 199, subsequent reduction of which with magnesium in boiling THF gives unsaturated spiro[cyclo- propane-1,30-indolin]-2-one, which was later used for the syn- thesis of compounds with potential pharmacological activity.129, 130Synthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment O 1) NaH, DMF, 25 8C 2) BrCH2CH2Br NH O O Mg THF, 18 h NH N (44%) 199 (15%) (CH2)2Br A scheme for the synthesis of spiro[1,4-benzothiazinecyclo- propan]-3-one 200 with the use of 2-aminobenzenethiol as the starting compound is presented below.The required functional- ised ethyl group is introduced in the initial condensation step, while the spirocyclopropane fragment is formed in the last step, i.e., cyclisation of mesylate 201.131 SH S (CH2)2OH a b, c, d, e O NH2 HN S S (CH2)2OMs f, g N O N 201 CH2CO2Me CH2CO2Me 200 (49%) Br , H+; (c) BrCH2CO2Me; , K2CO3, EtOH; (b) O (a)O O (d ) MeOH, TsOH; (e) MsCl, Et3N, CH2Cl2; ( f ) NaH, 20 8C, 30 min; (g) 70 8C, 15 min. Alkylation followed by 1,3-elimination was successfully used for a stereoselective synthesis of (R)- and (S)-isomers of 1-amino- 2,2-dideuteriocyclopropanecarboxylic acid. Spiranes 202 were used as the starting compounds which were then hydrolysed with HCl.These transformations could also be performed starting from chiral dihydropyrazine 203 and selectively deuterated 2-bro- moethyl triflates.132, 133 Metallation of compounds 203 followed by alkylation with deuterated 2-bromoethyl triflate first gives (2-bromoethyl)dihydropyrazine 204a,b (yield 86%± 88%); in this case, an isomer with a cis arrangement of the benzyl and bromoethyl substituents is formed as the main product. Subse- quent cyclisation of compounds 204a,b on treatment with BuLi in THF affords spiro[cyclopropanedihydropyrazines] 202a,b (yield 46%± 55%).132, 133 Me OMe N Bn BuLi 778 8C MeO N 203 Me Me OMe N OMe N a BuLi Bn H Bn N MeO N MeO CH2CD2Br 202a 204a D D Me Me OMe N OMe N b BuLi D Bn H Bn D MeO MeO CD2CH2Br N 202b N 204b (a) BrCD2CH2OTf; (b) BrCH2CD2OTf. In some cases, consecutive chemical transformations result in the formation of heterocyclic and then cyclopropane fragments.For example, the reaction of substituted thioureas 205a ± e with 2,4-dibromobutanoyl chloride occurs on treatment with 5% NaOH in the presence of benzyltriethylammonium chloride and results in a mixture of spiro[cyclopropane-1,50-dihydro- thiazol]-4-one derivatives 206a ± e (yields 18%± 40%) and tri- cyclic compounds 207a ± e.134 The reaction occurs in two steps, as shown for cyclohexylthiourea 205b. NHR NaOH CH2CH2Br C + S + Et3NCH2PhCl7 CHBrCOCl NH2 205a ± e O RNH N RN S N O + S 206a ± e (18% ± 40%) 207a ± e (24% ± 36%) N NaHCO3 NH 205b S (79%) (CH2)2Br R=Bu (a), cyclo-C6H11 (b), Bn (c), Ph (d), 4.Miscellaneous methods for the formation of a spiro-fused cyclopropane fragment A particular case of the formation of a cyclopropane ring spiro- fused with a thiazine fragment is represented by the transforma- tion of tricyclic benzothiazine salts 208a,b, which are obtained by chlorination of benzothiazinone 209 followed by treatment of the resulting a-chloro derivative 210 with 1,3-dienes in the presence of AgClO4.135 Treatment of the benzothiazinium salts 208a,b with reducing agents or bases results in 20-vinylspiro[cyclopropane- 1,20-thiazines] 211a,b in 56%± 90% yields. Electrolysis of the salt 208a in acetonitrile (1 h) also results in spiro[cyclopropane-1,20- thiazine] 211a in *60% yield.It was found by X-ray diffraction analysis that the vinyl group and the sulfur atom in compound 211a are syn-arranged. It was assumed 135 that the formation of spiro[cyclopropane-1,20-thiazines] 211a,b can follow both an ionic and a radical mechanism, although it was not specified which particular intermediates of radical nature can be generated in this system.135 Me N Me N O NCS 0 8C S S 210 209 O Me N H a or b +SClO¡4 R 208a,b RMe N O S R 211a,b R R=Me (a), H (b); (a) 20 8C: Mg, THF, or NaBH4, EtOH, or Zn, AcOH; (b) B7. A spirocyclopropane fragment is formed in the reaction of bromomalonodinitrile with the electron-deficient exocyclic dou- ble bond of 2-methylidene-substituted dihydrobenzoxazole 212.475 Br O + O Et3NCH2PhCl7 206b (e)., AgClO4 O R R MeCN, 0 8C Cl O Me N 7 +S R R476 Spiro[cyclopropane-1,20-dihydrobenzoxazole] 213 is formed when an equimolar mixture of the reactants is kept for 2 h at 25 8C in 95% ethanol in the absence of bases.136 COMe COMe HN HN EtOH COMe+BrCH(CN)2 COMe CN O 213 (82%) O 212 CN The reaction of polycyclic enamines 214 with methyl 1-bro- moacrylate or 1-chloroacrylonitrile results in spirocyclopropane- containing hexahydroindoloindolizine (215a) or hexahydroindo- loquinolizine (215b) salts. Treatment of these salts with NaBH4 or other reducing agents results either in compounds 216 containing a spirocyclopropane fragment (in moderate yields) or in deeper reduction with the cyclopropane ring opening.137, 138 N (CH2)n+H2C C(X)Z NH 214a,b + X7 N N NaBH4 (CH2)n (CH2)n HN HN 216a,b 215a,b Z Z n = 1 (a), 2 (b); X=Cl, Br; Z=COOMe, CN.Desulfurisation of thietane derivatives can serve as yet another method for the formation of a cyclopropane fragment spiro-fused with an azaheterocycle. In particular, photolysis of a mixture of N-methylmonothiophthalimide (217) with 1,1-diphe- nylethylene or trans-stilbene results in spiro-fused thietanes 218 or 219a,b,139 desulfurisation of which with Raney nickel (Ni/Ra) in ethanol affords spiro[cyclopropane-1,30-isoindolin]-1-ones 220 and 221; a mixture of two isomeric compounds, viz., trans- and cis-221, is formed from the isomer 219a under these conditions.However, only one derivative, viz., trans-221, is obtained in almost quantitative yield if thietane 219a is first oxidised with hydrogen peroxide in acetic acid to give sulfone 222, which is then subject to photolysis.139SNMe 217 O S Ph Ph Ph Ph Ph Ni/Ra NMe NMe Ph hn, 10 h EtOH 220 (54%) O 218 (34%) O Ph S S Ph Ph Ph Ph Ph NMe NMe + hn, 1 h 219b (44%) O 219a (36%) O Ph Ph Ph Ph 219a NMe NMe + Ni/Ra EtOH O cis-221 (27%) O trans-221 (20%) Yu V Tomilov, I V Kostyuchenko, OMNefedov Ph O2S Ph H2O2 hn 219a trans-221 NMe MeCO2H 222 (66%) O IV. Functionalisation of heterocyclic compounds containing a spirocyclopropane fragment 32b In this Section, we consider chemical transformations of azahe- terocycles containing a spirocyclopropane fragment, which is preserved in these reactions. In particular, chemical modifications of 5-bromospiro[cyclopropane-1,30-4,5-dihydro-3H-pyrazole] (32b) and 3-R-spiro[cyclopropane-1,50-4,5-dihydro-1H-pyr- azoles] 36a,b, which have recently become accessible (see Section II), were studied.33, 36 It was found 33, 140 that the bromine atom in compound 32b can be replaced by nucleophiles such as PhO, PhS or N3 to give compounds 223, in which the spiro[cyclo- propane-1,50-dihydropyrazole] structure remains intact.XH X7 7Br7 N N 223 (50% ± 65%) X=OPh (a), SPh (b), N3 (c).It was shown recently 32, 140 that 4,5-dihydro-3H-pyrazoles 32a,b, 35 and 223c add phthalimidonitrene, which is obtained in situ upon oxidation of N-aminophthalimide with Pb(OAc)4, to give pyrazolinio-N-phthaloimidoamides (azimines) 224a,b ± 227a,b with retention of the cyclopropane ring. In this case, the regioisomers a are formed preferentially from all 4,5-dihydro-3H- pyrazoles (or exclusively from ester 35). O R1 + NNH2 Pb(OAc)4, CH2Cl2 720 to730 8C R2 O N N 32a,b, 35, 223c R1 R1 R2 R2 N N + N N N N N N O O O O 224b ± 227b 224a ± 227a Ratio a : b Yield (%) R2 Compound R1 HHMe 5.5 : 1 see a 1 : 0 3.3 : 1 70 ± 75 30 ± 35 50 ± 55 60 ± 65 Ph Br COOMe H N3 224 225 226 227 a The isomer 225b is unstable under the reaction conditions.Thermolysis of the azimines 224 and 226 (o-dichlorobenzene, 170 8C) results in the elimination of one nitrogen molecule to give fused heterocyclic systems (compounds 228a,b) with retention of the cyclopropane fragment; in addition, deeper partial dedinitro- genation of the azimines to give spiropentane derivatives 229a,b is observed.32 It is assumed 141 that spiro{cyclopropanetetrahydro- pyrazolo[1,2-b]phthalazine}diones 228 are formed due to the preliminary dissociation of azimines 224, 226 to the starting dihydropyrazoles 32a, 35 and phthalimidonitrene 230. The nitrene 230 eliminates a nitrogen molecule to give benzocyclobutenedioneSynthesis and properties of nitrogenous heterocycles containing a spiro-fused cyclopropane fragment 231, which is in equilibrium with its open diketene form.The latter reacts with dihydropyrazoles 32, 35 to give compounds 228a,b in 25%± 28% yields. The 4,5-dihydro-3H-pyrazoles formed upon the destruction of azimines undergo dedinitrogenation to give the corresponding spiropentanes 229a,b. O O D NN 224, 226 732a,735 O O 231 230 O O R2 R1 C R1 N 32, 35 + R2 N C O 229a,b 228a,b O R1=H,R2=Ph (a); R1=Me, R2=COOMe (b). 3-Cyanospiro[cyclopropane-4,5-dihydro-1H-pyrazole] 36a, like other 4,5-dihydro-1H-pyrazoles, can be acylated with benzoyl or cyclopropanoyl chloride in the presence of pyridine to give 1-acyl-4,5-dihydro-1H-pyrazoles 232.142 On the other hand, the anions 38a,b generated from 4,5-dihydro-1H-pyrazoles 36a,b add to alkenes containing electron-withdrawing substituents exclu- sively as C(3)-nucleophiles [compounds 37a,b are formed similarly (see Section II)].36 For example, dihydropyrazole 36a reacts with dimethyl maleate or dimethyl fumarate in the presence of MeONa to give a mixture of diastereomeric cyanodiesters 233a,b (ratio *1.5 : 1, overall yield*70%).37, 38 CN CN RCOCl Py N N HN N 36a COR 232 (60% ± 70%) R=Ph, cyclo-C3H5.MeONa MeO2CHC CHCO2Me 38a 36a CNCH2CO2Me CNCH2CO2Me + N N N N CO2Me CO2Me 233b 233a Unexpectedly, spiro[cyclopropane-1,50-4,5-dihydro-1H-pyr- azoles] 36a,b readily react with diazocyclopropane (1) generated in situ. For example, decomposition of cyclopropylnitrosourea (2a) on treatment with MeONa or K2CO3 in the presence of dihydropyrazoles 36a,b results in hitherto unknown (E)-cyclo- propylazodihydropyrazoles 234a,b as the main reaction prod- ucts.36, 42 A reaction scheme was suggested which is similar to that of the formation of azo compounds through azo-coupling of aromatic diazonium salts with various substrates, including 4,5- dihydro-1H-pyrazoles.143 The reaction of the 38a,b anions can probably involve diazocyclopropane precursors such as cyclo- propyldiazohydroxide or the cyclopropyldiazonium cation formed upon alkaline decomposition of nitrosourea 2a, rather than compound 1 itself.1 This scheme is supported by the fact that aliphatic diazo compounds, e.g.diazomethane or methyl diazo- acetate, do not enter into similar reactions with 4,5-dihydro-1H- pyrazoles 36a,b. R N 36a,b N 2a,MeONa,720 to715 8C CH2Cl2 H N N 234a,b (72% ± 77%) R=CN (a), COOMe (b). 477 It should be noted that azodihydropyrazoles 234a,b can be obtained in one step by treating acrylonitrile or methyl acrylate with a two- to three-fold excess of cyclopropylnitrosourea (2a).36 An attempt at isolation of azodihydropyrazole 234b by TLC on Al2O3 resulted in its transformation to cyclopropylhydrazone 235 (probably due to hydrolysis of the ester groups followed by decarboxylation); the spiro[cyclopropane-1,50-4,5-dihydro-3H- pyrazole] structure is retained under these conditions. O C OH Al2O3 N NH N 234b N N N 235 (89%) N N Thermolysis of azodihydropyrazole 234a (110 8C, 2 h) is accompanied by elimination of the ring nitrogen atoms to give 1-cyano-1-(cyclopropylazo)spiropentane (236), which undergoes azocyclopropane ± dihydropyrazole rearrangement at higher tem- perature (180 8C, 40 min) 144, 145 to give dihydropyrazole 237 with a spirocyclopropane fragment at position 4 of the heterocycle.36 C6H4Cl2 N N N 232a PhMe 110 8C 180 8C N NC CN 237 (87%) 236 (>85%) Substituted diazocyclopropanes generated by decomposition of N-nitrosoureas 47a or 50 on treatment with sodium methoxide react with dihydropyrazole 36a similarly to the unsubstituted compound 1 to give (E)-azodihydropyrazoles 238a or 238b (each as a mixture of two diastereomers in the ratio*1 : 1).42 R R MeONa,720 to715 8C NCONH2+36a CH2Cl2 47a, 50 NO CN R R N N H N N238a,b R=Me (238a, 70%); R7R=CH2CH2 (238b, 65%).Bromination of cyanodihydropyrazole 36a with N-bromosuc- cinimide (NBS) at 20 8C in the absence of radical initiators occurs at position C(3) of the heterocycle to give 3-bromo-3-cyanospiro- [cyclopropane-1,50-4,5-dihydro-3H-pyrazole] (239) in high yield. However, the resulting bromodihydropyrazole 239 has low stabil- ity and is transformed to the isomeric (2-bromoethyl)cyanopyr- azole (240) in 3 ± 4 days at room temperature.142 Br CN Br(CH2)2 20 8C 36a CN NBS CCl4, 20 8C 3 ± 4 days N N N N 239 (80%) H 240 (*60%) The introduction of chlorine atoms in the cyclopropane ring makes it more stable with respect to electrophilic reagents, in particular Br2 in methanol; this enables functionalisation of the heterocyclic part of the molecule.For example, bromomethox- ylation of a quinoline derivative 241 at room temperature affords a high yield of compound 242 which retains the spiro-fused cyclopropane fragment.146478 Cl Br2, MeOH Cl N 241 CHO Certain transformations of spiro[cyclopropane-1,20-indolin]- 3-one derivatives, in particular of compounds 198, also occur with retention of the cyclopropane fragment; some functional deriva- tives showing antiinflammatory and analgesic activities were synthesised from them.100, 128 For example, the reduction of compound 198a with sodium borohydride results in the hydroxy derivative 243; its reactions with Grignard reagents give alcohols 244a,b.Saponification of N-acetylindolinone 198a on treatment with MeONa or KOH in methanol results in unsubstituted spiro[cy- clopropane-1,20-indolin]-3-one 245 in an almost quantitative yield. The latter was used as the starting compound for the syntheses of alkyl-, acyl-, alkoxycarbonyl- and sulfonylspiro[cy- clopropane-1,20-indolin]-3-ones.128 OH NaBH4, EtOH 4 h Ac N 243 (49%) OH R RMgBr 198a Ac N 244a,b O H+ HN 245 (99%) R=Ph (244a, 67%), Bn (244b, 79%). Nitration of compounds 198a with copper nitrate gives the 5-nitro derivative 246, catalytic hydrogenation of which affords 5-aminoindolinone 247. The acetylamino and mesitylamino deriv- atives of the latter show biological activities.It is of note that treatment of the spirane compound 198a with trifluoroacetic anhydride in acetic acid results not only in cyclopropane ring opening to give substituted indole 248, but also in skeletal isomer- isation of compound 198a, probably through Wagner ± Meerwein rearrangement. The rearrangement product 249 is formed in 40% yield.100 O Cu(NO3)2, NO2 Ac2O 60 8C, 1.5 h Ac N 246 (44%) 198a OAc AcOH, (CF3CO)2O + (CH2)2OCOCF3 Ac N 248 (46%) OMe Br Cl Cl N 242 (89%) CHO O H2N PtO2, H2 MeOH Ac N 247 (80%)O Ac N 249 (40%) Yu V Tomilov, I V Kostyuchenko, OMNefedov V. Conclusion It is evident from this review that the methods for the synthesis of nitrogenous heterocycles containing a spirocyclopropane frag- ment are quite diverse though rather laborious; this restricts considerably the study of the properties of these compounds.The interest in heterocyclic compounds incorporating a spiro- fused cyclopropane fragment stems from the search for new medicines and biologically active compounds. Some heterocycles with a spirocyclopropane fragment, such as derivatives of dihydroisoxazoles, indoline-2(3)-ones, cephalosporins and penicillanates, are of interest as potential pharmaceutical com- pounds. References 1. W Kirmse, H SchuÈ tte Chem. Ber. 101 1674 (1968) 2. 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Russian Chemical Reviews 69 (6) 481 ± 489 (2000) Incommensurate suprastructures: new problems of inorganic solid-state chemistry V S Pervov, E V Makhonina Contents I. Introduction II. Synthesis and structures of misfit compounds III. Physical properties of misfit suprastructures IV. Interactions of substructures and phase stabilities of layered misfit compounds V. Conclusion Abstract. incommensurate inorganic of class new a on Data Data on a new class of inorganic incommensurate intergrowth are compounds, misfit layered intergrowth suprastructures, suprastructures, viz., layered misfit compounds, are surveyed misfit of properties Physical systematised. and surveyed and systematised. Physical properties of misfit supra- supra- structures of effects the of mechanisms Possible discussed.are structures are discussed. Possible mechanisms of the effects of the the electronic the on incommensurability and structure electronic structure and incommensurability on the structural structural elements in recognition their on and suprastructures of elements of suprastructures and on their recognition in molecular molecular ensembles for criteria general The considered. are ensembles are considered. The general criteria for self-organisa- self-organisa- tion and proposed are suprastructures incommensurate of tion of incommensurate suprastructures are proposed and con- con- ditions sublattices the of one of fragmentation the for ditions for the fragmentation of one of the sublattices (i.e., conditions for the formation of nanocomposites) are given.The conditions for the formation of nanocomposites) are given. The bibliography references 82 includes bibliography includes 82 references. I. Introduction The term `supramolecular chemistry' was introduced by the Nobel laureate J-M Lehn in 1978. He defined this field as the chemistry beyond the molecule, which describes complex aggregates formed as a result of association of two (or more) chemical species linked by intermolecular forces.1 In succeeding years, this new interdisci- plinary science whose language, definitions and concepts are still in their developmental stage has been progressing rapidly.2 It should be noted that the range of subjects studied in supramolecular chemistry is being steadily extended, which gen- erates a need for the discussion of some limitations on their choice, in particular, restrictions imposed by the requirements of the geometric and topological correspondence of structural elements upon self-organisation of supramolecular ensembles.As shown below, these limitations are of fundamental importance partic- ularly in the case of inorganic suprastructures because their structures are substantially affected by the rigidity of conjugated extended structural elements. Thus it was demonstrated 3 that a guest ± host system, which governs differences in the principles of construction of supramolecules based on the structural organisa- tion of the host (three-, two-, one- or zero-dimensional structures), V S Pervov Moscow State University of Engineering Ecology, ul.Staraya Basmannaya 21/4, 107884 Moscow, Russian Federation. Fax (7-095) 261 49 61. Tel. (7-095) 267 19 47. E-mail: pervov@ionchran.rinet.ru E V Makhonina N S Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninsky prosp. 31, 117907 Moscow, Russian Federation. Fax (7-095) 952 20 62. E-mail: evma@ionchran.rinet.ru Received 27 January 2000 Uspekhi Khimii 69 (6) 528 ± 537 (2000); translated by T N Safonova #2000 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2000v069n06ABEH000573 481 482 483 485 487 is better suited to the classification of inorganic subjects of supramolecular chemistry. Incommensurability between a guest and a host is rather frequently observed in inorganic guest ± host systems, which can lead to structural and morphological changes in the supramolec- ular ensemble as a whole.The problem of incommensurability has been stated and considered in most detail within the framework of supramolecular chemistry dealing with incommensurate inter- growth structures. Studies in this field were started more than a decade ago.4 Among these structures are inorganic compounds with crystal lattices consisting of two (or more) sublattices whose periods are noticeably different (at least in one direction). The term `misfit' is finding increasing use for the description of such compounds. Two types of compounds with incommensurate structural elements, viz., linear (one-dimensional) and layered (two-dimen- sional) structures, are known.5 Systems characterised by a one- dimensional (chain) structure of the guest sublattice (substruc- ture) belong to the linear type (these structures are also said to be columnar misfit structures).Generally, the sizes of the `columns' correspond to the size of the host matrix in the ab plane perpendicular to the axis of the column, whereas the incommen- surability is associated with its c axis. These structures are exepmlified in crystals of Hg37x AsF6 containing 7Hg7Hg7 chains, which are located in cavities formed by AsF6 octahedra,4 and in compounds of the A17x Cr2X47x series (A=Ba, Sr, Eu or Pb; X=S or Se; x=0.29).6 The structure of one compound of this series, viz., Eu17x Cr2Se47x, is shown in Fig. 1.This com- pound is of interest because it contains two types of one-dimen- Cr Eu Se Figure 1. Structure of Eu17xCr2Se47x (projection along the incommen- surate axis).5482 sional guest sublattices, viz., Eu6Cr2Se6 and Eu3Se, which thread the framework of the host Cr21Se36. Suprastructures with incommensurate layers belong to lay- ered misfit structures. In these structures, as in columnar misfit substances, the incommensurability is manifested only in one crystallographic direction along which the layers are aligned. These subjects are not new, since different combinations of crystallographically incommensurate layers (for example, gallium adsorbate on the surface of single-crystal silicon 7 and some other epitaxial systems) have long been known and have been well characterised.Among layered misfit structures, synthetic complex chalcogenides of the general formula (MX)1+x (TX2)m (M=Sn, Pb, Bi, Sb or Ln; T=Ti, V, Nb, Ta or Cr; X=S or Se; x=0.08 ± 0.28; m=1, 2, 3...) have been studied in most detail. These compounds represent analogues of the well-known minerals, viz., cylindrite [(Pb,Sb)S]1.38(Sn,Fe)S2,8 franckeite Pb5FeSn3Sb2S14 (see Ref. 9) and some other minerals.10 The rather high thermodynamic stability of inorganic incom- mensurate compounds calls for revision of the existing concepts of the topological `laws' of construction of supramolecular struc- tures. When constructing incommensurate structures, researchers face two problems.The first problem is associated with the limiting values of the incommensurability up to which the structural elements (substructures) retain their capacity for self- organisation. The second problem is related to the consequences of this self-organisation. In the course of self-organisation of the suprastructure, forces responsible for the retention of the rigidity of its constituent substructures compete with forces linking these substructures to form a single suprastructure. This competition leads to various structural and morphological changes in the ensembles formed. Since the discovery of incommensurate intergrowth struc- tures, no structures possessing the incommensurability in more than one crystallographic directions have been found, i.e., the topological principles of the construction of these compounds are rejected only partially.Nevertheless, even `one-dimensional' incommensurability gives rise to very interesting properties of inorganic crystal structures. On the whole, problems associated with the structures, phase stabilities and properties of incommensurate intergrowth supra- structures have not been adequately investigated, though, in our opinion, these problems are of importance for both inorganic supramolecular and solid-state chemistry. In particular, one of the fruitful lines of investigation of incommensurate structures may be associated with an apparent analogy of the mechanisms of formation of intercalates AaTX2 (A is a donor species and TX2 is a layered dichalcogenide matrix) to those of layered misfit compounds (with the same matrices).It is also worthy of note that studies dealing with layered misfit compounds have been aimed mainly at searching for new combi- nations of incommensurate substructures, developing procedures for their structural identification and studying their physical properties. We believe that studies of layered misfit structures are of interest not only because of unusual properties of these compounds, but primarily because of considerable prospects of their application due to evident possibility of the preparation of materials possessing unique electrophysical and magnetic charac- teristics (if only due to the nontrivial behaviour of conduction electrons in incommensurate crystal fields).II. Synthesis and structures of misfit compounds Several procedures for the synthesis of incommensurate supra- structures are known. The majority of layered misfit structures (MX)1+x(TX2)m have been prepared by solid-phase high-temper- ature synthesis starting from the elements or the corresponding binary compounds (MX and TX2). Generally, suprastructures withM=Sn, Pb, Bi or Sb are formed at about 800 ± 900 8C,11 ± 16 whereas suprastructures with M=Ln are formed at 1050 ± V S Pervov, E V Makhonina 1350 8C.17 ± 20 In all cases, the syntheses are completed in several days. In a number of studies, layered misfit structures were prepared by slow heating of the starting mixtures to temperatures at which the synthesis started.Then the mixtures were kept at this temper- ature for several days and the resulting specimens were slowly cooled. Procedures for the synthesis of layered misfit compounds involving quenching of specimens from high temperatures (see, for example, Refs 12 and 16) were also reported. Unfortunately, the dependence of the properties of the resulting specimens on the mode of cooling was not examined. Most of the known misfit compounds were prepared using stoichiometric amounts of chalcogenides MX and TX2 (1 :m) based on the formula (MX)(TX2)m (i.e., at x=0), although the compositions of the resulting substances are described by the formula (MX)1+x(TX2)m, where x is distinct from zero. Gener- ally, syntheses of misfit compounds from the elements were carried out using a small excess of the corresponding chalcogen to accelerate the reaction (see, for example, Ref.15). A procedure for the preparation of layered misfit supra- structures (especially, based on REE) from the corresponding ternary oxides by their heating in a graphite boat under a stream of a mixture of hydrogen sulfide and an inert gas at 1300 ± 1350 8C was also described.5 In particular, this procedure was used for the preparation of (LaS)1.19CrS2. Single-crystalline specimens can be synthesised by the trans- port reaction method. Traditionally, iodine 19, 20 or chlorine 14 serves as the transporting agent. (It was mentioned that crystals were formed in the cooling zone of a furnace.) Crystals of `PbNbS3' and `LaNbS3' were grown with the use of an admixture of (NH4)2PbCl6, which decomposed at high temperature to form PbCl2, NH4Cl and Cl2.17 Apparently, the chlorine liberated acted as the transporting agent.As mentioned above, layered misfit suprastructures of the (MX)1+x(TX2)m type consist of layers of two substructures, viz., MX (guest) and TX2 (host). The guest layer (Q layer) has a pseudocubic NaCl-type lattice and the host layer (H layer) represents a `sandwich' of hexagonal networks built up from X atoms. Atoms of the transition metal T are either in trigonal- prismatic (Nb or Ta) or octahedral (Ti, V or Cr) environment formed by X atoms (Figs 2 and 3).21 ± 24 Thus the trigonal- prismatic and octahedral environments about the T atoms are observed in the structures (SnS)1.17NbS2 (see Ref.24) and (PbS)1.18TiS2,21 respectively. Layered misfit compounds differ in the number of the host layers per guest layer (for example, 1Q/1H, 1Q/2H or 1Q/3H).5 Therefore, these compounds are described by the general formula (MX)1+x(TX2)m, where the index m is the number of TX2 layers per unit cell of the suprastructure along the c axis. Mono- (m=1) and bilayer (m=2) structures (Fig. 4) prevail. The arrangement of the structural elements along the b axis can also be different due to the presence of two extreme stacking sequences for the substructures. In the case of a body-centred (CC) arrangement ofMXandTX2 substructures, their c axes coincide, whereas in the case of a face-centred (FF) arrangement, these axes are shifted aQ b b aH XT XM Figure 2.Substructures MX (Q layer) and TX2 (H layer) with incom- mensurate lattice parameters (aQ and aH).Incommensurate suprastructures: new problems of inorganic solid-state chemistry XT 2H 1T Figure 3. Coordination of the T atoms in the trigonal-prismatic (2H) and octahedral (1T) polytypes of the TX2 substructure. b a MX MX c TX2 TX2 b TX2 MX a MX TX2 Figure 4. Schematic representation of monolayer (a) and bilayer (b) misfit structures. relative to each other by a/2. Intermediate modes (CF and FC) of arrangement of MX and TX2 units were also found (Fig. 5).5 The limiting stoichiometry of the suprastructure (MX)1+x (TX2)m as a whole is determined by the ratio between the parameters a of the host and the guest (aH : aQ), which can change from 0.64 [for (YS)1.28CrS2) ]22 to 0.54 [for (BiS)1.08TaS2].23 Here, x=(4/2)(aH/aQ)71 (4/2 is the ratio between the numbers of the MX and TX2 formula units in the unit cell of the suprastructure).The parameters aH and aQ of the unit cells of selected layered misfit compounds are given in Table 1. The application of the X-ray powder method and X-ray structural analysis to studies of misfit structures presents prob- lems because the symmetry of these compounds should be described by four-dimensional space groups.4, 17 It was also demonstrated that the precise identification of misfit structures is complicated by the following interrelating facts: by the presence of c TX2 b MX T 1/2aH XM 1/2aQ X FF FC CF CC Figure 5.Different structural types of layered misfit compounds based on NbS2 and TaS2 (projections along the [100] direction).5 483 Table 1. Limiting stoichiometric ratios for the unit cells of some layered misfit compounds. Ref. Compound aQ /A aH /A x=2aH/aQ71 bQ=bH /A 24 17 21 5.751 5.797 5.881 (SnS)1.17NbS2 5.673 3.321 0.1708 (LaS)1.14NbS2 5.828 3.310 0.1359 5.800 3.410 0.1755 (PbS)1.18TiS2 several polytypes in the suprastructure, which hinders the for- mation of single crystals, and by the difference in morphology of crystalline particles of these suprastructures. Thus it was found that the synthesis and prolonged annealing (required for the attainment of thermodynamic equilibrium) of the misfit com- pounds (BiS)1+x(NbS2)m and (PbS)1+x(NbS2)m gave rise both to the usual layered crystals and species with the same composi- tion, which resemble an insulation tape bundle.11, 15 Beginning with a particular diameter of the species, the layers are twisted and the maximum radius of the bundle does not exceed 0.1 mm.III. Physical properties of misfit suprastructures The complexity of incommensurate suprastructures (in particular, layered misfit structures) and the characteristic features of inter- actions between their constituent substructures result in the diversity of the physical properties observed. Misfit structures are studied by different physical and physicochemical methods.The electrophysical and magnetic properties of misfit compounds were examined in a large number of studies. The superconductiv- ity of compounds based on some layered dichalcogenides with the 2H structure was also investigated. Valuable information on the physical properties of incommensurate suprastructures was also obtained in studies of X-ray photoelectron spectra, optical reflec- tance and Raman spectra as well as in studies with the use of some other methods. 1. Electrophysical properties Misfit compounds containing NbX2 or TaX2 as the host substructure possess metallic conductivity.11, 13, 19, 23 ± 26 In these structures, the resistivity (rab) in the ab plane is*1076 O.19, 23 ± 27 The ratio between the resistivities along the commensurate (b) and incommensurate (a) axes (ra/rb) is close to unity [for example, in the compound (CeS)1.16NbS2].27 This is also evident from the number of charge carriers along the a and b axes calculated for the suprastructure (PbS)1.13TaS2.These values were determined from optical reflectivity measurements.28 The resistivity along the c axis is substantially larger than that in the ab plane. The rc/rab ratio is equal to 50 for compounds based on chalcogenides of rare-earth elements 27 and it is even larger for suprastructures with M=Sn, Pb or Bi. Thus the rc/rab ratio for (SnS)1.18NbS2 is 250 and 800 at 300 and 4 K, respectively 3 (rc/rab'105 determined at 300 K for this compound previously 24 is, apparently, overestimated).Like some intercalates based on tantalum and niobium dichalcogenides, misfit suprastructures formed from TaS2 or NbS2 and PbS, SnS or BiS are characterised by a positive Hall coefficient and a negative Seebeck coefficient.23 ± 26 The number of holes calculated from the Hall coefficients at 4 K25, 26 suggest the occurrence of electron transfer from the MX layers to the TX2 layers in incommensurate suprastructures, as in intercalates, the dz2 band of the TX2 layer being more than half-filled. Taking into account the negative Seebeck coefficients, it should be noted that these data are only tentative. Suprastructures consisting of TaX2 or NbX2 layers and layers of REE chalcogenides are characterised by a substantially lower concentration of charge carriers compared to suprastructures containing Sn, Pb or Bi chalcogenides.These compounds possess positive Hall and Seebeck coefficients,29 ± 31 which is indicative of p-type conductivity in these compounds. The calculated degrees of electron density transfer in suprastructures with M=REE are484 substantially higher than those observed in compounds with M=Sn or Pb.31 The X-ray photoelectron specra of these com- pounds 32 ± 35 also revealed an essential electron transfer fromMX to TX2 layers. In this case, the M atoms exist virtually in the trivalent state. Metallic conductivity is also typical of suprastructures (MS)1+x (TiS2) with M=Sn or Pb.11, 36, 37 The temperature dependences of rab observed for (MS)1+x(TiS2) 36 is analogous to those found for the intercalates LixTiS2 (see Ref.38) and AgxTiS2.39 The Hall coefficient of the former is negative and corresponds to the partial filling of the conduction band of the TiS2 substructures by electrons from the MX substructure. How- ever, the character of the temperature dependence of rab indicates that holes in the valence band of MX are not involved in the conductivity. It was thus suggested 5 that holes are localised in the valence band of the MX substructure. This localisation occurs either due to a change in the lattice potential along the [100] direction giving rise to centres of hole localisation or due to the presence of defects and vacancies in the MX sublattice. The compounds (CeS)1.19(TiS2)m (m=1 or 2) 37 also possess metallic conductivity and exhibit antiferromagnetic ordering at 2.8 K, which is not accompanied by anomalous behaviour of the conductivity around this point.This indicates that the MX layers do not contribute to the conductivity of the above-mentioned compounds. The residual resistivities observed for the compounds (CeS)1.19(TiS2)m (*450 and 350 mO cm for m=1 and 2, respec- tively) are larger than that for LixTiS2 (see Ref. 38) whose structure is not incommensurate. The authors believed that this fact is indicative of a substantial effect of the incommensurability of misfit structures on the crystal lattice, which is manifested in its local modulations playing a significant role in scattering of charge carriers.37 The majority of compounds with the VX2 sublattice, for example, (PbS)1.12VS2 (see Ref.12) and (LnS)1+xVS2 (see Refs 37 and 40) (Ln=La, Ce, Nd or Sm), exhibit semiconducting properties. It was found that the conductivity of the compounds (LnS)1+xVS2 (Ln=La, Ce, Pr or Nd) changed from semicon- ducting to metallic at 150 ± 200 K.41 The V7V distances in the misfit compound (PbS)1.12VS2 possessing semiconducting properties 42 are close to those in the intercalates NaxVS2,43 which exhibit metallic conductivity. There- fore, the semiconducting properties of (PbS)1.12VS2 demonstrate that holes in the valence band of PbS are not involved in the conductivity. These holes are either localised or absent due to lattice defects. X-ray structural analysis of the compound (LaSe)1.21VSe2 within four-dimensional symmetry space groups 44 established that the LaSe sublattice contains*5% of lanthanum vacancies and the VSe2 sublattice is characterised by a large modulation of the V7V distances giving rise to centres of local- isation of charge carriers.Therefore, holes available in the valence band of LaSe layers do not contribute to the conductivity of the compound (LaSe)1.21VSe2. Based on the conductivity data, the temperature dependence of the thermoelectric power and the optical reflectivities for the compound (LaS)1.16VS2, it was con- cluded that charge carriers are localised in LaS layers.37 Misfit suprastructures with the CrS2 host substructure were prepared only for REE. The measurements of the conductivity of (GdS)1.27CrS2 (see Ref.45) demonstrated that this compound exhibits semiconducting properties; the activation energy is 0.34 eV. The suprastructure (LaS)1+xCrS2 also possesses semiconducting properties.45, 46 The X-ray photoelectron spectra and magnetic measurements performed for the compounds (LnS)1+xCrS2 demonstrated that chromium atoms occupying the CrS2 sublattice points exist in the trivalent state,47, 48 which is indicative of a substantial electron transfer from LnX layers to CrS2 layers. In this case, a portion of electrons (x) does remain in the LnX sublattice, which seemingly should give rise to metallic conductivity in these misfit compounds (at least, for elements of the first part of the REE series whose electrons are delocalised over 5d and 4f orbitals).However, the precise chemical analysis of V S Pervov, E V Makhonina the compound (LaS)1+xCrS2 (see Ref. 45) demonstrated that the lanthanum content in this compound is less than that expected. Based on the results of the analysis, the formula (La0.94[ ]0.06S)1.2CrS2 was assigned to the compound (LaS)1+xCrS2 because the charges of La3+, Cr3+ and S27 can be balanced out only if lanthanum vacancies are present in the LaS layers. An analogous situation was observed for the compound (GdS)1.27CrS2 to which the composition (Gd0.91[ ]0.09S)1.27CrS2 was assigned on the basis of the data from precise chemical analysis and X-ray structural analysis. In this case, charge balance between the ions is observed.Therefore, the semiconducting character of the compounds under consideration is attributable to partial localisation of electrons in the MX layers. 