摘要:

Chemisorption of Carbon Monoxide and Hydrogen on AgNa Mordenite BY HERMANN K. BEYER Central Research Institute of Chemistry, Hungarian Academy of Sciences, 11 Pustaszeri-ut 57-69, Budapest, Hungary AND PETER A. JACOBS* AND JAN B. UYTTERHOEVEN Centrum voor Oppervlaktescheikunde en Colloi'dale Scheikunde, Katholieke Univeristeit Leuven, De Croylaan 42, B-3030 Leuven (Heverlee), Belgium Received 12th April, 1978 It has been established, with the help of volumetric, i.r. and mass spectroscopic methods, that silver mordenites are capable of chemisorbing hydrogen and carbon monoxide. The silver ions in the large pores chemisorb one CO molecule, while only a quarter of them can retain hydrogen molecules. This amount corresponds to the occupancy of site VI. Hydrogen is also slowly chemisorbed in the side pockets of the structure in a similar way.A model for the chemisorption site is proposed. Carbon monoxide is known to be strongly retained by transition metal zeolites.'. In the case of silver and cuprous ions in Y zeolites, sorption of CO is used as a method for the titration of supercage cations, since it is supposed not to enter the sodalite cages through the six-membered ring^.^-^ Recently it was found that these concepts could be applied to the AgNaA system.6 It is the first aim of the present work to investigate if these concepts also apply to Ag Zeolon, a zeolite with a completely different structure and pore size. Previously, it was found that silver A zeolite was susceptible to autoreductioq6 with the concomitant formation of colour centres, due to the formation in the sodalite cages of linear clusters Agg+. It seemed that dissociative hydrogen chemisorption was possible at the ends of such a linear cluster.6 On Ag mordenite, it was also reported that important amounts of hydrogen could be chemisorbed, but no further details were given.7 This is a rather unusual observation, since Ag in none of its valency states is known to be a good hydrogenation catalyst and therefore is unable to chemisorb and activate hydrogen.We have therefore investigated the chemisorptive properties of AgNa mordenite zeolites in more detail, by varying zeolite parameters such as degree of ion exchange, outgassing temperature and %/A1 ratio of the framework; we have also studied competitive sorption with other small molecules. EXPERIMENTAL MATERIALS A commercial sample of Na Zeolon (Norton) with the following unit cell composition was used throughout this work and will be denoted as Z7.6: Na7.62 A17.62 Si40.40 0 9 6 .109110 CHEMISORPTION ON AgNa MORDENITE This composition does not take into account the 1.6 % by weight of Fez03 present as impurities. Samples with varying concentrations of Ag+ ions were prepared by contacting the parent sample with variable amounts of a diluted AgN03 solution as described earlier.,, After the necessary washings, the samples were air dried and stored in the dark. Only freshly prepared samples were used. For sample identification, the degree of ion exchange of the zeolite as usual follows the sample name. The second figure in brackets denotes the out- gassing temperature in K.Lattice aluminium was extracted by refluxing the parent zeolite with the appropriate amount of H4EDTA (ethylenediaminetetra-acetic acid) as described by Kerr. The following aluminium deficient materials were prepared : z5 NaS.1 A15.1 si40 0 9 0 . 2 23.9 Na3.9 Al3.9 si40 087.8 z2.0 Na2.0 Al2.0 si40 0 8 4 - They were exchanged for 100 % with Ag+ as described previo~sly.~ Part of the parent NaZ,,, sample was also treated with dithionite,' in order to reduce the iron content. A sample with only 0.74 % of iron (as Fe203) was obtained and ion exchanged. It will be denoted as Z*,.6. METHODS AND MATERIALS Gas uptake was measured in a low volume recirculation reactor as described earlier.' In some cases competitive adsorption measurements were performed in a similar system equipped with a sampling valve, allowing in this way gas chromatographic analyses of the gas phase.1.r. measurements were made in situ in a Beckman IR12 double beam grating spectrometer in the absorbance mode, using two identical cells in the sample and reference beam. A thermocouple was in the middle of the ultra-thin pellet in the sample beam (thickness: 2x lo2 kg m-2). Temperature programmed desorption experiments under flowing He were carried out in a Hewlett Packard GC/MS 5992A system using single ion monitoring techniques. RESULTS AND DISCUSSION ACTIVATION OF AgNaZ7.6 Upon slow degassing of AgNaZ,., under a stream of helium gas, water was the major desorption product. Above 573 K, small amounts