2. Magnetic properties The magnetic properties of layered misfit compounds based on TaX2 or NbX2 with the LnX guest substructure are determined primarily by the nature of the Ln atom. The strong effect of the crystal field was observed for mono- and bilayer misfit structures with M=Ce or Nd.19, 27, 34, 49 Studies of the magnetic properties of the compounds (LnS)1+x (TS2)m (T=Ta or Nb) demon- strated that these properties are substantially different in the directions perpendicular and parallel to the magnetic field (the direction of the field coincides with the c axis of the crystal).Thus the magnetic susceptibilities for the phases `NdNb2S5' and `SmNb2S5' along the field and in the transverse direction differ by factors of 1.5 and 2.5 ± 2.6, respectively.19 The small magnetic moments of the compounds (LaX)1+x (TX2)2 (see Refs 19, 49 and 50) indicate that lanthanum atoms exist in the trivalent state, which is indicative of a substantial electron transfer from LaX layers to TX2 layers. In suprastructures with M=Ce 51 or Sm,34 the electron density transfer from MX layers to TX2 layers is somewhat smaller than that observed in suprastructures with M=La. According to the results of measurements of magnetic moments, weak ferromagnetic interactions occur within the LnX layer and even weaker antiferromagnetic interactions occur between the LnX layers.At low temperature, antiferromagnetic ordering is observed in suprastructures (in this case, the temper- ature dependence of the magnetic moment does not obey the Curie ± Weiss law).19, 38, 45 For the suprastructure `GdNb2S5', the ordering occurs at 5 K.19 For the suprastructure (GdS)1.21NbS2, the ordering occurs at 12.8 and 4.6 K.38 Somewhat different results were obtained for compounds withM=Tb, Dy or Er. At low temperature, these compounds behave as paramagnetics and do not exhibit the anisotropy of magnetic properties.5, 19 This was attributed to the absence of the effect of the crystal field in the case of REE atoms located in the right part of the Periodic system due to a larger contraction of their 4f orbitals.The magnetic properties of the suprastructures (LnS)1+xVS2 also substantially depend on the nature of the Ln atom 40, 52 and are in many respects similar to the properties of the corresponding structures based on NbX2. However, the properties of the former compounds are distinguished by stronger antiferromagnetic inter- actions between LnS layers. The deviation of the temperature dependence of the magnetic moment from the Curie ± Weiss law at low temperatures is attributed to the effect of the crystal field. The magnetic properties of the compounds (LnS)1+xVS2 indicate that the Ln atoms in these compounds exist in the trivalent state. The magnetic behaviour of misfit structures containing CrS2 layers is more complex because of the contribution of Cr3+ ions.45, 47, 48 Thus the compound (LaS)1.20CrS2 behaves as a para- magnetic up to 110 ± 300 K.At low temperatures, two magnetic transitions (at 120 and 70 K) are observed for this compound.48 Such behaviour of (LaS)1.20CrS2 is conditioned by the spins of the Cr3+ ions. The results of magnetic measurements for structures containing CrS2 layers were interpreted taking into account the type of ordering of the magnetic structure at low temperature and possible antiferromagnetic interactions between the Cr ions in the CrS2 layer (depending on the Cr ±Cr distance) (see, for example, the review 5).Incommensurate suprastructures: new problems of inorganic solid-state chemistry 3. Superconductivity Of the known misfit suprastructures, only the compounds (MX)1+x(TX2)m (M=Sn, Pb, Bi or Ln; X=S or Se, m=1 or 2) based on layered tantalum or niobium dichalcogenides, which have 2H structures and possess their own superconductivity, exhibit superconducting properties.The superconducting transi- tion critical temperatures (Tc) for all these misfit compounds are lower than those for the corresponding dichalcogenides TX2, which is, apparently, attributable to the insulating properties of MX layers.53 ± 58 For example, the Tc values for the compounds (PbS)1.14(NbS2)2 and (PbS)1.14NbS2 are 3.4 54 and 2.475 K,53 respectively, whereas Tc for 2H-NbS2 is 6.3 K.5 Misfit compounds based on TX2, like dichalcogenides as such, exhibit anisotropy of the critical field, which depends on the nature of the metal M.Thus the anisotropy is *1.29 and 35 for (BiSe)1.10NbSe2 and (LaSe)1.14NbSe2, respectively. For mono- and bilayer suprastruc- tures, the critical fields also have differing anisotropy. For the monolayer compounds (SnS)1.17NbS2 and (PbS)1.14NbS2, the anisotropy is*8 ± 10,53, 56 whereas the anisotropy for the bilayer compound (PbSe)1.12(NbSe2)2 is *4± 5.54 Based on the fact that the compound (PbSe)1.12(NbSe2)2 exhibits anisotropy intermedi- ate between those of (PbS)1.14NbS2 and NbSe2 as such, it was suggested that the compound (PbSe)1.12(NbSe2)2 is a second-stage intercalate.57 * * * To sum up the discussion of the physical properties of layered misfit structures, it should be stated that these properties can be described to a first approximation by an additive scheme, viz., as a result of superposition of the properties of the TX2 and MX substructures.Thus studies of a number of misfit structures by X-ray photoelectron and Raman spectroscopy 21, 59 ± 62 demon- strated that these spectra can be described as a superposition of the spectra of the MX and TX2 substructures. In some respects, this is also true for the results of studies of the electrophysical properties of these compounds. When describ- ing suprastructures (MX)1+x(TX2)m within the framework of the rigid band model, one can use the fact that the TX2 andMXlayers in these structures are similar to the corresponding layers in crystals of TX2 and MX, with the difference that the Fermi level for the TX2 layer of the misfit structure is located higher than that in the crystal of TX2 and taking into account that the changes in the MX layer compared to the analogous layer in the crystal are caused by the electron transfer to the TX2 layer.(The charge transfer from the MX layers to the TX2 layers was quantitatively evaluated based on the Hall and Seebeck coefficients.) Needless to say the real situation goes beyond the scope of the simple additive scheme. For example, as mentioned above, the mutual effect of two substructures, which is manifested, in particular, in distortions and discontinuities of the crystal lattices of the TX2 and MX layers, cannot be ignored. On the whole, the data on the physical properties of layered misfit structures confirm the correctness of their comparison with intercalates of theAaTX2 type.IV. Interactions of substructures and phase stabilities of layered misfit compounds In this Section, we consider the nature of the interaction between substructures and the possibility of deformation of their lattices. In our opinion, it is worthwhile to perform a comparative analysis of conditions of the occurrence of layered misfit structures (MX)1+x(TX2)m and intercalatesAaTX2 (A is any metal) because this analysis can be based on the use of a unified approach determining the limits of the phase stability of the layered TX2 host matrix. Although intercalates, unlike misfit structures, do not imply incommensurability between the host and guest lattices (in the theory of intercalates,63 it is assumed that cavities in the host lattice topotactically correspond to the structure of the guest), both layered misfit structures and intercalates are characterised by Q7Hinteractions of the same type determined by charge transfer from MX to TX2 and from A to TX2, respectively.64, 65 The concept describing the conditions of phase stability of layered intercalates is based on the rigid band model.66 Depending on the coordination of the T atom, the TX2 matrix can exist in two structural modifications related to the electronic stabilisation of the conduction bands, viz., 1T (octahedral coordi- nation) and 2H(trigonal-prismatic coordination).The schemes of the conduction bands for layered dichalcogenides of Groups IV ±VI transition metals are shown in Fig.6. E s, p dxz; dyz EF2 dx2¡y2 , dxy dz2 EF1 ps N(E) Group IV Figure 6. Band structures of transition metal dichalcogenides TX2 (2H polytype).66 It was found 66 that the valence band of the TX2 layer consists of two subbands to which the s and p atomic orbitals (AO) of chalcogen X make the major contributions, whereas the conduc- tion band consists primarily of nonbonding d-AO of the transition metal T. The splitting of the conduction band by the crystal field of the X atoms determines its occupation by electrons and the energetics. In the 2H structures of TX2, the band formed by the dz2-AO of the T metal has the lowest energy. For the d 1 ions of Group V metals (for example, for Nb and Ta), this band is half-filled; the occupied and unoccupied levels of this band are not separated due to which these compounds exhibit metallic conductivity.Within the limits determined by the filling of the dz2-AO of the T atom, intercalation of the structures 2H-NbX2 and 2H-TaX2 does not lead to electron destabilisation of the system and occurs rather readily. We have demon- strated 67, 68 that destabilisation of the conduction band in the intercalates GaaNbSe2 and GaaTaSe2 occurs at a&0.12 and is accompanied by the transformation of a two-dimensional struc- ture into a three-dimensional (spinel) structure, which is associ- ated with a change in the valence states of gallium and niobium (tantalum) atoms caused by charge transfer from gallium to niobium (tantalum).Layered misfit structures (MX)1+x(TX2)m based on dichal- cogenides of Group V transition metals have been rather well studied. It was demonstrated that the degree of charge transfer from M to T depends on the properties of the MX guest layer.17, 19, 25, 26, 29 ± 35, 49 ± 51, 62, 64 In suprastructures containing lanthanide (M=Ln) sulfides (selenides) as the guest, substantial charge transfer was observed. Thus based on the temperature dependence of the conductivity and the data from X-ray photo- electron spectroscopy, it was established that the filling of the dz2 band in 2H-TaX2 for monolayer structures is 1.8 ± 1.97 electrons per T metal atom. A different situation occurs in misfit com- pounds with M=Sn or Pb.In the latter, the charge transfer is E E s, p s, p EF2 dz2 dz2 EF1 p p s s N(E) Group V 485 EF2 EF1 N(E) Group VI486 significantly smaller. According to the published data,24, 25, 64 the charge transfer in these suprastructures is 0.3 ± 0.5 electrons per T atom. Apparently, suprastructures with T=V are a special case.12, 37, 40, 44, 52, 61 In the phases (PbS)1.12VS2,12 (LnS)1+xVS2 (Ln=La, Ce, Nd or Sm) 37, 40 and (LaSe)1.12VSe2,44 vanadium atoms are in an octahedral environment. In these structures, as in compounds with T=Nb or Ta, electron density is transferred from MX layers to VX2 layers, this transfer being particularly significant for compounds with M=Ln.40, 52 As mentioned above, the V±V distances in these misfit structures are close to those in intercalates NaxVS2 (see Ref.43) possessing metallic conductivity. A consideration of the electronic structures of misfit suprastructures based on VX2 within the framework of the rigid band model assumes that these structures possess metallic con- ductivity. However, most of the suprastructures synthesised based on vanadium chalcogenides are actually semiconductors. This behaviour may be attributed either to the formation of an energy gap in the Fermi level due to splitting of the t2g orbitals 37 or to localisation of charge carriers in the MX layer at defects of different types 37, 44, 61 caused primarily by the incommensurabil- ity of substructure lattices. Layered matrices based on chalcogenides of Group VI metals, such asMoand W, belong to the 2Hpolytype and are high energy- gap semiconductors.The dz2 band in chalcogenides of Group VI metals with the 2H structure, unlike that in chalcogenides of Group V metals, is completely filled. The energy gap between this band and the nearest unoccupied levels is *1.5 eV.66 Hence, intercalation of these compounds with A donors is very hindered. Therefore, it is reasonable that layered misfit structures based on 2Hlayers of MoX2 orWX2 are as yet unknown. At the same time, misfit compounds based on chromium sulfide, viz., (LnS)1+x(CrS2)m, with the 1T structure of the host matrix have been characterised in sufficient detail. These compounds are semiconductors with an energy gap of *0.5 eV.In these compounds, as in the compounds (LnS)1+x (VS2)m , the M and T atoms exist in the trivalent states due to a substantial charge transfer from Ln to Cr and the presence of vacancies in Ln positions.37, 45, 46 Layered misfit suprastructures withM=Bi or Sb are a special case. Although these compounds are very similar in structure and properties to compounds with M=Pb or Sn, the charge transfer in the former compounds determined from electrophysical data 23, 26 is substantially smaller than that in misfit structures withM=Pb or Sn, unless a strong acceptor, such as CrS2, serves as the host matrix.64 The X-ray photoelectron spectra 69 of the compounds (SbS)1+xCrS2 and the Bi7S bond lengths in (BiS)1.23CrS2 (see Ref.70) demonstrate that the Sb and Bi atoms in these compounds exist in the trivalent state. A number of characteristic structural features of the compounds (BiS)1.08TaS2 and (BiSe)1.09TaSe2 containing short Bi7Bi bonds were men- tioned.15 Of Group IV transition metals, only titanium atoms form layered dichalcogenide structures with a crystal lattice of the 1T-CdI type (with octahedral coordination about the T atom, see Fig. 3). Generally, their intercalation with donors (metals) is accompanied by a 1T?2H phase transition.63 The atomic t2g orbitals of titanium ions with the d0 electronic configuration are unoccupied. However, intercalation of the TiX2 matrix with A donor atoms leads to the electron transfer fromAatoms to Ti ions and to the occupation of the t2g orbitals.In this case, their degeneracy is eliminated because the trigonal-prismatic (2H) coordination about Ti atoms with the lower-energy dz2 band becomes energetically more favourable. A rather surprising thing is that the Ti atoms retain an octahedral coordination in spite of the difference in the character of theMXlayers and the conditions of charge transfer. Titanium dichalcogenides form layered misfit compounds with Pb, Sn,11, 21, 36, 61, 71, 72 Ce 37 or Ag.73 Electrophysical meas- urements 36, 37 and analysis of photoelectron spectra 21, 61, 74, 75 and V S Pervov, E V Makhonina Raman spectra 61 indicate charge transfer fromMXlayers to TiX2 layers. The nature and bond strengths between the layers in such misfit structures were interpreted differently.Thus, in some studies 3, 64, 69 it was assumed that the MX and TiX2 layers are covalently bound (viz., that there are covalent bonds between the Matoms of theMXlayers and the X atoms of the TiX2 layers). In other studies, it was reported that there are Coulombic interac- tions between the positively charged metal atomsMfrom theMX layers and the negatively charged chalcogen atoms from the TX2 layers, as, for example, in the compounds (PbS)1.18(TiS2)m (m=1 or 2). Electron probe microanalysis of this compound 71 revealed a deficiency of lead ions in the PbS layers, which was interpreted as the replacement of 8%± 10% of Pb2+ ions by Ti3+ ions, which may lead to stabilisation of the misfit suprastructure.The stability of the compounds (CeS)1.19(TiS2)m (m=1 or 2) was estimated within the framework of the rigid band model based on the results of measurements of the electrical resistivity, thermoelectric power and optical reflectivity.37 However, the results of the majority of studies, in our opinion, indicate that the interaction between the MX and TX2 substruc- tures occurs through charge transfer from the MX layers to the TX2 layers. For example, calculations of the band structure of (LaS)(SrS)0.2CrS2 demonstrated 46 that there is no more or less significant charge density between the lanthanum atoms from the LaS layer and the sulfur atoms from the CrS2 layer. On the contrary, the lone electron pairs of the sulfur atoms of the CrS2 layer are directed toward the free space rather than toward the lanthanum atoms of the adjacent layer.In this case, the factors determining the polytype of the TX2 layer in the resulting supra- structures remain unclear. In our opinion, the energy character- istics of the structures under consideration play here a decisive role. These characteristics can be described based on the concept of electronic stabilisation of the suprastructure. This concept was confirmed by the results of the study 45 in which the formation of defects inMXsubstructures due to the transfer of an excess charge from the MX layer to the TX2 layer was experimentally observed and theoretically justified. One would expect that intercalation of layered misfit struc- tures with donor species will be accompanied by phase transitions associated with changes in substructures. Analogous processes were observed, for example, on the formation of intercalates of the AaTX2 type.67, 68 The formation of defects (discontinuities) in the MX substructure may be yet another consequence of intercala- tion.As mentioned above, intercalates based on layered misfit compounds are formed due to charge transfer and filling of unoccupied levels of the suprastructure. Unfortunately, examples of the existence of such intercalates, their structural features and properties are limited in number.However, to a first approxima- tion it can be stated that the rule of electronic stabilisation is fulfilled for these compounds, as in the case of intercalation of typical layered matrices.At the same time, it is important to keep in mind the differences associated with the charge transfer in the above-mentioned intercalates and in the corresponding misfit structures. Studies of intercalation of the suprastructures `PbVS3', `PbTiS3', `PbTi2S5' and `SnTiS3' with lithium (from solutions of n-butyllithium in hexane at room temperature) 14 demonstrated that intercalation of monolayer misfit structures occurs with greater difficulty than that of the corresponding bilayer structures. Analogous results were obtained in the study 76 in which the electrochemical intercalation of the com- pounds (PbS)1.18TiS2 and (PbS)1.18(TiS2)2 with silver was exam- ined.It was demonstrated that the insertion of silver into the structure (PbS)1.18TiS2 resulted in disproportionation of the latter into Agx(PbS)1.18(TiS2)2 and PbS. Similar results were obtained upon intercalation of iron and nickel into layered misfit structures based on TiS2 and LaS or CeS.77 Monolayer intercalates could not be prepared, whereas the bilayer structures of the Aa(LaS)1.18(TiS2)2 type were synthesised and studied. Presumably, the formation of intercalates (in the caseIncommensurate suprastructures: new problems of inorganic solid-state chemistry of a comparable donor ability of the intercalant) becomes easier as the charge transfer fromMXto TX2 decreases and as the electron `capacitivity' of the unoccupied band is increased. In this respect, the probability of intercalation of layered misfit compounds possessing the 1T structure is higher than that of compounds with the 2H structure because a metal atom with octahedral coordination can accept a larger number of electrons than an atom with trigonal-prismatic coordination. Intercalation of metals into the synthetic matrix Ta17xRexSe2 was also studied.78, 79 The electronic structure of this matrix can be changed by varying its composition, i.e., by varying the x value.For x=0.5, this matrix is isoelectronic and isostructural to the matrix 2H-MoSe2, viz., the dz2 band in this matrix is filled and intercalation is accompanied by disproportionation of the layered structure. The results of a study 46 in which the possibility of the replacement of a portion of lanthanum atoms in (LaS)1+xCrS2 by `inert' Sr was examined can be cited as supporting evidence for the above concept of electronic stabilisation.The results obtained demonstrated that the structure (LaS)1+xCrS2 contains a substantial amount (*0.2) of lanthanum vacancies, i.e., the corresponding suprastructure is a nanocomposite. This fact was indirectly confirmed by the results of another study,16 where it was attempted to obtain images of LaS layers in the suprastructure (LaS)1.14NbS2 by scanning tunnelling electron and atomic-force microscopy; however, the attempts were unsuccessful. Probably, the differences in the morphology of the synthesised crystalline species (BiS)1+x (NbS)m are also associated with the conditions of the interaction between the constituent substruc- tures. Among the specimens obtained, layered structures as well as structures of the `insulation-tape bundle' type were found.As mentioned above, no noticeable electron density transfer was observed in layered misfit structures with M=Bi or Sb, unlike those with M=Ln. In the case of the former stuctures, single crystals are deformed and take the shape of an `insulation-tape bundle' or a bent tube (because stresses due to the incommensur- ability of the layers in one direction result in the curvature) due to the incommensurability of the intercalant MS and the nonrigidity of the TS2 matrix.80 ± 82 The optimum inner and outer radii of `bundles' are determined by the force balance retaining the matrix rigidity as well as by the conditions of the interaction between substructures.Unfortunately, data on the thermodynamic properties of layered misfit structures are lacking in the literature. We suggested that the formation of defects (discontinuities) in intergrowth incommensurate substructures and the degree of additivity of the substructure contributions to the observed properties of the suprastructure can be studied by thermal analysis and differential scanning calorimetry. We established that the specific heats of the compounds (SnS)1+xTaS2 and (PbS)1+xTaS2 cannot be described in the context of the additivity. Anomalies were also found for the temperature dependence of the specific heat due to first-order phase transition.Thus it was demonstrated that compounds with the nonextreme stoichiometry (x=0) did not give a low-temper- ature (35 ± 70 8C) specific-heat peak, whereas these peaks for quenched and nonquenched samples of (SnS)1.15TaS2 differ in height. For all compounds based on TaS2, the specific-heat peak was observed at 350 8C. The peak height depends on the stoichio- metry and the conditions of cooling of the samples. Probably, these effects are associated with disruptions in one of the sub- lattices. Our studies demonstrated that the compounds (SnS)1+xTaS2 actively decomposed at above*600 8C in an inert atmosphere to liberate elementary sulfur. Apparently, the intercalates SnxTaS2 were the final decomposition products.In the future, we hope to confirm the fact that the observed phase transitions are associated with discontinuities in one of the sublattices (MX). In our opinion, these compounds are thermodynamically unstable due to the effect of the incommensurability on the crystal structure. Appa- 487 rently, strengthening of the interaction between substructures (for a given incommensurability) leads to an increase in the instability of the suprastructure due to a change in the energy of the bonds between the metal and chalcogen atoms in one of the substruc- tures. We have presented sufficiently convincing evidence for the possibility of fragmentation of one of the sublattices in the misfit structure (MX)1+x(TS2)m. The equation of motion was solved within the framework of the Frenkel ± Kontorova model taking into account the anharmonicity of the elastic sublattice and the incommensurability between the period of this sublattice and the corresponding lattice parameter of the crystal environment.The corrections for the known solutions of the equation of motion in the harmonic approximation were also found. It was demon- strated that under conditions of anharmonicity of the interaction between the sublattice and the host lattice, two reasons for its possible fragmentation into particles of finite length exist, viz., the incommensurability and doubling of the period of solutions of the nonlinear problem describing this model. The solution obtained determines the conditions of formation of one-dimensional nano- composite structures and the limiting parameters at which the suprastructure of the ensemble changes from regular to random.V. Conclusion Incommensurate suprastructures, which have been studied thus far, are limited only to compounds in which one lattice parameter of intergrowth substructures is incommensurate (a one-dimen- sional case). Apparently, eutectics can serve as abundant examples of suprastructures characterised by incommensurability along all three crystallographic directions. As it usually is, the transforma- tion from a one-dimensional model to a three-dimensional system, presents problems. However, it can be said that some general criteria for the formation of suprastructures with the three-dimen- sional incommensurability were revealed.First, it is apparent that the incommensurability of inter- growth substructures in real suprastructures occurs within partic- ular limits. Apparently, for some incommensurability parameters, the interaction between sublattices can lead to the formation of defects of different types, including fragmentation of one of the substructures. We failed to find literature data on the dependence of the properties and structures of layered misfit structures on the incommensurability. However, it is apparent that the character of the interaction between substructures should depend on the stoichiometric ratio, i.e., on the x and m values. As mentioned above, indirect evidence is available for the fact that monolayer structures undergo disproportionation to form bilayer and simple structures as the x parameter changes (see the data on intercala- tion of misfit structures 14, 76, 77).Other data (tubular morphology of particles,15 the results of studies by scanning tunnelling electron and atomic-force microscopy 70 and results of our investigations of thermodynamic properties of misfit structures) indicate that defects in substructures comprising the misfit structure or in one of these substructures are frequently observed. Second, it was proved that it is important to meet the conditions of electronic stabilisation of suprastructures. Since the charge transfer is the major mechanism responsible for the interaction between structural elements in misfit suprastructures, the conditions of electronic stabilisation determine both the stabilities of substructures and the existence of a suprastructure as a whole.The above-considered differences in the character of the interaction between substructures MX and TX2 determine both the possibility of formation of defects in the substructures and their character [see the data 44, 45, 69 on the structures (LaS)1+xCrS2, (LaSe)1+xVSe2 and (PbS)1+x TiS2]. The differ- ences in the morphology of misfit particles are also attributable to these facts.15 Third, it was established that the nonrigidity of substructures is of importance, at least it was demonstrated that deformations of sublattices due to their incommensurability should be taken into488 account both in structural studies and in investigations of physicochemical properties of incommensurate compounds.For example, it can be suggested that bonds in one sublattice can be cleaved at particular tensile stresses and new bonds in another sublattice can be formed at particular compression stresses. The latter possibility is supported by the results of the study of the structures (BiS)1.08TaS2 and (BiSe)1.09TaSe2 15 in which short (as in metals) Bi7Bi bonds were found. The results of the study 16 provided indirect evidence for the cleavage of bonds in MX substructures. Finally, approaches and procedures, which allow one to determine the conditions of fragmentation of substructures, were theoretically justified. In the present review, we call attention to some apparent relationships responsible for the structural characteristics, struc- ture imperfection and morphology of particles of crystalline suprastructures formed from incommensurate elements. Although it is evident that this problem is of importance in solid- state chemistry and in many fields of materials science, it has not been discussed previously in the literature.Evidently, three situations can occur upon formation of incommensurate intergrowth suprastructures. In the first case, the nonrigidity of the lattices compensates for their insignificant incommensurability. In this case, the formation of a suprastruc- ture is accompanied by stresses, but it does not disturb the stoichiometry. In the second situation, rigid substructures exist and the interaction between these substructures are rather weak.In this case, rather well-organised crystalline suprastructures are formed at any incommensurability. Their limiting stoichiometry is determined by the incommensurability, and the properties, most likely, additively depend on the properties of the constituent elements. The third situation is associated with mechanisms of structural compensation. Due to the strong interaction between substructures, their nonrigidity and substantial incommensur- ability, discontinuities can appear in one of the sublattices accompanied by the formation of nanocomposites. The structural compensation of the resulting stresses may lead to the formation of unusual defects or give rise to an unusual morphology of particles of suprastructural aggregates. 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出版商:RSC    

年代:2000

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Russian Chemical Reviews 69 (6) 491 ± 522 (2000) Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds G G Furin Contents I. Introduction II. The use of perfluoroalkyl halides in the synthesis of partially fluorinated compounds III. Reactions of perfluoroalkyl halides with organic substrates occurring by a single-electron transfer mechanism IV. Conclusion Abstract. perfluoroalkyl of activation the to approaches The The approaches to the activation of perfluoroalkyl halides partially of synthesis the in intermediates as used halides used as intermediates in the synthesis of partially fluori- fluori- nated reactions for conditions The considered. are compounds nated compounds are considered. The conditions for reactions of of organic compounds with perfluoroalkyl iodides in the presence of organic compounds with perfluoroalkyl iodides in the presence of reductants salts, metal and metals HOCH reductants (Na (Na2S2O4, HOCH2SO2Na), Na), metals and metal salts, redox FeSO Pb(OAc) systems redox systems (Na (Na , B 2S2O8, ButOOH, OOH, Pb(OAc)4, H2O2 ± FeSO4, Ce(SO The described.are complexes metal transition and 4)2) and transition metal complexes are described. The generation of perfluoroalkyl radicals by a single-electron transfer generation of perfluoroalkyl radicals by a single-electron transfer mechanism of introduction The discussed. are mechanism are discussed. The introduction of perfluoroalkyl perfluoroalkyl groups compounds organic unsaturated and aromatic into groups into aromatic and unsaturated organic compounds and and functionalisation particularly, iodides, perfluoroalkyl of functionalisation of perfluoroalkyl iodides, particularly, their their transformation and perfluoroalkanesulfinic into transformation into perfluoroalkanesulfinic and perfluoroal- perfluoroal- kanecarboxylic acids and aldehydes, are considered.The bibliog- kanecarboxylic acids and aldehydes, are considered. The bibliog- raphy references 442 includes raphy includes 442 references. I. Introduction The introduction of fluorine atoms into the molecules of organic compounds not only changes their physical and chemical proper- ties but also forms the basis for the development of new synthetic procedures, sometimes unusual for organic chemistry, for the generation of C7C bonds and cyclic systems.1±6 Partially fluorinated organic compounds, particularly those containing perfluoroalkyl groups, find wide application in the synthesis of novel materials, in the design of medicinal and agricultural preparations and in different branches of technol- ogy.7± 24 This, in turn, stimulates the development of novel, and the perfection of the existing methods for the introduction of polyfluorinated fragments into organic substrates.The interest of investigators in the possibility of direct introduction of such fragments into organic molecules is determined by diverse applic- ability of fluorine-containing compounds and unique physical and biological properties imparted to these compounds by fluorine, because regioselective substitution of a perfluoroalkyl group for the hydrogen atom in aromatic or heterocyclic systems may significantly influence their properties.G G Furin N N Vorozhtsov Novosibirsk Institute of Organic Chemistry, Siberian Branch of the Russian Academy of Sciences, prosp. Akad. Lavrent'eva 9, 630090 Novosibirsk, Russian Federation. Fax (7-383) 234 47 52. Tel. (7-383) 234 47 47. E-mail: furin@nioch.nsc.ru, root@orchem.nsk.su Received 27 September 1999 Uspekhi Khimii 69 (6) 538 ± 571 (2000); translated by R L Birnova #2000 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2000v069n06ABEH000353 491 492 496 517 The introduction of perfluoroalkyl groups, in the first place, of CF3, into organic molecules is based on three main types of chemical transformations, viz., those involving electrophilic (see, e.g., Refs 2, 25, 26), nucleophilic 27 and radical 28 ± 30 species.Thus, the availability of perfluoroalkyl iodides and the feasibility of their use in the synthesis of organometallic compounds made it possible to develop novel procedures for the generation of perfluoroalkyl radicals and to study their reactions.28 ± 30 The addition of perfluoroalkyl halides to alkenes and alkynes is one of the most fundamental procedures for introducing perfluoroalkyl groups into the molecules of organic substrates. Perfluoroalkyl radicals are traditionally generated photochemi- cally,31 ± 41 thermally 42 or electrolytically,43, 44 viz., by: (i) photolysis or thermolysis of perfluoroalkyl halides, per- fluoroalkanesulfonyl chlorides and organometallic compounds containing perfluoroalkyl substituents;45 ± 50 (ii) decomposition of polyfluorinated acyl peroxides of the general formula (CnF2n+1COO)2 51 ± 64 and electrolysis of per- fluoroalkanecarboxylic acids.65 ± 69 These methods have successfully been used in the perfluoro- alkylation of alkenes, aromatic, natural and heterocyclic com- pounds.Their advantages and disadvantages have been described in detail.45, 65 ± 68 To the main disadvantages of these methods one may relate the difficulty in their implementation under conditions of large-scale manufacture, low selectivity and low yields of the target products.Moreover, the preparation of the starting build- ing blocks, which are often toxic and expensive, demands special conditions.19 These circumstances together have made it necessary to develop efficient methods for introducing perfluoroalkyl groups { into organic molecules. The main emphasis in these studies was laid on their direct incorporation by in situ generation of perfluoroalkyl radicals. This, in turn, required simple, available and inexpensive reagents and simplification of the procedure of direct introduction of perfluoroalkyl groups into organic mole- cules. This search culminated in the development of novel approaches to the generation of perfluoroalkyl radicals from perfluoroalkyl halides in reactions occurring by a single-electron transfer mechanism.A variety of initiators for such reactions are currently known. The ease of performance and high efficiency of the perfluoroalkylation reaction as well as high accessibility of the reagents leave hope that this reaction will be very efficient in the synthesis of fluoroorganic compounds. The present work is an overview of the published data concerning perfluoroalkylation { The electrophilic nature of the perfluoroalkyl radical was reported by Baum et al.70492 reactions, it highlights the key events in the methodology of introduction of perfluoroalkyl groups into organic compounds. II. The use of perfluoroalkyl halides in the synthesis of partially fluorinated compounds Perfluoroalkyl iodides and bromides have recently received con- siderable attention owing to their accessibility, high reactivity and ability to be used in perfluoroalkylation reactions, including new ones.These reactions can be initiated in various ways, viz., ther- mally,42,71 ± 74 electrochemically,43, 44 photolytically,31 ± 41, 75, 76 or in the presence of free radical inducers, e.g., hydrogen peroxide,77 a,a-azobis(dimethylpentanonitrile),78 ± 80 a,a-azobis(cyclohexa- necarbonitrile) 81 and a,a-azobis(isobutyronitrile) (AIBN).79 ± 85 By selecting appropriate reaction conditions (viz., solvent, tem- perature, reaction time), one may carry out perfluoroalkylation of various organic compounds. These reactions are accompanied by the cleavage of C7I and C7Br bonds, but not of C7F bonds because the latter possess greater strength.Under certain conditions, perfluoroalkyl halides act as radical reagents, which perfluoroalkylate unsaturated organic compounds. This approach was repeatedly used in the chemistry of fluoroorganic compounds.36, 86 ± 93 Perfluoroalkyl iodides (RFI) are widely used as a source of perfluoroalkyl radicals, their addition to alkenes 46 and reactions with aromatic hydrocarbons under thermolysis conditions have been described, e.g.: [RFCH2CHR] ., RF. +CH2 CHR RFCH2CHIR +RF. , [RFCH2CHR] .+RFI ArH+2RFI 190 ± 250 8C ArRF+RFH+I2. 1. Reactions of perfluoroalkyl iodides with organic substrates in the presence of nucleophilic agents This methodology was first used 94 ± 102 in reactions of alkene- and arene-thiols with perfluoroalkyl iodides in liquid ammonia upon UV-irradiation.The corresponding aryl perfluoroalkyl sulfides were isolated in high yields. NH3(liquid) n-C8F17SPh+NaI PhSNa+n-C8F17I DMF, 25 8C (92%) Reactions with perfluoroalkyl bromides and diiodoperfluoro- alkanes were conducted in a similar way, this was further extended to selenium and tellurium derivatives and representatives of other classes.103 ± 108 Later, it was shown that reactions of perfluoroalkyl iodides with trialkylammonium and sodium salts of benzenethiols (Table 1) 102 or sodium benzothiazole-2-thiolate 108, 109 do not always require UV-irradiation. These reactions may occur in bipolar aprotic solvents at room temperature and are character- ised by high yields.NaH R R SRF SH+RFI Yield (%) RF R RF Yield (%) R 93 93 90 68 C6F13 C8F17 C4F9(CH2)2 C6F13(CH2)2 NO2 NO2 NO2 NO2 H C4F9 66 Me OH Cl NO2 77 30 83 99 C4F9 C4F9 C4F9 C4F9 Alkali metal benzenethiolates are convenient reagents, but in this case substitution reactions occur only on irradiation.110 ± 112 Nitrobenzene can be used as an initiator of this reaction. For example, the reactions of perfluorohexyl bromide with potassium G G Furin Table 1. Reactions of perfluoroalkyl iodides with triethylammonium arenethiolates.102 + Et3N ArS7NHEt3 +RFI ArSRF+ArSSAr B A Yield (%) Reaction conditions Ar t /h solvent T / 8C A B other products Ph DMF 4-MeO2CNHC6H4 DMF DMF 3 127 730 54 traces 7 2 83 3 17 5 30 0.5 98 19 ± 20 0 ± 5 0 ± 22 MeCN 21 ± 22 O 82 21 ± 22 2 2 7 21 ± 22 103 2-NH2C6H4 DMF 4-MeOC6H4 4-ClC6H4 DMF 763 12 O THF HMPAa 21 ± 22 MeCN 21 ± 30 23 ± 24 MeCN 22 ± 40 22 MeCN 21 ± 22 22 ± 30 20 50 ± 55 77 7 77779 traces traces 13 traces 6 DMF DMF DMF 780 1.5 64 3 75 0.5 84 1.5 66 2 88 2 72 4 40 0.5 72 3 39 5 4-HO2CC6H4 4-MeO2CC6H4 4-NO2C6H4 S SH DMF DMF traces traces 87 20 20 ± 22 48 20 ± 22 120 58.8 N 3.8 72.2 DMF 20 ± 22 24 7 N SH aHMPA is hexamethylphosphoramide. benzenethiolates in DMFin the presence of nitrobenzene result in aryl perfluorohexyl sulfides.113 PhNO2 ArSRF ArSK+RFBr Yield (%) Yield (%) Ar Ar RF RF Ph Ph 4-MeC6H4 4-MeC6H4 Ph 83 40 23 34 13 33 72 75 77 45 CF3 CF3 CF3 CF3 CF3 4-MeOC6H4 3-MeOC6H4 3-NH2C6H4 4-ClC6H4 4-CF3C6H4 C2F5 n-C6F13 CF3 n-C6F13 CF3 The reaction of CF3(CF2)9I with sodium 4-fluorobenzene- thiolate in DMF at 30 ± 45 8C gives 4-FC6H4S(CF2)9CF3 (yield 94%).114 On the other hand, benzenethiol,115, 116 benzenesele- nol 117 ± 119 and benzenetellurol 120, 121 anions, which are known to be strong nucleophiles, generate the corresponding perfluoro- alkyl radicals from perfluoroalkyl iodides introduced into the reaction with alkenes.In this way, efficient perfluoroalkylselen- ylation (Table 2) 117 ± 119 and perfluoroalkyltellurylation (Table 3) 120, 121 of a series of alkenes were carried out.In PhSeNa7RFX and PhTeNa7RFI systems, perfluoroalkyl radicals are generated from perfluoroalkyl halides at room temperature. This property was used in the development of a new approach to the generation of perfluoroalkyl radicals at low temperatures. The yields of perfluroalkyl phenyl sulfides (RFSPh) depend on the length of the alkyl chain. In the case ofCnF2n+1I, where n=4, 6 and 8, the yields are 78%, 84% and 86%, respectively. Perfluoroalkyl radicals add to the multiple bond regioselectively.1 A procedure for the synthesis of aryl perfluoroalkyl sulfides from perfluoroalkyl halides and benzenethiols was proposed bySome new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Table 2.Perfluoroalkylselenylation of alkenes.117 ± 119 R1 R2 Alkene OS O Table 3. Perfluoroalkyltellurylation of alkenes.120, 121 PhTeNa ±RFX R AlkeneCN CH2 CH2O Koshechko et al.105 who used MV2+7SO2 (MV2+ is methyl- viologen, N,N 0-dimethyl-4,40-bipyridinium salt) and I27SO2 sys- tems as electron carriers. XRF=CF3, Hal=I: X=H (91.2%), NHCO2Me (88.5%), Cl (53%), NO2 (9.2%);104 RF=CF3, Hal=Br: X=H (74%), Me (41%);105 RF=CFCl2CF2, Hal=Cl, X=H (34%);105 RF=CF3,Hal=Br: X=NHCO2Me (94%), H (78%), Br (64%), Cl (60%), This reaction was studied in detail using spectrophotometry and cyclic voltamperometry 105 and provided conclusive evidence for the intermediate formation of the .CF3 radical.Kinetic studies revealed that this reaction is of the second order with respect to the reagents, i.e., u=k2[ArSH][MV2+2I7]. The k2 values for PhSH and 4-MeC6H4SH were equal to 4.6 and 7.1 litre mol71 s71, respectively, at 30 8C. After addition of SO2 to the system, the reaction is controlled by the radical anion SO¡2 . generated from SO2 by the radical R1 RF PhSeNa ±RFX +RFSePh+(PhSe)2 PhSe R2 AYield (%) RFX A (PhSe)2 RFSePh C8F17I 59 19 21 C6F13I 57 17 13 CF3Br 26 34 31 traces 20 C8F17I 86 7 C6F13I 84 6 CF3Br 38 32 C8F17I 63 25 15 trifluoromethylating agent in polar solvents. The ionisation C6F13I 55 20 19 potential of TDAE is equal to 6.13 eV,122 being close to that of zinc, which is known to be a potent reductant [the standard electrode potential (E) of zinc is 70.763 V].TDAE is also known to be a very potent electron donor; its ionisation energy (591 kJ mol71) is lower than that of zinc (906 kJ mol71) and is close to that for lithium (521 kJ mol71). Electrochemical oxida- tion of TDAE in acetonitrile occurs in two reversible single- electron steps and results in [TDAE]+.and [TDAE]2+ (E =70.78 and70.61 V, respectively).123 30 traces 66 C8F17I Later, this methodology was used in the synthesis of dialkyl- (trifluoromethyl)amines by the reaction of CF2Br2 with secondary C8F17I 15 60 17 amines in the presence of TDAE124 and in reactions of 2-(bromo- C8F17I 39 42 9 TePh RF R Yields for different RFX (%) C4F9I C8F17I CF3Br 59 81 57 39 58 44 47 63 44 54 64 30 MV2+±SO2 SH+RFHal X SRF DMF, 20 8C NO2 (24%) (reaction with benzenethiols).107 493 cationMV+., which, in turn, is generated upon action of ArS7 on MV2+.The interaction of the intermediate radical anion [CF3SPh]7. with MV2+ gives the reaction product and MV+.. It is noteworthy that SO2 is an efficient electron carrier in the electrochemical cathode trifluoromethylation of benzenethiols with trifluoromethyl bromide.106, 107 Tetrakis(dimethylamino)ethylene (TDAE) proved to be an efficient reductant initiating the cleavage of C7I and C7Br bonds in reactions with unsaturated compounds. Thus TDAE forms a complex (e.g., with CF3I), which can act as a nucleophilic chlorodifluoromethyl and difluoromethyl)benzooxazole 125 ketones with aromatic aldehydes in the presence of TDAE.126 N NMe2 Me2N DMF ArCHO+ CF2Br+ 720 to 208C O NMe2 Me2N F N Me2N + + F+ O NMe22Br7 NMe2 Me2N Ar Ar 4-CNC6H4 4-CF3C6H4 4-PhC6H4 Ph 4-FC6H4 61 63 45 Yield (%) 62 67 Ar R R TDAE ArCHO+O OH O DMF, 720 to 208C CF2Cl F F NMe2 NMe2 NMe2 NMe2 N R Ph N Ph Ph Ph Ar 4-CF3C6H4 4-FC6H4 N 57 55 58 55 Yield 55 45 (%)The acyldifluoromethyl anion generated from chlorodifluoro- methyl ketone reacts with aromatic aldehydes to give the corre- sponding hydroxy ketones containing a CF2 fragment in the a- position.126 In the presence of alcoholates, perfluoroalkyl iodides and -bromides react with alkenes to yield the addition products.127 ± 131 This suggests that alcoholates, as is the case with the Cannizzaro reaction with aldehydes, act as reducing agents rather than induce splitting of perfluoroalkyl halides by the haloformic pathway. RFI HO7 RFCH2CHIR +RFCH CHR RF=n-C3F7, iso-C3F7, C2F5CFCF3 CHR CH2 EtOH RFBr RFCH2CHBrR RF=C6F13, C4F9 R=n-C5H11, CH2OH.494 Phosphines [PPh3, PBun3 , P(NEt2)3, P(OEt)3] are used as activators in the reaction of perfluoroalkyl iodides with alkenes.132 ± 145 PPh3 RFCH2CHIR CHR+RFI CH2 70 ± 75 8C, 4 h R=n-C4H9, n-C6H13.Yield (%) Yield (%) RF RF 72 28 87 79 81 83 C8F17 FSO2(CF2)2O(CF2)2 FSO2(CF2)2O(CF2)8 C6F13 Cl(CF2)4 Cl(CF2)6 In the presence of P(NEt2)3, perfluoroalkyl iodides R(CF2)nI (R=CF3, n=477) react with alkenes 140 or benzoyl chloride derivatives 141 with the formation of addition products at the multiple bond and the corresponding ketones (yields 32%± 43%).The hexamethyldisiloxane ± sodium methoxide system in THF is also effective to this goal.142 The reaction of perfluoroalkyl iodides with nucleophiles manifests the features of a SRN1 reaction 44, 146 and proceeds smoothly under relatively mild conditions. The stereochemistry of the reaction of perfluoroalkyl iodides with alkenes suggests that it is the perfluoroalkyl radical that initially attacks the alkene. Presumably, the initiation consists in electron transfer from the nucleophile to the perfluoroalkyl iodide resulting in the gener- ation of the radical anion [RFI]7.;147, 148 the process is exothermic.The radical anion formed must be rapidly decomposed into the perfluoroalkyl radical and the iodide ion. The efficiency of the free-radical chain growth in the reaction with alkenes is provided under conditions such that the decomposition of the radical anion [RFI]7. is a fast reaction; apparently, the polar effect in the translocation of the iodine favours the decomposition: Rd¡ F _I_RdHá. The radical anion [CF3I]7. has been detected in a solid state as a stable species at 77 K. At 100 K, it dissociates into the trifluoromethyl radical and the iodide ion.149 ± 155 The reaction of the perfluoroalkyl radical with an anionic substrate generates a radical anion which further reacts with perfluoroalkyl iodide to give [RFI]7.according to the SRN1 mechanism.152 ± 155 A more detailed description of these reactions is given in Refs 116, 156 ± 160. Further transformations of the radical anion [RFX]7. may proceed in two pathways (routes a and b), which depends on thermodynamic factors. a X7+RF. Nu7 [RFNu]7. RX [RFR]7.+NuX [RFX]7. b RF¡ +X. Nu is nucleophile. It was shown 47 that the RF .and I fragments (but not the radical anions [RFI]7.) are formed in polar solvents. Hence a question arises about the pathways of generation of the radical RF .. It is quite probable that only the C7I bonds are involved in the formation of donor ± acceptor complexes with perfluoroalkyl iodides, which favours the manifestation of electrophilic proper- ties of RFI in solvents of the hexamethylphosphoramide (HMPA) andDMFtype.Presumably, the translocation of the radical anion centre to RFI followed by the generation of the RF .radical is the limiting step in this reaction. The formation of radicals from perfluoroalkyl halides by the SRN1 mechanism is one of the most characteristic features of electron transfer reactions in organic chemistry.161 The SRN1 mechanism is especially favourable for perfluoroalkyl halides, since the latter manifest very low activity in nucleophilic reactions of the SN1 and SN2 type. Studies of perfluoroalkyl halides reactions occurring via the SRN1 mechanism were begun in the 1970's.162 ± 170 G G Furin RS7+RFI [RF I]7.+RS., RF. + I7, [RFI]7.[RSRF]7., RF.+RS7 RSRF+[RFI]7.. [RSRF]7.+RFI The values of the radical formation energy (E) in the gas phase were found to be as follows:89 E /eV Radical E /eV Radical 3.39 3.61 3.37 3.06 2.10 2.10 2.65 3.40 F. Cl. Br I. . C .F3 CF3C .F2 (CF3)2C .F (CF3)3C. Therefore, route a in the transformation of radical anions is probable for compounds CF3X, C2F5X, (CF3)2CFX (but not for X=I), while route b is probable for (CF3)3CX (at all values of X) and R. The direction of a reaction in solution depends on the value of free energy of solvation (DG). For example, in water DG has the following values: Anion Anion DG /kJ mol71 DG /kJ mol71 I7 F7 7283 7200 R¡F 7472 7347 7321 Cl7 Br7In this case, route a seems to be preferable for all RFX [probably, with the exception of (CF3)3CCl] and, perhaps, (CF3)2CFI.The transfer of electrons from the charged nucleophile to ButBr leads to the formation of a radical anion ± radical pair; its further transformations differ from those for an analogous pair in the case of RFBr, which is decomposed by the route b, resulting in the radical anion [RFX]7.. Quantum-chemical calculations using the AM1 method revealed that the formation of the radical anion generating the ternary perfluoroalkyl carbanion (CF3)3C7 and the radical Br. (see Refs 146, 165) is due to higher electronega- tivity of the tertiary group of the perfluoroalkyl radical.The enthalpy of formation of this anion and the Br. radical (DH1) is 17.6 kcal mol71, whereas that of the tertiary perfluoroalkyl radical and the bromide ion (DH2) is much higher, i.e., 57.9 kcal mol71 (see Ref. 166). RF=CF3 [(RF)3C].+Br7 [(RF)3CBr]7. [(RF)3C]7+Br. CF3, F F F . RF =(CF3)3C, C3F7(CF3)2C, The occurrence of this reaction through the formation of a radical anion was confirmed experimentally.166 The reactions of (RF)3CBr with nucleophiles, e.g., Na2S, NaSH, KSCN, KCN, R4NX (X=Cl, Br, I), in organic solvents (e.g., MeCN, DMF, CH2Cl2, EtOAc) result in the quantitative formation of mixtures of (RF)3CH and perfluoroalkene. This can be attributed to the reaction of the perfluoroalkyl halide with the proton from the medium as well as to stabilisation of the perfluoroalkyl carbanion due to elimination of the fluorine anion from the CF2 fragment in the a-position.Solv C3F7(CF3)2CBr+Nu7 C3F7(CF3)2CH+C2F5CF C(CF3)2 Nu is nucleophile, Solv is solvent. The electron transfer from the reductant to perfluoroalkyl halide resulting in the formation of the corresponding radical anions is highly efficient, since free s*-orbitals of the C7Hal bonds (Hal=Cl, Br, I) lie fairly low on the energy axis. Active generation of such radical anions requires a reductant the stand- ard reduction potential (Ered) of which is higher than that of the495 Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds nated carbon chain are easily substituted and the target product is formed in a high yield.More recent studies confirmed the efficacy of this approach.178 ± 192 alkyl halide involved in the reaction. Depending on the structure of the alkyl fragment and the nature of the halogen, the reducing potentials (E1/2 relative to SCE) of perfluoroalkyl halides (Pt electrode in MeCN) vary from71.10 to +0.71 V.171 Na2S2O4 ±NaHCO3 Cl(CF2)4I E1/2 /V RFHal E1/2 /V RFHal MeCN, 85 8C, 9 h Cl(CF2)4SO2Na (84%) 70.14 70.09 0.12 Later, it was found that other nucleophilic sulfur derivatives also react with perfluoroalkyl iodides to give salts of perfluoro- alkanesulfinic acid (Table 4).22, 143, 144, 184 0.71 Presumably, these reactions occur via a single-electron trans- fer (SET) mechanism as can be evidenced from the trapping of perfluoroalkyl radicals by alkenes and nitroso compounds.54 71.02 S2O2¡ 2SO2¡.4 70.95 (CF3)3CBr C3F7CBr(CF3)2 1-bromo-1-methylperfluoro- cyclopentane 1-bromoperfluorobicyclo- [4.4.0]decane 1-chloro-1-methylperfluoro- cyclopentane 1-chloroperfluorobicyclo- [4.4.0]decane 71.10 71.00 70.96 70.66 70.36 0.10 0.14 0.32 70.97 71.05 CF3I C3F7I I(CF2)4I (CF3)2CFI cyclo-C6F11I I2 (CF3)3CI C3F7CI(CF3)2 C3F7CCl(CF3)2 (CF3)2CFBr [RFISO2]7. (or [RFI]7.) SO2¡.+RFI S2O2¡ 4 RF ButNO RF .+ I7+SO2 alkene RFSO2¡ +SO2¡. N O. But adduct (1 : 1) Consequently, the presence in the reaction mixture of a compound with a higher (in comparison with perfluoroalkyl halide) value of Ered makes possible the generation of the radical anion [RFX]7.; its decomposition results in the perfluoroalkyl radical.The latter can be further involved in reactions with organic compounds. In the subsequent sections, this process will be exemplified with both classical reductants and redox systems. 2. Sulfinylation of perfluoroalkyl iodides The sulfonylation with sodium dithionite gives an access to perfluoroalkanesulfonic acids, which are valuable intermediates in the synthesis of surfactants, without recourse to electrochemical fluorination and using accessible perfluoroalkyl iodid- es.134, 173, 184, 185, 193 For example, I(CF2)2O(CF2)2SO3Na can be prepared from I(CF2)2O(CF2)2I using phase-transfer catalysis in polyethylene glycols-200 and -600 or in acetonitrile, ethanol or diglyme.Perfluoroalkyl bromides also react with sodium dithion- ite.172 ± 176, 194, 195 Thus, CF3Br gives sodium trifluoromethanesul- finate in 90% yield, and sulfinylation products are formed from 1,1,1-trichloroperfluoroalkanes in yields of 90% and higher. Na2S2O4 ±NaHCO3 Cl2 RCCl2SO2Cl RCCl2SO2Na RCCl3 MeCN±H2O R=Cl, F, CF3, Cl(CF2)2, Cl(CF2)4, Cl(CF2)6. The addition of perfluoroalkyl halides to the C=C bond of alkenes is the most promising approach to the generation of C7C bonds in the synthesis of polyfluorinated compounds. Numerous synthetic procedures for perfluoroalkylation of alkenes, especially by RFI, have been developed.One of them includes thermal or photochemical induction of free-radical reactions. This approach was developed by a group of Chinese inves- tigators who studied sulfinatodehalogenation of halogen-contain- ing hydrocarbons. Thus it was demonstrated for the first time 54, 172 ± 177 that perfluoroalkyl iodides react with sodium dithionite (Na2S2O4) to yield sulfinic acid derivatives. The chem- istry of perfluoroalkanesulfinates including their synthesis, prop- erties, reactions and applications is described in the reviews (see Refs 158 ± 160). The reactions of a,o-diiodoperfluoroalkanes 183 and a,o- dibromoperfluoroalkanes189 with 1 or 2 equiv. of Na2S2O4 in aqueous MeCN in the presence of sodium hydrogencarbonate result in sulfinates, e.g., I(CF2)nSO2Na and NaSO2(CF2)nSO2Na, which in turn give the corresponding sulfonyl chlorides, e.g., I(CF2)nSO2Cl and ClSO2(CF2)nSO2Cl (n=3, 4, 6) upon chlori- nation at 0 8C (Table 5).The inexpensive reducing agent Na2S2O4 can be used for the preparation of perfluoroalkanesulfinic acid salts from perfluoro- alkyl halides (RFX, where X=Br, I, or RFCCl3) under relatively mild conditions. This method is widely employed in reactions of these salts with alkenes, dienes, alkynes and aromatic compounds. On the other hand, this system is efficient mostly for polyfluori- nated alkyl halides.172 Bromine and iodine atoms in the perfluori- Table 4. Synthesis of sodium perfluoroalkanesulfinates. Product Reaction conditions Nucleophile RFX Yield (%) solvent T /8C Na2S2O4 MeCN±H2O MeCN±H2O HOCH2SO2Na NaHSO3±K3Fe(CN)6 NaHSO3 ± FeCl3 Na2S2O5 NaHSO3 95 91 73 96 65 75 88 63 85 79 95 90 80 ± 85 20 MeCN±H2O 2585 85 85 70 ± 80 70 80 80 70 ± 80 70 ± 80 70 F(CF2)8SO2Na F(CF2)8SO2Na CF3 CCl2SO2Na NaSO2(CF2)2OCF2CO2Na Cl(CF2)6SO2Na Cl(CF2)8SO2Na Cl(CF2)8SO2Na F(CF2)6SO2Na Cl(CF2)4SO2Na Cl(CF2)6SO2Na NaSO2(CF2)2O(CF2)2SO2Na F(CF2)6SO2Na KSO2(CF2)2O(CF2)2SO2F 90 F(CF2)8I F(CF2)8Br CF3CCl3 I(CF2)2OCF2CO2Na Cl(CF2)6I Cl(CF2)8I Cl(CF2)8I F(CF2)6I Cl(CF2)4I Cl(CF2)6Br I(CF2)2O(CF2)2SO2F F(CF2)6Br I(CF2)2O(CF2)2SO2F H2O MeCN±H2O MeCN±H2O DMF±H2O DMF±H2O DMF±H2O DMF±H2O DMF±H2O DMF±H2O dioxane ±H2O K2SO3496 Table 5.Sulfinylation with subsequent chlorination of a,o-diiodoper- fluoroalkanes I(CF2)nI.183, 189 Product Yield (%) b n I(CF2)nI : MeCN: :Na2S2O4 (see a) :H2 O(see a) 10 : 3 10 : 3 20 : 3 1 : 1 1 : 1 1 : 1 I(CF2)3SO2Cl I(CF2)4SO2Cl I(CF2)6SO2Cl ClSO2(CF2)3SO2Cl ClSO2(CF2)4SO2Cl ClSO2(CF2)6SO2Cl 3 1 : 1 4 1 : 1 6 1 : 1 3 1 : 2 4 1 : 2 6 1 : 2 28 (80) 25 (90) 39 (84) 73 (100) 83 (100) 75 (>95) a Molar ratio. b The figures in parentheses correspond to the yields according to 19F NMR spectroscopy data. Na2S2O4±NaHCO3 I(CF2)nI MeCN±H2O, 20 8C Cl2, H2O I(CF2)nSO2Na and/or NaO2S(CF2)nSO2Na 0 8C I(CF2)nSO2Cl and/or ClO2S(CF2)nSO2Cl One should bear in mind that dimerisation of a perfluoroalkyl radical is also possible.For example, heating of perfluoroalkyl iodide in the presence of the Na2S2O47NaHCO3 system in MeCN for 48 h gives a dimeric product.93 Na2S2O4 ±NaHCO3 RFRF 2 RFI MeCN, D The sulfinatodehalogenation reaction has opened up new opportunities for the synthesis of perfluoroalkanesulfinic and -sulfonic acids and their derivatives, since it permits direct trans- formation of perfluoroalkyl halide into perfluoroalkyl sulfinate and thus eliminates the necessity for the intermediate step, i.e., the synthesis of an organometallic derivative. There is no doubt that this approach holds great promise for wide-scale technological application.172 ± 175, 178 ± 181, 189, 195 III.Reactions of perfluoroalkyl halides with organic substrates occurring by a single-electron transfer mechanism The addition of perfluoroalkyl iodides to alkenes and alkynes is one of the most important methods for the synthesis of commer- cially valuable fluorohydrocarbons used as intermediates in the preparation of novel materials and products.20 In this Section, we shall consider a novel approach to the functionalisation of the accessible perfluoroalkyl iodides, which consists in the involve- ment of an intermediate perfluoroalkyl radical generated under the action of various initiators. This reaction is described by a well-known mechanism, SRN1. The possibility to alter the direc- tion of the reaction by varying reaction conditions and using appropriate initiators permits one to perform directed synthesis of fluorinated compounds of various compositions. Reactions of perfluoroalkyl iodides with organic substrates can be initiated in three different ways, viz.: (1) by treating perfluoroalkyl iodides with reductants.The key steps in this process are the initial formation of the intermediate radical anion of perfluoroalkyl iodide and its dissociation into the perfluoroalkyl radical and the iodide anion; (2) by treating perfluoroalkyl iodides with oxidants. As a result the reactant, possessing electrophilic properties, generates a radical cation. The latter reacts with perfluoroalkyl iodide to generate a radical anion [RFI]7., which is further decomposed to give a perfluoroalkyl radical; (3) by treating perfluoroalkyl iodides with systems which generate alkyl or any other radicals themselves.The reaction of the latter with perfluoroalkyl iodide yields perfluoroalkyl radicals by-passing the formation of radical anions. G G Furin A vast body of experimental evidence on each of these approaches provides a guideline for new applications of per- fluoroalkyl iodides. It seems therefore expedient to lay the main emphasis on these particular pathways of chemical transforma- tions of perfluoroalkyl halides and sodium perfluoroalkanesulfi- nates. 1. Reactions of perfluoroalkyl iodides in the presence of reducing systems The presence of an appropriate reductant is a main requirement for the activation of perfluoroalkyl halides and the intermediate formation of perfluoroalkyl radicals.Its specific function consists primarily in the generation of the corresponding radical anions from perfluoroalkyl halides. Various systems have been tested for this purpose, viz., (1) formaldehyde ± sodium sulfoxylate;190 (2) sodium dithionite; (3) thiourea dioxide;170, 185 (4) metals and metal salts; (5) tran- sition metal complexes. Each of these systems has characteristic features of its own; therefore, their effects must be considered in more detail. a. The formaldehyde ± sodium sulfoxylate system The formaldehyde ± sodium sulfoxylate system or rongalite (HOCH2SO2Na), is widely used in industry as a reductant.Its reaction with perfluoroalkyl iodides and bromides gives the corresponding salts of sulfinic acids. It was found that under special conditions this reagent can generate perfluoroalkyl radi- cals from both perfluoroalkyl iodides and perfluoroalkanesulfinic acid salts. The reaction of perfluoroalkyl iodides and bromides with ethylene, ethylene derivatives and acetylene in polar solvents in the presence of compounds containing the SO¡2 anion (e.g., Na2S2O4, HOCH2SO2Na, etc.) (3 h, room temperature) yields addition products at the multiple bond in nearly quantitative yields.101 Rongalite was used for perfluoroalkylation of pyridine deriv- atives under the action of perfluoroalkyl iodides.191, 192, 196, 197 HOCH2SO2Na +RFX RF R1 R2 R1 R2 MeCN±H2O N N X=I, Br; R1=H: R2=H, 3-Me, 4-Me, 4-NH2; R1=3-Me, R2=5-Me; R1±R2=2,3-CH=CHCH=CH (quinoline); R1±R2=3,4-CH=CHCH=CH (isoquinoline).It is worth noting that the reaction of the perfluoroalkyl iodides RFI with pyridine in the presence of the Na2S2O4 ± NaHCO3 system does not result in the formation of perfluoroal- kylation products in acceptable yields, whereas an addition of HOCH2SO2Na affords a mixture of a-, b- and g-perfluoroalkyl- pyridines in sufficiently good yields.191, 192 HOCH2SO2Na ±NaHCO3 +RFX RF MeCN±H2O, 70 ± 75 8C, 6 h N N (42% ± 68%) RFX=C6F13I, C7F15I, C8F17I, ClC8F16I, C7F15Br, ClC6F12Br. This reaction applied to coumarin gives 3-perfluoroalkylcou- marin; its S- and N-analogues can also be prepared in good yields.198, 199 However, in the case of the Na2S2O47cetyltrime- thylammonium bromide (CTMAB) system the yield of the target product is low.62R R RF HOCH2SO2Na X O E X E +RFI O E=O (63%), S, NH; RF=F(CF2)6; X=H, OH.Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Polyfluorination of pyrrole in the presence of rongalite was carried out in a similar way.192 HOCH2SO2Na +Cl(CF2)4I MeCN±H2O, 60 8C, 5 h (CF2)4Cl NH NH (68%) Reactions involving rongalite occur in accordance with the following tentative scheme: HOCH2SO¡2 HSO¡2 +CH2O, RF .+SO¡2 .+I7+H2O.RFI+HSO¡2 +OH7 Perfluoroalkyl halides react with disulfides in the presence of reductants, e.g., HOCH2SO2Na, Na2S2O4, formate7SO2, to give perfluoroalkyl thioethers.62, 200, 201 For example, the reaction of diphenyl disulfide with bromotrifluoromethane in the presence of Na2S2O4 in DMF containing Na2HPO4 at 20 8C gives trifluoro- methyl phenyl sulfide in 65% yield.The reaction of polyfluoroalkyl iodides and -bromides con- taining 3 to 12 carbon atoms, viz., Cl(CF2)nI (n=4, 6, 8), CF3(CF2)nI (n=577) and Cl(CF2)nNBr (n=4, 6), with the rongalite7NaHCO3 system in bipolar aprotic solvents (MeCN, DMF) results in the formation of sodium polyfluorocarboxylates in high yields.185, 2017205 This approach is more convenient than the conventional method based on electrochemical fluorination of carboxylic acids and their derivatives.H+ CF3(CF2)nHal CF3(CF2)n71CO¡2 HOCH2SO2Na ±NaHCO3 80 ± 85 8C, 15 ± 22 h CF3(CF2)n71CO2H n n Yield (%) Hal Yield (%) Hal 6 2 7 3 11 5 74 80 82 779 84 IBr IBr IBr IBr IBr IBr 82 70 70 86 51 7 These results gave an impetus to further investigations of perfluoroalkylation of various organic substrates using perfluoro- alkyl iodide7reductant systems.2067210 b. The use of sodium dithionite Reactions of perfluoroalkyl iodides with ethylene and acetylene in polar solvents induced by sodium dithionite (Na2S2O4) also permit the introduction of the perfluoroalkyl group into organic molecules. Thus the reaction of Cl(CF2)6I with ethylene in the presence of the Na2S2O47NaHCO3 system (3 h, room temper- ature) gives an addition product at the multiple bond, Cl(CF2)6CH2CH2I, in a nearly quantitative yield.186, 187, 211, 212 A similar reaction involves secondary perfluoroalkyl iodides, such as CF3CFI(CF2)4SO2F, CF3CFI(CF2)nCl (n=2, 4), CF3CFI(CF2)2O(CF2)2SO3Na and CF3(CF2)2OCFICF3.2137215 Na2S2O4 R1CH CR2R3+RFI RFR1CHCIR2R3 MeCN R1=R2=H: R3=(CH2)4Me, (CH2)2CH=CH2, CH2OH, OAc, (CF2)4Cl, CH2OCH2CH=CH2; R1=H, R2=R3=F; R1±R2=(CH2)4, R3=H.In the presence of sodium dithionite, perfluoroalkyl bromides react vigorously with alkenes in aqueous isopropyl alcohol at 60 ± 70 8C to give addition products in good yields.215 497 R R RF RF Na2S2O4 Cl2 CHR +RFBr CH2 PriOH±H2O SO2Cl SO2Na (64% ± 74%) R=H, (CH2)3Me, (CH2)5Me, (CH2)7Me; RF=H(CF2)6, F(CF2)8, Cl(CF2)4, Cl(CF2)6.The reaction of perfluoroalkyl iodides (RFI=CF3I, Cl(CF2)2I, Cl(CF2)4I) with aryl isocyanides (RC6H4NC) in the presence of the Na2S2O47NaHCO3 system results in polyfluoro- alkylimidoyl iodides RC6H4N=CIRF.216 Dibromodifluoromethane is used as the starting compound in the synthesis of compounds containing the bromodifluoromethyl group. In the presence of sodium dithionite, rongalite or thiourea dioxide, CF2Br2 and CHF2I react with terminal alkenes in aqueous acetonitrile or tert-butyl alcohol at room temperature or on cooling to give the corresponding adducts.196, 217, 218 Na2S2O4±NaHCO3 CH2 CHBun+CHF2I MeCN±H2O, 20 8C, 14 h CHF2CH2CHIBun (86%) HOCH2SO2Na, CuCl CHC6H13+CF2Br2 CH2 ButOH, 20 8C, 24 h CBrF2CH2CHBrC6H13 (68%) Compounds containing different halogen atoms can also be used as fluoroalkylating reagents in the presence of the Na2S2O4 ± NaHCO3 system.For example, Freon-113 reacts with alkenes, dienes and hex-1-yne at moderate temperatures resulting in fluoroalkylation products, albeit, in low yields.219 Na2S2O4 ±NaHCO3 CF2ClCFCl2 MeCN±H2O CH2 CH(CH2)3Me CF2ClCFCl(CH2)5Me 40 ± 45 8C, 20 h CH(CH2)nCH CH2 CH2HC C(CH2)3Me CF2ClCFClCH2CHCl(CH2)nCH CH2 n=2 (48%), 4 (56%) CF2ClCFClCH CH(CH2)3Me 40 ± 45 8C, 20 h In the presence of sodium dithionite, CF2Br2 reacts with diethylallyl malonate, alkenes and alkynes; in the latter case, mixtures of E- and Z-isomers are formed in moderate yields (Table 6).196, 220 Na2S2O4±NaHCO3 CF2Br2 CHCH2CH(CO2Et)2 CH2 CF2BrCH2CHBrCH2CH(CO2Et)2 HC CR CF2BrCH CRBr R=(CH2)3Me (55%), (CH2)4Me (53%), (CH2)5Me (50%).The reaction of difluorodiiodomethane with alkenes in the presence of iron at 40 ± 50 8C gives compounds carrying the ICF2 group.221, 222 CH2 CH(CH2)3Me ICF2CH2CHI(CH2)3Me Fe (73%) CF2I2 CHCN CH2 ICF2(CH2)2CN (57%) The latter also react with alkenes and alkynes inMeCN7H2O in the presence of the Na2S2O47NaHCO3 system at 30 8C, resulting in the formation of addition products at the multiple bond.222498 Table 6. Reactions of alkenes and alkynes with CF2Br2 induced by reductants. Substrate Hex-1-ene Oct-1-ene Cyclohexene Cyclooctene Styrene Diallyl ether a-Pinene b-Pinene Diethyl allylmalonate Hex-1-yne Hept-1-yne Oct-1-yne 2,3-Dihydrofuran 3,4-Dihydro-2H-pyran 3,4-Dihydro-2H-pyran (excess) Na2S2O4±NaHCO3 ICF2(CH2)2CN MeCN±H2O, 24 h CH2 CHR HC CR The reaction of Cl(CF2)4I with a-phenylstyrene in aqueous MeCN induced by the Na2S2O47NaHCO3 system (4 h, 40 8C) gives the products 1 and 2 which contain no iodine atom.223 Ph Na2S2O4±NaHCO3 +RFI X X RF Ph Ph Ph Ph 4-MeOC6H4 But 30 35 26 32 18 38 H 68 Cl(CF2)4 Cl(CF2)6 Cl(CF2)2 CF3(CF2)5 Cl(CF2)4 Cl(CF2)4 Cl(CF2)4 However, if styrene is used as a substrate, fluorine-containing oligomers are formed together with compound 1.196 Cyclohexene and cyclooctene manifest similar behaviour.196 Under these con- ditions, CF2Br2 also reacts with a- and b-pinenes.196, 220Yield (%) Reductant 85 80 92 87 88 70 75 75 80 50 85 68 75 80 55 53 50 78 72 76 HOCH2SO2Na (NH2)2C=SO2 Na2S2O4 HOCH2SO2Na Na2S2O4 HOCH2SO2Na (NH2)2C=SO2 Na2S2O4 Na2S2O4 HOCH2SO2Na Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 Na2S2O4 R(CH2)2CF2(CH2)2CN R=CH2OH (72.5%), CO2Et (56%) RCI CHCF2(CH2)2CN R=CH2OH (51%, E:Z=57 : 43), CH2CO2Et (66%, E:Z=63 : 37) Ph Ph RF + RFH2C MeCN±H2O X X H 1 2 Yield (%) 1 2 33 36 24 31 19 36 G G Furin b-pinene CH2CF2Br Na2S2O4±NaHCO3 Br CF2Br2 a-pinene Br CF2Br It was shown 224 ± 229 that the use of compounds containing different halogen atoms in the reaction of 1,1,1-tribromotrifluoro- ethane with alkenes yields addition products at the multiple bond.Na2S2O4±NaHCO3 CF3CBr3 MeCN±H2O, 20 8C CH2 CHOEt CF3CBr2CH2CHO CH2 CHCH2CN CF3CBr2CH2CHBrCH2CN The mechanism of generation of perfluoroalkyl radicals under the action of sodium dithionite and its subsequent reaction with alkenes is now well-established.158 The transformations of the intermediate radical C were shown to occur in three different ways. S2O2¡ 4 2 SO2¡. RFI RF .+ I7 + SO2 , Ph Ph Ph RFI I +RF . R R RF RF R C . SO¡2 H. 7H. Ph H Ph Ph 7 R R R RF RF RF The reaction of perfluoroalkyl iodides with alkynes under sulfinatodehalogenation conditions gives a mixture of E- and Z-adducts in very high yields.230 A similar reaction with alkenes was used in the synthesis of an a,a-difluoro-g-lactone.231 O Na2S2O4±NaHCO3 CR1R2 + CH2 MeCN±H2O, 20 8C CF2I Et2N F O F SiO2 R1 R1 CF2 Et2N R2 O O I R2 R1=R2=Alk, H.The reaction of CF2=CFCF2Cl with allyl alcohol in aqueous acetonitrile in the presence of the Na2S2O47NaHCO3 system affords an adduct (1 : 1); treatment of the latter with zinc at 130 ± 140 8C in ethylene glycol results in 1,1,2,3,3-pentafluoro- 1,5-hexadiene,232 which is further used in the synthesis of poly- fluorinated polymers. In the presence of sodium dithionite, perfluoroalkyl iodides react also with allyl alcohol and unsaturated carboxylic acids to give addition products at the multiple bonds in high yields.233 A convenient and efficient procedure was developed for the direct introduction of the perfluoroalkyl group into unsaturated compounds which is based on the reaction of perfluoroalkyl iodides with alkene and alkyne derivatives induced by sulfur- containing systems.The main advantages of this method are its simplicity, high variability of functional groups, easy isolation of reaction products and regioselectivity. Moreover, these reagentsSome new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds are neither toxic nor explosive, which makes them environmen- tally safe. The presence of two multiple bonds in the substrate molecule favours the addition of RF and I fragments to the alkene and the formation of a five-membered heterocycle of the type 3.This reaction is regioselective.201 Its strategy consists in the generation of a radical centre due to the cleavage of the F2C7I bond, the addition of the radical formed at the double bond and subsequent cyclisation involving the radical centre and the multiple bond as a donor. Polyfluoroalkylated 3-iodoalkylidenetetrahydrofuran-2- one is formed as a result of generation of the perfluoroalkyl radical initiated by the reaction of RF with Na2S2O4 and sub- sequent formation of a five-membered heterocycle. This reaction occurs with high regioselectivity.201 OO R RF Yield (%) H CF3 44 47 50 80 83 82 92 HHMe Me Me n-C8H17 Similarly, perfluoroalkyl derivatives of 3-iodoalkylidene-2- pyrrolidone 4 and the acyclic amide 5 are formed in the perfluoro- alkylation of N-allylprop-2-en- and N-allylbut-3-enamides by perfluoroalkyl iodides (or by polyfluorohalogenalkyl iodides) in the presence of the Na2S2O47NaHCO3 system.201, 211 R2 R1 Me Me Me Prn Prn HMe Me Me Me Presumably, this reaction occurs by the following scheme: R2 R Na2S2O4 ±NaHCO3 +RFI MeCN±H2O Cl(CF2)2 Cl(CF2)4 CF3 Cl(CF2)2 Cl(CF2)4 Cl(CF2)2 O R1 N +RFI R1 I RF O N 4 R2 R2 RF Me Bn Bn Bn Bn MeCO PhCO PhCO OTs OTs Cl(CF2)2 Cl(CF2)2 Cl(CF2)4 Cl(CF2)2 Cl(CF2)4 Cl(CF2)2 Cl(CF2)2 Cl(CF2)4 CF3 Cl(CF2)4 O R1 +RF .N R I RF O O 3 E:Z 32 : 68 60 : 40 52 : 48 95 : 5 >97: 3 >97: 3 >97: 3 Na2S2O4 ±NaHCO3 MeCN±H2O O R1 I N R2 + RF 5 E:Z Yield (%) 4 5 >97: 3 >97: 3 >97: 3 >97: 3 >97: 3 52 : 48 >97: 3 >97: 3 >97: 3 >97: 3 19 35 29 23 2700000 53 50 49 41 43 46 70 60 72 83O R1 N R2 RF 499 O R1 RFI R2 I N RF 5 I R1 R1 RF RF RFI O O N N R2 R2 4 Cyclisation induced by the intermediate radical is successfully used for the construction of cyclic systems.234 It is worth noting that in reactions with alkynes perfluoroalkyl iodides form mixtures of E- and Z-adducts in the presence of sodium dithionite, whereas perfluoroalkyl bromides and tri- chloro-1,1,1-trifluoroethane yield exclusively sulfinates.230 Generally, if the starting compound contains a double bond, its treatment with perfluoroalkyl iodides in the presence of the Na2S2O47NaHCO3 system results in the formation of addition products as is the case in the reaction of perfluoroalkyl iodides with O-allyl-O-isopropylideneglycerol and crown ethers contain- ing multiple bonds in a CH2Cl27H2O mixture.235, 236 O O Na2S2O4, CH2Cl2±H2O O O +RFI 30 8C, 3 h O O RF I RF=F(CF2)8 (72%), F(CF2)6 (59%), Cl(CF2)6 (55%), Cl(CF2)8 (68%).The addition products of perfluoroalkyl iodides at the triple bond can be used in the synthesis of heterocyclic compounds, e.g., 5-perfluoroalkyl-substituted isoxazoles.237, 238 Na2S2O4 ±NaHCO3 CF3CF2I + R1C CR2 MeCN±H2O, 0 8C NH2OH.HCl, NaHCO3 CF3CF2R1C CIR2 EtOH ±H2O, 60 8C R2 R1 CF3CF2CHR1 CR2 N NOH F3C O R1=H,R2=CH2OH. O Na2S2O4±NaHCO3 P CRI CF2I+HC CR MeCN±H2O EtO EtODiethyl difluoroiodomethylphosphonate was also introduced in the reaction with alkynes 222 to give a mixture of isomers the ratio of which depends on the nature of the substituent at the triple bond (Table 7). OPOEt CF2CH OEt Perfluoroalkyl derivatives of alkynes are formed in the reac- tion of alkynes with perfluoroalkyl iodides and subsequent treat- ment with a base as a result of elimination of HI from the adducts formed.235 ± 240 RFC CR HC CR+RFI R R RF RF 1) Na2S2O4 ±NaHCO3, MeCN±H2O, 10 ± 15 8C 2) ButOK±Et2O,720 8C Yield (%) Yield (%) n-C6H13 n-C8H17 73 76 78 n-Ê 5H11 (CH2)6OH Prn Cl(CF2)4 Cl(CF2)4 Cl(CF2)8 47 74 (CH2)9OH 82 52 Cl(CF2)2 Cl(CF2)2 Cl(CF2)2 Cl(CF2)4 Prn500 Table 7.The reaction of diethyl difluoroiodomethylphosphonate with alkynes HC:CR in the presence of the Na2S2O4 ±NaHCO3 system in MeCN±H2O.222 E:Z Yield (%) t /h R(CH2)3Me CH2OH CO2Me CO2Et 82 : 18 52 : 48 50 : 50 100 : 0 100 : 0 100 : 0 57 : 43 72 : 28 59 : 41 100 : 0 79 41 74 65 67 26 75 62 72 56 30.17 3440.17 3334 CH2OMe Ph CH2OEt CONMe2 ratio is Note. The ICF2P(O)(OEt)2:HC:CR:Na2S2O4 :NaHCO3 1 : 2 : 1 : 1.The reaction of silylenol ethers with perfluoroalkyl iodides in the presence of the Na2S2O47NaHCO3 system results in the formation of perfluoroalkylated a,b-unsaturated aldehydes and ketones.241 ± 245 Heating of the latter with HNEt2 (or piperidine) and acid hydrolysis give the corresponding b-dicarbonyl com- pounds. Na2S2O4 ±NaHCO3 Me(CH2)nCH CHOSiMe3+X(CF2)nI MeCN±H2O, 40 8C Me(CH2)n C CF(CF2)n71X , CHONa2S2O4±NaHCO3 Me C CH2+X(CF2)nI MeCN±H2O, 40 8C OSiMe3Me 1) HNEt2 2) HCl, H2O CH CF(CF2)n71X OMe (CF2)n71X CH2 O O X=Cl: n=4, 6, 8; X = F: n=6, 8. Trimethylsilyl ethers of the enol forms of acetophenone and methyl vinyl ketone react with perfluoroalkyl iodides in the presence of the Na2S2O47NaHCO3 system to give hydrogen substitution products at the double bond.242 Ph Ph (CF2)6F Na2S2O4 ±NaHCO3 +F(CF2)6I H Me3SiO Me3SiO (58%) It should be noted that the intermediate radical is capable of dimerisation; thus the dimeric products 6 and 7 are formed from butadiene derivatives in reactions involving allylic radicals 8.246 R1 R2 H2C Na2S2O4±NaHCO3 RF +RFI CH2 R1 R2 8 RF R2 R1 R2 R1 + RF R1 RF R2 R2 R1 RF 7 6 RF=Cl(CF2)n (n=2, 4), CF3(CF2)3; R1=R2=H, Me.G G Furin The rates of reactions of perfluoroalkyl halides with alkenes and alkynes can be increased by sonication.206, 235 R CHR CH2 C4F9-n n-C4F9I Na2S2O4 ±NaHCO3 MeCN±H2O, Sonication IR=CH2COMe (68%), CH2OH (61%), CH2OAc (70%), (CH2)5Me (90%) R HC CR I C4F9-n R=(CH2)5Et (95%) a-Perfluoroalkyl derivatives of aldehydes formed as inter- mediate products in the synthesis of valuable fluorine-containing blocks 226 are further used in the synthesis of heterocyclic com- pounds.227, 240 Polyfluorinated aldehydes or ketones are formed in reactions of vinyl ethers with perfluoroalkyl iodides and are further transformed into either the corresponding acids 9 or alcohols 10.247 RCH CHOEt+RFI Na2S2O4 ±NaHCO3 MeCN±H2O, 20 8C RFCHRCHO [O] RFCHRCOOH 9 [H] RFCHRCH2OH 10 Me Me Na2S2O4±NaHCO3 RFCH2 +RFI CH2 DMF, H2O, 5 8C O OEt Compound 11 containing the allene group, like dienes, form an intermediate radical in the reaction with perfluoroalkyl iodides; its dimerisation yields the diether 12.236RF Na2S2O4±NaHCO3 OMe CH2 MeCN, H2O, 20 8C C CHOMe+RFI 11 RF MeO OMe 12 RF Perfluoroalkyl iodides n-C6F13I and Cl(CF2)nI (n=2, 4, 6, 8) react with 4-methylenedioxolane in the presence of the Na2S2O47 NaHCO3 system resulting in ring opening.248 O Me Na2S2O4 ±NaHCO3 RFCH2COCH2OH +RFI Me O Cyclic ethers (2,3-dihydrofuran and 3,4-dihydro-2H-pyran) react with RFI [RF=Cl(CF2)n, where n=4, 6, 8; F(CF2)n, where n=6, 8] 226 or with CF2Br2 196, 225 in the presence of the Na2S2O47NaHCO3 system to produce 2-polyfluoroalkylhemi- acetals 13 which can be oxidised to the corresponding lactones 14 or reduced to the diols 15.226, 249 On the other hand, the hydrogen substitution product at the multiple bond 16 is formed in the presence of p-toluenesulfonic acid (Scheme 1).Na2S2O4 ±NaHCO3 +RFI RF MeCN±H2O, 20 8C O OH O 17 OH RF O RF=n-C6F13, Cl(CF2)n (n=2, 4, 6, 8). Perfluoroalkyl iodides react with heterocyclic compounds 17 ± 20 containing an a-methylene substituent in the presence ofSome new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds RF (CH2)n Na2S2O4 ±NaHCO3 HO (CH2)n O 13 (72% ± 78%) + RFI O RF (CH2)n TsOH O16 n=1, 2. the Na2S2O47NaHCO3 system with the formation of ring-open- ing products.250 O O O O O O O 20 19 18 OH Carbohydrates containing perfluoroalkyl substituents, e.g., 2-RF-2-deoxy-D-glucose, are prepared by perfluoroalkylation of glycals by perfluoroalkyl iodides induced by the Na2S2O47 NaHCO3 system.197, 207, 251 ± 258 OAc O O HO HO AcO AcO +RFI Na2S2O4 ±NaHCO3 MeCN±H2O, 20 8C OH RF Perfluoroalkyl-substituted carbohydrates, e.g., 2-iodo-3- perfluoroalkylpropyl-2,3,4,6-tetra-O-acetyl-b-D-glucopyranoside (21), can be synthesised by perfluoroalkylation of allyl gluco- pyranoside 22.These compounds were found to be useful inter- mediates and can be used as surfactants and emulsifiers.250, 259 ± 266 AcO Na2S2O4±NaHCO3 O +RFI AcO AcO O MeCN±H2O, 0 ± 20 8C, 1±4 h OAc 22 AcO I O AcO AcO O RF OAc 21 RF=C4F9 (86%), C6F13 (83%), C8F17 (78%), C10F21 (71%). Perfluoroalkyl iodides add at the multiple bond of hex-5- enopyranose and -furanose (R=CH2Ph, Me) in the presence of Na2S2O4.262 CH2 Me O O Me O H2C O OR O O Me Me O O Me Me Under ordinary conditions, benzene does not react with perfluoroalkyl iodides; however, under conditions of phase-trans- fer catalysis with CTMAB it yields perfluoroalkylation products and dimerisation products of intermediate cationic s-com- plexes.212, 267 ± 269 Perfluoroalkylation of aromatic compounds containing amino or hydroxy substituents with bromotrifluoro- 501 Scheme 1 RF (CH2)n [O] O O14 [H] HOCH2CHRF(CH2)n+1OH 15 methane or long-chain perfluoroalkyl iodides occurs at the ortho- and para-positions.212, 267 ± 269 Na2S2O4 ±NaHCO3±H2O PhH+RFI CTMAB RFH H H PhRF+ H RF H +RF H RF RF RF (35%) NH2 Na2S2O4 CF3 PhNH2+CF3Br ortho : para=23 : 11 Ortho- and para-perfluoroalkylphenols can easily be prepared from phenol 270 and its para-substituted derivatives 252, 271 in the presence of an alkali.For example, in the presence of NaOH p-cresol reacts with Cl(CF2)6I in DMF containing Na2S2O4 ± NaHCO3 to give 2-o-chloroperfluorohexyl-p-cresol in 60% yield.270 2,6-Diperfluoroalkyl derivatives can also be formed.271 The Na2S2O47NaHCO3 system was efficient in the per- fluoroalkylation of biologically active compounds containing a phenolic fragment. A procedure was developed for introducing perfluoroalkyl substituents into the aromatic ring of tyrosine.272 CH2CH(NH2)CO2H CH2CH(NH2)CO2H Na2S2O4 ±NaHCO3 +RFI MeCN±H2O RF OH OHa-Perfluoroalkyl-substituted derivatives are formed in high yields upon treatment of pyrrole with perfluoroalkyl iodides in the presence of the Na2S2O47NaHCO3 system.273 However, high hydrolytic lability of the fluorine atoms of the a-CF2 group should be kept in mind. It is of note that 2,5-dimethylpyrrole yields both addition (23) and substitution products of the hydrogen atom of the pyrrole ring (24).274 ± 277 NH, Na2S2O4±NaHCO3 RF RFI MeCN±H2O NH502 Me NH, Na2S2O4 ±NaHCO3 RFI MeMeCN±H2O Me Perfluoroalkylation of other nitrogen-containing heterocyclic compounds is also possible.273 Na2S2O4 ±NaHCO3 RFI MeCN±H2O RF N NH NH RF Perfluoroalkyl sulfones are synthesised in the reaction of alkenes H2C=CHR (R=CN, MeCO) with sodium perfluoroal- kanesulfinates RFSO2Na (RF=C4F9, ClC4F8) obtained by treat- ment of perfluoroalkyl iodides with sodium dithionite.188 It may thus be concluded that perfluoroalkyl radicals can be formed from perfluoroalkyl halides under the action of other radical anions capable of generating radical anions of perfluoro- alkyl halides. Indeed, Medebielle et al.239 who studied the reduc- tion of CF3Br, n-C4F9I, n-C6F13I and I(CF2)4I using terephtha- lonitrile, nitrobenzene and 4-nitropyridine N-oxide as messengers (E =71.60, 71.10 and 70.79 V rel.SCE, respectively) demonstrated the efficiency of perfluoroalkylation of N-anions of the heterocyclic series (e.g., imidazole, adenine, xanthine, uracil, cytosine, barbituric acid, lumazine, theophylline) by inter- mediate perfluoroalkyl radicals.O2N N CHO+n-C6F13I 7N (E=70.90 V rel. SCE) O DMSO HN +I(CF2)4I N 7O (E=71.60 V rel. SCE) This reaction occurs in accordance with the following scheme. The initial electrochemically generated 4-nitropyridine N-oxide (P) radical anion induces the reduction of perfluoroalkyl halide to the corresponding radical anion which is further transformed into the perfluoroalkyl radical. The latter reacts with the N-anion to yield a new radical anion which ultimately yields the final product and the radical anion of the `messenger', viz., P+e7 P7., P7.+RFI RF .+ I7+P, RFNu7., RF .+Nu7 RFNu7.+P RFNu+P7.. In the case of perfluoroalkyl halides, the reaction mechanism represents a modified version of the classical SRN1 mechanism where the electron transfer occurs without the intermediate formation of the substrate radical anion.The perfluoroalkyl RF RF Me Me +Me NH NH 23 (67%) 24 (20%) N N + RF NH NH (55%) (10%) RF + NH NH (35%) (5%) O2N N DMSO CHO F13C6 NH (35%) O (CF2)3CF2I HN O (35%) NH G G Furin radical thus generated attacks the carbon atom of the N-anion of the heterocyclic compound, eventually resulting in the formation of the reaction product. This methodology describes the perfluoroalkylation of organic substrates by perfluoroalkyl halides as a reduction in the presence of catalysts of the 4-nitropyridine N-oxide type.c. Reactions of perfluoroalkyl iodides and -bromides catalysed by transition metals and their derivatives Catalytic effects of metals and their salts. Various initiators of addition reactions of perfluoroalkyl iodides and -bromides to the multiple bonds C=C are presently known. An important role in the generation of perfluoroalkyl radicals is played by transition metal derivatives (mostly, zero-valent compounds) 278, 279 and their complexes180, 280 ± 283 used as both reagents and catalysts of diverse reactions.180, 278, 282, 283 Reactions of perfluoroalkyl iodides with alkenes and alkynes are especially efficient in the presence of Ru, Ni, W, Mo,180, 282, 283 Sn,284, 285 Fe,286, 287 Mg,288, 289 Cu,290 ± 294 Raney Ni (RaNi),295 ± 297 Pt0,298, 299 MnII, HgI,300 RuII,301 Rh,302 Me3Al,217 Et3B,303 ± 308 Zn,197, 309 and Pd0 (see Refs 197, 278, 310) and result in the formation of addition products at the multiple bond.278, 279 Reactions of perfluoroalkyl iodides with benzene in the presence of metals (Rh, Pd, Pt, Ru, Cu, RaNi, Co) and aqueous potassium hydrogencarbonate give per- fluoroalkylbenzenes.311, 312 It is noteworthy that disubstitution occurs with low yields.The role of metals consists in reductive generation of the radical RF .from RFI. Further transformations depend on the type of the substrate and may occur either as subsequent addition of the radical RF .at the multiple bond (C=C) or as substitution of a halogen or hydrogen atom at the carbon atom of the multiple bond. Thus perfluoroalkyl iodides give perfluoroalkanes in the presence of zinc in sulfolane or in H2O;313 inDMFthey react with aldehydes to give the corresponding alcohols.314 SO2 RF RF 120 8C, 6 h Zn RFI R RCHO DMF, 5 ± 20 8C, 1.5 h RF OH The reaction of bromotrifluoromethane with aldehydes and zinc in N-methylpyrrolidone yields alcohols;315 trifluoroacetalde- hyde is formed from DMF under conditions of cathode syn- thesis.316 It should be noted that reactions of perfluoroalkyl iodides and -bromides with electrophiles can also be catalysed by other metals.Thus the reaction of bromotrifluoromethane with chlorotrime- thylsilane in the presence of aluminium powder in N-methylpyr- rolidone yields trimethyl(trifluoromethyl)silane (yield 62%).317 In the presence of cadmium, perfluoroalkanes are formed in 72% to 90% yield.318 The reaction of Cl(CF2)4I with BunCH=CH2 in the presence of Mg results in the addition product BunCHICH2(CF2)4Cl in high yield, the reaction with BunC:CH yields a mixture of (E)- and (Z)-Cl(CF2)4CH=CIBun (Ref. 288).Various reactions of perfluoroalkyl iodides with aromatic compounds (Table 8) and alkenes in the presence of copper have been described.319 ± 322 In these reactions, diethylene glycol, ace- tonitrile and acetic anhydride are used as solvents. The reaction of perfluoroalkyl iodides with cyclohexene in the presence of catalytic amounts of copper gives addition products at the multiple bond and reduction products.RF RF Cu +RFH + +RFI Ac2O, 100 8C, 6.5 h I RF=(CF2)4Cl, (CF2)4O(CF2)2SO2F, (CF2)2O(CF2)2SO2F.Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Table 8. Reactions of bromo- and iodoaromatic compounds with perfluoroalkyl iodides RFI in the presence of copper.321 Reaction conditions ArHal RF solvent T /8C PhI C10H7Br C10H7I DMSO DMSO DMSO DMSO C5H5N n-C7F15 n-C8F17 n-C7F15 n-C7F15 n-C8F17 The reactions catalysed by metals (e.g., Zn, Cd) seem to occur via the intermediate formation of organometallic compounds, viz., an organozinc compound of the CF3ZnBr . Ln type (see Ref. 314) or an organocadmium compound,318 which further generate perfluoroalkyl radicals.MeCN (RF)2Cd+CdI2 Cd+RFI 2RFCdI 80 8C, 2±5 h RF RF (72% ± 90%) RF=F(CF3)2C(CF2)6, n-C6F13, n-C8F17, F(CF3)2CO(CF2)2, F(CF3)2CO(CF2)8, EtOC(O)(CF2)4O(CF2)2. Hence the initiation of the cleavage of the C7Hal bond under the action of metals is one of the simplest and convenient methods for the activation of reactions of RFI with alkenes and alkynes.288 It would be natural to expect that a similar effect will be produced by a combination of transition metal salts and zero- valent metals. Indeed, the NiCl2 .6 H2O7Al system efficiently initiates the reactions of RFI with RFCH=CH2 resulting in the formation of addition products at the multiple bond, albeit, in moderate yields.323 For example, the yields of the adducts formed in the reaction of alkenes with RFI in MeCN in the presence of 20 mol.% of NiCl2 .6 H2O and 2 equiv.Al (25 ± 30 8C, 12 h) (Table 9) were 45%± 60%.323 Zinc can replace aluminium in this reaction.324 NiCl2 .H2O, Al CH2 R2FCH2CHICF2R1F CHCF2R1F +R2FI MeCN, 25 ± 30 8C R1F =C3F6Cl, C5F10Cl, C3F7; R2F =ClC4F8, ClC6F12, ClC8F16. An interesting transformation occurred when perfluoroalkyl iodides, -bromides and -chlorides were heated in DMF in the presence of aluminium-promoted SnII (SnCl27Al) 325 or PbII (PbBr27Al).326 ± 329 This reaction resulted in the formation of perfluoroalkylaldehyde monohydrates.325 ± 329 Me2NCHO P2O5 RFCHO RFCH(OH)2 RFX a or b Yield (%) Yield Reagents RFX (%) Reagents RFX and con- ditions and con- ditions Al Cl(CF2)6I 97 (a) SnCl2, Cl(CF2)4I 80 (b) PbCl2, H(CF2)4Cl Al, 20 8C, Cl(CF2)8I 88 10 h H(CF2)6Cl H(CF2)8Cl CH2 =CH(CF2)4Cl CH2=CH(CF2)6Cl C4F9I 9084 89 C6F13Br C8F17Br 80 85 88 82 86 BunCHICH2(CF2)4Cl 91 BunCHICH2(CF2)6Cl 93 The yields of reaction products and reaction conditions are listed in Tables 10 and 11.The perfluoroalkylation of DMF by perfluoroalkyl iodides and a,o-dibromoperfluoroalkanes in the presence of Al7SnCl2 or Al7PbBr2 is strongly accelerated by sonication 330 which has recently found wide application in the activation of organic reactions.331 ± 333 Thus the reaction occurring under normal con- ditions usually lasts from 4 to 24 h, whereas that subjected to sonication is completed within 0.25 ± 3 h.The possibility of performing perfluoroalkylation with perfluoroalkyl iodides in 503 Yield (%) Product t /h 125 130 125 125 120 n-C7F15Ph n-C8F17Ph n-C7F15C10H7 n-C7F15C10H7 n-C8F17C10H7 78 83 45 89 96 23 15 34 48 16 the presence of metals (e.g., zinc, magnesium, etc.) using sonica- tion has been demonstrated.255, 334 ± 337 The reaction of cyclohexanone with C4F9I in hexane catalysed by magnesium and activated by sonication results in 1-perfluoro- butylcyclohexanol (yield*81%).336 Perfluoroalkylation occurs in the presence of zinc in THF and is catalysed by the triphenylphosphine ± palladium complex. In the absence of catalysts, the reactions of perfluoroalkyl iodides with compounds containing a carbonyl group are carried out using zinc in DMF.For example, the reaction of perfluoroalkyl iodides with the o-tolualdehyde ± chromium tricarbonyl 25 com- plex yields the corresponding alcohols 26 which eliminate Cr(CO)3 to give the alcohols 27.338 Me Me Me RF RF CHO+RFI OH Zn, DMF, 20 8C 0.5 ± 2.5 h, sonication Cr(CO)3 OH Cr(CO)3 26 (85%) 27 25 Table 9. Reactions of fluorine-containing alkenes CH2=CHCF2R1F with perfluoroalkyl iodides R2FI (25 ± 30 8C, 12 h, molar ratio R2FI : NiCl2:6H2O=2.0 : 1.0 : 0.2 or 5.0 : 1.0 : 0.2).323 Yield (%) Product R2 R1 F F C3F6Cl C5F10Cl C3F7 55 56 55 58 60 59 45 50 ClC4F8CH2CH=CFC3F6Cl ClC6F12CH2CH=CFC3F6Cl ClC8F16CH2CH=CFC3F6Cl ClC4F8CH2CH=CFC5F10Cl ClC6F12CH2CH=CFC5F10Cl ClC8F16CH2CH=CFC5F10Cl ClC6F12CH2CH=CFC3F7 ClC8F16CH2CH=CFC3F7 ClC4F8 ClC6F12 ClC8F16 ClC4F8 ClC6F12 ClC8F16 ClC6F12 ClC8F16 Table 10.The reaction of perfluoroalkyl iodides withDMFin the presence of the SnE27Al system.325 Product SnE2 RFX Yield (%) Reaction conditions T /8C t /h Cl(CF2)4I Cl(CF2)6I 6 106895 Cl(CF2)8I F(CF2)4I F(CF2)6Br F(CF2)8Br 16 15 15 15 15 15 15 15 15 15 15 15 Cl(CF2)4CHO 80 Cl(CF2)4CHO 88 Cl(CF2)4CHO 83 Cl(CF2)6CHO 97 Cl(CF2)6CHO 75 Cl(CF2)6CHO 85 Cl(CF2)8CHO 79 90 84 89 74 90 SnCl2 SnCl2 SnBr2 SnCl2 SnBr2 SnF2 SnBr2 SnCl2 SnCl2 SnCl2 SnBr2 SnF2 108 12 12 156 F(CF2)4CHO F(CF2)6CHO F(CF2)8CHO F(CF2)8CHO F(CF2)8CHO504 Table 11.The synthesis of polyfluorinated aldehydes and their monohy- drates from perfluoroalkyl halides and DMF in the presence of alumi- nium-activated salts with and without sonication.330 RFX Sonication Time /h Catalyst�SnCl2 0.25 24 +7 C4F9I C6F13I 0.25 + 0.25 + C8F17I2 3 BrC8F16Br + Catalyst�PbBr2 0.25 16 +7 C4F9I C6F13I 0.25 + 0.25 + C8F17I 4 BrC6F12Br 7 1.5 + 1.5 BrC8F16Br + More recent studies 338 demonstrated that sonication can be used in reactions of perfluoroalkyl iodides and -bromides with various carbonyl compounds and alkyl halides in the presence of MnCl27Na and AgBr7Li systems.339 This finding has led to the development of a simple procedure for the synthesis of perfluoro- carboxylic acids and partially fluorinated secondary alcohols using carbon dioxide and aldehydes, respectively.In this case, sodium and lithium are used as reductants for the formation of active metals (manganese and silver), which yield reactive organo- metallic derivatives with perfluoroalkyl halides. The organome- tallic derivatives enter into the reaction with the carbonyl compound. 1) CO2 2) H3O+ RFX MnCl2, 2 equiv. Na, DMF, sonication i-C3F7I n-C4F9I n-C4F9Br n-C6F13I n-C8F17I n-C8F17Br RFX 39 52 Yield 41 (%) RCHO RFX MnCl2, 2 equiv. Na, DMF, sonication RFX CF3 I n-C4F9Br n-C4F9I n-C8F17Br R Ph Ph C5H11 Et 38 51 Yield (%) 52 The activity of perfluoroalkyl halides decreases in the follow- ing order: RFI>RFBr RFCl. The Sn7AgOAc and Sn7Cu2Cl2 systems effectively catalyse reactions of perfluoroalkyl iodides with alkenes under relatively mild conditions.284 Methanol is the most suitable solvent for these reactions.Joint use of metallic Sn and Al produces the same effect. G G Furin Sn0 RFCH2CHIR CHR+RFI CH2 MeOH, 20 8C, 24 h Product R=Me(CH2)5, MeO(CH2)2, HOCH2, PhCH2, HO(CH2)4, (EtO2C)2CHCH2, Me2CHCH2; RF=n-C4F9, n-C6F13. Yield (%) It was found that the copper acetate ± hydrazine hydrate system catalyses reactions of perfluoroalkyl iodides with alkenes and alkynes;340 the yields of the target products vary from 65% to 90%.CH2 CHR RFCH2CHIR Cu(2±H2NNH2 .H2O RFI RF=C2F5, n-C3F7, iso-C3F7, n-C6F13, C3F7OCFCF3 R=CH2OH, Bun, n-C6F13. PriOH C4F9CHO 41 C6F13CH(OH)2, 80, C6F13CHO 65 C6F13CH(OH)2, 60, C8F17CHO 65 C8F17CH(OH)2, 78, C8F17CHO 65 (HO)2CHC8F16CH(OH)2, 90, OCHC6F12CHO 69 HC CR RFCH CIR RF=n-C3F7, iso-C3F7, R=CH2OH. The KI7CuSO4 system is also active in these reactions.341 In the presence of this system, cupric perfluoroalkanesulfinates react with alkenes with the formation of addition products at the multiple bond, viz., RFSO2CH2CHIR. Nickel complexes effectively catalyse the perfluoroalkylation of aromatic compounds under the action of polyfluoroalkyl iodides.342 NH2 NH2 NH2 (CF2)nCl Ni(PPh3)4 + +Cl(CF2)nI C4F9CHO 50 C6F13CH(OH)2, 74, C6F13CHO 65 C6F13CH(OH)2, 70, C6F13CHO 62 C8F17CH(OH)2, 70, C8F17CHO 60 (HO)2CHC6F12CH(OH)2, 80, OCHC6F12CHO 65 (HO)2CHC6F12CH(OH)2, 87, OCHC6F12CHO 60 (HO)2CHC8F16CH(OH)2, 83, OCHC8F16CHO 60 Dioxane, 80 8C, 6 h (CF2)nCl (45%) (40%) n=2, 6.It was found 343 that the Cp2TiCl27Fe system catalyses the reactions of perfluoroalkyl iodides XCF2CF2I (X=Cl, Br) with alkenes and alkynes which yield 1 : 1 adducts.343 ± 345 The use of octa-1,7-diene (28) as an alkene results in the involvement of only one multiple bond and the formation of the adduct 29. Cp2TiCl2±Fe CH(CH2)4CH CH2+RFI CH2 50765 8C, 8 ± 15 h 28 RFCH2CHI(CH2)4CH CH2 29 RF=ClC4F8 (87%), C4F9 (88%), (CF2)2CF (92%), CF2ClCF2 (90%).RFCO2H 46 61 62 R RF OH In the presence of 30 mol.-equiv. of Fe and 2 mol.-equiv. of Cp2TiCl2, 1,2-dihalogenotetrafluoroethane CF2BrCF2X (X=I, Br) reacts with alkenes in EtOH under a nitrogen atmosphere to give addition products in excellent yields (Table 12). The exper- imental results provide support for a radical mechanism of this reaction. In the perfluoroalkylation induced by CF2BrCF2X in the presence of Cp2TiCl2 as a catalyst, 2-bromotetrafluoroethyl radical can be formed, apparently according to the following scheme:346, 347 TiIII +FeI, TiIV+Fe0 32 CF2BrCF2X7.+TiIV TiIII +CF2BrCF2X . CF2BrCF2+X7, CF2BrCF2X . CF2BrCF2+R1CH CHR2 . CF2BrCF2CHR1CHR2 . CF2BrCF2CHR1CHXR2+CF2BrCF2 .Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Table 12.Reactions of alkenes with 1,2-dihalogenotetrafluoroethane induced by the Cp2TiCl27Fe system.345 CF2BrCF2CHR1CHXR2 CF2BrCF2X+R1CH CHR2 t /h Alkene RFX T /8C Oct-1-ene CF2BrCF2I 55 10 CF2 BrCF2CH2CHIC6H13 CF2BrCF2I 25 15 CF2 BrCF2CH2CHIC6H13 15 15 26 CF2BrCF2Br CF2BrCF2Br CF2BrCF2Br Hex-1-ene Hexa-1,5-diene 55 60 60 36 70 Cyclohexene CF2BrCF2Br CF2BrCF2I 65 24 Allyl alcohol CF2BrCF2I 65 13 CF2 BrCF2CH2CHICH2OH 8 60 Diallyl ether CF2BrCF2Br CF2BrCF2I 55 7 Dichlorobis(cyclopentadienyl)titanium(IV) catalyses the per- fluoroalkylation of isoprene by perfluoroalkyl iodides in the presence of zinc in THF or DMF at room temperature, resulting in the reductive addition product at one multiple bond.334 This reaction is activated by sonication.Cp2TiCl2 +RFI RF Zn, THF, 20 8C, 1 h Zinc used as a catalyst in the reaction of perfluoroalkyl iodides with alkenes initiates addition and reduction reactions as well as dimerisation of transient radicals.335 The ratio of reaction prod- ucts changes when the reaction is carried out in CH2Cl2. As in the case with AIBN, only the addition product is formed in the presence of iron in DMF. CH(CH2)mR+RFI CH2 Zn RFCH2CH2(CH2)mR+RFCH2CH(CH2)mR H+ RFCH2CH(CH2)mR Fe RFCH2CHI(CH2)mR DMF RF=C6F13, C8F17; R = CO2H, CH2OH; m=0, 2, 8. The cyclopentanedienyldicarbonyl iron dimer is yet another efficient catalyst of the reaction of perfluoroalkyl iodides with alkene derivatives.348, 349 CHR+RFI CH2 [CpFe (CO)2]2 Et3N, EtOH, 25 8C RFCH2CH2R RF=F(CF2)n (n=4, 6, 8), Cl(CF2)6; R = CO2Et, CN, COMe.[CpFe(CO)2]2 CHOEt+CF3(CF2)5I CF3(CF2)5CH2CH2OEt CH2 Et3N, EtOH, 25 8C (63% ± 95%) RF=C8F17, C3F7, CF(CF3)2. Successful perfluoroalkylation of alkenes containing electron- accepting substituents (e.g., acrylates, acrylonitrile, methyl vinyl ketone, etc.) was carried out with Zn-bis(dimethylglyoxymate)- pyridinecobalt(II) bromide [BrCo(dmgH)2Py, 30] in ethanol as a 505 Yield (%) Product CF2BrCF2CH2CHBrC6H13 CF2BrCF2CH2CHBrC4H9 CF2BrCF2CH2CHBr(CH2)2CH=CH2 96 91 95 93 78 Br 92 CF2CF2Br I 92 CF2CF2Br 96 Br CF2CF2Br 95 O I CF2CF2Br 94 O catalyst (Table 13).205, 256, 259, 343, 350 ± 354 This reaction also involved ozone-destroying bromoperfluoroalkanes (bromo- freons), which are now prohibited for use.Owing to relatively mild reaction conditions, this method is especially convenient for the synthesis of carboxylic acid esters, nitriles and ketones containing a perfluoroalkyl fragment. Zinc powder was used as a reductant in the reaction catalysed by BrCo(dmgH)2Py (30).205, 343 H O O Co NPy N N BrNO O H 30 The system 307Zn was found to be efficient in reactions of BrCF2CF2CH=CHCH2X (X=Cl, AcO) with alkynes HC:CR (R=Ph, CH2OH, C5H11). The yield of the cyclisation products, viz., 4,4,5,5-tetrafluoro-3-vinylcyclopentenes, varied from 40% to 50%.343 In the presence of this system, cyclic polyfluoroalkyl bromides react smoothly with alkenes.(CF2)2(CH2)2CO2R CF2CF2Br Br Br + CO2R BrCo(dmgH)2Py ± Zn EtOH, 20 8C, 24 h Zinc itself can exert a pronounced effect on the reactions of alkenes with perfluoroalkyl iodides. For example, the reaction of Me(CH2)4CH=CH2 with CF3(CF2)3I yielded 90% of Me(CH2)4. .CHICH2(CF2)3CF3.351 The system 307Zn was used for perfluoroalkylation of alkenes by perfluoroalkyl iodides and -bromides.256, 259, 344 Thus perfluoroalkylation of various cyclic, linear, symmetric or asym- metric alkenes with Freon-2402 (1,2-dibromo-1,1,2,2-tetrafluoro- ethane) resulted in derivatives containing a CF2CF2 fragment.354, 355 It may be noted that the activation of the C7Br bond, e.g., in RCF2CF2Br, by cobalt in the low valent state generated in situ occurs with high efficiency, which made it possible to induce reactions of these compounds with unsaturated substrates.259506 Table 13.Perfluoroalkylation of alkenes by perfluoroalkyl iodides in the presence of the catalytic system 307Zn.354 Alkene H2C=CHCO2Et H2C=CHCN H2C=CHC(O)Me HC:CCO2Et 7 10 a The reaction was carried out in the presence of the catalytic system Cp2TiCl27Fe. The (diethoxyphosphoryl)difluoromethyl group was success- fully introduced into alkenes containing electron-withdrawing substituents by the reaction with (EtO)2P(O)CF2Br in the pres- ence of the system 307Zn.344, 346 ± 348 30±Zn, (EtO)2PCF2Br CHX CH2 X=CO2Et, CO2H, CN, CH2Cl, CONH2, COMe, OAc, OEt, CO2Me, Bun.The yield of the reaction products increases after addition of 1 equiv. of HCOONH4. Apparently, the surface of zinc is acti- vated by ammonium ions. Other ammonium salts, e.g., NH4Cl, NH4Br and NH4OAc, can also be used for this purpose; however, the yields of the reaction products are lower. Reduction of commercial Freon-1301 (bromotrifluorome- thane) to the trifluoromethyl radical possessing electrophilic character using the Zn7SO2 system in DMF in the presence of Na2S2O5 and bases (Na2HPO4, 2-methylpyridine) was a step forward on the way to trifluoromethylation of aromatic and heterocyclic compounds.138, 171, 267, 353, 355 ± 357 Thus the reaction of CF3Br with aniline in the presence of this system gives a mixture of ortho- and para-trifluoromethylanilines with the ortho-isomer prevailing.NH2 +CF3Br Trifluoromethylation of pyrrole and N-methylpyrrole occurs at position 2. In the presence of this system, perfluoroalkyl iodides F(CF2)nI (n=1, 2, 4, 6, 8) efficiently react with aromatic compounds RFX T /8C Cl(CF2)6I F(CF2)4I F(CF2)6I F(CF2)8I CF2ClCF2I a CF2BrCF2Br CF2BrCFClBr CF2Br2 15 20 20 20 65 75 50 70 CF2BrCF2I 6530 C6F13I 30 30 C6F13I C6F13Br C8F17Br 30 45 45 RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et RFCH2CH2CO2Et Cl(CF2)4I 30 2 RF CH2CH2CN 10 RF CH2CH2CO2Et 2.5 C8F17I 30 3 RF CH2CH2CN C6F13Br C8F17Br Cl(CF2)6I 30 5 RF CH2CH2C(O)Me C4F9I 25 4 RF CH2CH2C(O)Me RFCH2CH2C(O)Me RFCH2CH2C(O)Me RFCH2CH2C(O)Me ClC4F8I 25 8 RF CH=CHCO2Et C4F9I 20 7 RF CH=CHCO2Et RFCH=CHCO2Et RFCH=CHCO2Et C6F13Br C8F17Br 30 30 O O (EtO)2PCF2(CH2)2X NH2 NH2 CF3 Zn ± SO2, DMF + Na2S2O5, 2-MeC5H4N, 20 8C (36%) CF3 (20%) Product t /h 0.5 0.5 0.5 0.5 10 11 10 24 RFCH2CH2CN RFCH2CH2CN RFCH2CH2CN 3.5 43.5 55 containing electron ± donor substituents (phenols, anisole, ani- lines, aminophenols, toluene) and pyrrole.Zn ± SO2 ArRF+BH+. I7 ArH+RFI B: The reaction of perfluoroalkyl iodides with CO2 in the presence of the Zn/Cu couple in DMSO results in perfluorinated carboxylic acid, this presents special interest.358 ± 360 An analogous reaction with SO2 gives the corresponding perfluoroalkanesul- fonyl chlorides.360 CO2 RFCO2H DMSO Zn/Cu RFI RF=C4F9 (40%), C6F13 (45%), C8F17 (47%) 1) SO2 2) Cl2,MeOH DMSO RFSO2Cl RF=C4F9 (40%), C6F13 (40%), C8F17 (52%) Some metal halides can effectively catalyse perfluoroalkyla- tion reactions.Thus the redox system CrCl37Fe in ethanol promotes the perfluoroalkylation of alkenes containing electron- withdrawing substituents 256, 347, 361, 362 under the action of CF2Br2 (Table 14),205 CF3Cl or ICHFCO2R (R=Me, Et) at 60 ± 70 8C.287 CrCl3±Fe . 6H2O R2O2CCHFCH2CH2R1 CH2 CHR1+ICHFCO2R2 EtOH R1=CO2Me (71%), CO2Et (78%), CN (74%), COMe (75%); R2=Me, Et.The CrCl37Fe system is efficient in the reaction of perfluoro- alkyl iodides Cl(CF2)nI (n=2, 4, 6, 8), C4F9I, C6F13I and C8F17I with methyl a-acetylaminoacrylate resulting in b-perfluoroalkyl- a-amino acid derivatives RFCH2CH(NHAc)CO2Me in 65% to 80% yields. The reaction of perfluoroalkyl iodides with diethyl allylmalonate and its analogues in the presence of the CrCl37Fe system gives perfluoroalkylmethyl-substituted derivatives of G G Furin Yield (%) (E :Z) 56 71 72 75 92 93 90 90 61 93 71 69 75 70 45 49 64 72 53 85 (26 : 74) 73 (9 : 91) 76 (30 : 70) 65 (28 : 72)507 Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Table 14.Reactions of alkenes containing electron-withdrawing substituents with CF2Br2 in the presence of the FeCrCl3 system in EtOH.205 Yield (%) Product t /h Alkene T /8C 72 62 80 43 20 20 24 24 60 60 60 75 CF2Br(CH2)2CO2Et CF2Br(CH2)2CO2Me CF2BrCH2CH(Me)CO2Et CF2BrCH(Me)CH2CO2Et CH2=CHCO2Et CH2=CHCO2Me CH2=C(Me)CO2Et MeCH=CHCO2Et CH2=CHCO2H 65 20 CF2 Br(CH2)2CO2H 64 CH2=CHCONH2 CH2=CHCN CH2=CHCOMe CH2=CHBun CH2=CHC6H13-n CH2=CH(CH2)2CH=CH2 CH2=CH(CH2)2Ac CH2=CH(CH2)8CO2Me CH2=CHCH2OAc 72 62 60 96 84 72 64 64 30 20 18 20 10 106 138 12 70 60 60 60 60 60 60 60 60 CF2Br(CH2)2CONH2 CF2Br(CH2)2CN CF2Br(CH2)2COMe CF2BrCH2CHBrBun CF2BrCH2CHBrC6H13-n CF2BrCH2CHBr(CH2)2CH=CH2 CF2BrCH2CHBr(CH2)2Ac CF2BrCH2CHBr(CH2)8CO2Me CF2BrCH2CHBrCH2OAc 74 8 12 CF2BrCH2CHBr(CH2)3Me cyclopropane 31 in high yields.355, 356 Ethanol is the best solvent for this reaction.3-iodomethyl-4-perfluoroalkylmethyl-1,1-di(ethoxycarbonyl)cyc- lopentanes (4 : 1).138 E E RF CrCl3±Fe +RFI I. CO2Et RF LaCl3±Zn or SmCl3±Zn THF, 50 ± 67 8C CO2Et+RFI EtOH, 60 ± 79 8C 31 EtO2C CO2Et EtO2C CO2Et I RF RF E Yield (%) E Yield (%) RF RF I. EtO2C CO2Et EtO2C CO2Et 92 76 70 69 COMe CN CN CN C6F13 C4F9 C8F17 C6F13 89 92 85 87 85 CO2Et CO2Et CO2Et COMe COMe C2F5 C6F13 C8F17 C4F9 C8F17 RF=ClC4F8, ClC6F12, C6F13, C8F17. The NiCl2 .6 H2O7Zn system in THF proved to be efficient in the reaction of iodofluoroacetates with alkenes resulting in d-iodo esters in good yields.251 ± 253 In the case of perfluoroalkyl chlorides, the hydrogen atom is substituted for chlorine.252 The YbCl37Zn and LnCl37Zn systems produce a similar effect.138, 251, 254, 256 Thus the reaction of perfluorohexyl iodide with CH2=CHCH2OAc in THF in the presence of the YbCl37Zn system results in F(CF2)6(CH2)3OAc in 95% yield.This can be explained by the fact that the primary addition product to the double bond undergoes reductive deiodination. Activation of perfluoroalkyl iodides by transition metal com- plexes. Transition metal complexes can also efficiently activate perfluoroalkyl iodides. The efficiency of the YbCl37Zn system in catalytic reactions of perfluoroalkyl iodides with alkenes was studied (Table 15).250 ± 256 This reaction is completed within several minutes in tetrahydrofuran but does not take place in EtOH or benzene.Perfluoroalkanesulfonyl chlorides F(CF2)nSO2Cl (n=1 ± 20) and pentafluorobenzenesulfonyl chloride can replace perfluoro- alkyl iodides in perfluoroalkylation and arylation reactions of aromatic and heterocyclic compounds and alkenes with (Ph3P)3RuCl2 as a catalyst.355, 363 ± 367 LnCl3±Zn RF +RFI CO2Me CO2Me OMe THF, 50 ± 79 8C OMe (65% ± 80%) C6F5 (Ph3P)3RuCl2 +C6F5SO2Cl (73%) OMe OMe The reaction of substituted hepta-1,6-diene with perfluoro- alkyl iodide in the presence of the LaCl37Zn or SmCl37Zn system is accompanied by cyclisation involving the second double bond and results in a mixture of the corresponding cis- and trans- Table 15.Perfluoroalkylation of alkenes with perfluoroalkyl iodides in the presence of the YbCl3Zn system.251 Yield (%) Product Time /min Alkene RF 95 56 60 58 F(CF2)6(CH2)3OAc F(CF2)6(CH2)3OH F(CF2)6(CH2)3P(O)(OEt)2 Cl(CF2)8(CH2)2C6H13 F(CF2)6 F(CF2)6 F(CF2)6 Cl(CF2)8 CH2=CHCH2OAc CH2=CHCH2OH CH2=CHCH2P(O)(OEt)2 CH2=CHC6H13-n 67 10 10 Note: The alkene :RFI : YbCl3 : Zn molar ratio is 1.00 : 1.00 : 0.05 : 0.50.508 (Ph3P)3RuCl2 ArRF + SO2 ArH+RFSO2Cl 120 8C, 19 h Ar Ar RF Yield (%) Yield RF (%) 44 54 59 41 Ph MeC6H4 MeOC6H4 1,4-Me2C6H3 C6F13 C6F13 C6F13 C6F13 41 36 58 63 Ph MeC6H4 MeOC6H4 1,4-Me2C6H3 1,4-(MeO)2C6H3 71 CF3 CF3 CF3 CF3 C6F13 The addition product to the double bond is formed in the reaction with alkenes.301, 368, 369 This catalytic system was effective in perfluoroalkylation of arenes 363, 364, 370, 371 and enol silyl ethers by perfluoroalkanesul- fonyl chlorides (Table 16).366 Table 16.Reactions of aromatic compounds with pentafluorobenzenesul- fonyl chloride in the presence of (Ph3P)3RuCl2 at 240 8C.366 Yield (%) Time /h Product Substrate 73 14 87 39 59 145 24 C6F5Ph 4 C6F5C6H4OMeoà 8 C6F5C6H4Cl b 4 C6F5C6H4CNc 4 C6F5C6H3Me2 4 MeC6H3(C6F5)CHMe2 2 C6F5C6H3(OMe)2 PhH PhOMe PhCl PhCN p-Me2C6H4 p-MeC6H4CHMe2 p-(MeO)2C6H4 a The ratio of the ortho : meta : para isomers is 43 : 16 : 41.b The ratio of the ortho : meta : para isomers is 42 : 31 : 27. c The ratio of the ortho : meta : para isomers is 27 : 43 : 30. Perfluorophenylation of various thiophene derivatives by C6F5SO2Cl in the presence of the (Ph3P)3RuCl2 complex was studied under similar conditions. The results of these studies are listed in Table 17.366, 367 C6F5 (Ph3P)3RuCl2 + +C6F5SO2Cl C6F5 240 8C S S S 33 32 Perfluoroalkyl iodides add to alkenes in the presence of the Wilkinson catalyst [tris(triphenylphosphine)rhodium chloride] at 80 8C.298, 372 This catalyst ensures high chemoselectivity under mild reaction conditions. (Ph3P)3RhCl CH2 CHC5H11+Cl(CF2)4I PhH, 1.5 h Cl(CF2)4CH2CHIC5H11 (75%) (Ph3P)3RhCl CR1R2+RFI CH2 RFCH2CIR1R2 (80% ± 95%) RF=Cl(CF2)4, F(CF2)4, Cl(CF2)6, Cl(CF2)2; R1=n-C5H11, n-C6H13, Bun, Me2CHCH2, Et; R2=H, Me.Perfluoroalkyl iodides RFI [RF =Cl(CF2)4, Cl(CF2)6, CF3(CF2)3] react with alkenes and alkynes in the presence of Ir(H)(CO)(PPh3)3. The addition reaction to the triple bond yields predominantly E-isomers.358 The perfluoroalkyl radical RF .generated from perfluoroalkyl iodides in the presence of metals or transition metal complexes reacts smoothly with alkenes containing both electron-donor and electron-withdrawing substituents. As in the case of sulfinatode- G G Furin Table 17. Reactions of thiophene and its derivatives with pentafluoroben- zenesulfonyl chloride in the presence of (Ph3P)3RuCl2.366 Yield (%) Product Substrate 22 C6F5 S S C6F5 6 S 14 Me Me C6F5 S S C6F5 5 Me S C6F5 7 Me S 39 C6F5 Me3Si SiMe3 S S C6F5 17 S Me3Si C6F5 11 SiMe3 S halogenation, these complexes effectively catalyse the addition of perfluoroalkyl halides to both types of alkenes.Tetrakis(triphenylphosphine)palladium is also efficient in reactions of perfluoroalkyl iodides with alkenes and alkynes in hexane.278, 302, 305, 310, 373 ± 376 CH2=CHR RFCH2CHIR (70% ± 80%) Pd(PPh3)4 RFI C6H14 H I HC:CR 60 ± 67 8C, 24 h R RF RF=CF3(CF2)3, CF3(CF2)2, CF3(CF2)5; R=(CH2)2OH, Ph, n-C6H13, SiMe3, Bun, CH2SiMe3, (CH2)2CO2Me, CH2OH. For example, chlorododecafluorohexyl iodide reacts with hept-2-ene in the presence of 0.5 mol.% Pd0 (20 min, 20 8C) resulting in the addition product (yield 97%).An increase in temperature from 20 to 100 8C has little effect on this reaction. The trialkylstannyl group at the carbon atom of the multiple bond can be replaced by the perfluoroalkyl group by treatment with perfluoroalkyl iodide in the presence of Pd(PPh3)4.377 Thus the reaction of (E)-PhCH=CHSnBun3 with perfluorobutyl iodide in the presence of Pd(PPh3)4 in hexane with boiling for 4 min results in (E)-PhCH=CHC4F9 in 68% yield.297, 377 A mixture of cis- and trans-ethers RFCH=CHOR (yields 51%± 86%) is formed in the reaction of RFI (RF=CF3, C3F7, C6F13) with CH2=CHOR(R=H, Bun) in hexane in the presence of Pd(PPh3)4 and Et3N.378 a,a-Difluoro-substituted esters of carboxylic and phosphonic acids are prepared by the reaction of iodo-substituted derivatives of these acids with alkenes in the presence of Pd(PPh3)4.Sub- sequent treatment of the iodo-substituted derivative with NiCl2 .6 H2O results in the formation of the reduction prod- uct.158, 250 ± 256Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Pd(PPh3)4 CHR CH2 THF, 20 8C ICF2P(O)(OEt)2 RCHICH2CF2P(O)(OEt)2 (75% ± 82%)NiCl2 .6H2O ICF2C(O)R RCHICH2CF2COR 20 8C, 30 min R(CH2)2CF2COR (60% ± 80%) R=Ph, Bun, n-C6H13. Zero-valent palladium also catalyses the reactions of aryl- or alkenyl halides with alkenes resulting in addition products.379 Most probably, the complex 34, which is formed first, yields an organopalladium derivative 35 in reactions with alkene.380 Its further transformations can include reduction of palladium to Pd0 with the formation of an addition product to the multiple bond (route a) or elimination of the hydrogen atom from the b-position under the action of palladium eventually resulting in a new alkene (route b).CH2 CHR RFI + Pd0 RFCH2CHRPdI 35 RFPdI 34 a RFCH2CHIR+Pd0 b RFCH CHR+HPdI Palladium(0) is the only possible reagent in the formation of a radical anion of perfluoroalkyl iodide (reduction) which yields the perfluoroalkyl radical initiating further conversions. The forma- tion of a cyclic system in the reaction of perfluoroalkyl iodide with diallyl ether in the presence of Pd0 provides strong evidence in favour of the radical mechanism of this reaction.On the other hand, this reaction may occur via the generation of the perfluoroalkyl radical upon decomposition of the complex 34. The perfluoroalkyl radical further reacts with alkene to give the target product. RF .+PdI, RFPdI 34 34 RF .+PdI RFI + Pd0 RFI7.+Pd+ RFI RFCH2CHIR+RF . RF .CH2 CHR RFCH2CHR . PdI RFCH2CHIR+Pd0 The EPR spectra of perfluoroalkyl radicals generated in these reactions could not be recorded because of their high reactivity and low concentration.278 However, the use of N-benzylidene- tert-butylamine N-oxide as a spin trap made it possible to obtain well-resolved EPR spectra in which the trapped [Cl(CF2)4].radical could be detected as the radical [Cl(CF2)4CH(Ph)N(O.)But].278 These findings provide evidence both for the electron transfer in this reaction and the oxidation of Pd0 by perfluoroalkyl iodide resulting in the formation of a perfluoroalkyl palladium complex of the type 34 as occurring with the formation of a transient radical. Fluorine-containing aliphatic mono- and dicarboxylic acids were obtained by the reaction of perfluoroalkyl iodides or -bromides with CO2 in the presence of the Group VIII transition metal complexes and subsequent hydrolysis of the reaction products.381, 382 Thus CF3(CF2)7CO2H was isolated in 40% yield upon hydrolysis of the reaction product of CF3(CF2)7I with CO2 in DMF in an autoclave in the presence of Pd(PPh3)4 at 60 8C.This suggests the intermediate formation of the perfluoroalkyl radical which further reacts with carbon dioxide. When the reaction is carried out in the presence of alkenes and a CO2 source, the intermediate radical formed as the product of addition of the perfluoroalkyl radical to the multiple bond reacts further with CO2 to yield a carboxylic acid. With alcohol as a solvent, this reaction gives the corresponding ester. Thus the 509 reaction of hex-1-ene with C8F17I in the presence of K2CO3 and dichlorobis(triphenylphosphine)palladium in ethanol (12 h, 80 8C) gives C8F17CH2CHBuCO2Et in 67% yield.383, 384 Perfluoroalkylation of aromatic compounds by perfluoro- alkyl iodides can be carried out in the presence of zero-valent transition metals (e.g., Rh, Pd, Pt, Ru, Cu, Ni, Re) and aqueous K2CO3.385 The yields of disubstituted products are usually low.2% Pd, 0.1% Pt PhH+CF3(CF2)3I K2CO3, 170 8C Ph(CF2)3CF3+C6H4[(CF2)3CF3]2 (93%) (5%) On the other hand, the reaction of perfluorovinyl- and polyfluoroaryl iodides with alkynes in the presence of the (Ph3P)2PdCl27CuI complex results in the formation of addition products to the triple bond and elimination of HI.361, 373 ± 376 R2CF CFI R1C CCF CFR2 (50% ± 87%) (Ph3P)2PdCl2 R1C CH F R2 I CuI, NEt3, 770 to 20 8C F C R1C R2 R1=OMe, NMe2, F, Br; R2=(CH2)nMe (n=3 ± 6), Ph, (CH2)3CN, CH2OPh, CH2OH, CH(OH)Me. The reaction of perfluoroalkyl iodides with alkynes in the presence of a palladium catalyst and bases (e.g., K2CO3, Et3N) yields mixtures of enynes and alkenes.386 The co-catalyst CuI increases the yield of enynes.The best results are attained when the CHCl37EtOH mixture (5 : 1) is used as a solvent. (Ph3P)2PdCl2, CuI 2HC CR+RFI CHCl3 ± EtOH, 50 8C, 17 h RFCH CRC CR+RFCH CHR+(RC C)2 38 37 36 Yield (%) R RF 38 37 36 3 7 7 7 74 70 Bun SiMe3 n-C8F17 n-C3F7 These reactions occur smoothly without complications and allow for high variability of functional groups without resorting to the use of toxic or hazardous reagents. Palladium derivatives efficiently catalyse the reactions of perfluoroalkyl halides with allylic alcohols which occur in the presence ofK2CO3 and result in the formation of polyfluoroalkyl- substituted oxiranes (Table 18).386 R1 R2 R1 (PPh3)2PdCl2 RFX+H2C K2CO3, EtOH, 80 8C R3 C(OH)R2R3 RFH2C O Table 18.Reactions of allylic alcohols H2C=CR1C(OH)R2R3 with perfluoroalkyl iodides RFI in EtOH in the presence of (Ph3P)2PdCl2.386 R3 R2 R1 RF Yield of oxirane (%) 70 71 79 63 71 77 72 74 56 Me HHHHHH H H H n-C8 F17 H H Me n-C8 F17 H Me n-C8F17 n-C6H13 H CF3 H n-C6H13 C2F5 H n-C6H13 n-C3F7 H n-C6H13 n-C4F9 n-C6H13 H n-C6F13 H CF2ClCFCl n-C6H13510 Similarly, perfluorooctylmethyl-substituted aziridines are obtained in the reaction of perfluorooctyl iodide with allylamines under identical conditions. NR (PPh3)2PdCl2 CH CH2NHR n-C8F17I + CH2 K2CO3, EtOH CH2C8F17-n R=H (35%), Ph (41%).On the other hand, the addition product to the multiple bond is formed in the reaction of perfluoroalkyl halides with allyl acetate in the presence of Pd(PPh3)4.382 Pd(PPh3)4 CHCH2OAc ClCF2CFCl(CF2)2I + CH2 ClCF2CFCl(CF2)2CH2CHICH2OAc (74.5%) It was found 328 that the dichlorobis(Z-cyclopentadienyl)tita- nium(IV)7iron system efficiently catalyses the reactions of per- fluoroalkyl iodides and -bromides with octa-1,7-diene (39). This reaction gives addition products to one multiple bond (40). Cp2TiCl2±Fe CH2 50 ± 65 8C, 8 ± 15 h CH2 CH(CH2)4CH CH2+RFI 39 RFCH2CHI(CH2)4CH 40 RF=ClC4F8 (87%), C4F9 (88%), (CF2)2CF (92%), CF2ClCF2 (90%), CF2BrCF2 (91%), CF2ClCFCl (81%). The Cp2TiCl27Zn system is also efficient in reactions of allyl bromide with carbonyl compounds.329 Ethyl-4,4,4-trifluoro-3-iodo-(Z)-crotonate (41) is a valuable synthon in the synthesis of compounds containing the trifluoro- methyl group.The reaction of alkynes with the ester 41 in the presence of Pd(PPh3)2Cl2 results in compound 42 which contains a conjugated system of double and triple bonds in addition to the CF3 group.387, 388 H F3C CF3 (Ph3P)2PdCl2 C RC +HC CR I CO2Et H CuI, Et3N 20 8C, 24 h EtO2C 42 41 R=SiMe3 (76%), Ph (87%), (CH2)7Me (92%), 4-MeOC6H4 (93%), 4-NO2C6H4 (88%), (CH2)5Me (93%), (CH2)3Me (91%). The reaction of (E )- and (Z)-1,2-difluoro-1-iodoalkenes and (E )- and (Z)-a,b-difluoro-b-iodostyrenes with carbon monoxide in the presence of Pd(PPh3)2Cl2 as the catalyst, an alcohol and trialkylamine on heating yields carboxylic acid esters.389 (Ph3P)2PdCl2 (3% ± 5%) R1CF CFI+CO R1CF CFCO2R2 R2OH, Et3N, 70 ± 105 8C Product T /8C Yield (%) Con- R1 figura- tion (E)-ButCF=CFCO2Bu (E)-BusCF=CFCO2Bu (E)-PhCF=CFCO2Bu (Z)-BunCF=CFCO2Et 4-CNC6H4 4-CF3C6H4 105 105 105 95 80 80 80 70 But Bus Ph Bun 4-MeOC6H4 (E)-4-MeOC6H4CF=CFCO2Bu (E)-4-CNC6H4CF=CFCO2Bu (E)-4-CF3C6H4CF=CFCO2Bu 4-MeOC6H4 (Z)-4-MeOC6H4CF=CFCO2Bu ZZZEZZZE 85 92 89 82 86 96 89 86 Nickel complexes also efficiently catalyse perfluoroalkylation of aromatic compounds.342 G G Furin NH2 NH2 NH2 (CF2)nCl Ni(PPh3)4 +Cl(CF2)nI + O O, 80 8C, 6 h (40%) (CF2)nCl (45%) n=2, 6.The search for novel methods for the synthesis of fluoroor- ganic compounds was based on the use of accessible carbonyls of zero-valent metals. It was found that carbonyl complexes of the Group VIII transition metals can efficiently catalyse the reaction of RFI with alkenes and alkynes.180, 382, 383 For example, per- fluoroalkyl iodides react with phenylacetylene in the presence of transition metal carbonyls, e.g., Ni(CO)2(PPh3)3, resulting in b-perfluoroalkylstyrenes (yield 89% ± 96%) (Table 19). Table 19. Reactions of phenylacetylene with perfluoroalkyl iodides.180 Yield (%) t /h Catalyst T /8C Conver- sion (%) 93 94 94.5 96 89 92 98.6 99.8 99.7 100 95.7 97.9 12 12 11655 120 100 125 70 90 80 Ru/C Pt/C Ag/Al2O3 Ni(CO)2(PPh3)3 W(CO)5[P(OEt)3] Mo(CO)5(PPh3) Depending on the reaction conditions, iron pentacarbonyl converts the primary perfluoroalkyl iodide into 1-iodoperfluoro- alk-1-ene or to a perfluoroalkyl radical which both can further perfluoroalkylate aromatic compounds and alkenes.233, 390, 391 The addition of I(CF2)4I to CH2 =CH2 in the presence of Fe(CO)5 and HOCH2CH2NH2 in an autoclave at 100 8C results in ICH2CH2(CF2)4CH2CH2I (yield 78%).Perfluoroalkyl iodides enter into addition or substitution reactions with alkenes 346, 348 and dihydropyran 348 in the presence of [CpFe(CO2)]2. O RF Et2O, Et3N O RF=C8F17 (46%) RF O [CpFe(CO)2]2 RFI MeOH, Et3N OMe O RF=C8F17 (83%) CHR CH2 RFCH2CH2R Et3N, EtOH, 25 8CR=CO2Et, CN, COMe; RF=F(CF2)n (n=4, 6, 8), Cl(CF2)6 The reactions of trialkylsilyl derivatives of alkenes with perfluoroalkyl iodides in the presence of iron carbonyl, Fe3(CO)12 result in the substitution of the perfluoroalkyl group for the trialkylsilyl group.392, 393Fe3(CO)12 CHCH2SiMe3+RFI CH2 RFCH2CH CH2 60 8C, 12 h (40% ± 85%) RF=n-C3F7, n-C8F17, CF2CF2Br, CFClCF2Br, CFClCF2Cl, CHFCF2Cl.In the presence of Fe(CO)5 in DMF, alkenes react with RFI with the formation of addition products to the double bond.281511 Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Fe(CO)5 CHR+RFI CH2 RFCH2CHIR product to the multiple bond, viz., Cl(CF2)nCH2C5H11, in 45% yield.396 DMF CH2 CHBun, RF=(CF3)2CFCF=CFCF2, NCCF2, MeCO2CF2, C3F7, CF3(CF2)4CF2, FSO2CF2CF2, (CF3)2CFOCF2CF2; R = Bun, CO2Me.Pb(OAc)4 Ac2O± AcOH, 80 8C Cl(CF2)nCH2C5H11 (45%) Cl(CF2)nSO2Na (NH4)2Ce(NO3)6 MeCN Cl(CF2)2nCl (75% ± 90%) n=3, 5. Some peroxides are effective in reactions of perfluoroalkyl iodides with alkenes.397 It was shown 394 that nickel carbonyls are efficient in the reaction of substitution of the perfluoroalkyl group of a-chloro- fluoroketones for chlorine. When these reactions are carried out in donor solvents, organometallic compounds possessing perfluoro- alkylating properties can be formed. For example, the reaction of perfluoroalkyl iodides with nickel tetracarbonyl in acetonitrile at 25 ± 60 8C yields either dimeric products or unsaturated com- pounds.392 Me(CH2)mCH CH2+CF3(CF2)nI F F (CF2)6F (CF2)5F 1) n-C6H13C(O)OOBut, 85 ± 100 8C, 6 h 2) Zn, EtOH F(CF2)6I + CF3(CF2)n(CH2)m+2Me 120 8C F(CF2)4 F F(CF2)5 F n=1 ± 21; m =3 ± 25. I(CF2)6I F MeCN Ni(CO)4 7CO Potassium permanganate can also initiate the reaction of perfluoroalkyl iodides with alkenes in aqueousMeCNat 80 8C.398 CFCF2I CF2 CF3CF CFCF CFCF3 KMnO4 CHR+RFI CH2 MeCN±H2O RFCH2CHIR (CF3)2CFI CF3CF CF2 RF=Cl(CF2)4, Cl(CF2)6; R = Bun, CH2OH, n-C6H13, n-C10H21, Me3Si, CH2OCH2CH=CH2, n-C14H29.This reaction probably occurs via the intermediate formation of the nickel-containing compound 43.MeCN F(CF2)6I+Ni(CO)4 F(CF2)6NiI(MeCN)2 43 Some salts of CeIV efficiently induce perfluoroalkylation by perfluoroalkyl iodides. In the presence of Ce(SO4)2 .4 H2O or (NH4)2Ce(NO3)6, perfluoroalkyl halides RFX [RF =Cl(CF2)n (n=4, 6), F3C(CF2)5, X=I; RF=CF2Br, X=Br] react smoothly with alkenes RCH=CH2 (R=Bun, CH2 OH, n-C8H17, etc.) (Tables 20 and 21) and alkynes to give perfluoro- alkylation products.398, 399 Table 20. The effect of the solvent on the reaction of but-1-ene and hex-1- ene with Cl(CF2)4I and Cl(CF2)6I in the presence of Ce(SO4)2 .4H2O.398 The reaction of perfluoroallyl iodide with nickel tetracarbonyl is exotermic. The nickel compound formed reacts with the original substrate to give an isomeric mixture of perfluorohexa-2,4-diene.The reaction of perfluorohexyl iodide with nickel tetracarbonyl carried out at temperatures >120 8C yields a mixture of two dodecenes, viz., trans-perfluorododec-6-ene and trans-perfluoro- dodec-5-ene (1 : 1) and perfluorocyclohexene. Yield (%) Conversion (%) Solvent A B C D 2. Reactions of perfluoroalkyl halides with unsaturated organic compounds in the presence of redox systems 100 100 60 4000 82 80 38 3000 81 78 31 3400 DMF 100 MeOH 95 DMF±MeOH 50 DMSO 45 AcOH 0 [MeO(CH2)2]2O 0 Note: A is Cl(CF2)4I, B is Cl(CF2)6I, C is RCHICH2(CF2)4Cl, D is RCHICH2(CF2)6Cl. Studies of reactions of perfluoroalkyl halides with unsaturated organic compounds in the presence of reducing and oxidising systems revealed many specific features in their behaviour which can be rationalised by generation of perfluoroalkyl radicals.These radicals can be formed in different ways, predominantly by the reduction of perfluoroalkyl iodide to the radical anion. Hence a question arises as to whether the radicalRF .can be generated by an alternative route. According to some data, the reaction of per- fluoroalkyl iodides with alkenes can be efficiently initiated by some oxidants, e.g., Pb(OAc)4, (NH4)2S2O87HCO2Na, CrCl37Fe. Thus lead tetraacetate initiates the reaction of diio- dodifluoromethane with alkenes and alkynes.395 Table 21. The reaction of alkenes RCH=CH2 with perfluoroalkyl halides RFX in the presence of Ce(SO4)2 .4H2O in DMF.398 CHR1 CH2 ICF2CH2CH2R1 R Yields for different RFX(%) [MeO(CH2)2]2O, Pb(OAc)4 60 8C, 4 h CF2I2 Cl(CF2)6I CF3 (CF2)5I CF2 Br2 Cl(CF2)4I H R2 I R3O2C HC CR2 R3OH, 80 8C, 24 h 83 786 786 79 73 74 85 78 81 83 R1=(CH2)3Me (95%), CH2OH (93%), SiMe3 (95%), CH2OEt (92%), (CF2)4Cl (80%), (CF2)4Br (78%); R2=Bun: R3=Bun (72%), Et (78%); R2=C5H11, R3=Et (76%); R2=CH2OMe: R3=Bun (70%), Me (64%).83 784 56 82 84 77 7 7 7 817 7 7 Bun CH2OH n-C6H13 n-C8H17 n-C9H19 n-C10H21 Me3Si CH2OCH=CH2 n-C14H29 81 73 82 84 84 80 68 65 78 Note. The reaction was carried out at 80 8C for 8 h (100% conversion). In addition to perfluoroalkyl iodides, these reactions occur with sodium perfluoroalkanesulfinates.For example, heating of Cl(CF2)nSO2Na with hex-1-ene in Ac2O7AcOH in the presence of Pb(OAc)4 at 80 8C results in the formation of an addition512 In the presence of Mn(OAc)3 .2 H2O or Ce(SO4)2, sodium polyfluoroalkanesulfinates can be used in these reactions instead of perfluoroalkyl iodides. In this case, the perfluoroalkyl radical formed reacts with aromatic compounds 400 and alkenes,250 which results in the formation of either substitution products of the hydrogen atom in the benzene ring or in the formation of adducts to the multiple bond. This approach was used for introducing perfluoroalkyl groups into the benzene rings of benzocrown ethers under the action of sodium perfluorosulfinates.401 Tetrahydrofuran 45 derivatives (see Table 21) were prepared using diallyl ether (44) as a substrate; this reaction resulted in the formation of a free radical intermediate as could be evidenced from the EPR spectra.234 I RF Ce(SO4)2 .4H2O O +RFI DMF O 45 44 Reactions of perfluoroalkyl iodides with alkynes in the presence of CeIV salts (Table 22) proceed at a higher temperature (120 8C) and are slower (the reaction time varies from 18 to 20 h) than the corresponding reactions with alkenes.398, 399 Ce(SO4)2 .4H2O RFCH CRI CR+RFI HC DMF RF=Cl(CF2)4, Cl(CF2)6, CF3(CF2)5; R=Bun, Ph, n-C6H13, n-C7H15, CH2OH, MeOCH2. Table 22. The reaction of acetylene derivatives HC:CR with Cl(CF2)4I and Cl(CF2)6I in the presence of CeIV salts in DMF.398 Yield of RFCH=CRI (%) (E :Z) Inducer R Cl(CF2)6 Cl(CF2)4 Bun Ph 73 (3 : 1) 55 (3 : 1) 53 (6 : 1) n-C6H13 n-C7H15 CH2OH 52 (4 : 1) 59 (4 : 1) 61 (6 : 1) 48 (10 : 1) 7 71 (1 : 1) 74 (11 : 1) 78 (5 : 1) 7776 (3 : 1) 71 (5 : 1) 65 (65 : 0) 67 (9 : 1) 7 Ce(SO4)2 .4H2O Ce(SO4)2 .4H2O (NH4)2Ce(NO3)6 Ce(SO4)2 .4H2O 68(3:1) (NH4)2Ce(NO3)6 Ce(SO4)2 .4H2O (NH4)2Ce(NO3)6 Ce(SO4)2 .4H2O (NH4)2Ce(NO3)6 Ce(SO4)2 .4H2O 48(2:5) CH2OMe Note.The reaction was carried out at 120 8C for 18 ± 20 h. Butadiene undergoes perfluoroalkylation under the action of perfluoroalkanesulfonyl bromide RFSO2Br in the presence of dibenzoyl peroxide to give a mixture of isomeric unsaturated addition products.402 CHCH CH2+RFSO2Br (PhCOO)2 CH2 RFCH2CHBrCH CHR0F +RFCH2CH CHCHBrR0F RF, R0F =Cl(CF2)4, Cl(CF2)5, F(CF2)5.Dibenzoyl peroxide can also be used for perfluoroalkylation of aromatic compounds.268 The use of hydrogen peroxide, di-tert-butyl peroxide and dibenzoyl peroxide as inducers gave encouraging results. Thus the reaction of trimethylsilylacetylene with 1,6-diiodoperfluoro- hexane in the presence of di-tert-butyl peroxide results in 1,10-diiodo-1,10-bis(trimethylsilyl)dodecafluorodeca-1,9-diene in 92% yield.70 G G Furin I(CF2)nI, (ButO)2 Me3SiCI CH(CF2)nCH HC CSiMe3 CISiMe3 120 8C, 85 h n=6, 8, 10, 12. Treatment of phenylacetylene with perfluoroheptyl iodide in the presence of di-tert-butyl peroxide results in (E)-1-iodo-1- phenylpentanedecafluoronon-1-ene.70 (ButO)2 PhC CH+CF3(CF2)6I 120 8C, 48 h PhIC CH(CF2)6CF3 (89%) The reaction of alkenes with perfluoroalkyl iodides in the presence of hydrogen peroxide in acetone, acetonitrile or ethanol gives addition products to the multiple bond in good yields.403 Potassium superoxide (KO2) reacts with 1,4-diiodoperfluor- obutane in benzene containing dicyclohexano-18-crown-6 (its role in this reaction is ambiguous) to give I(CF2)3CO2H.404, 405 Sodium perfluoroalkanesulfinates of the type Cl(CF2)nSO2Na (n=4, 6, 8) the reduction potentials of which are equal to 0.95 ± 1.00 V generate perfluoroalkyl radicals in the presence of oxidants, e.g., Mn(OAc)3 .2 H2O, Ce(SO4)2, HgSO4 and Co2O3.250 ± 256 The radicals formed react with aromatic com- pounds to give monoperfluoroalkylation products.For example, the reaction of 1,4-dimethoxybenzene with Cl(CF2)4SO2Na in the presence of Mn(OAc)3 inH2O, MeCN or AcOH at 80 8C gave the adduct 1,4-(MeO)2C6H3(CF2)4Cl-2 in 50% yield.406 The reaction of sodium perfluoroalkanesulfinates with cou- marin gives the 3-perfuoroalkyl derivatives 46.257 3,6-Bis(per- fluoroalkyl)- (47) and 3,6,8-tris(perfluoroalkyl) derivatives (48) are formed when the perfluoroalkylating reagent is used in excess. These compounds have found applications as fluorescent dyes and for laser systems. O O RF 1 equiv. of RFSO2Na MeCN±AcOH ± Ac2O O O 46 RF=F(CF2)6 (60%), F(CF2)7 (62%), F(CF2)8 (65%), Cl(CF2)4 (52%), Cl(CF2)6 (67%) RF RF RF RF RFSO2Na (excess) + O O O O 47 48 RF The reaction of perfluoroalkyl iodides RFI [RF=CF3(CF2)5, H(CF2)4, Cl(CF2)n (n=4, 6, 8), I(CF2)m (m=4, 6), NaO3S..(CF2)2O(CF2)m (m=2, 4)] with NaHSO3 in the presence of (NH4)2Ce(NO3)6 in aqueous acetonitrile at 70 8C results in the salts RFSO2Na in 70% to 88% yields.156 The CeIV7NaHCO3 and FeIII7NaHSO3 systems efficiently catalyse the reactions of perfluoroalkyl iodides with alkenes. These reactions give high yields of addition products to the double bond.353, 407 K2[Fe(CN)6] was found to be an excellent inducer of reactions of addition of perfluoroalkyl iodides to alkenes and their derivatives.244CH2 CHCH2OH 125 8C, 6 h Cl(CF2)nCH2CHICH2OH n=2 (70%), 4 (72%), 6 (64%), 8 (72%) CH2 CHCH2OAc Cl(CF2)nI 60 8C, 4 h Cl(CF2)nCH2CHICH2OAc n=2 (85%), 4 (84%), 6 (80%), 8 (80%) CH2 CHOAc Cl(CF2)nCH2CHIOAc 50 ± 60 8C, 4 h n=4 (83%), 6 (81%)Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds Let us now discuss the tentative reaction mechanisms under- lying reactions of perfluoroalkyl halides and sodium perfluoroal- kanesulfinates with unsaturated compounds in the presence of redox systems.These reactions were surveyed by Hu et al.30 Two schemes are probable. According to the first of them, a radical cation is generated from perfluoroalkyl iodide under the action of an oxidant and is transformed to a perfluoroalkyl radical. The second route includes initial oxidation of the unsatu- rated substrate to the radical cation, which then reacts with perfluoroalkyl iodide to produce the perfluoroalkyl radical.The latter was proposed by Huang and Xie 400 for the reaction with styrene in the presence of lead tetraacetate. + Ox RFI CHR CHR + CH2 RCHCH2I +RF .CH2 RFI RFCH2CHIR +RF. RFCH2CHR Ox, oxidant. However, standard oxidation potentials (E ox) of the alkenes used are too high to ensure their oxidation to the corresponding radical cations. For instance, Eox of oct-1-ene is 2.70 V relative to Ag+/AgNO3,408 although polar effects can to certain degree compensate for this stability. An alternative intermediate, viz., the radical cation of per- fluoroalkyl iodide [RFI]+., can be formed under the action of a strong oxidant.Indeed, the same radical cation is formed in the electrochemical 409 oxidation of perfluoroalkyl iodide in the presence of perfluoroalkanesulfinic acid. Efficient catalysis of the reaction of perfluoroalkyl iodide with alkenes [e.g., Eox of MeOC6H4C(Me)=CH2 is 1.49 V (see Ref. 410), E ox of a-phenylstyrene is 1.22 V relative to SCE 411] requires an oxidant with a reduction potential, E ox, of >1.6 V (rel. SCE). In this case, the radical cation [RFI] +. can be formed. The radical cation [RFI]+. is rapidly decomposed into RF .and the iodonium cation. The radical RF .was detected in its reaction with alkene, which resulted in the generation of a new radical. The latter detached iodine from RFI to yield the reaction product and the radical RF ..The reduction potentials of some oxidants are listed in Table 23.412, 413 If the reduction potential of an oxidant is 51.60 V (rel. SCE), this can efficiently initiate the reaction with alkenes. Table 23. Standard reduction potentials (Ered) of different oxidants. Ion Oxidant Ref. Ered /V 8 4 S2O2¡ MnO¡ Pb4+ Ce4+ Mn3+ Cr2O2¡ 7 Fe3+ 412 412 412 412 412 412 412 413 413 413 414 2.01 1.695 1.69 1.61 1.51 1.33 0.771 0.02 1.14 0.70 1.06 Na2S2O8, (NH4)2S2O8 KMnO4 Pb(OAc)4, PbO2 Ce(SO4)2, (NH4)2Ce(NO3)6 Mn2(OAc)3 K2Cr2O7 FeCl3 Chloranil [N(C6H3Br2-2,4)3]+ [N(C6H4Br-3)3]+ [C6H4Br-4]3N+ Thus, the reactions of perfluoroalkyl halides with alkenes or alkynes in the presence of oxidants appear to be a convenient method for fluoroalkylation of alkenes or alkynes.Perfluoroalkyl iodides successfully react with alkenes in aqueous MeCN (6 ± 8 h, 60 8C) in the presence of Na2S2O8 or (NH4)2S2O8 (Table 24).398 Cyclohexene and cyclopentene also react with RFI to produce the 1 : 1 adducts in good yields. The reaction of a-chloro-o-iodoperfluoroalkanes with alkenes in the presence of the (NH4)2S2O87HCO2Na system gives addition products at the expense of the C7I bond without involving the 513 Table 24. Reactions of RFI with alkenes RCH=CH2 in the presence of Na2S2O8 in MeCN7H2O.398 R Yield of RCHICH2RF for different RFI (%) Cl(CF2)6I CF3 (CF2)5I Cl(CF2)4I 84 83 83 85 87 84 81 61 83 85 88 7 7 7 Bun CH2OH C6H13 C8H17 C9H19 C10H21 C14H29 81 73 85 83 85 83 78 Note.Reactions were carried out at 60 8C for 6 ± 8 h. C7Cl bond.415, 416 The reaction of perfluoroalkyl iodides with a-phenylstyrene carried out under identical conditions gives the corresponding adduct.223 RF Ph2C CH2 50 8C, 8 h S2O2¡ S2O2¡ 8 8 Ph2ClCH2RF RF=Cl(CF2)4 I RF RFI CHR CH2 MeCN, H2O MeCN, H2O RFCH2CHIR I RF=Cl(CF2)4, Cl(CF2)6, CF3(CF2)5; R=Bun, CH2OH, n-C6H13, n-C8H17, n-C9H19, n-C10H21, Me3Si, CH2OCH2CH=CH2. Reactions of sodium perfluoroalkanesulfinates RFCF2SO2Na with allyl halide and propargyl halide in the presence of (NH4)2S2O8 result in good yields of 3-(perfluoroalkyl)prop-1-ene and 3-(perfluoroalkyl)allene, respectively.326 An interesting transformation of perfluoroalkyl iodides and -bromides as well as of compounds containing a CCl3 group at the end of the perfluorinated carbon chain into the corresponding perfluorocarboxylic acids was observed in the presence of a redox system.132 ± 144, 159, 193, 401, 417, 418 CF3CCl3 Ox DMF, 40 8C CF3CO2H Ox=(NH4)2S2O8 ±HCO2Na .2H2O, (NH4)2S2O8 ± oxalate, H2O2 ± FeSO4 .7H2O, (NH4)2S2O8±Na2S2O4, H2O2±Na2S2O4, KBrO3±Na2S2O4, (PhCO)2O2 ±PhNMe2. CF3CCl=CHCH2Cl is the reaction product of CF3CCl3 with ethylene in the presence of Cr2O3.419 Perfluoroalkylation by perfluoroalkyl iodides and sodium perfluoroalkanesulfinates was performed using a variety of redox reagents and systems, e.g., Ce(SO4)2, H2O2 ± FeSO4, (NH4)2Ce(NO3)6, Pb(OAc)4 ±HOAc± Ac2O, Mn(OAc)3 .H2O, etc.This reaction occurs via the inter- mediate formation of the perfluoroalkyl radical, since the intro- duction of compounds containing labile (C7Hal) bonds yields products of substitution of the RFCF2 group for the halogen atom.420 (NH4)2S2O8 RFCF2SO2Na DMF, 40 8C CH2 CHCH2X RFCF2CH2CH CH2+RFCO2H+RFCF2X HC CCH2X C CH2+RFCO2H+RFCF2X RFCF2CH X=Cl, Br; RF=Cl(CF2)n (n=2, 4, 6), CF3(CF2)n (n=3, 5, 7). The optimum conditions for this reaction are as follows: temperature below 40 8C and DMF as a solvent. The use of redox systems allows for selective transformation of perfluoroalkyl iodides, a,o-diiodoperfluoroalkanes and com-514 Table 25.Conversion of polyfluoroalkyl halides into the corresponding acids under the action of the (NH4)2S2O87HCO2Na .2H2O system in DMF.421 t /h Substrate T /8C 14 14 12 12 10455 C6F13I 55 12 C5 F11CO2H Cl(CF2)4I Cl(CF2)6I I(CF2)6I I(CF2)8I CF3CCl3 CF3CBr2Cl CCl3CF2CFClBr CF2(CCl3)2 CF2ClCFCl2 CF2BrCFClBr CF2ClCFClCF2CFCl2 50 50 50 50 25 50 30 30 20 15 30 10 205 pounds of the type RFCCl3, RFCFBrCl, RFCBr2Cl, RFCFCl2, etc., into the corresponding acids (Table 25).421 ± 423 X(CF2)nCF2I (NH4)2S2O8 ±HCO2Na . 2H2O X(CF2)nCO2H X=F, n=5; X=Cl, n=4, 6 ICF2(CF2)nCF2I HO2C(CF2)nCO2H n=4, 6 Oxidising systems based on sulfur-containing acids have been studied by physicochemical methods.424, 425 Perfluorocarboxylic acids can also be prepared from sodium perfluoroalkanesulfinates in the presence of a redox reagent.159 RFCF2SO2Na (NH4)2S2O8, H2O 60 8C RFCO2H+RFCHF2 (68%) The AgNO37HCO2Na system in aqueous acetonitrile catal- yses the reaction in a similar way.426 AgNO3 ±HCO2Na RFCO2H RFCF2I MeCN±H2O, 20 8C, 24 h RF=ClCF2 (50%), Cl(CF2)3 (65%), Cl(CF2)5 (72%), F(CF2)7 (85%), F(CF2)5 (89%).1,1,1-Trichlorotrifluoroethane can be converted into tri- fluoroacetic acid in the presence of various oxidants (Table 26).421 The reaction induced by (NH4)2S2O87HCO2Na presumably occurs in accordance with the following scheme:421 S2O2¡ 8 2SO4¡., SO4¡.+HCO¡2 HSO4¡ +CO2¡., .RFCCl2+CO2+Cl¡, RFCCl3+CO2¡. H. RFCHCl2 . RFCCl2 O2 H2O RFCO2H RFCOCl RFCCl2OOH 7HOCl In this case, the generation of the polyfluoroalkyl radical by the radical anion CO2¡. is the key step of this reaction. In the presence of alkenes and alkynes, the acids are not formed, the addition to multiple bonds occurs instead. CF2ClCFCl2+CH2 CHR (NH4)2S2O8 ±HCO2Na CF2ClCFCl(CH2)2R R=Bun, n-C5H11, CH2Br, CH2OH, OAc, (CH2)4CH=CH2. It is known that other radical anions can initiate such trans- formations. Thus in the presence of an electrochemically gener- G G Furin Yield (%) Conversion (%) Acid 83.9 78.7 81.2 92.0 89.0 72.5 71.8 74.6 69.8 55.6 63.4 78.6 75 69 70 50 62 100 100 100 100 100 100 100 Cl(CF2)3CO2H Cl(CF2)5CO2H (CF2)4(CO2H)2 (CF2)6(CO2H)2 CF3CO2H CF3CO2H CF2(CO2H)2 CF2(CO2H)2 ClCF2CO2H BrCF2CO2H CF2ClCFClCF2CO2H ated radical anion of molecular oxygen O¡2 ., perfluorobutyl iodide, perfluorooctyl iodide and a,o-diiodoperfluorobutane pro- duce the corresponding acids in up to 50% yields.417 DMF CF3(CF2)2CF2I + 4e7+O2 CF3(CF2)2CO¡2 + I7+2F7 This reaction occurs according to the following scheme: O2 + e7 O¡2 ., RFOO.+ I7, RFI +O2¡. . O¡2RFOO7+O2 R0FCO2H RFOO. dimerisation RFO4RF R0FCO2H. This system can also be used for the activation of inert Freon-113.422, 423 The redox system (NH4)2S2O87HCO2Na . 2H2O manifests high selectivity.421, 426 Selective reduction of perfluorochloroalkanes by the (NH4)2S2O87HCO2NH4 or the (NH4)2S2O87NaH2PO4 .H2O system is of considerable practical importance because it yields products which can further be used as inhalation anesthetics similar to the widely employed ethers CHF2OCF2CHClF (influ- rane) and CHF2OCHClCF3 (isoflurane).421 ± 423 (NH4)2S2O8 ±HCO2NH4 CF2ClCFClCF2CFCl2 CF2ClCFClCF2CHClF+ (44%) +CF2ClCHFCF2CFCl2+CF2ClCHFCF2CHClF (16%) (14%) In contrast with perfluoroalkyl iodides which are oxidised at the CF2I fragment to yield carboxylic acids, perfluoroalkyl chlorides smoothly yield addition products to the multiple bond under identical conditions.Table 26. Conversion of CF3CCl3 into trifluoroacetic acid in the presence of various redox systems.421 System Reaction conditions Con- Yield version (%) (%) solvent T /8C t /h 95 100 100 100 100 100 25 40 35 40 45 30 (NH4)2S2O8 ±HCO2Na DMF DMF±H2O DMF±H2O DMF±H2O DMF±H2O DMF H2O2 ± FeSO4 (NH4)2S2O8±Na2S2O4 H2O2±Na2S2O4 KBrO3±Na2S2O4 (PhCO2)2 ± PhNMe2 25 10 100 0.5 100 5 100 1 100 3 85 16515 Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds CH2 CHR The reaction of perfluoroalkyl iodides with alkenes in the presence of H2O2 in acetone, MeCN or EtOH gives an addition product to the multiple bond in high yield.403 (NH4)2S2O8 ± HCO2Na .2H2O RFCl RFCH2CH2R RF=(CF2)8OCF2CF2SO2Na, (CF2)8OCF2CF3, (CF2)nCOONa (n=6, 7); R=Bun, n-C5H11, CH2Br, CH2OAc, CH2SiMe3 The reagent RF(CF2)nSO2Na7MoO2(acac)2 is effective in perfluoroalkylation, e.g., of disulfides, which occurs in the pres- ence of M2S2O8 (M=K, Na, NH4) or ButOOH in a mixture of water and a polar aprotic solvent, such as MeCN, DMF, dimethylacetamide, sulfolan, glymes, HMPT, etc.429 ± 431 CH2 CH(CH2)4Me ButOOH RSCF3+RSO2SR RSSR +CF3SO2Na RF(CH2)6Me RF=Cl(CH2)2(CF2)4 MeCN, 208C R Yield of RSCF3 (%) The intermediate perfluoroalkyl radical not only reacts with alkenes, but can undergo other transformations depending on the reaction conditions and the oxidant type. For example, reactions of sodium chloropolyfluoroalkanesulfinates yield dimerisation products, carboxylic acids and adducts to the multiple bond.396 95 75 100 Perfluoroalkylated alkenes are the main products in the reaction of sodium perfluoroalkanesulfinates with conjugated dienes in the presence ofM2S2O8.159, 427, 428 60 47 55 Me(CH2)6CH2 (CH2)2CO2Et (CH2)2CO2Et CH2CO2Et CH2CH(N+H3)CO2Me (CH2)2CH(N+H3)CO2Me Trifluoroalkylation of vinyl esters in the presence of ButOOH results in a-trifluoromethyl ketones.432 The nature of other functional groups in the molecule can influence the lability of the C7Cl bond.For example, the activity of compounds of the type Cl(CF2)7X (X=CO2 Na, CO2Me, CO2H) in the reaction with hept-1-ene decreases in the following order: Cl(CF2)7CO2Na>Cl(CF2)7CO2Me>Cl(CF2)7CO2H. OC(O)R Cu2+ OC(O)R In polyhalogenopolyfluoroalkanes containing I and Cl atoms, CF3SO2Na ButOOH F3C.F3C OC(O)R O the latter is much less active than iodine. The chlorine atom reacts with hept-1-ene only after substitution of the SO3Na group for iodine. H2O + F3C F3C The perfluoroalkylation reaction can occur with different redox reagents and systems, e.g., (NH4)2Ce(NO3)6, H2O2 ± FeSO4, Ce(SO4)2, Pb(OAc)4 ±HOAc±Ac2O, Mn(OAc)3 .H2O, etc. This reaction proceeds through the generation of the per- fluoroalkyl radical and results in the products of substitution of the RFCF2 group for the halogen atom (Table 27).325, 326 (NH4)2S2O8 ±HCO2Na Trifluoromethyl derivatives are formed in reactions of CF3SO2Na with vinyl sulfides. The sulfur atom effectively stabil- ises the carbocation, which can be trapped by the reaction with a nucleophile, particularly, with an alcohol.a-Trifluoromethyl thioketals are the end products in this reaction. CHR CF2ClCFCl(CH2)2R CF2ClCFCl2+CH2 SPh R=Bun, n-C5H11, CH2Br, CH2OH, MeCO2, (CH2)4CH=CH2. Cu2+ SPh ButOOH F3C. CF3SO2Na F3C Table 27. Synthesis of 3-(perfluoroalkyl)prop-1-enes and 3-(perfluoroal- kyl)allenes.326 SPh ROH + SPh OR+ Yield (%) Substrate RFCF2X SPh F3C F3C F3C A B CH2=CHCH2X Aromatic compounds also undergo perfluoroalkylation in the presence of ButOOH.433 The trifluoromethyl radical can also be generated in the oxidation of the sodium trifluoromethanesulfinate by aqueous tert-butyl hydroxyperoxide in the presence of Cu2+ (Refs 326, 432) and M2S2O8 (M=K, Na, NH4).430, 432 ± 435 Some of these reactions are depicted in Scheme 2.The CF3SO2Na7ButOOH7Cu2+ system can be used as a formal `cationoid' reagent in the trifluoromethylation of arenes (Table 28).250, 253, 430, 432 Perfluoroalkanesulfinates react with mono- and disubstituted alkenes in air or in oxygen with UV irradiation resulting in a-perfluoroalkyl ketones.253 HC:CCH2X RF UV-irradiation +RFSO2Na O2, DMF, 20 8C O RF=X(CF2)n, n=4, 6, 8; X = F, Cl. 10 16 33 14 10 18 15 16 10 12 15 17 12 20 30 15 10 17 25 75 34 46 53 62 65 28 40 72 67 74 32 32 46 27 47 42 54 50 Cl(CF2)8CF2CF2Br Cl(CF2)8OCF2CF2Cl CF3CCl2Br Cl(CF2)2Br Cl(CF2)4Br Cl(CF2)6Br Cl(CF2)4Cl Cl(CF2)6Cl CF3(CF2)3Br CF3(CF2)5Br CF3(CF2)7Br CF3(CF2)7Cl Cl(CF2)2Br Cl(CF2)4Br Cl(CF2)4Cl Cl(CF2)6Br CF3(CF2)3Br CF3(CF2)5Br CF3(CF2)7Br Note: A is RFCF2CH=CH2, B is RFCF2CH=C=CH2.516 OAc OCF3 The reactions of terminal alkenes with sodium perfluoroalka- nesulfinates in the presence of (NH4)2S2O8 or the Fenton reagent (H2O27FeSO4 .7H2O) proceed rather vigorously.In the pres- ence of additional nucleophiles, side reactions of the intermediate carbocations are possible, which has been used for the synthesis of secondary amines.436 H2O2 ± FeSO4 .7H2O CHR+RFSO2Na CH2 NaN3 RFCH2CHRNH2 RF=Cl(CF2)n (n=4, 6), CF3(CF2)5; R = Bun, n-C7H15, n-C8H17, AcO, CH2OAc, (CH2)8CO2Et.Pyrrole and its derivatives undergo perfluoroalkylation under the action of perfluoroalkyl iodides in the presence of the H2O27FeSO4 system in DMSO (Table 29).437 Table 28. Synthesis of trifluoromethylarenes.253 CF3SO2Na ±ButOOH±Cu2+ ArH ArCF3 Product Substrate OH PhOH CF3 OH OH CF3 CO2Me CO2Me NH2 NH2 Cl Cl Cl CF3 NH2 PhNH2 CF3 NHAc PhNHAc CF3 a The ratio of ortho : meta : para isomers is 4 : 1 : 6. b The ratio of ortho : meta : para isomers is 4 : 1 : 2. Me O CH2CF3 CF3SO2Na ±ButOOH± Cu(OSO2CF3)2 ArH RSSR RSCF3 ArCF3 [H] RFCH2CHRN3 (50% ± 70%) Yield (%) 45 a 21 Cl 20 13 52 b Me OAc (SCH2CH2CO2Et)2 CF3SCH2CH2CO2Et Table 29. Homolytic perfluoroalkylation of pyrrole by perfluoroalkyl iodides in the presence of hydrogen peroxide and FeSO4.437 Substrate NH CHO NH COMe Me N CO2Me NH CHO Me NHNH 3.Activation of perfluoroalkyl iodides by radicals The above data suggest that under different reaction conditions perfluoroalkyl iodides can generate perfluoroalkyl radicals which further react with alkenes and aromatic compounds by a free- radical mechanism. Bravo et al.438 found that the radical Ph. can rapidly detach the iodine atom from secondary perfluoroalkyl iodides. This can be explained by the fact that the Ph7I bond is stronger than the RF7I bond. The kinetics of the reaction of perfluoroalkyl iodides with the phenyl radical was studied by Kryger et al.439 RFI + Ph. sec-RI +Ph. sec-R is secondary alkyl.In other words, it is the iodide ion that is responsible for the electron transfer. It was thus suggested that perfluoroalkyl iodides can be activated by radicals generated from other substrates. For example, the methyl radical can activate the C7I bond. In turn, the methyl radical is formed in the reaction of acetone or DMSO with hydrogen peroxide in trifluoroacetic acid or in the presence of Fe2+ salts, respectively. The methyl radical reacts with perfluoroalkyl iodide to produce a perfluoroalkyl radical. The G G Furin Scheme 2 OH OH F3C O O O O Product RFI Yield (%) 78 I(CF2)3CF3 (CF2)3CF3 NH CHO RF I(CF2)3CF3 ICF(CF3)2 I(CF2)2CF3 55 73 64 NH 71 I(CF2)3CF3 MeOC (CF2)3CF3 Me N 73 I(CF2)3CF3 (CF2)3CF3 MeO2C NH 36 I(CF2)2CF3 OHC (CF2)2CF3 NH 30 I(CF2)2CF3 (CF2)2CF3 NH RF .+PhI, sec-R.+PhI (k=109 litre mol71 s71)Some new aspects in the application of perfluoroalkyl halides in the synthesis of fluorine-containing organic compounds latter initiates further perfluoroalkylation of unsaturated or aromatic compounds.. RF.+MeI, RFI +CH3 ArC4F9+MeI+MeCO2H+H2O. ArH+C4F9I H2O2, Me2CO CF3CO2H Perfluoroalkyl radicals were generated by the following sys- tems: ButOOH± Fe(OAc)2OH, Me2CO±H2O2, Me2SO ±H2O2 ± Fe2+.440 These systems effect smooth perfluoroalkylation of aromatic compounds and alkenes (e.g., oct-1-ene, cyclohexene). CHCH2R+C4F9I CH2 (PhCOO)2 C4F9CH2CH CHR+PhI+PhCO2H+CO2 ButOOH C4F9CH2CH CHR+MeI+Me2CO+H2O ButOOH ArC4F9 FeIII ArH+C4F9I H2O2, Me2SO ArC4F9+MeI+MeSO2H+H2O FeII The ratio of isomers formed in perfluoroalkylation of aro- matic compounds and the relative rates of these reactions suggest the radical mechanism of this reaction.438 Reductive perfluoroalkylation of alkenes with perfluoroalkyl iodides can be carried out in the presence of tert-butyl hydro- peroxide in acetic acid (Table 30).441 Table 30. Reductive perfluoroalkylation of alkenes by perfluoroalkyl iodides RFI in the presence of ButOOH.441 Alkene Yield (%) RF Hex-1-ene Oct-1-ene 3,3-Dimethylbut-1-ene Cyclohexene C4F9 C8F17 C4F9 C8F17 C4F9 C8F17 C4F9 C8F17 77 72 73 71 83 86 85 73 It should be noted that this approach was first used in reactions of some aromatic compounds with perfluoroalkyl iodides and equimolar amounts of the peroxide.442 It may be expected that after optimal conditions for such reactions are found, their role in perfluoroalkylation will increase.IV. Conclusion The data presented above testify to the increasing interest of investigators in the development of new approaches to the introduction of perfluorinated fragments into organic molecules and the transformation of simple substituents into complex func- tional groups. The novel perfluoroalkylating reagents considered above can be regarded as an alternative to classical and popular reagents. In particular, perfluoroalkyl iodides are widely used in perfluorination of unsaturated and aromatic organic substrates in the presence of initiators and catalysts. Radical perfluoroalkyla- tion, syntheses of perfluoroalkanesulfinic and perfluorocarbox- ylic acids and polyfluorinated aldehydes as well as electrochemical synthesis of perfluoroalkyl derivatives offer obvious advantages because of simplicity and possibility to be used on an industrial scale. It remains to be hoped that further investigations will culminate in the discovery of other approaches to the synthesis of fluorine-containing compounds. 517 In this review, we made an attempt to demonstrate the most recent approaches and synthetic potentialities of novel reagents and to outline the main trends in the synthesis of perfluoroorganic compounds containing various molecular backbones and func- tional groups.This form of presentation of the experimental material makes it possible to contemplate the problem from the unusual for traditional chemistry standpoint and to propose certain original solutions based on the use of novel approaches to the generation of perfluoroalkyl radicals and their involvement in reactions with various compounds. Needless to say, the practical implementation of the above- mentioned ideas and processes occurring by a single-electron transfer mechanism presents special interest not only for practi- tioners in fluoroorganic chemistry but also for specialists in organic synthesis and investigators elaborating radically new approaches to directed synthesis of organic molecules with the ultimate goal to develop new technologies.It should be noted that perfluoroorganic compounds often represent convenient, even unique models for the formulation and solution of fundamental problems of theoretical organic chemistry. In this context, the role of perfluorinated organic materials is steadily increasing, although the number of perfluoroalkylating agents which are suitable for large-scale production is still too small. A break- through in this area can be expected in the nearest future. 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Russian Chemical Reviews 69 (6) 523 ± 549 (2000) Structure and properties of polymers in terms of the fractal approach V U Novikov, G V Kozlov Contents I. Introduction II. Fractal analysis of the polymer structure III. Modelling of the structure and properties of polymers IV. Experimental determination of the fractal dimension V. Conclusion Abstract. fractality of manifestations various considers review The The review considers various manifestations of fractality in and macromolecules of synthesis the of description the in the description of the synthesis of macromolecules and the the formation polymers, in state quasi-equilibrium the of formation of the quasi-equilibrium state in polymers, fluctuation fluctuation free volume, macromolecular frameworks, order parameters, and free volume, macromolecular frameworks, order parameters, and dissipative in stress shear of centres as acting structures, dissipative structures, acting as centres of shear stress in clusters.clusters. The of properties the of modelling numerical of possibility The possibility of numerical modelling of the properties of net- net- work formalism fractal of framework the within polymers work polymers within the framework of fractal formalism is is demonstrated. The methods for determination of the fractal demonstrated. The methods for determination of the fractal dimension 248 includes bibliography The described. are dimension are described. The bibliography includes 248 referen- referen- ces. I. Introduction The use in investigations of only Euclidean geometry, which describes objects with integer dimensions, restricts the possibility of adequate description of real (both natural and artificial) objects because it leaves numerous objects with fractional (fractal) dimensions beyond the scope of consideration.The properties of such objects can be described using fractal geometry.1, 2 Frequently encountered natural and synthetic polymers belong to the class of fractal objects. A polymer consists of long- chain macromolecules. Owing to this structure, polymers possess properties differing from those of other classes of solids. The most important parameters characterising a macromolecular chain are length and rigidity.3±5 The structure of a vitreous polymer is thermodynamically unstable.Thermodynamically nonequilibrium processes result in the formation of fractal structures.6 A classical example support- ing this statement is a fractured surface of a polymer. It has been found experimentally that the fractal properties of a fractured surface do not depend on the thermodynamic state of the solid.7 This is due to the thermodynamically nonequilibrium character of the fracture process.8 In the syntheses of polymers in solution (which is the most widely used variant 9) the main structural unit is a macromolecular coil, which is known 10 to be a fractal. To describe an object in terms of Euclidean geometry, only one V U Novikov Moscow State Open University, ul. P Korchagina 22/2, 129805 Moscow, Russian Federation.Fax (7-095) 283 80 71. E-mail: vknovik@cityline.ru G V Kozlov Kabardino-Balkarian State University, ul. Chernyshevskogo 173, 360004 Nal'chik, Russian Federation. Fax (7-866) 225 44 75. Tel. (7-866) 222 41 44 Received 12 April 2000 Uspekhi Khimii 69 (6) 572 ± 599 (2000); translated by Z P Bobkova #2000 Russian Academy of Sciences and Turpion Ltd DOI 10.1070/RC2000v069n06ABEH000592 523 523 537 544 546 parameter, namely, the Euclidean dimension d, is needed, whereas description of fractal objects requires at least three parameters: the dimension d and the Hausdorff and spectral (fracton, ds) dimen- sions.11 Thus, the question of whether or not the methods of fractal analysis should be used to describe the structure of a macromolecular coil and a polymer is not a matter of researcher's choice but is dictated by the requirements of correct approach to the problem.{ The methods of fractal analysis and the models of irreversible aggregation provide a new understanding of the processes of synthesis and provide results which are difficult to obtain (or cannot be obtained) by other methods.All the foregoing has stipulated the scope of this review the purpose of which is to summarise the results of the use of fractal approach to the synthesis and analysis of the structures and properties of vitreous polymers. II. Fractal analysis of the polymer structure 1. A model and the structure of a macromolecular coil In order to develop a physically substantiated description for processes such as flocculation, polymerisation, etc., various irre- versible aggregation models, based on the physical pattern of formation of larger objects from smaller ones, have been devel- oped.15 ± 18 The necessity of using models of this type in this review is due to the fact that the processes they describe result in the formation of fractal objects.The fractal dimension of a macromolecular coil in solution (D) is determined by two types of interaction: interactions of the coil elements with one another and solvent ± polymer interactions.19 These types of interaction have been considered in detail.20 In particular, the D value was found to depend on the chain rigidity, characterised by the Kuhn segment length (A).Linear D(A) dependences have been found for flexible-, semirigid- and rigid- chain polymers (Fig. 1). An increase in the chain rigidity (an increase in A) is accompanied by a decrease in D; this implies transition to less compact macromolecular coils.10, 21 TheDvalues obtained by extrapolation to A=0 are different. The lowest value is obtained for rigid-chain polymers, which reflects the difficulty of formation of macromolecular coils in this case.22 For flexible- and semirigid-chain polymers, the D(A) plot at A=0 extrapolates to D=2, which corresponds to the dimension of the coil in a Y-solvent.20 Thus, only a hypothetical absolutely { The required concepts and definitions which reflect the specific features of the results outlined below can be found in Refs 12 ± 14.524 D 2.0 1.8 1.6 Figure 1.Fractal dimension D of a macromolecular coil vs. length of the Kuhn segment A for flexible- and semirigid-chain (correlation coefficient 0.82) (1) and rigid-chain polymers (correlation coefficient 0.85) (2). flexible macromolecule (A=0) can have an ideal conformation in a good solvent. In real polymer chains (for A>0, i.e. actually, for an isolated macromolecular coil), this conformation can be attained by choosing a solvent which would counterbalance the effect of excluded volume.19 A similar extrapolation to A=0 for rigid-chain polymers gives D ^ 1.67. This corresponds to the dimension of a coil in a good solvent.10 However, it should be noted that for these polymers, Y-conditions can be created when the index in the Mark ¡¾ Kuhn ¡¾ Houwink equation a=0.5 (or D=2).For instance, Y-conditions for polyarylate have been attained 22 at a=0.8, which is equivalent to D^1.67 in con- formity with the equation D=1 a a 3 Thus, different D values obtained for the above classes of polymers by extrapolation of the D(A) plot to A=0 can imply different criteria for the attainment of Y-conditions. Two alternative analytical expressions have been reported 20, 23 for evaluation of D as a function of the molecular characteristics of a polymer, C? and S (C? is the characteristic ratio, which is a measure of the statistical chain flexibility 24 and S is the cross-section area of the macromolecule) C?= D=274 The D values determined from Eqns (2) and (3) were found to be in good agreement with those determined using Eqn (1).20 The polymer ¡¾ solvent interactions, which also influence the D value of a macromolecular coil in solution, can be characterised in several ways.One way is to use the Huggins constant kH, which reflects the extent of polymer ¡¾ solvent interaction.24 The equation derived in terms of this approach shows the variation of D as a function of molecular mass Mof the polymer 22 D=lnMa lnO7:14kH ¢§ 1U ¢§ lnkZ ¢§ lnkH , 3lnM where kZ is the constant in the Mark ¡¾ Kuhn ¡¾ Houwink equation. TheD(k¢§2 H ) dependence obtained experimentally 20 shows that both an increase in the rigidity and improvement of the thermo- dynamic quality of the solvent with respect to the polymer result in 0 40 80 2 1 0 1 2 3 .2 C?S 3O2D¢§ DU a 43 , 1=2 A /nm D1.6 1.4 1.2 1.0 A /nm (1) (2) (3) (4) V U Novikov, G V Kozlov 10 20 t /min 0 50 D D 2.0 2.4 2 1 1.8 1.9 18 14 22 1073ds /J1/2m73/2 Figure 2. Fractal dimension D of a macromolecular coil for polyarylate vs. solubility parameter ds of the solvent used in the synthesis (1) and vs. reaction time t (2). higher kH. This in turn, decreases both k¢§2 H and D. The correlation limits of D(k¢§2 H ) correspond to the range 1.5<D<2.286; hence, this correlation can be used for predicting the structure of a macromolecular coil in dilute solutions. Yet another parameter used to characterise the polymer ¡¾ solvent interaction is the difference between the solubility param- eters of the polymer and the solvent.25 The plot for the variation of D of polyarylate vs.the solubility parameter of the solvent used in the synthesis of the polymer has a dome-like shape, typical of this type of dependence (Fig. 2, curve 1); this confirms the increase in D (an increase in the compactness of the macromolecular coil) following deterioration of the thermodynamic quality of the solvent. The fractal dimension of a macromolecular coil D can serve simultaneously as a measure of volume interactions of this coil: for a coil in a Y-solvent, D equal to 2 implies the absence of these interactions (the interaction parameter e=0), D<2 corresponds to repulsive interactions (e>0), and D>2 means attractive interactions (e<0).A simple procedure for the determination of D is based on the equation 26 , D= (5) 3aZa 5aZa ¢§ 2!¢§1 ¢§ 3! aZa2=3 Y aZa2=3 Y where [Z] and [Z]Y are intrinsic viscosities of the polymer dissolved in an arbitrary solvent and in a Y-solvent, respectively. By virtue of fractal analysis, one can gain some useful information, in addition to the data on molecular hydrodynamics, from the same experimental data.27 This statement is illustrated below by some examples. The fractal dimension D characterises the degree of `openness' of the fractal structure �¢ the lower D, the more efficient the penetration of particles into a fractal cluster (the more `accessible' is the cluster for a reaction).28 This is expressed analytically as follows:29 (6) Q!t (37D)/2, where Q is the degree of conversion of a polymer and t is the current reaction time.Equation (6) is the main scaling relation used to describe polymerisation kinetics.30 ¡¾ 37 It is noteworthy that the process cannot take place for Euclidean coils (compact globules) because for them, D=d=3 and Q=const. It is clear than in the general case, Eqn (6) should also contain diffusion parameters and the initial reactant concentrations. An aspect related directly to the problem of macromolecular coil structure considered here is the dependence of aggregation processes on the concentration of aggregating particles c (initial concentration c0) in some space.38 If the density r of a cluster (macromolecular coil) decreases during the growth down to the density of the surrounding medium (the polymer ¡¾ monomer solution), one type of universality of diffusion-limited aggregationStructure and properties of polymers in terms of the fractal approach (DLA) is replaced by another type, namely, the particle ± cluster aggregation switches to aggregation according to the Eden model;39 subsequently, growth of the macromolecular coil ceases, having reached the critical radius Rc.37 This variation of r is possible only for fractals because their density depends on the radius of gyration Rg, which is the critical radius for them 37 (7) r!bRD¡d, g where b is a proportionality factor.In the case of Euclidean objects, D=d and r=const. The transition between the classes of universality considered in terms of the DLA model is preceded by yet another transition, namely, the cluster ± cluster aggregation is replaced by the particle ± cluster aggregation; this markedly decreases the rate of the reaction but does not stop it.40 In terms of the cluster ± cluster DLA, the synthesis of a polymer can be described using the relation 40 ± 42 , (8) 1=D 4c Rg! 0kT t 3Z0m0 where k is the Boltzmann constant, T is temperature, Z0 is the initial viscosity of the medium, t is the reaction time, and m0 is the mass of a unit. An increase inDimplies an increase in the degree of branching of a macromolecular coil.22 This statement is illustrated by calculation of the spectral dimension ds, which characterises the degree of connectivity of a fractal.The ds value for a swollen fractal with allowance for the effect of excluded volume can be estimated from the following equation:43 D=d (9) s d ¡ 2 . d á 2 Note that for linear polymers, ds=1, while for branched polymers, ds=1.33.42, 43 The coil structure formed during the synthesis largely determines the molecular mass of the polymer formed. As D increases, the coil becomes more compact and the density of the coil diminishes.44 The main models suitable in this case include the formation of a close packing of macromolecular coils, the appearance of an entanglement network, and the description of the self-acceleration effect with allowance for the concept of free volume.According to each of these models, the increase in the viscosity in the monomer ± polymer system is the main reason for the formation of a macromolecular coil.45 To describe the limiting regimes of the dynamics of the growth of aggregates in a reaction vessel with the initial monomer concentration c0, the characteristic length scale x was intro- duced,46 which determines the qualitative transition from a fractal object to a non-fractal object (10) x!c¡1=Öd¡DÜ. 0 The former regime is realised for Rg 55 x, for a coil density much greater than the density of the medium in the reaction vessel and for the aggregate size (the degree of polymerisation for a macromolecular coil) N; it can be written that 46 (11) N(c0, t)!(c0t)D/(2+D7d). The latter regime is observed when Rg 44 x, the densities of the aggregate and the medium in the reaction vessel are nearly equal, and (12) N(c0, t)!cÖ1ádÜ=Öd¡DÜt d.0 The relationship between N and Q in terms of the irreversible aggregation models can be elucidated using the main scaling relation (6) and relation (8), in which all the parameters, except for c0, Z0 and t, are assumed to be constant, (13) 0 Q!cÖD¡1Ü=2ZÖ5¡DÜ=2NÖ3¡DÜ=2. 0 The resulting equation can be used to estimate the dependence of Q on t for the two regimes considered above. All these depend- 525 ences are non-linear and imply an increase in the reaction rate with an increase in t, that is, a self-acceleration effect.A possible reason for self-acceleration is interpenetration of macromolecular coils compressed to theY-size with the formation of a stable network of molecular entanglements.47, 48 In some cases, under certain conditions of synthesis, in particular, for low c0 and Z0, the absence of self-acceleration is assumed.45 It should be noted that the above variant for the calculation of Q(t) does not take into account the exhaustion of the monomer during the reaction. Exhaustion of the monomer appreciably decreases the reaction rate. In other words, the effects of self- acceleration and exhaustion of the monomer act in the opposite directions. When c0 values are low, the latter effect can suppress the former one. An important process occurring during the synthesis of polymers is gelation; traditionally, it attracts considerable atten- tion.However, there are several definitions of the gelation point and several methods for locating it on theQ(t) curve. For example, the gelation point is found as the point in which the solution starts to exhibit some properties of a solid (elastity, fragility, etc.).48 In polymer syntheses, transition from the initial stage of polymer- isation to the self-acceleration stage is referred to as gelation point.49 The concept of gelation point used in polymer physics implies the point where the cluster which tightens the system (and extends from one system edge to the other) is formed.36 Kolb and Herrmann 50 calculated the gelation point on the Q(t) curve in terms of an approach based on the DLA models. Different approaches and different definitions of gelation cause uncertainty in its interpretation.If the gelation effect is interpreted as the formation of a cluster tightening the system, the parameters describing this system change substantially.36 Thus the velocity u of the migration of clusters (macromolecular coils) with mass m is assumed to be 50 (14) u=ma, where a is a scaling index. At the point of gelation, the sign of a changes from negative to positive. This means that below the gelation point, smaller clusters are more mobile, whereas after the gelation point, the tightening cluster has the highest mobility. Statistical geometric characteristics of the system also change in the gelation point.It has been shown both theoretically and experimentally 36 that D values of about 1.6 ± 2.1, typical of a macromolecular coil in a solution, increase to*2.5 (see Ref. 21), which is a value characterising a Witten ± Sander cluster.15 In terms of the cluster ± cluster DLA, the time dependence of Rg is written as 51 (15) Rg!t1/z, where the index z is related to D and a by the expression (16) z=D(17a)7(d72). Polymeric systems are often described using the size distribu- tion function of clusters (macromolecular coils). In the physical chemistry of polymers, this function is defined as the molecular- mass distribution (MMD) function. The fractal dimension D provides little information on aggregation (polymerisation); this is a static value which does not describe the aggregation dynamics.In addition, D characterises the geometric properties of only one cluster (macromolecular coil) and cannot be used to describe sets of clusters in the system. For this purpose, one has to study the cluster size distribution function ns(t), where ns is the number of clusters consisting of s units at time t.52 The description of the cluster size distribution in the cluster ± cluster DLA model has been analysed.40, 50, 52, 53 This model is completely suitable, for example, for the description of polymer- isation of polymethyldiammonium chloride (PMDAC). The D value of this polymer, estimated to be 1.65 using Eqn (1), is a typical fractal dimension of aggregates formed during the clus-526 ter ¡¾ cluster DLA.37 In view of this fact, the molecular mass distribution of PMDAC is described using the function 52 ns(t)!s72tz. (17) Let us consider methods used to estimate the parameters appearing in relation (17).The ns(t0) values for the gelation point are found from the experimental MMD curves, Wi(N), in the following way. It is assumed that N=s and the part of the polymer corresponding to si is roughly equal to the total weight proportion of the polymer fractionWi. By dividingWi into si and by multiplying the ratio by the maximum degree of conversion Qi, we obtain the ns(t0) value. The index z is found from Eqn (16). In terms of the DLA model, the diffusion coefficient Ds is usually represented, by analogy with Eqn (14), in the form51, 52 (18) Ds!s a.(19) In view of the definition of Ds (see Ref. 54), it can be easily found from Eqn (18) that a!7ln Z0 . It was shown 51, 52 that a determines the pattern of the MMD function. For a<70.5, dome-shaped distribution curves having a maximum were obtained, and for a > 70.5, the curves decay monotonically. The MMD curves for PMDAC are also dome- shaped. If we assume the equality sign in relation (19), a would vary from 71 to 73, which completely complies with the experimental MMDcurves. The position of the MMDmaximum Nmax is determined by the relation 55 (20) Nmax! ¢§a 1 ¢§ a . An increase in c0 results in an increase in Z0 as well as in a and Nmax. Figure 3 presents the variation of ln(s2ns) vs.ln(stz) for PMDAC samples synthesised at different c0. It can be seen that all experimental points fit in one curve. This is the most important result which confirms the legitimacy of using irreversible aggrega- tion models for the description of polymerisation. ln(s2ns) 3 �¢1 �¢2 �¢3 �¢4 1 71 1 ln(stz) 3 2 Figure 3. Generalised MMD curve as the function ln(s2ns) vs. ln(stz) for PMDAC synthesised at c0 of 1.0 (1), 2.5 (2), 4.0 (3) and 5.0 (4) mol litre71. The general curve shown in Fig. 3 can be used to predict the kinetics of MMD as a function of t. For this purpose, the s=N value is first specified and the stz value is determined for an arbitrary t. After that, the corresponding s2ns value is found using the plot in Fig. 3 and then Wi is calculated.The same calculation should be repeated for a different s, and so on. The relationship between the structures of the macromolecu- lar coil and a solid polymer and its influence on the glass transition temperature Tg have been analysed in relation to a series of vitreous amorphous copolymers�¢aromatic copolyestersulfono- formals (APESF). Transition to the condensed state implies a change in the environment of a macromolecular coil; the solvent V U Novikov, G V Kozlov molecules surrounding the coil are replaced by similar coils. This changes the fractal dimension of the coil 44 and, correspondingly, the fractal dimension of the polymer structure as a whole.56 To derive an analytical expression representing the relation- ship between the structure and properties of polymers, a definite quantitative model of the structure is required.The cluster model for the structure of the amorphous state of polymers was used for this purpose.57 This model is based on the concept of local (short- range) order. The proportion of segments densely packed in the clusters jcl is a parameter of order, which is related to Tg by the following expression:58 (21) jcl ^ 0.03(Tg7T)0.55, 1=2, (22) df=d76 jcl SC? where T is the testing temperature. Within the framework of the cluster model, the glass ¡¾ liquid transition is regarded as the thermofluctuational decomposition of clusters at T=Tg.59 Fractal concepts are interrelated with the cluster model; the relationship between the main characteristics of these models is given in the form 60 where df is the fractal dimension of the supermolecular (super- segmental) structure of the polymer (23) df=(d71) (1+m), where m is the Poisson coefficient. The S values for the sulfone and formal fragments which constitute APESF were assumed to be 35 and 23 A2, respec- tively,48 and S values for copolymers were estimated using the condition of additivity.The C? values were calculated from the equation 60 f (24) C?=dOd ¢§ dfU a 4=3 . d Using Eqns (21) ¡¾ (24), one can calculate Tg proceeding only from the structure of the macromolecular coil in solution, which is characterised by D, and from the molecular parameter S.The Tg values calculated by this procedure are in good agreement with experimental values; the discrepancy between them does not exceed 4% (Fig. 4). Tg /K 423 373 0 60 30 cs (mol.%) Figure 4. Glass transition temperature Tg vs. the content of sulfone fragment. The curve corresponds to experimental results and the points are calculated values.14 2. Hierarchy and evolution of dissipative structures in polymers In recent years, principles of synergetics of nonequilibrium systems and fractal analysis have been used to study the relation- ship between the structures and properties of vitreous polymers,61 ¡¾ 64 because an amorphous polymer is a thermody- namically nonequilibrium system.Structure and properties of polymers in terms of the fractal approach The main feature distinguishing polymers from other classes of solids is that they consist of long-chain macromolecules.Therefore, it is natural to assume that the structural hierarchy of polymers (including network polyld be based on their molecular structure. In recent years, the characteristic ratio C? has been used more and more frequently as a molecular parameter to describe the properties of polymers, instead of some other characteristics such as a/s (a is the chain `thickness' and s is the chain rigidity).65, 66 According to Boyer and Miller,67 this is due to the fact that s has greater uncertainty than C?. Indeed, s depends on the bond angles in the macromolecule, while C? depends on the bond lengths, which are normally determined much more precisely than the bond angles.Without objecting to the legiti- macy of this conclusion, we believe, nevertheless, that the reasons for the wide use of the parameter C? are much more fundamental (see, for example, a number of studies 60 ¡À 64, 68 ¡À 71). This can be demonstrated in relation to the epoxy polymers based on bisphe- nol A and cured by diamine (EP-1) and anhydride (EP-2). For example, to estimate the Bragg interval dB for these polymers, wide-angle X-ray diffractometry has been used.71 The resulting value was used to determine the diameter (and, hence, the cross- section area S) of the molecule, simulated by a cylinder, from the following relation: (25) &1.22 dB. 1=2, (26) Tg&129 S C? Subsequently, using the empirical relation 71 where Tg is expressed in Kelvins and S is expressed in A2, one can calculate the C? values for epoxy polymers.The behaviour of a solid subjected to mechanical treatment is determined by the processes of formation (disintegration) and evolution of dissipative structures (DS), which ensure the opti- mum mode of dissipation of the supplied energy.60, 72, 73 This general statement is valid for all polymers. Polymers have local order, which occurs as DS.74, 75 However, direct application of the fundamental principles of thermodynamics and statistical physics of nonequilibrium systems to the investigation of the deformation of materials of a particular class is often difficult or even impossible without the knowledge of a definite quantitative model for the structure of this material.In the case of amorphous polymers, the cluster model is suitable for this purpose.57, 74 Aspecific feature of the DSformed in polymers is the existence of a universal hierarchy of space scales (structural levels), which is also reflected in the hierarchy of linear dimensions of the struc- ture.60, 63 Even elastically isotropic solids are characterised by at least three independent length scales, l1, l2 and l3, which are related to one another 73 l1=a, l2=aL0, (27) (28) (29) l3=aL0Li, where a is the minimum scale, L0 and Li are automodelling coefficients. When choosing these length scales as applied to polymers, one should reject the atomic-size level because a polymer consists of long macromolecules. Therefore, the bond length in the macro- molecular backbone l0, which is of the order of several angstroms, should be taken as the minimum scale a for polymers.62, 76 Then the next (segmental) structural level would be determined by the length of statistical segment lst, which is found from the equation lst=l0C?.Hence, provided that l1=l0, it can be written for this structural level that 77 ¡À 79 L0=C?. The next structural level for polymers is the topological level, the parameters of which are determined by characteristics of the network of macromolecular entanglements (`loops') in linear polymers or the network of chemical cross-links in cross-linked polymers. The characteristic length for this level is the distance between the entanglement points or chemical cross-linking points Rs cl , 2V ¡¦1=3 Rs=18 F where Vcl is the density of the cluster network of entanglements, F is the cluster functionality.If the equality L0=C? is retained for the subsequent struc- tural levels, Eqns (27) ¡À (29) for polymers can be written in the forml1=l0, l2=lst=l0C?, l3=Rs=l0C2?. Figure 5 shows the dependence of Rs vs C2?. Splitting of the plot into two straight lines is due, first, to the great scatter of the published data 62, 76, 80 and, second, to different approaches to the interpretation of the l2=lst value.62, 81 Nevertheless, the fact that Rs is proportional to C2? confirms that C? is the automodelling coefficient for the transition of the scale of DS dimensions from lst to Rs.Rs /nm 8.0 4.00 40 Figure 5.Distance between entanglements (chemical cross-linking points) vs. characteristic ratio for amorphous vitreous (1), amorphous- crystalline (2) and cross-linked (3) polymers.79 Figure 6 illustrates the relationship between the Rs values calculated from Eqns (30) and (33). Aharoni 76 noted an increase in Rs following an increase in the chain flexibility (increase in C?) for a large number of linear polymers Rs (30) /nm 1050 5 10Rs (33) /nm Figure 6. Relationship between the distances between entanglements (chemical cross-linking points) Rs calculated from Eqns (30) and (33) for amorphous glassy (1), amorphous-crystalline (2) and cross-linked (3) polymers.79 527 (30) (31) (32) (33) D1 D2 D3 80 C2? D1 D2 D3528 (34) Rs^10C?.A similar relation holds for cross-linked polymers Rs^5C?. (35) Thus, the C? value, which is correlated with Rs, appears to be controlled by the polymer topology, which can be varied by varying the cross-linking density ns. Polymers are characterised by one more, specific length scale; this is the section of a macromolecule between entanglement points or chemical cross-linking points Ls, which can be deter- mined from the equation (36) Ls= Fch , 2Svs where Fch is the functionality of a chemical cross-linking point (Fch=4).14 Figure 7 shows the variation of Ls vs. C3?, which can be approximated by a straight line passing through the origin of coordinates.The Ls/C3? ratio has the order of l0.62, 76 Hence, for this structural level, typical of polymers,C?can be accepted as the automodelling coefficient.82 ¡À 84 Ls /nm 60 20 D1 D2 D3 C3 600 200 ? Figure 7. Length of the section of a macromolecule between entangle- ments (chemical cross-linking points) Ls vs. characteristic ratio C3? for amorphous glassy (1), amorphous-crystalline (2) and cross-linked (3) polymers.79 Let us consider the evolution of DS in network polymers during deformation. It has been shown 74 that plastic yield in amorphous polymers occurs exactly in clusters, the yield point being dependent only on the density of the cluster network of entanglements (nen), i.e.on the number of closely packed segments in unit volume of the polymer. Yield can be regarded as the loss of stability of clusters in the field of mechanical stress, while cold flow is the deformation of a devitrified loosely packed matrix in which the role of chemical cross-links is played by the cluster network of entanglements.85 This interpretation permits one to specify the structural changes occurring during deformation of network polymers in terms of the percolation cluster model.60, 72 ¡À 74 As noted above, the DS formed (or existing) in a solid subjected to deformation are distinguished by a universal hier- archy of structural levels.86 Balankin 87, 88 suggested that the hierarchical structure of the DS in a solid is based on a funda- mental feature, i.e.shear stability, which stipulates the difference between the characteristic space scales of the regions of local- isation and dissipation of energy `pumped' into the solid on external treatment. The characteristic scale of the regions (ls) in which excess energy is dissipated is proportional to the shear modulus G. Since, in terms of the cluster model, these regions can be associated with clusters, it is expedient to use the characteristic size lst as ls. Figure 8 illustrates the relationship between G and lst, which is approximated by a straight line that passes through the origin of coordinates. This confirms the legitimacy of using lst as ls. V U Novikov, G V Kozlov lst /nm 0.8 0.6 D1 D2 D3 D4 0.4 1.0 G /GPa 1.5 Figure 8.Relationship between the length of statistical segment lst and the shear modulus G for EP-1 (1), EP-2 (2) and for EP-1 (3) and EP-2 (4) samples cured at a hydrostatic pressure of 200 MPa.78 With allowance for the above interpretation of cold flow and for Eqn (30), the distance between the clusters Rcl should be accepted as the next level in the hierarchy of structural levels. The characteristic size of the regions of localisation of the `pumped-in' energy is (37) le!B �¢ 43G, Li�¢1 (38) L G¡¦1 �� Li. i �� le �� B �¢ 4 ls 3G where B is the bulk modulus.73 The possibility of equating Rcl and le is verified in the following way. The ratio of the space scales of the DS of adjacent structural levels, Li and Li+1, is expressed as follows:73 It is clear that the multiplication of the ratio [B+(4/3)G]/G by ls, which is equal to lst, gives le.The Rcl value can be estimated using Eqn (30). The dependence of le on [B+(4/3)G] also proved to be linear (Fig. 9), which implies that the parameter le can, in principle, be used as the characteristic size of the regions of localisation of the pumped-in energy. However, this assumption can be ultimately confirmed by comparing le and Rcl. A correlation between these parameters has been found;60 it was shown that Rcl regularly exceeds le by*0.8 nm. This relationship between le and Rcl can be interpreted by virtue of the cluster structure model for an amorphous polymer (Fig.10).89 Evidently, the decrease in Rcl by *0.8 nm, which is roughly equal to lst, means that the pumped-in energy does not spread throughout the whole polymer bulk but is localised only in the loosely packed matrix because a cluster with the characteristic size lst is excluded from consideration. Compar- le /nm 32 D1 D2 D3 D4 2 1 4 [B+(4/3)G] /GPa Figure 9. Relationship between the characteristic size of the regions of localisation of the pumped-in energy le and the parameter [B+(4/3)G]. For designations, see Fig. 8.78Structure and properties of polymers in terms of the fractal approach Rcl Rcl7lst Figure 10. Parameters of the cluster structure model for an amorphous polymer. le /nm 3 2 �¢1 �¢2 �¢3 �¢4 1 (Rcl7lst) /nm 2 Figure 11.Relationship between the characteristic size of the regions of localisation of the pumped-in energy le and the (Rcl7lst) value. For designations, see Fig. 8. ison of the le value and the difference Rcl 7 lst (Fig. 11) confirms this conclusion. Hence, the structural characteristics le and Rcl 7 lst, estimated within the framework of the cluster model and regarded as the space scales of the DS of adjacent levels [see Eqn (38)], allow one to estimate the automodelling coefficient for the mechanical deformation of a network polymer Li, which is equal to the fractal dimension Df of the regions of localisation of excess energy in a plastically deformed medium. In a first approximation, the Df value can be expressed in terms of the Poisson coefficient m in the following way:72 (39) Df=2 1 ¢§ m 1 ¢§ 2m .The relationship between the dimension Df and the automod- elling coefficient Li for the network polymers under consideration is illustrated in Fig. 12. It can be seen that both the magnitudes Df 4 �¢1 �¢2 �¢3 �¢4 2 4 Li Figure 12. Relationship between the fractal dimension of the regions of localisation of excess energy Df and the automodelling coefficient Li. For designations, see Fig. 8. 529 D Rs , (40) a lst st and the patterns of variation for these parameters coincide. Thus, plastic yield and cold flow of network polymers are adequately described in terms of the thermodynamics of nonequilibrium processes and the cluster model of amorphous polymers provides a correct description of the structure of network polymers.It is also evident that clusters are identified as DS. Similar results have been obtained for film samples of a linear polymer�¢polyarylatesulfone.90 Using Eqn (38) and the ratio 14 Ls l it can be shown that . (41) lst 1=D Ls Li=Df& Figure 13 shows that the Ls values estimated from Eqns (36) and (41) are in good agreement with each other. This implies that the sections of a macromolecule between entanglements and between clusters also obey (are controlled by) the DS hierarchy.90 Ls (36) /nm 840 L 4 s (41) /nm Figure 13. Relationship between the lengths of macromolecule sections between entanglements determined using Eqns (36) and (41) for polyar- ylatesulfone.90 In view of the foregoing, it can be suggested that the automodelling coefficient Li in Eqn (38) is equal to C?.Then this equation assumes the form (42) GB a 43 a C? . The B and G values can be expressed in terms of Young's modulus (E) and the fractal dimension of the polymer structure df in the following way:91 (43) B=dOd ¢§ dfU , E (44) G=EOd ¢§ 1U , 2df where d = 3. Using Eqns (42) ¡¾ (44), one can estimate quantitatively the relationship between the molecular parameter C? and the fractal dimension df.92 (45) dOd ¢§ 1UOfd ¢§ dfU a 43 a C?. 2d The dependences of df found from Eqns (23) and (45) for various classes of polymers are presented in Fig. 14.It can be seen that the results are in good agreement with each other. It is noteworthy that the methods of calculation are completely independent �¢ Eqn (23) employs the results of mechanical test- ing, while Eqn (45) is based on published data for C?.92530 df 2.9 2.5 2.10 5 10 Figure 14. Fractal dimension of the structure df of polymers vs. character- istic ratio C?. Solid lineDcalculation from Eqn (45); dotsDcalculation from Eqn (23): (1) linear polymers, impact testing; (2) linear polymers, calculation of df from the data of Ref. 60; (3) cross-linked epoxy polymers; (4) super-high- molecular-mass polyethylene produced by solid-phase extrusion; (5) poly- arylate prepared by solid-phase extrusion at T>Tg; (6) linear polymers, stretching testing; (7) linear polymers, calculation of df from small-angle X-ray diffraction data.For sample (7) experimental data on the inaccur- acy are given.60 The evolution of DS induced by various types of treatment of the polymer has been considered.64, 93, 94 Figure 15 shows the dependence of the cluster functionality F on the curing agent : oligomer ratio (Kst) for epoxy polymers in deformed and non- deformed states. The most characteristic distinction between the plots being compared is the substantial increase in F after the yield point. The simultaneous decrease in Vcl and increase in F upon deformation of polymers up to the yield point 63, 64 implies decomposition of unstable clusters characterised by relatively low F to leave only stable clusters with large F.95 The decay of unstable clusters induces mechanical devitrification of the loosely packed matrix; this explains the plastic behaviour of the polymer in the plateau of forced rubber-like elasticity (cold flow).96, 97 The opposite situation is observed during heat ageing, namely, the local order (Vcl) increases and the molecular mobility of chains is suppressed (D decreases).94 Experimental evidence for the fractality of the cluster struc- ture (or DS) has been obtained using wide-angle X-ray diffraction analysis.98 ¡À 100 The integral intensity of the amorphous halo Icl can be regarded as a measure of distributed particles (clusters), while its half-width can be taken as a measure of their effective size; the relationship between these values is illustrated in Fig.16 F 40 200 1.0 0.5 Figure 15. Functionality of clusters vs. the curing agent : oligomer ratio for epoxy polymers EP-1 (1, 3) and EP-2 (2, 4) before (1, 2) and after (3, 4) the yield point has been attained. D1 D2 D3 D4 D5 D6 D7 18 23C? 4 312 Kst V U Novikov, G V Kozlov ln I ¡¦1 cl 1.2 0.4 28 26 ln lcl Figure 16. Reciprocal integral intensity of X-ray scattering vs. cluster half-width for EP-1.98 in relation to EP-1. The I ¡¦1 cl (lcl) dependence presented in the logarithmic coordinates is readily transformed into the form 98 (46) I ¡¦1 cl !l dclf , where df ^ 2.70. This type of dependence is typical of fractal structures; it can serve as experimental evidence confirming the fractality of the polymer structure.In addition, the df value is in good agreement wther epoxy polymers (see, for example, Ref. 69). A fundamental description of the process of polymer fracture which includes the dilaton concept 101 ¡À 103 as a constituent has been proposed.104 The dilaton model assumes the formation of a negative density fluctuation, dilaton, the length of which is determined by the free path of phonons Lf. In this case, the overload factor w on the bonds being ruptured depends on Lf and on the interatomic distance aat:101 (47) w �� Lf . aat The Lf values found for oriented polymers are about 10 nm and w are about 30 ¡À 40.103 However, for nonoriented polymers, it was found that w 4 1, i.e.Lf 4 aat. These dilatons were called `degenerate' (practically, this means that phonons have no free path).105 ¡À 107 The use of the fracton concept 28 provided a fundamental interpretation for this seeming contradiction. Fractons are vibra- tional excitations localised on a fractal. Since the chain section between entanglements or cross-links is a fractal, a phonon localised on this section becomes a fracton. Localisation of a phonon means that it has no free path; this accounts for the fact that w41. During orientation of a polymer, the chain section in question is stretched; finally, it becomes straight. In this case, its Hausdorff dimension is equal to the topological dimension (48) D=dt=1 and the fractal behaviour switches to the Euclidean behaviour: the phonon becomes delocalised and acquires some free path con- trolled by the structure of the oriented polymer.Now w>1. Thus, the dilaton concept is actually a specific case of the fracton theory (for D=1).104 The following relationship between the parameters w and D has been obtained:104 (49) w ^ D72. An increase in the molecular mobility (increase in D) results in stress relaxation on the non-oriented polymer chains (w<1).108 Since characteristics of fractal analysis are general, the rela- tionship between the structures of different aggregation (physical) states of the polymer can be established. For example, a macro- molecular coil (cluster) in solution and the polymer structure in the condensed state are fractals with the dimensions D and df, respectively.44, 109 This fact can be used to predict the structure of a solid polymer even at the stage of synthesis.110 ¡À 112 The D value,Structure and properties of polymers in terms of the fractal approach with allowance for the effect of excluded volume, is determined by Eqn (9).For linear polymers, it should be accepted that ds in this equation is equal to 1.43 Transition to the condensed state is accompanied by the change in the environment of a macro- molecular coil; a coil becomes surrounded by similar coils instead of solvent molecules. This results in the change of the fractal dimension df for the condensed state 44 (50) df=dsOd a 2U .2 (51) For linear polymers, provided that ds=1 and d=3, it follows from Eqns (9) and (50) that 111 df=1.5D. Equation (51) clearly demonstrates the relationship between the coil structure in solution and the structure of the condensed polymer. 3. Quasi-equilibrium state of polymers Neither completely ordered nor completely disordered polymers have been obtained to date. One reason for this situation is the chain nature of polymer molecules (in particular, the formation of loops during crystallisation).113 The tendency for transition to a more equilibrated state in polymers is often attributed to an increase in the degree of ordering.114 Therefore, it can be assumed that processes in which this tendency is manifested (for example, heat ageing, thermosetting, etc.) are subject to a competition of two opposing mechanisms.An increase in the degree of ordering is counteracted by the entropy of `stretching' of macromolecules. When the thermodynamic forces of these mechanisms have been balanced, the polymer reaches some quasi-equilibrium state.60 Perturbation of the balance in either direction governs the pattern of changes in the polymer structure. In other words, under certain conditions, a polymer can be transformed not only towards a more equilibrated state but also away from equilibrium. Accord- ing to its physical essence, the latter process can be called `antirelaxation'. Some causes and consequencies of this process are considered below in terms of the cluster model of the structure of the amorphous state of polymers and cluster analysis.Thermosetting of extruded specimens of polyarylate occurs in the loosely packed matrix;112 therefore, the Df value should be taken as the fractal dimension which determines the process in a structural element (for example, in a tube). Figure 17 a shows the variation of the thermosetting c as a function ofDf for extrudates, which implies that the thermal shrinkage changes its sign when Df ^ 3. This fact is very interesting by itself. In the case of extrudates with Df>3, a less closely packed structure (having greaterDf) is transformed during relaxation (thermosetting) into a more closely packed structure (having smaller Df), which is, therefore, closer to equilibrium.The behaviour of specimens with Df<3 requires clarification. At the first glance, it seems that asDf decreases and the structure changes, c=0 should imply termination of thermosetting. However, this does not occur; instead, c only changes its sign. This effect can be easily explained b a c c 70.1 0.2 0 0 5 3 3.0 0.1 0.22.6 Df 7 l Figure 17. Thermosetting c vs. the dimension of the regions of local- isation of excess energy Df (a) and extrusion draw ratio l (b) for polyarylate extrudates. 531 by two specific features of the cluster model �¢ arbitrary orienta- tion of the cluster axes in space and connection of clusters by `interpenetrating' chains, which are subject to the limitations of the Gaussian statistics.97 This means that it is impossible to attain a close packing of clusters, i.e.conditions of thermodynamic equilibrium cannot be reached in an amorphous polymer. This has been the reason for the introduction of the above-mentioned concept of `quasi-equilibrium state',115 in which forces due to which a polymer tends to a thermodynamic equilibrium and, hence, to an increase in the degree of local ordering are counter- balanced by entropy forces of the `interpenetrating chains'. The last-mentioned fact can induce transition of an amorphous polymer from a thermodynamically more equilibrated state to a less equilibrated state. Experimental dependence of c on the draw ratio l confirms this direction of the thermosetting process (Fig. 17 b).The most characteristic feature of the relationship between D and df (Fig. 18) is the fact that the limiting value D =1 is attained at df=2.5 rather than at df=2. Recalling that the dimension D characterises the mobility (deformability) of the section of a macromolecule between chemical cross-linking points (entangle- ment points) and D=1 implies the loss of molecular mobility by this section. The quasi-equilibrium state corresponds to `freezing' of the molecular mobility of polymer chains and, as a conse- quence, to the transition to brittle fracture, which is realised at Df<3.87 Since Df and df are related to each other as follows 87 (52) f Df=1a 3 ¢§ d , 1 it can be readily seen that df=2.5 corresponds to Df =3.When examining the dependence of df on the relative portion of the loosely packed matrix jlp in poly(methyl methacrylate), high-density polyethylene, polycarbonate, and polyarylate (Fig. 19), attention is drawn by the fact that for jlp=0 (the hypothetical state characterised by full local ordering), the df values are extrapolated to certain d 0f values (which are different for different polymers), exceeding the lower limiting value, equal to 2. Using published data for C?(see, for example, Ref. 113), one can calculate the theoretical d tf values from Eqn (45) and compare them with the limiting d 0f value (see Fig. 19). The parameters d tfand d 0f are well correlated (Table 1), which reflects the occurrence of a quasi-equilibrium state.Using Eqn (45) and the relation (53) jcl=C?l0SVcl, the following limits can be iden: for C? > 3, a quasi- equilibrium state cannot be attained at all; for C?=2 ¡¾ 3, it may happen that Df<3; the value df=2, corresponding to Df=2 is reachable only for a polymer with C?=2. Analysis of the results obtained in terms of Eqn (45) as well as the data given in Fig. 19 and in Table 1 show that Eqn (45) determines the minimum df values possible for a given C?. D 1.8 1.4 �¢1 �¢2 1.0 df 2.6 2.8 Figure 18. Relationship between the fractal dimensions of the macro- molecule section between cross-linking points D and of the structure df for epoxy polymers EP-1 (1) and EP-2 (2).532 df 2.7 D1 D2 D3 D4 D5 2.3 0 0.8 0.4 jlp Figure 19. Fractal dimension of the structure df vs.proportion of the loosely packed matrix jlp for poly(methyl methacrylate) (1), high-density polyethylene (2), polycarbonate (3), polyarylate (4), and polyarylate extrudates (5). Table 1. Fractal dimensions of the polymer structures d tf and d 0f . Polymer d tf d 0f 2.60 2.49 2.31 2.27 2.51 2.55 2.53 2.29 2.23 2.58 Poly(methyl methacrylate) High-density polyethylene Polycarbonate Polyarylate Epoxy polymer This accounts for the discrepancies between the df values found from relations (23) and (45) D the former gives the real df value and the latter gives the minimum possible one. The dependences of Df on the curing agent : oligomer ratio (Fig.20) for EP-2 specimens immediately after the manufacture (curve 1) and after keeping at room temperature for 1.5 years (physical ageing) (curve 2) show that during ageing,Df approaches 3, this effect being more pronounced for nonequilibrium systems with a deficiency or an excess of a curing agent. The minimum C? value for the epoxy polymer with Kst=1.0 is equal to 3.38.71 With allowance for this fact, an estimate of the minimum Df value also gave *3.38. This estimate is in good agreement with the exper- imental Df value for the aged polymer (Df ^ 3.16). The existence of the quasi-equilibrium state is also confirmed by the temperature dependences of the density fluctuations hDr/ri2 (Fig. 21), which diminish as the temperature rises and tend to zero for T=0, which corresponds to an ideal structure.However, there occurs a transition at temperature T * below which hDr/ri2 deviates from the predicted pattern 116 and remains constant as the temperature varies. The density fluctuations above T * are supposed to be due to the local mobility of the sequences in the polymer backbone but below T * this mobility becomes `frozen'. This interpretation is fully consistent with the concept Df 5 1 4 2 3 1.25 0.75 Kst Figure 20. Dimensions of the regions of localisation of excess energyDf vs. the curing agent : oligomer ratio Kst for EP-2 samples immediately after preparation (1) and after physical ageing (2). V U Novikov, G V Kozlov 103hDr/ri2 1 15 2 5 T* T /K 100 300 Figure 21.Temperature dependences of the density fluctuations hDr/ri2 for poly(methyl methacrylate) (1) and poly(ethylene terephthalate) (2).117 of quasi-equilibrium state (D=1). The nature of the temperature T * has been considered in detail.117 Thus, the introduction of the concept of quasi-equilibrium state in polymers provides interpretation of some experimental facts. The application of the cluster model and fractal analysis makes it possible to specify the direction of the process of synthesis and to estimate its main characteristics. 4. Fluctuation free volume in polymers The properties of polymers are mainly related to the molecular mobility and structure, which is determined by the degree of ordering of macromolecules.118 Free volume, or, more precisely, one of its components, fluctuation free volume, is one of the parameters most suitable for phenomenological description of a structure.119 As a rule, the fraction of the fluctuation free volume ffv is estimated on the basis of polymer properties rather than from structure characteristics.Within the framework of the cluster model of the amorphous state of polymers,74, 120, 121 it has been shown 57 that a microcavity of fluctuation free volume is formed upon detachment (dissociation) of a segment from a region of local order (cluster) and `collapses' upon attachment of a segment to a cluster. If this mechanism is accepted, at least two aspects need to be considered. One aspect concerns the energy characteristics of the process.The cluster model for the structure of the amorphous state of polymers postulates the thermofluctuational character of local ordering, according to which the number of segments in clusters diminishes as the temperature increases;122 this results in the formation of new microcavities of the fluctuation free volume (their nature has been considered in detail 123) and in an increase in ffv. It is evident that the energy of thermal fluctuations is of the order of kT; the energy of formation of a microcavity (eh) can be estimated from the equation (54) eh=kTg ln 1 . ffv Since the maximum ffv value expected in the vitreous state is 0.159 (according to the most `rigorous' estimates 124) and T<Tg, it is obvious that the energy of thermal fluctuations is insufficient for the formation of a microcavity.The second point is determination of the ffv value. This can be done by virtue of the following equation: (55) ffv^0:017 1 �¢ m 1 ¡¦ 2m . For amorphous vitreous polymers, ffv ^ 0.050 ¡À 0.090,121 which is much greater than the value ffv ^ 0.0250.003, which has been found in terms of the Williams ¡À Landell ¡À Ferry (WLF) concept and is generally accepted for most polymers.118 Evaluation of some polymer properties requires not only the integral characteristic ffv but also the parameters of a separateStructure and properties of polymers in terms of the fractal approach microcavity of fluctuation free volume, which is traditionally represented as a sphere with volume Vh.119 Recalling that the fractal dimension of the polymer structure is in the range 24df43, it can be suggested that the fluctuation free volume as a structural unit also possesses fractal properties.Using relations (55) and (23), the dependence of ffv on df has been elucidated 60 f . (56) ffv ^ 8.561073 f d 3 ¢§ d If the above assumption is correct, the following general relation should hold:125 (57) Nh!rDffv , h where Nh is the number of microcavities, rh is their characteristic size, and Dffv is the fractal dimension of the fluctuation free volume. As a first approximation, the rh value can be expressed in h , the volume being found terms of the microcavity volume as V1=3 from the equation (58) Vh=3O1 ¢§ mUkTg .ffvE Although this approximation introduces some inaccuracy to the quantitative results, it does not deteriorate the generality of the conclusions. The number of microcavities Nh is expressed as the ratio 119 (59) Nh= ffv . Vh h Figure 22 presents the variation of lnNh as a function of lnV1=3 for specimens of three epoxy polymers, EP-1, EP-2, and aged EP-2, which is designated by EP-3. It can be seen that the plots are linear; this is a typical feature of fractal behaviour. The Dffv values found from relation (57) for EP-1 and EP-2 were 5.9; that for EP-3 was 2.7. It is clear that Dffv calculated in this way are averaged values; nevertheless, they provide grounds for an important conclusion: in the general case, a microcavity of fluctuation free volume can be represented by a Dffv-dimensional sphere, modelling by a three- dimensional sphere being a specific case.The Dffv values are close to the corresponding dimensions Df of the regions of localisation of excess energy, which are determined from Eqn (39). In addi- tion, Df is equal to the automodelling coefficient Li and, hence, to C?. The fractal dimension Dffv interpreted in this way is closely related to the characteristics of the polymer structure. Now we consider the energy criterion for the formation of a microcavity with the volume Vh. For this purpose, we use the concept of free fracture of solids,126 according to which a limited amount of potential energy with density A* can be accumulated in lnNh 0 71 �¢1 �¢2 �¢3 72 1.3 ln (V1=3 0.9 h ) mber of microcavities of fluctuation free volume vs. their size for EP-1 (1), EP-2 (2) and EP-3 (3). 533 (60) (61) a limited volume V and the formation of a new surface requires work equal to the product of the surface area Sn and the specific surface energy sn. In the case of free fracture,127 A*V=snSn. As applied to the formation of a microcavity with the volume V=Vh, relation (60) can be represented as follows:87 VS a sn A . n (62) For a Dffv-dimensional sphere, it can be written that 87 VS a rh . D n ffv The sn value can be represented as follows:119 eh (63) , sn= h 2V2=3 where eh is estimated from Eqn (54).Finally, by determining A* as the ratio (64) A*=kT , Vh and using Eqns (61) and (63), we obtain (65) Dffv a TglnO1=ffvU . 4pT Since ageing can be interpreted as a tendency towards ther- modynamic equilibrium,114 it is assumed that the condition Dffv=3 corresponds to a certain quasi-equilibrium state of the polymer. This allows one to draw several conclusions. First, an increase in temperature, all other factors being the same, implies an increase in Df and, hence, enhancement of the thermodynamic nonequilibrium of the polymer as a system. It follows from Eqn (39) that an increase in Df is accompanied by an increase in m; this accounts for the well-known fact that the Poisson coef- ficient of polymers increases with temperature.74, 127, 128 Second, an increase in m implies a decrease in the degree of local ordering of amorphous polymers,70, 129 which is manifested as a decrease in the density of the cluster network of entanglements Ven.In other words, an increase in Ven reflects the trend of a polymer towads thermodynamic equilibrium.114 Third, in the case where Dffv=3, one can calculate the relative portion of the `quasi-equilibrium' free volume (f 0fv); for the epoxy polymers in question, it falls in the range *0.028 ¡¾ 0.042, which is rather close to the ffv value in the WLF equation mentioned above. Thus, the estimation of ffv using Eqn (55) is correct and the considerable magnitudes of ffv reflect a relatively high degree of thermodynamic nonequilibrium in epoxy polymers.Let us consider the general statements of the concept of fluctuation free volume in relation to cross-linked systems. Figure 23 a illustrates the relationship between the fractal dimen- sions of the regions of localisation of excess energy Df [see Eqn (39)] and the fluctuation free volume Dffv [see Eqn (65)]. It can be seen that these two values are fairly close to each other.{ Thus, the ffv value can actually be used to characterise the polymer structure. (66) The formation of a microcavity with the volume Vh requires local critical deformation ec130 lnO1=ffvU , 3g ec a 13 where g is the GruE neisen parameter, characterising the anharmo- nicity of the intermolecular bonds in a polymer and the factor 3 was introduced under the assumption that a microcavity is three- dimensional. In view of this fact, this factor should be replaced by Dffv and thus Eqn (66) assumes the form { Some discrepancy is due to the fluctuation nature of free volume.534 b a Df D¢§1 ffv 5 �¢1 �¢2 �¢3 0.35 3 4 3 Dffv 0.35 0.2 ec Figure 23.Relationships between the fractal dimensions of the regions of localisation of excess energy Df and the fluctuation free volume Dffv (a) and between the dimension of the fluctuation free volume and the critical deformation in the formation of microcavities ec (b) for EP-1 (1), EP-2 (2) and EP-3 (3). (67) ec a lnO1=ffvU . 3gDffv Thus, the more pronounced the fractality of the fluctuation free volume (the greater Dffv), the smaller ec and the easier the formation of the microcavity.This fact is reflected in the depend- ence of ec on D¢§1 ffv (Fig. 23 b). The g value was found from the relation 130 (68) g^0:74 1 a m 1 ¢§ 2m . It is noteworthy that the GruE neisen parameter varies in parallel with Dffv and is related to the dimension of the fluctuation free volume by the following simple relation: (69) g^Dffv71. In other words, the GruE neisen parameter is also a fractal characteristic; for quasi-equilibrium conditions, g=2. The values g>2 mean an enhanced nonequilibrium character of the sys- tem.131 Figure 24 shows the dependence of g on Dffv and the depend- ence ofVh onKst for three epoxy polymers. TheVh values for EP-1 and EP-2 vary from 0.97 to 7.31 nm3 but those for EP-3 are greater and lie in the range of 5.45 ¡¾ 10.1 nm3.In terms of the free fracture concept, this implies that the formation of a microcavity in a system the state of which is close to quasi-equilibrium requires more thermal fluctuations with the energy kT than that in non- equilibrium systems (EP-1 or EP-2). The same requirement is valid for each particular composition, which is confirmed by the presence of a maximum on the dependence of Vh on Kst at Kst=1. The degree of equilibration can be estimated as the difference b a g Vh/ nm3 4 �¢1 �¢2 �¢3 7.5 2 0 1.0 0.5 Kst 3 4Dffv 2 Figure 24. Relationship between the GruE neisen parameter g and the dimension of the fluctuation free volume Dffv (a) and the dependence of Vh on Kst (b) for EP-1 (1), EP-2 (2) and EP-3 (3). V U Novikov, G V Kozlov a ffv, f 0 b fv 10727Ven /m73 1 0.08 3 2 �¢1 �¢2 �¢3 0.04 3 1 0.06 0.02 Kst 1.0 0.5 1.5 Dffv Figure 25.Variation of ffv vs. Kst (a) and of the density of the cluster network of entanglements Ven vs. Dffv (b) for epoxy polymers. (a): (1 ) EP-1, f 0fv(Kst); (2) EP-1, ffv(Kst); (3) EP-3, ffv(Kst); (b): (1) EP-1, (2) EP-2, (3) EP-3. (70) Dffv=ffv7f 0fv. The meaning of this estimate becomes evident if one compares the ffv(Kst) and f 0fv(Kst) plots for EP-1 and EP-3 (Fig. 25 a). As noted above, samples with Kst=1 are closest to the quasi- equilibrium state. The aged EP-3 samples at Kst=1 have already reached this state and further ageing does not change the struc- ture.The samples with Kst40.50 and those with Kst51.50 possess the lowest stability during physical ageing, which is displayed as the corresponding change in their properties. The decrease in the elastic modulus during ageing of EP-1 amounted to 1.7 GPa for Kst=1.50 and 1.1 GPa for Kst=1.0. Thus, by comparing the ffv(Kst) and f 0fv(Kst) plots, one can demonstrate the degree of thermodynamic nonequilibrium of cross-linked systems and predict the possible changes in their structure and properties during physical ageing. The closeness of a polymer to the equilibrium state can be characterised by the degree of ordering. Using the cluster model, this trend can be quantitatively described fairly easily in terms of the parameters Ven or jcl.57,132 The dependence of Ven on Dffv (Fig.25 b) shows that the degree of local ordering can serve as an indication of the thermodynamic nonequilibrium of the polymer structure. Extrapolation of the straight line Ven(Dffv) to Dffv=0 gives Ven ^ 3.861027 m73, which is about 1.5 times lower than the maximum Ven value found as the ratio of the total length of the macromolecule per unit volume of the polymer to the length of the statistical segment.133 This discrepancy stipulates the legitimacy of applying the term `quasi-equilibrium state' to the polymer struc- ture with Dffv=0. It is clear that an equilibrium state implies that all macromolecules are packed in the regions of local ordering. It has been shown 70 that the condition Dffv=0 cannot be attained for the epoxy polymers in question even for the maximum possible Ven value.Yet another important feature of the quasi-equilibrium state is temperature dependence of parameters, in particular, ffv [see Eqn (65)]. When Ven=0, the straight line Ven(Dffv) is extrapolated to Dffv ^ 0.077, which also has a definite physical meaning. For f 0fv=0.035 (see Fig. 25 a) and Dffv ^ 0.077, the ffv value is equal to 0.112, which is close to the fluctuation free volume at Tg.118, 119 Thus, the destruction of clusters can be identified with glass transition of cross-linked polymers. Thus, the above results point to the fractality of the fluctua- tion free volume in cross-linked polymers. In this connection, one important fact should be noted, which has not recention before.In accordance with Eqn (58), Vh decreases with an increase in ffv. For pores with sizes of the order of several nanometers, it has been shown 134, 135 that (71) ¢§ dV dr !r27D0, where V is the total pore volume, r is the average pore radius, and D0 is the fractal dimension of the structure of a porous material.Structure and properties of polymers in terms of the fractal approach ffv 0.06 0.04 0.23 0.21 Figure 26. Relative fluctuation free volume ffv vs. radius of the free volume microcavities rh for EP-1 (1) and EP-2 (2). According to different estimates, the linear sizes of micro- cavities of free volume rh vary from 0.2 to 1.5 nm.136 ± 142 If we assume that Vh=ffv and r=rh, for Eqn (71) to have a physical meaning, it is evidently required that the slope of the ffv(rh) plot be negative.The calculated D0 values for EP-1 and EP-2 vary from 4.78 to 5.31, which is consistent with the above estimates of Dffv and Df. Figure 26 presents the dependence of ffv on rh, which is linear and has a negative slope. Figure 27 illustrates the relation- ship between Df and D0. It can be seen that D0 values are regularly greater thanDf but both values vary according to the same pattern and the deviations do not exceed 25%. This also attests to the fractality of the free volume the dimension of which reflects the extent of `pumping' of energy into the polymer and does not coincide with the corresponding dimension of the polymer struc- ture.D0 54 �1 �2 3 4 5 Figure 27.Relationship between the fractal dimensions D0 and Df calcu- lated from Eqns (71) and (39), respectively, for EP-1 (1) and EP-2 (2). Let us consider the influence of the `pumping' of energy (mechanical or thermal) on the formation of free volume in epoxy polymers. Within the framework of the Frenkel' kinetic theory,115 the radius of a microcavity of free volume rh depends on the surface tension s r h 2à eh 4ps . Equation (72), which is an analogue of relation (63), permits calculation of s provided that rh and eh are known. The depend- ence of the s values thus found on Df for EP-1 and EP-2 is plotted in Fig. 28. An increase in Df (enhancement of energy pumping from the outside) results in a decrease in s, which facilitates the formation of a microcavity of the fluctuation free volume.Note that for Df=7.7, the s value becomes equal to zero. This is unlikely from the physical viewpoint; nevertheless, it is evident that s sharply diminishes on moving towards Df ^ 7.7. This Df value is matched by m ^ 0.425 [according to Eqn (39)], which corresponds to the mechanical 74 and thermal 143 glass transition process. It has been shown experimentally that Vh sharply increases (and, hence, s decreases) 136 and the yield point increases144 at Tg. �1 �2rh /nm Df (72) 535 s /kJm72 0.3 �1 �2 0.2 0.1 2 Df 4 Figure 28. Surface tension vs. fractal dimension of the regions of local- isation of excess energy for EP-1 (1) and EP-2 (2).The variation of ffv as a function of Df is presented in Fig. 29. The straight line was drawn with the assumption that for m=0 (which corresponds to close packing of an amorphous poly- mer 129), Df=2 and ffv=0, whereas for the maximum possible ffv value at Tg [ f t fv^ 0.159 (see Ref. 124)], m ^ 0.44 and Dtf ^9.3. The ffv values found using relation (55) for EP-1 and EP-2 correspond to the proposed model. Thus, `pumping' of energy into a polymer increases the dimensions of the regions in which it is localised and increases the fluctuation free volume. ffv f tfv �1 �2 0.10 0.05 4 8Dt Df f Figure 29. Relationship between the relative fluctuation free volume ffv and the dimension of the regions of localisation of excess energy Df.The points correspond to the calculation of ffv from Eqn (55) for EP-1 (1) and EP-2 (2). The explanations are in the text.153 Thus, the fluctuation free volume in vitreous polymers has a fractal structure; therefore, the microcavities that constitute the free volume can be modelled by a Dffv-dimensional sphere. The sizes of microcavities are controlled by the volume in which the energy of thermal fluctuations needed for their formation is accumulated. The absolute magnitudes of ffv can characterise the thermodynamic nonequilibrium of the polymer structure. For quasi-equilibrium structures, it is assumed to be equal to ffv in the known WLF equation. The dimension of the free volume regions (which coincides with the corresponding dimension of the regions of localisation of energy pumped from the outside) reflects the extent of energetic excitation of the polymer structure.5. Fractal characteristics of polymers in time-dependent processes Polymers obey the principle of temperature ± time superposi- tion,145, 146 according to which structural (including fractal) characteristics of polymers are functions of the time scale of testing. In this connection, we shall consider the influence of the536 (73) jcl (t)=j0cl exp ¡¦ t , t0 time factor on the fractal characteristics in processes typical of polymers such as thermal ageing or relaxation. The dependences of the dielectric loss tangent (tan d) on the Hausdorff dimension for several copolymers have different slopes at measurement frequencies of 1 and 10 kHz.This hampers correct prediction of tan d. This difference can be easily explained in terms of the cluster model. The jcl value is a parameter of the order of the polymer structure;60 due to the thermodynamic nonequili- brium of the structure, it is also a function of the time scale t. In the general case, the time-dependent order parameter jcl(t) is deter- mined as follows:147 where j0cl is the jcl value at very large t and t0 is the relaxation time under normal conditions. If the time scale of the experiment is expressed in terms of p/o (o is the frequency of measurements) and the relaxation time is assumed to be t ^ 10 ms, the jcl value can be estimated as a function of frequency and, hence, different D values for frequen- cies of 1 and 10 kHz can be obtained.An increase in D (decrease in t) results in higher jcl [according to Eqn (73)] and in lower D.14 Therefore, the dependence of tan d on D is described by one straight line for both frequencies mentioned above.26 Thus clusters can be generally defined as regions in which relaxation processes are impossible. Physical ageing of amorphous vitreous polymers consists in the variation of the structure and properties with time, which reflects the thermodynamically nonequilibrium nature of these polymers.114 At relatively low temperatures (about room temper- ature), this process is fairly slow; it takes several years for substantial changes in the properties to occur.94, 148 Therefore, forecasting of these phenomena should be performed with allow- ance for both spatial and temporal disorder of systems.The spatial non-uniformity of the structure of amorphous vitreous polymers accounts for the rather broad range of the rates of relaxation processes. Spatial disorder results in temporal disorder. The variation of the properties and structure of polymers during ageing can be described quantitatively within the framework of fractal analysis. Study of the reaction dynamics in disordered systems has shown that for most reactions at long times, subordination expressed by the following general relation is obeyed:149 (74) F!t ag, where F is an arbitrary function dependent on time t and a and g are coefficients taking into account the spatial and temporal disorder.As applied to physical ageing, the variation of structure with time can be described, on the basis of general relation (74), in the following way:150 (75) clt ag, Vcl=CV0 where Vcl and V0cl are the densities of the cluster network of entanglements in the aged and initial polymers, respectively; C is a proportionality coefficient. The index a can be defined in terms of fractal analysis as the difference df72, where df is the fractal dimension of the structure of the initial epoxy polymer, with allowance for the following considerations: the 2<df43 range characterises the degree of disorder of the polymer structure;151 most information on this point is carried by the fractiothe greater the magnitude of df, the lower the local order and, hence, the higher the spatial disorder of the system.152 The quasi-equilibrium state of polymers is characterised by df ^ 2.5.This value corresponds to a fully relaxed polymer with a narrow size distribution of free volume cavities 153 and, hence, to the least temporal disorder, characterised by a spectrum of relaxation times. Therefore, the following approximation has been used:150 V U Novikov, G V Kozlov (76) g=df72.5. Thus, Eqn (75) can be finally written in the form (77) Vcl=V0clCt(df72)(df72.5), where the coefficient C determined empirically is equal to *0.14 and the time of ageing is expressed in seconds.Figure 30 shows the dependences of jcl on Kst for the initial (EP-2) and aged (EP-3) epoxy polymers. In the case of EP-3, the jcl values determined experimentally and calculated using Eqn (77) are given. It can be seen that the experimental and calculated values are in good agreement. The maximum devia- tions for Kst equal to 0.50 and 1.50 do not exceed *25%. It is assumed 150 that the main reason for the inaccuracy is the high power dependence of Vcl on df in Eqn (77). jcl 0.8 2 3 0.6 D1 D2 D3 1 0.4 0.2 1.0 1.5 Kst 0.5 Figure 30. Relative portion of clusters jcl vs. the curing agent : oligomer ratio Kst for EP-2 (1) and EP-3 (2, 3); (1, 2) experimental data, (3) calculation using Eqn (77).150 Yet another important aspect of physical ageing is also associated with the dependence of jcl on Kst (see Fig.30). The ageing rate expressed as the difference between the jcl values for EP-2 and EP-3 varies substantially for different Kst (and, hence, for different chemical cross-linking densities ns). The minimum ageing rate is observed for a system with Kst=1.0; 152 deviations from this value towards both greater and lower values result in an increase in the ageing rate.101 This is due to an increase in both a and g [see Eqn (77)] or, in other words, to an increase in the fractal dimension of the structure df. Parameters which vary during physical ageing include not only supermolecular structure characteristics (df and Df) but also the statistical chain flexibility index C?.Using Eqns (39) and (41), it can be written that (78) Li=C?=Df=2 1 ¡¦ m 1 ¡¦ 2m . The physical ageing results ultimately in the formation of similar structures for all the epoxy polymers considered, irrespec- tive of the density of chemical cross-linking points (ns varies by approximately an order of magnitude).154 Naturally, this struc- ture equalisation also determines substantial convegence of the properties of EP-2 and EP-3.94 From the practical viewpoint, it is important to predict the properties of polymers during physical ageing. A procedure suitable for this purpose has been reported.150 This procedure is based on Eqn (77). Knowing the Vcl and C? values, one can estimate Df and calculate E.155 Then the yield point sp 142, 148 and some characteristics of polymers64, 156 can be determined.In recent years, considerable attention has been paid to investigation of the relaxation processes in complex condensed systems. An example of this type of system is amorphous- crystalline polyethylene, the structure of which under normal conditions consists of crystalline regions, regions of local ordering and a devitrified loosely packed matrix.157, 158 The interest in theseStructure and properties of polymers in terms of the fractal approach studies is caused by the experimental fact that the correlation functions for many different systems vary in accordance with the same exponential dependence (79) , 0<b<1. t j(t)=exp ¡¦ t b The parameters b and t depend both on the material and on the environmental conditions, for example, temperature.The law described by Eqn (79) was first proposed by Kohl- rausch and has later been used by Williams and Watts to describe the dielectric relaxation in polymers (M Schlesinger, J Klafter, see Ref. 149, p. 553). The main difficulty in the case of polymers is to identify the parameters of Eqn (79) in terms of characteristics describing the polymer structure. This identification has been performed within the framework of fractal analysis.39 In the impact testing of polymers, the elastic modulus decreases with an increase in the time scale of testing (in the case of brittle fracture, this is time to fracture t0) and can be described by the empirical relation 159, 160 E=E0(t 0)7m, (80) where E0 is the `unity' modulus, i.e.the E value for t0=1 on the time scale chosen, and m is an empirical index characterising the degree of completeness of relaxation processes. Figure 31 shows the variation of E as a function of t 0 corresponding to Eqn (80) for high-density polyethylene samples with different lengths of a sharp notch (an increase in the length decreases t 0) at a testing temperature of 293 K. The slope of the straight line can be used to estimate the index m, while extrap- olation of the plot to t 0=1 gives the E0 value. It should be noted that at certain t 0 values (for example, t), the variation of lnE vs. ln(1/t 0) has a breakDat t 0<t the elastic modulus increases faster than at t 0>t, which reflects an increase in m.This finding is related to the extent of completeness of relaxation processes: at t 0>t this extent is high and, correspondingly, the increase in E is insignificant. ln E 6.9 6.5 6.5 6.16.0 ln (1/t 0) t Figure 31. Elastic modulus E vs. time to fracture t 0 [see Eqn (80)] for high- density polyethylene samples with a sharp notch; t=t0 is relaxation time.153 The difficulty in describing the variation of E according to Eqn (80) is due to the presence of two empirical constants (E0 and m), which, moreover, can change discretely. Therefore, an alter- native approach based on the use of the Kohlrausch equation (79) has been chosen.153 To describe E, this equation should be written in the form (81) E=E 00 exp 0 b , 0<b<1, t 0 ¡¦ t where E00 is a constant.Let us consider the physical meaning of the parameters appearing in Eqn (81). It is evident that the t value can be taken 537 as t0 (see Fig. 31). The constant E 00 determines the maximum elastic modulus Emax which can be attained for a given polymer without relaxation. The range of variation of this parameter for very high testing frequencies (several megahertz) was found 161 to be 1.1 ¡À 2.6 GPa for high- and low-density polyethylene. Finally, the index b, characterising the width of the relaxation spectrum (spatial disorder of the system), can be associated with the fractional part of df, i.e. it is taken to be equal to df72.Note that both b and df72 vary over the same limits. Thus, the final form of the Kohlrausch equation for determining the elastic modulus of polymers under high-speed loading (brittle fracture) can be written as follows 153 t 0 d (82) E=Emax exp f¡¦2 ¡¦ , 0<(df72)<1. t Figure 32 shows the dependences of the E values, both experimental and calculated from Eqn (82), on the sharp notch length l for high-density polyethylene samples at different temper- atures. Good agreement between the theoretical and experimental results is obvious. 1 E /GPa 1.0 2 D5 D6 D7 D8 0.6 34 0.2 l /mm 1.0 0.5 Figure 32. Experimental (1 ¡À 4) and calculated [Eqn (82)] (5 ¡À 8) elastic moduli E vs. length of the sharp notch l for high-density polyethylene at testing temperatures of 293 (1, 5), 313 (2, 6), 333 (3, 7) and 353K (4, 8).153 Thus, methods of fractal analysis in combination with the cluster model of the structure of amorphous polymers provide a quantitative description of time-dependent processes.The fact that the fractal dimension of the structure df takes into account both the spatial and temporal disorder accounts for the simplicity of the resulting equations.150 III. Modelling of the structure and properties of polymers 1. Modelling in terms of the percolation theory Percolation models are widely used to describe critical phenom- ena 162 including those in polymers.162 ¡À 166 Percolation clusters are homogeneous fractals when x=xc (x is the current coordinate, xc is the coordinate of the percolation transition).For example, the structure of vitreous polymers is a fractal when T = Tg or, with allowance for the foregoing, when T<Tg. It should be borne in mind that the fractal properties of the polymer structure are due to the presence of the cluster structure or, more precisely, of `frozen' ordering. However, as has already been mentioned, the magnitude of the fractal dimension of the structure df for amorphous polymers is debated, the overall range being 24df43.125 Thus on the basis of theoretical statements of Alexander and Orbach,43 it has been concluded 167 that for an ideal disordered linear polymer, df is equal to 2, while for real amorphous polymers, this value is 2.0 ¡À 2.2.Let us make several rather simple estimates of df for epoxy polymers EP-1 and EP-2. For a percolation system, the following relation holds:162538 (83) df=d7bn , where d is the dimension of the Euclidean space in which the fractal is inserted and b and n are critical indices of a percolation system related to each other as (84) dn=2b+gc, where gc is also a critical index of the percolation system. The parameters calculated from Eqn (83) are listed in Table 2. Table 2. Parameters of percolation systems for epoxy polymers. Calculation using Eqn (83) Experiment Parameter EP-2 EP-1 0.88 0.455 2.545 nb / n df 1.15 0.504 2.50 0.67 0.537 2.46 The evaluation of the index n for EP-1 and EP-2 for d=3 using Eqn (84) and the b and gc values determined previously gives 0.67 and 1.15, respectively, which is consistent with the theoretical value n =0.88 (see Table 2).The df values for epoxy polymers estimated using Eqn (23) fall in the range from 2.56 to 2.73, which is in good agreement with the estimates made in this review but is substantially greater than has been assumed previously.43, 167 The following ratio for percolation clusters has been reported: (85) dsuper= df , ds where dsuper>1 is so-called superlocalised index. Using the dsuper and ds values found experimentally for epoxy polymers based on bisphenol A,167, 168 we calculated df, which proved to be 2.55. This value is close to the above estimates. Note that the application of Eqn (85) to the calculation of dsuper of epoxy polymers became possible owing to the representation of their structure as a percolation system.The df value can also be estimated without experimental ds but using only the index dsuper. For example, the random walk dimension dw can be represented, with allowance for Eqn (85), in the following form: (86) dw=2dsuper. The df values for the epoxy polymer at dsuper=1.85 167 amounted to 2.47 and 2.70 in accordance with the Alexander ± Orbach and Aharoni ± Stauffer hypotheses,48 respectively. These values are close to the estimates made using Eqn (23).167 The fractal dimension is determined by the disorder which is generated by deterministic chaos. This statement can be expressed in the analytical form 169 (87) df=Sl , (88) where S is the entropy of the system, l is the Lyapunov index.The entropy change DS in a chaotic process can be determined using the following simple formula:170, 171 DS^3k ffv ln ffv , where ffv is determined from Eqn (55) and k is the Boltzmann constant. Figure 33 shows the variation of df [calculated in terms of Eqn (23)] as a function of DS [calculated using Eqn (88)] for the epoxy polymers under consideration. This plot has some interest- ing features. First, extrapolation of the df(DS) straight line to DS=0 yields the value df=2. Relation (88) indicates that the condition DS=0 is matched by ffv=0. This implies close packing V U Novikov, G V Kozlov df 2.6 2.4 �1 �2 0.5 1.0 10721DS /J mol71K71 Figure 33.Fractal dimension df of the structure vs. entropy for EP-1 (1) and EP-2 (2).170 of the structure of epoxy polymers. In other words, the value df=2 is attained for an amorphous polymer in the case of close packing rather than in the case of ideal disorder, as has been suggested in a previous publication.167 Second, df=3 is attained at a DS value corresponding to ffv ^ 0.157. This is known to be the greatest theoretical value relative to the free volume at Tg.124 This means that df=3 corresponds to the devitrified state of the polymer, i.e. to destruction of the local `frozen' order. This fact confirms the relationship between local order and fractality of amorphous polymers. Third, in accordance with relation (87), the linear dependence of df on DS means that l=const. Thus, the chaotic component of the dynamics of structure formation is the same for the epoxy polymers considered.172 Thus, the structure formed in epoxy polymers at the glass transition temperatutre Tg is a percolation cluster, which is described adequately in terms of the cluster model.57, 173 There- fore, it can be assumed that glass transition of a polymer is a phase transition and jcl is an order parameter.In addition, this fact can serve as evidence confirming fractality of the structure of network polymers (for T<Tg) in the range of length scales of *0.3 ± 5.0 nm. The fractal dimension of the structure of epoxy polymers is much greater than it has been believed previously (see, for example, Ref.60); it is determined by the disorder generated by deterministic chaos. The loss of fractality by the epoxy polymer structure, i.e. the situation when df=d is attained at the glass transition temperature. It is worth noting that the model of percolation cluster proposed by Kozlov et al.166, 170 is similar in essence to the concept of critical thermal transition.19 According to this concept, the portion of system elements belonging to the greatest cluster is proportional to the order parameter, which varies near the critical temperature T* as eb, where e=(T7T*)/T *. 2. The model of diffusion-limited aggregation The general description of the models of irreversible aggregation has been reported in several publications.12, 162, 174 Here we shall consider particular aspects of using the model of diffusion-limited aggregation (DLA) for describing the structure of amorphous polymers.Note that the computer simulation procedures, widely used for this purpose, should be made more specific. If the cluster model of the structure of amorphous polymers 173 ± 175 can be described as the Witten ± Sander (WS) cluster, this means that the model and the WS cluster belong to the same class of universality. There exist numerous reasons for representing the structure of an amorphous polymer as WS clusters and for assigning them to one class of universality. These reasons have been considered in detail;60 here we mention only three most important ones.176 The first reason is that the aggregation mechanism belongs to one class of universality; for WS clusters, this is attachment of separate particles to the growing clusters (aggregation of the particle ±Structure and properties of polymers in terms of the fractal approach cluster type).In terms of the cluster model, this mechanism is attachment of a statistical segment to a region of local order; this event is equivalent to the `collapse' of a microcavity of the fluctuation free volume.57, 121 The second reason follows from the first one: due to the identical aggregation mechanisms, the structures of amorphous polymers and the WS clusters have the same scaling indices, namely, the dimensions df (see Refs 170 and 171) and D (see Ref. 172), respectively.The third reason is as follows. It is known 44 that during the synthesis of polymers, the class of universality changes in the gelation point, namely, the cluster ¡À cluster mechanism is replaced by the particle ¡À cluster mechanism; the latter affords WS clusters. The model representation (in terms of the DLA model) made it possible to describe the structures of EP-1 and EP-2; this was done using the same scaling index, namely, the dimension df.175 It should be mentioned that the word `cluster' is interpreted in different ways in the cluster model 177 and in the WS cluster model. In terms of the latter, the term `cluster' denotes both the region of local ordering and chains protruding from it, while in the former case, only statistical segments incorporated in the region of local ordering are meant.It is evident that the structure of a polymer sample cannot be regarded as a single WS cluster. Therefore, by analogy with Belousov et al.,177 who proposed a modified variant of the WS model, we represent the structure of epoxy polymers by a set of WS clusters, the size of each cluster ranging from lst to Rcl. Therefore, the model of multiple growth sites is the most plausible modification of the WS model. Accord- ing to the WS model, the growth of a WS cluster takes place on a large number of seeds, the cluster size Rcl being related to the concentration of free diffusing particles N in the following way: (89) N^RD¡¦d. cl Only those statistical segments that are located in the loosely packed matrix are able to join the region of local ordering.An increase in the degree of local ordering decreases the temperature; for Rcl=const, this means a decrease in the difference D¡À d or a decrease in D. The N value was taken to be equal to the product of the number of particles (statistical segments) per unit volume and the proportion of the loosely packed matrix. Figure 34 shows the plots for the variation of the fractal dimensions of the epoxy polymer structures 156 and of the WS cluster, calculated using relation (89), vs. the curing agent : oligomer ratio. One can notice good correspondence between df and D.175 Thus, a modified version of the particle ¡À cluster aggregation model178 allows the structures of network polymers to be described in terms of D.This stipulates the assignment of the structure of network polymers to the given class of universality and, hence, description of its properties by relations developed for this class of universality.175 Description of the local ordering of the structure of amor- phous polymers (in relation to polycarbonate and high-density polyethylene) in terms of the WS model has been reported.176 The following equation characterises the variation of the density of the df, D df, D 2.8 D3 D4 2.8 1 2.7 2 2.7 2.6 0.5 1.0 Kst Figure 34. Fractal dimensions of the structure df (1, 2) and of the WS clusters D (3, 4) vs. the curing agent : oligomer ratio Kst for EP-1 (1, 3) and EP-2 (2, 4).156 539 WS cluster rWS as a function of its radius RWS and the dimension D:179 RWS , (90) a rWS=r D¡¦d where r is the density of the material of the WS cluster in the state of close packing, a is the lower boundary of the fractal behaviour of the WS cluster, which can be identified with the length of an elementary unit in the polymer chain.A WS cluster obeys the relations D<d and rWS<r, which determine the condition a<RWS. Replacement of the signs in the first two inequalities by equality signs implies transition of the cluster to another class of universality, for example, transition to the Eden cluster.87 Meanwhile, since rWS =0 and r=0, a cannot be equal to zero. Thus, a compact region (D ^ d) with size a, identified as a region of local ordering for the structure of an amorphous polymer, always exists in the centre of the WS cluster.This statement is a necessary condition for the existence of the WS cluster.180 Two remarks on this point are pertinent. First, the cause for the appearance of the compact region at initial stages of formation of a WS cluster can be easily under- stood. Indeed, the fractal nature of the WS cluster is determined by the shielding effect of its `branches', which prevent the access of particles into the inner regions of the cluster.180, 181 However, in initial stages of the growth, these `branches' are poorly developed and the shielding effect is low. Second, the polymer structure, as any real (physical) fractal, possesses fractal properties only in a particular range of length scales.87 It has been shown experimen- tally 167, 182 that this range for polymers is from several A �º ngstrom to several tens of A �º ngstrom.This implies the presence of a density gradient in the polymer in this range of length scales, which, in turn, means alternation of blobs and rarefied sections in the material.183 The cluster model 173, 177 satisfies this condition, whereas, for example, the `felt' model of the polymer structure proposed by Flory 113 cannot account for the experimentally observed fractal properties.167, 182, 183 Thus, interpretation of the structure of an amorphous poly- mer as a WS cluster (more precisely, as a set of these clusters) assumes necessarily the existence of regions of local order.This has been confirmed 176 by comparing the a values calculated from Eqn (90) and the size of the region of local order rcl (Fig. 35). The rcl value can be found from the following equation (under the assumption of close packing):184 , (91) rcl= nclS pZ 1=2 where ncl is the number of statistical segments in the cluster, Z is the density of packing of the element, equal to 0.74.184 Figure 36 shows the variations of the size of the regions of local order rcl in the cluster model 173 and the compact regions a in the WS model vs. testing temperature for polycarbonate and high- density polyethylene. In studies by Kozlov et al.,176, 185 the density of the loosely packed polymer matrix, which coincides with the density of the polymer above the glass transition (melting) temperature, was taken as rWS and the density of the crystalline dm 2 rcl Figure 35. Cross-section of the region of local order incorporating seven statistical segments (dm is the diameter of the polymer macromolecule).175540 a rcl, a /nm 2 2.0 1.5 1.0 0.5 333 293 373 rcl, a /nm b 1.0 0.5 333 293 Figure 36.Size of the regions of local ordering rcl (curve) in the cluster model and size of the compact regions a (dots) in the WS model vs. temperature for polycarbonate (a) and high-density polyethylene (b). regions of polycarbonate and polyethylene was used as r. In addition, it was assumed in calculations that Rcl=RWS, D=df. The absolute magnitudes and the patterns of temperature variation of the parameters rcl and a are in good agreement. Some scatter in the a values relative to rcl is due to the inaccuracy in the determination of df using Eqn (23), caused by the power depend- ence of a on D, which markedly affects the accuracy of compar- ison.Thus, it can be inferred that experimental results also indicate the obligatory existence of regions of local order in the structure of an amorphous polymer in terms of the DLA model. The structure of amorphous polymers can also be studied using the method of autocorrelation functions 176 C(r)=hp(r 0)7p(r 0+r)i, where p(r 0) and p(r0+r) are probabilities that particles compos- ing a cluster are located at points r 0 and r 0+r (the probability is equal to unity when the point does contain a particle and to zero when no particle is present).The autocorrelation function for distances r greater than several lattice spacings can be represented by the scaling relation 186 C(r)!r7a , where a=d7D. In the case of a linear autocorrelation function, having determined a, one can estimate the fractal dimension D of the object. The autocorrelation function for the structure of an amor- phous polymer (in particular, polycarbonate) is shown schemati- cally in Fig. 37; the density variation is presented as a function of distance, the reference point (r=0) being placed at the centre of a local order region (see Fig. 35). Over an interval from 0 to rcl the r value remains constant and equal to the density of the region of local order, which has been assumed, as a first approximation, to be equal to the rcr value for crystalline polycarbonate.187 In the range from rcl to Rcl, the density is supposed to decrease linearly to reach rmin, which is estimated as follows.Litt et al.187 have reported the averaged density of amorphous polycarbonate ra, 1T /K T /K (92) (93) (94) (95) (96) V U Novikov, G V Kozlov r rcr ra rmin 0 r rcl Rcl Figure 37. Autocorrelation function r(r) for polycarbonate. The explan- ations are in the text. (97) which corresponds to the centre of the sloping section in Fig. 37. From simple geometricsiderations, we obtain rmin=ra7(rcr7ra). ¡a (98) , (rcr7rmin)7a ^ 2 ¡ rcl Now one can estimate the a value from the relation Rcl and then calculate the df value for the polymer structure using Eqn (96) because modelling of this structure by a WS cluster assumes that equality (93) is valid.178 The temperature dependences of the fractal dimension of the polycarbonate structure obtained experimentally and calculated in terms of the WS model taking account of relations (95) and (98) are presented in Fig.38. It can be seen that the results correspond rather well to each other. However, the agreement can be improved by using so-called `true' yield point. Kozlov et al.166 determined df for polycarbonate at 293K using five different procedures; the average value was found to be df ^ 2.51. This result is in good agreement with the value df ^ 2.56 determined for 293K in terms of the WS model.df 123 2.65 2.60 T /K 373 333 293 Figure 38. Fractal dimensions df of the structures of polycarbonate (1, 2) and WS cluster (3) vs. temperature. Determined with allowance for real (1) and `true' (2) yield point. Recalling that the quasi-equilibrium state of a polymer structure is characterised, in the general case, by df=2.5, the same fractal dimension is typical of a WS cluster in a three- dimensional space when N ??.186 Therefore, below we consider the correspondence between the conditions of formation of a quasi-equilibrium state in the cluster model of an amorphous polymer structure and in the WS model. The modification of the WS model discussed above (growth on a large number of `seeds') 177 uses the term `diffusion distance' x, which depends on the local environment of each `seed'.The growth of a WS clusterStructure and properties of polymers in terms of the fractal approach continues until the condition x ^ Rcl is attained. The x and Rcl values are related to the concentration of free particles (cfr) in the following way:178 (99) x^c¢§1 fr Rcl D¢§da2. (100) Taking into account the condition for termination of the cluster growth, it can be written that cfr^RD¢§d. cl This relation allows one to determine the concentration of free particles at the moment when theWScluster stops growing having reached the size Rcl (subsequently, this concentration is designated by cWS) or when the quasi-equilibrium state in terms of the WS model has been attained because in this case, too, the diffusion growth is restricted by interaction of the neighbouring WS clusters.The concentration of particles in the cluster can be determined in terms of the cluster model.173 Using relations (45) and (53), df can be related to the fraction of clusters jcl. Assuming that df=2.5, one can estimate the jcl value for the quasi-equilibrium state of polymers.15 The Rcl value in the model 178 is limited by the number of `seeds', which is, in turn, equal to the number of WS clusters, nWS. According to the cluster model, the number of statistical segments incorporated in the regions of local order per unit volume of the polymer is assumed to be equal to the density of cluster network Vcl.The functionality F of such a region is the number of chains protruding from it. Since this region (cluster) is an analogue of a crystallite with extended chains, the number of segments in one cluster is equal to F/2. The number of regions of local order Ncl, equal to nWS, in unit volume of the polymer can be found from the equation 113 (101) Ncl=2Vcl . F In addition to the cluster network of entanglements, polymers are known to contain a network of traditional `loops'; unlike the cluster network, the latter is retained above Tg.146 The numbers of entanglements in this network, determined above Tg, have been reported (see, for example, Refs 62, 76, 188). The density of the network of these `loops' (Ven) can be found from the equation (102) Ven=rNA , Men where Men is the molecular mass of the chain between entangle- ments.10726Ncl /m73 2 1 7 8 0.3 6 5 4 3 0.10 10726Ven /m73 0.2 Figure 39. Relationship between the densities of clusters Ncl and the network of macromolecular `loops' Ven for various polymers; (1) poly(ethylene terephthalate), (2) polyamide-6, (3) polyethylene, (4) polypropylene, (5) polystyrene, (6) poly(methyl methacrylate), (7) poly(vinyl chloride), (8) polycarbonate. 541 Figure 39 illustrates the relationship between the Ncl and Ven values for eight polymers. It can be seen that these parameters correspond to each other both in magnitude and in the pattern of variation. The rather large scatter is due to the discrepancies between theMen values taken from different sources for the same polymer [for instance, for polyethylene, Men=737 g mol71 (see Ref.62) or 1900 g mol71 (see Ref. 188)]. Nevertheless, under the assumption that Ncl ^Ven, the Ven value can be identified as the density of `seeds' and the Rcl value can be found using Eqn (30). The use of dimensional Rcl values in relation (100) results in the cWS value being dependent on the dimension of Rcl. Therefore, the lower limit (b) at which the fractal properties are manifested (b ^ 0.5 nm173) was chosen as the scale, and the dimensionless parameter Rcl/b was used in Eqn (100). When a different b value is employed, cWS somewhat changes but the trend of its variation is retained.It has been shown 189 that the minimum value dfmin=2.5 is typical only of polymers with C?=3. The dfmin value can be determined by modification of the equation 190 (103) 3O3 ¢§f min df minU a 43 a C? . d For polymers with C?>3, the calculation gives incorrect jcl values (greater than unity). Therefore, the dfmin values found for polymers using Eqn (103) are greater than 2.5. Thus, the chain rigidity has a substantial influence on the formation of the polymer structure. Only segments incorporated in the loosely packed matrix have the opportunity to join the regions of local ordering. Thus, in terms of the WS model, it is these segments that should be considered as free particles. Therefore, csf=17jcl=jlp, where jlp is the volume fraction of the loosely packed matrix.Figure 40 illustrates the good correspondence between the cWS and csf values for twelve polymers, which attests that the inter- pretations of the quasi-equilibrium state of the polymer structure in the cluster model 173 and in the WS model 178 are equivalent. The cWS values are somewhat greater than csf because the scale b was chosen arbitrarily. Thus, the concepts of quasi-equilibrium state involved in the DLA and cluster models of the structure of amorphous polymers are similar in physical essence, the quantitative estimations in terms of these two models providing consistent results. The csf 11 6 9 0.6 7 10 5 12 1 2 8 4 3 0.4 0.4 0.6 cWS Figure 40.Relationship between the concentrations of free particles cWS and statistical segments in the loosely packed matrix csf for the quasi- equilibrium state; (1) polyethylene, (2) poly(methyl methacrylate), (3) polystyrene, (4) poly- tetrafluoroethylene, (5) polypropylene, (6) polycarbonate, (7) poly(ethy- lene terephthalate), (8) poly(vinyl acetate), (9) poly(ethylene oxide), (10) polycaprolactam, (11) polyestersulfone, (12) poly(vinyl chloride).542 macromolecular `loops', which restrict the mobility of polymer chains act as the `seeds' in the WS model.178 3. Order and fractality in polymers The temperature dependences of Vcl for different polymers are similar. Raising the temperature results in a decrease in Vcl, the rate of thermofluctuational decomposition of clusters sharply increasing as T approaches Tg (or Tm).This general regularity is illustrated by the plots for Vcl vs. testing temperature for poly- carbonate, poly(methyl methacrylate) and high-density polyethy- lene (Fig. 41). Note that similar temperature dependences are obeyed by the mechanical properties of polymers (elastic mod- ulus, yield point, etc.).191 This similarity implies the possibility of superposition of the Vcl(T) curves for different polymers, which is due to the common pattern of variation of the degree of local ordering vs. temperature. Below we construct this superposition and consider some its consequences in terms of the cluster model resorting to percolation theory and fractal analysis.60 10727Vcl /m73 3 D1 D2 D3 10 100 50 DT /K Figure 41.Density of the cluster network of entanglements Vcl vs. reduced testing temperature DT=Tg7T for polycarbonate (1), poly(methyl methacrylate) (2) and DT=Tm7T for high-density polyethylene (3).60 (104) The dependences of Vcl on the reduced temperature DT=Tg7T for some polymers follow similar patterns (see Ref. 41); therefore, a scaling relation of the following type can be applied: Vcl!DT x, where x is a generalised index. However, the degree of local ordering is reflected more precisely by the relative portion of clusters jcl, determined from Eqn (53). An obvious advantage of Eqn (53) is the fact that it includes the main molecular characteristics of polymers. Figure 42 shows the lnjcl(lnDT) plots for the three polymers mentioned above and for the epoxy polymer EP-1, which are approximated by a common straight line.It can be easily seen that lnjcl 71 D1 D2 D3 D4 72 2 4 3 ln DT Figure 42. Relative portion of the clusters jcl vs. reduced testing temper- ature DT for polycarbonate (1), poly(methyl methacrylate) (2), high- density polyethylene (3) and EP-1 (4).60 V U Novikov, G V Kozlov these data comply well with the known relation of percolation models in the case of critical transition 162 (105) P?!(Tg7T) b. In this interpretation, the jcl value corresponds to the `power' of an infinite cluster, i.e. the probability P? that a unit belongs to the infinite cluster. Thus, at Tg (or Tm), the cluster network of entanglements appears (or vanishes); simultaneously, the struc- ture of a vitreous polymer sample as a system is formed (or destroyed).Several other important points related to the possibi- lity of describing a polymer structure in terms of Eqn (105) deserve attention. In the cluster model, the statistical segment lst is taken as the `section of rigidity' of a chain. The lst value is several times smaller than the Kuhn segment length A, which character- ises the rigidity of a freely jointed chain.91 When the A value is chosen as the `section of rigidity', the jcl values prove to be greater than unity in most cases, which is devoid of physical meaning. The relationship between A and lst can be written in the following form: (106) lst=Acos yv 2 , where yv is the bond angle.Thus, the shorter length of the chain section of rigidity lst in the vitreous state is due to the conformational rearrangements pecu- liar to this state. In the case of amorphous-crystalline high-density polyethy- lene, the reduced j0cl value was used; this parameter characterises jcl with respect to the whole polymer bulk rather than to the amorphous phase alone (107) j0cl= jcl 1 ¡¦ k , where k is the degree of crystallinity. The relation modified for the case of amorphous-crystalline 1=2 jcl , (108) df=d75.98610710 C? S polymers is represented by Eqn (53). Using Eqns (53) and (23), one can elucidate the relationship between df and jcl where S is expressed in A2.As has been shown above, Eqn (45) provides the minimum values for the fractal dimension of structure (d tf ) possible for a given polymer, which are in good agreement with the d 0f values (see Table 1). Hence, by substituting d tf or d 0f into Eqn (108), one can estimate the limiting degree of local ordering (j0cl) possible for a given polymer as a function of the most important molecular characteristics of the polymer, C? and S. When the temperature decreases below T0 (at which the j 0cl value is attained), the degree of local ordering does not change; therefore, T0 can be regarded as an analogue of the temperature T?at which the polymer reaches a constant free volume.106, 173, 191, 192 Meanwhile, T0 can be found from Eqn (104) provided that jcl=j 0cl.The T0 and T? values thus obtained, together with the temperatures of transition to a state with a constant value of density fluctuations T *,106, 193 for eight polymers are listed in Table 3. It can be seen that T0 and T? are in good agreement for all polymers except polycarbonate, for which the calculation gave DT=670 K, which has no physical meaning. For real polymers, the tendency towards a thermody- namically more equilibrium state should be counterbalanced at a certain point by the force of chain `tightening.' Therefore, the value df=2.5 should be used instead of d tf . In addition, the value jlp=1 (i.e. jcl=0) is attained at df=2.92 rather than at df=3, as could be suggested in view of Eqn (108). With allowance for these corrections, calculation in terms of Eqn (105) affords T0 ^318K for polycarbonate, which is consistent with the value T?=323K (see Table 3).The correspondence between T0 and T * is poorer than that between T0 and T? but the patterns of their variation for polymers fully coincide.Structure and properties of polymers in terms of the fractal approach Table 3. Temperatures of the transitions to the `frozen' free volume T?, quasi-equilibrium state T0 and a constant density fluctuation T *. T*/ K Polymer T0/ K T?/ K 220 ¡¾ 250 200 140 ¡¾ 150 210 270 250 ¡¾ 280 220 200 ¡¾ 220 300 304 243 199 320 269 333 318 280 277 227 227 324 290 270 323 Poly(ethylene terephthalate) Polyamide-6 Polyethylene Polypropylene Polystyrene Poly(methyl methacrylate) Poly(vinyl chloride) Polycarbonate The following empirical relation between the change in the specific Gibbs function of the formation of the supermolecular structure DG during the self-assembly of the cluster structure and jcl has been derived 194 (109) DG!jcl .(110) Substitution of this relation into Eqn (108) gave the expres- sionDG!C?S(37df)2. The DG value for the supercooled liquid ¡¾ solid nonequili- brium phase transition has been reported.195 It follows from relation (110) that DG=0 when df=3, i.e. when the fractal properties are lost. In other words, the fact that fractal structures are formed only in nonequilibrium processes has been confirmed once again.12 4.The possibility of numerical modelling of polymer properties Little is known about a polymer synthesised from monomers or prepared by curing an oligomer; as a rule, the known data include the trademarks of monomers, oligomers, and curing agents and their ratios. Evidently, in this situation, for example, in the case of network polymers, the main initial parameter �¢ cross-linking density ns�¢can be either calculated 154 or determined experimen- tally.192 In the latter case, the molecular mass of the chain section between the cross-linking points Ms is calculated using the equation (111) 1 Ms a Fim 2W , where Fi is the functionality of the curing agent,mis the number of moles of the curing agent in the sample, and W is the sample weight.Comparison of the Tg(ns) plots for different epoxy polymers for which the ns values were determined by both methods mentioned above shows that the experimental values are some- what lower than the calculated ones. This discrepancy can be eliminated by introducing the correction factor C. The discrep- ancy is due to two reasons; one reason is the use of different batches of epoxy resins and curing agents and the other reason is that the calculation implies completeness of the curing reaction, i.e. that the curing agent has been entirely consumed, which does not occur in reality. Apart from ns, it is necessary to estimate the cross-section area of the macromolecule S and the length of a real bond in the backbone l0.The S value is either taken from reference data (if they do exist) or estimated by comparison with the S value of a linear polymer with a similar chemical structure. For example, the chemical structures of the epoxy resins and polycarbonate are similar because they both are based on bisphenol A. Therefore, the value S=0.31 nm2, determined for polycarbonates, was used for these epoxy polymers.76 Experimental estimates have shown 71 that this approximation is correct to within*5%. As regards the l0 value, it characterises a class of polymers rather than a 543 particular polymer, which makes its determination easier.ce epoxy resins are heterochain polymers, l0=0.125 nm.76 Using the above parameters, one can estimate the length of the section of a macromolecule between chemical cross-linking points and the distance between chemical cross-linking points.14 The subsequent stage is to solve a set of three equations with three variables, namely, the characteristic ratio C? and the fractal dimensions of the macromolecule section between chemical cross-linking points D and of the cluster structure df.By solving this set of equations, one can find these structural characteristics of the epoxy polymers. After that, the Poisson coefficient should be found from Eqn (23) and the cluster network densityVcl should be determined from the relation (112) m=0.572.98610710(Vcl l0)1/2. Finally, the relative portion of clusters is calculated as (113) jcl=Vcl V (114) where V is the polymer volume.For the loosely packed matrix,60 jlp=17jcl . Thus, we have obtained a complete set of characteristics of the molecular, topological, and supermolecular levels of the structure of cross-linked polymers, which permits one to model and predict their properties. The properties chosen include three character- istics for applications (elastic modulus E, yield point sp and glass transition temperature Tg), which are needed to develop new materials, and three characteristics which are regarded conven- tionally as theoretical (GruE neisen parameter g, thermal expansion coefficient at and yield strain e). fv It should be taken into account that one order parameter (for example, jcl) is inadequate to describe the structure and proper- ties of an amorphous polymer. It has been shown in relation to linear polymers 196 that the need for a second order parameter is due to the thermodynamic nonequilibrium of the loosely packed matrix.In other words, ffv=f 0fv. Therefore, a second order parameter was introduced for linear polymers, namely, (f 0fv7ffv)/ffv. In the case of cross-linked polymers, the constant contribution to ffv caused by the presence of chemical cross- linking points should be additionally taken into account as f (f fv=0.024, see Refs 70, 185). The use of percolation models 197 results in the relation (115) cl ¢§ f 0fv ¢§ f fv ¢§ ffv , ffv G! j A where G is the shear modulus, A ^ 1.5. Having determined f 0fv from relation (70) and ffv from relation (55), one can find the shear modulus and then, using Eqn (44), the elastic modulus.The relation for determining the yield point derived using relations (23) and (44) has the form (116) sp=EO3 ¢§ dfU . 3df The sp value can also be estimated using the equation 198, 199 (117) sp=31=2GbOlstVclU1=2 , 2p where b is the Burgers vector, determined from the empirical relation 129 . b= (118) C? 1=2 52:2 The glass transition temperature Tg can be found either using an empirical equation 71 or in terms of the fractal approach to glass transition. This is done either using a general model or a544 model which takes into account the stabilising influence of chemical cross-links via the factor ns1=2 (see Ref. 200). The GruE neisen parameter g can be determined by one of the following methods: calculation in terms of relation (69) using the parameter Df (equal to Dffv), determined previously from Eqn (39); calculation in terms of Eqn (68); or calculation using the relation (119) g=4OS1=2 a l9p2 0UOlstVclU1=2 ¢§ 0:25.The thermal expansion coefficient at can be found from the equation (120) g=3 a atTO3 a atTU . 6at The yield strain e is found from relation (67) provided that e=ec. Thus, the approach making use of the cluster model of the structure of amorphous polymers and fractal analysis provides the possibility of numerical modelling of the structures and properties of network polymers. An obvious advantage of this procedure is the fact that only ns and S are actually used as calculation parameters. It should be noted that the simplicity of choosing the input data is combined with the strict physical interpretation of these data and, hence, no empirical adjusting coefficients are required.IV. Experimental determination of the fractal dimension 1. A brief survey of the methods Various methods are used to determine the fractal dimen- sion,61, 201 which can be conventionally divided into two groups: fractographical and physical methods, based on the relationship between the fractal dimension and physical properties. The former group includes the methods of horizontal sections (cut islets),202 ¡¾ 207 vertical sections,13, 208 ¡¾ 211 profile Fourier analy- sis,203, 212 decentration, expansion, and cell counting,61, 213 sim- ilarity transformation,214, 215 etc.The fractographic methods used to gain fractal information on the irregularity of fractured surfaces make it possible to investigate profiles as horizontal or vertical sections of the surface. This requires additional hypoth- eses to attain reliability of the relationships between the surface fractal properties and size.208, 216, 217 The main goal of fractographic measurements is to determine the fractal dimension of, for example, chipped (fractured) surface and the limits in which the surface exhibits fractal properties. The main problem is the legitimacy of measuring the fractal dimension of self-affine fractured surfaces. The horizontal profile of a fractured surface can be statistically self-similar but the vertical profile is usually self-affine.218, 219 Thus, the horizontal and vertical surface sections have absolutely different scaling charac- teristics, which need to be estimated using different procedures of measurements.In the case of statistically self-similar horizontal contours, any sensible procedure for determination of the fractal dimension should give the same value.87 The question is how this fractal dimension is correlated with the fractal properties of the self-affine fractured surface. Self-affine vertical profiles can be characterised by many fractal dimensions, for example, local and global fractal dimensions. The latter are always equal to the topological dimension of the profile, while the local dimensions of the profile irregularities can be represented as exponential functions.220 The second group of methods comprises various physical methods used most often for fractal analysis of surfaces (mainly, fractured surfaces).They include porometry,211, 222 scattering procedures (e.g., small-angle neutron scattering),13 optical dif- fraction methods,13, 61, 182, 223 secondary electron emission meas- urement,13 adsorption ¡¾ desorption measurements (adsorption V U Novikov, G V Kozlov probe method),13, 224 ¡¾ 227 methods of thermodynamics,228 the deposit experiment method,229 electro- and thermochemical methods,229, 230 NMR measurements of the pore distribution,231 procedures based on the results of mechanical measure- ments,61, 232 etc.} 2. Small-angle X-ray diffraction As an example, we shall consider the practical application of one method, small-angle X-ray scattering (SAXS), which is widely used to study the fractal structure of solids.227, 233 ¡¾ 245 Polymers are mainly studied by this method during cross-linking in solu- tions.233 ¡¾ 235 The theoretical grounds of the method have been developed fairly well by now.238, 241, 242 The fractal structures of block polystyrene, poly(methyl methacrylate), and polycarbonate have been studied by the SAXS method.153 These particular polymers were chosen because they are often used as model systems and, therefore, they are well characterised and because the structures of macromolecules 76 and, as a consequence, the properties of these polymers are different.244 The use of the SAXS method is based on the characteristic power dependence of the scattering intensity I on the scattering vector (121) I(k)!k7x, where x is a Porod index, the interpretation of which depends on the nature of the scattering source (122) k=4pl71 sin y2 , where l is the X-ray radiation wavelength and y is the scattering angle.224 In the case of bulk fractals (i.e. structures like polymers), this index coincides with the fractal dimension of the structure df.224, 242 (123) For a fractal phase interface with the dimension Di, the following relation holds:238 I(k)!kDi76, 2<Di<6. Figure 43 shows the ln I (ln k) plots, while Fig.44 presents the dependences of ln I on k2 for the polymers mentioned above.245 Two linear sections present for each polymer of Fig.43 point to the existence of two regions with different fractal dimensions. These plots differ from the analogous plots for silicates, for which the slope of the ln I (ln k) plots increases discretely with an increase in k (which implies the loss of fractal properties), but are similar to the dependences obtained for amorphous chalcogenide films.242 To identify the structural regions responsible for the observed change in the slope, the cluster model for the structure of } Experimental methods for determining the fractal dimension are consid- ered in detail, for example, in a monograph.237 ln I 5.5 �¢1 �¢2 �¢3 3.7 1.9 ln k 74.0 73.4 74.6 Figure 43.SAXS intensity vs. scattering vector k for poly(methyl metha- crylate) (1), polystyrene (2), polycarbonate (3).39Structure and properties of polymers in terms of the fractal approach ln I 6.4 �¢1 �¢2 �¢3 4.6 2.8 20 1073k2 / nm71 0 Figure 44. SAXS intensity vs. k2 for poly(methyl methacrylate) (1), polystyrene (2), polycarbonate (3).39 amorphous polymers was used. The region of local order and the sections of macromolecules protruding from it should be consid- ered as the fractal cluster.125 The size of this cluster is twice the distance between the regions of local order, and its fractal dimension characterises the structure of the whole polymer, which is a set of generalised fractal clusters.Another structural region is represented by the loosely packed matrix located between the local order regions; all the fluctuation free volume is accumu- lated in this region. The Rcl values for the polymers considered are listed in Table 4. Using the plots presented in Fig. 44 one can calculate the Guinier radii.245 Attention is drawn by the facts that RG and Rcl are close in magnitude and that RG increases twofold on passing from one linear section to the other (Fig. 43), which corresponds to the transition from Rcl to 2Rcl. This suggests that the RG and Rcl values reflect the same structural parameter. The condition for the fractality of particles which scatter X-rays in the range of small angles is known 224 to be represented by the inequality RGk51.Table 4. Structural and fractal characteristics of amorphous polymers. Polymer dfp Df Dfp df Rcl/ RG/ nm nm k<0.02871 k>0.028712.80 5.12 2.75 5.0 2.80 5.20 2.70 4.33 5.0 5.0 4.1 10.0 3.7 10.0 Polystyrene Poly(methyl methacrylate) Polycarbonate 3.0 2.40 4.40 2.62 3.63 4.0 8.0 The presence of two RG values implies the existence of a boundary between fractal structural regions, which can be found from the condition RGk51. For a fractal cluster with the size 2Rcl ^ 7.0 nm, this corresponds to k ^ 0.00143 nm71 or ln k ^ 4.25, which is the upper limit of fractality of the polymer structure. When RG ^ Rcl ^ 3.5 nm, we have ln k ^ 73.56, which is consistent with the ln k value at which the slope of the plots in Fig.43 changes. Thus, the section of the dependence of lnI on ln k for ln k ranging from 4.25 to 73.56 can be associated with the cluster structure of an amorphous polymer and the section for ln k>73.56 is matched by the loosely packed matrix. The existence of these boundaries is due to a known feature of real fractals �¢ the fractal behaviour is realised only within a definite scale range. Several ranges have been determined for amorphous solids;242 we shall distinguish two of them which correspond to the k values used. If the size of a cluster of pores } is designated by Zp and the size of a pore is designated by ap, the } In amorphous polymers, the term `pores' is used in relation to micro- cavities of free volume and the term `cluster of pores' refers to the loosely packed matrix in which they are concentrated.545 dimension of structural elements will be estimated in the following ranges of k. When k<Z¢§1 p , the dimension of the structure itself is determined, while for Z¢§1 p <k<ap, the dimension of the cluster of pores is found. It has been shown 189 that the fluctuation free volume in a polymer is a fractal object, its dimension being equal to the dimension of the regions of localisation of excess energy Df.246 In other words, Df characterises the degree of energy excitation of the loosely packed matrix. The dimensions df and Df can be found from relations (23) and (39), respectively. The dfp values estimated from Eqn (123) with allowance for the slope of the plots shown in Fig.43 (ln k is74.25 to73.56) are summarised in Table 4. The df values found using Eqn (23) are given for comparison. The fact that the values thus obtained are close confirms the validity of this interpretation. The slope of the plot sections for ln k>73.56 is close to unity; it cannot be interpreted as the fractal dimension of a structural element if for no other reason than its magnitude. Therefore, Eqn (123) was used to determine the fractal dimension. Compar- ison of the Dfp and Df values obtained in this way [see Eqn (39)] showed that they are in good agreement (see Table 4). Note that a slope of the order of unity (70.75 to 70.80) has also been obtained for a similar k range for amorphous chalcogenide films; however, this result was not interpreted.242 The condition RGk51 is usually obeyed for larger angles in the small-angle region.However, in the case of relatively large structural elements, the region of fractality and the Guinier region can overlap. Apparently, this overlap also takes place for the polymers under consideration. The range of linearity of the plots shown in Figs 43 and 44 is (1 ¡¾ 3)6103 nm71 and RG ^ 10 nm, i.e. the product RGk falls in the range from 1 to 3. The overlap of the fractality and Guinier regions may imply a relationship between the fractal dimension df and the Guinier radius RG. This can be demonstrated analytically in the following way. According to the small-angle Guinier approximation, the following relation holds:245 (124) I=I0 ln ¢§R2Gk2 , 3 while in the range of the Porod large angles, the relation 153 I=Ck7d f, (125) is valid, where I0 and C are constants.For equal I, there exists a formal relationship between df and RG 153 (126) df=OR2G=3Uk ¢§ lnOI0=CU . lnk It is noteworthy that this relationship is not obligatory in terms of the cluster model. An increase in RG means an increase in the distance between the clusters, a decrease in Vcl, an increase in m, and the corresponding increase in df, which is reflected by relation (126). We would like to note yet another important aspect of determination of df by the SAXS method. Based on the data of previous publications,238, 246 Novikov et al.167, 182 estimated the df values for amorphous vitreous polymers to be 2.0 ¡¾ 2.2.In another study,247 polystyrene has been tested at 16 K; as shown above, transfer of this result to the temperature range of about 293K is improper. Studies of the silicate colloid aggregates 224, 241, 248 showed that their porosity influences appreciably the df value. Thus pressing (i.e. an increase in the density) of samples results in markedly higher df ranging from 2.55 to 2.65.241 Feder 13 obtained df=2.56 for protein aggregates. These results are in good agree- ment with the data obtained in terms of Eqn (23) and with the above SAXS data. Therefore, any estimates assuming a priori, without sufficient grounds, df ^ 2 for amorphous vitreous poly- mers can induce substantial errors, for example, in the calculation of ds.167, 182546 Thus, the SAXS methods make it possible to confirm the fractality of different structural components of amorphous vitre- ous polymers and to measure their fractal dimensions.The upper limit of the fractal behaviour of polymers, equal to*2Rcl, is also in good agreement with the estimate of this value reported by Novikov et al.167 V. Conclusion A feature distinguishing thoach from the physical models of polymer synthesis developed previously is that it takes into account the structure of the macromolecular coil, which determines the polymer structure, and characterises simultane- ously the fractal dimension of the coil and the particular mecha- nism of the coil formation.The results obtained along this line indicate that the growth of macromolecules during the polymer structure formation stops when the macromolecular coil has reached the density of the reaction medium rather than due to exhaustion of the chemical reactants, i.e. the reaction is termi- nated by purely physical factors. This conclusion is impossible in terms of the Euclidean geometry. Based on fundamental physical principles, the multilevel polymer structure has been described and the equations relating the molecular characteristics, topology, and parameters of the supermolecular structure of polymers are analysed. The applica- tion of principles of nonequilibrium thermodynamics and treat- ment of vitreous polymers as structurally inhomogeneous solids provided understanding of the fact that the mechanical energy applied during deformation is `pumped' into the loosely packed regions of the polymer and dissipated in the closely packed regions (clusters). The dissipation of mechanical energy induces shear stress in the clusters; the clusters lose their stability, which causes the polymer to yield.Analysis of the concept of the fluctuation free volume in a vitreous polymer has shown that it possesses fractal properties; hence, the microcavities composing this volume can be modelled by a Dffv-dimensional sphere. The microcavity size is restricted by the volume in which the energy of thermal fluctuations needed for their formation is accumulated.It is shown that `stretching' of macromolecules hampers an increase in the degree of ordering. When the thermodynamic forces inducing these effects are coun- terbalanced, the polymer reaches a certain quasi-equilibrium state, which is explained by a density fluctuation above a partic- ular temperature below the glass transition temperature. The introduction of the concept of the quasi-equilibrium state of polymers provides a better understanding of several experimental findings. The results of modelling the polymer structure using percola- tion and aggregation theory showed that the structure formed at the glass transition temperature is a percolation cluster. Glass transition is assumed to be a phase transition. The fractal dimension of these structures is determined by the disorder generated by deterministic chaos.Simultaneously, it was shown that the polymer structure can be modelled by a modified model of the diffusion-limited irreversible aggregation. The superposition of the cluster volume ± temperature curves for amorphous and amorphous-crystalline polymers and the relationship between fractality and local order in the structure of vitreous polymers were described within the framework of the cluster model resort- ing to the percolation theory. The importance of calculation of the properties of polymers is demonstrated by presenting a procedure based on the cluster model of the amorphous state structure and fractal analysis. This procedure allows one to perform numerical modelling of properties of, for example, cross-linked polymers.An obvious advantage of this method is the simplicity of choosing the input data in combination with strict physical interpretation and the absence of adjusting coefficients. 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ISSN:0036-021X    

出版商:RSC    

年代:2000

数据来源: RSC