of oxygen were also desorbed.However, even the sample AgZ,. ,-lOO(773) did not release appreciable amounts of oxygen, corresponding only to a degree of autoreduction of silver lower than 2 %. During the same treatment, the white colour of the samples remained unchanged. This behaviour is totally in contrast to AgA-100 zeolite, where under the same conditions about 11 % of the silver ions present are reduced, and the colour of the sample gradually turns to bright red.6 A D S OR P TI 0 N I SOT HER MS Adsorption isotherms of hydrogen, carbon monoxide, oxygen and nitrogen on both AgZ7.,-100(673) and NaZ7.,-(673) are shown in fig. 1. The adsorption isotherms for nitrogen and oxygen are reversible and almost identical for both samples. This excludes the existence of any specific interaction of these molecules with the Ag+ ions.For carbon monoxide and hydrogen the behaviour is totally different. The presence of silver ions considerably enhances the sorption capacity of theH. K. BEYER, P. A. JACOBS AND J . B. UYTTERHOEVEN 111 mordenite for these molecules. Under the present conditions, almost no hydrogen was adsorbed on the parent Na mordenite. For COY the adsorption isotherm on Na mordenite is also completely reversible. The data therefore clearly indicate that the specific interactions with CO and hydrogen are related exclusively to the presence of 13.33 39.99 66.65 adsorbate pressure/kN m-2 FIG. 1.-Adsorption isotherms of carbon monoxide (a), oxygen (c), nitrogen (6) and hydrogen ( d ) on AgNaZ7.6-76(673) (full lines) and on NaZ,.6-(673) (dotted lines) at 298 K.Full points refer to AgNaZ” ,. 6-76(673). silver ions. Indeed, the iron content of the sample does not influence the amount of hydrogen or carbon monoxide adsorbed (compare samples Z and Z*). Such interactions were also observed for silver A, but not for other small pore zeolites such as Ag+-chabasite, Ag+-clinoptilolite and Ag+-stilbite.6 CARBON MONOXIDE SORPTION The amount of carbon monoxide sorbed was arbitrarily divided into two parts. CO was considered to be chemisorbed if it could not be removed by room temperature degassing (293 K) for 30 min in a vacuum of 1.33 mN m-2. The excess taken up was considered to be reversibly sorbed (physisorbed). The amount CO chemisorbed on AgNaZ7.,-76 is given in fig. 2 and remains unchanged for thoroughly degassed samples.The ratio of carbon monoxide chemisorbed to the Agf content of the sample amounts to 0.56. The slightly lower value obtained after outgassing at 473 K has to be related to the last traces of water retained by the sample under these condi- tions. Thus only 56 % of the silver ions are accessible for the strong interaction with CO, and the cations located in the “ side pockets ” of the structure are not available for this interaction. There is, however, no structure analysis available, which would allow direct comparison and verification of the statement. Data for K+ exchanged mordenite reveal that the ratio of pore cations to total cations is equal to 0.64. Furthermore, the data obtained for hydrogen reduction of the same system point also in this direction.In general for Ag zeolites, ions in the hidden sites of the structure are more difficult to reduce. In faujasite these sites are in the hexagonal prism^,^ and in mordenite they are in the side pockets of the struct~re.~ In the latter zeolite, the fraction of easily reducible silver ions is 0.65. All this constitutes firm arguments for the statement that only silver ions located in the big pores of mordenite are centres for strong sorption of carbon monoxide.112 CHEMISORPTION ON AgNa MORDENITE The variation of the chemisorptive properties of AgNaZ,. ,-(673) with the degree of cation exchange is shown in fig. 3. There is a lower than linear increase in the amount chemisorbed with the Ag+ content. The fraction of exposed cations declines linearly from 0.72 to almost 0.55.It seems, therefore, that in the monoionic silver mordenite, there is almost equal repartition of the cations between the hidden and the 0.5 2 4 I M 4: - + \ 8 1 % 2 x !l M s. 8 0.25 Y 0 0.0 0 473 573 673 773 degassing temperature/K FIG. 2.-Carbon monoxide chemisorption at 293 K on AgNaZ7.6-76 at different outgassing tempera- tures. 0 50 100 I .o +M 3.5 u 4 0 \ 1.0 Ag+ exchange / % FIG. 3.-Carbon monoxide chemisorbed at 293 K on AgNaZ7,6-(673) at different degrees of silver exchange.H . K . BEYER, P . A . JACOBS AND J . B. UYTTERHOEVEN 113 exposed sites. At lower degrees of exchange, there seems to be a slight preference of the smaller cation (Na+) for the hidden sites. The influence of the degree of dealumination on the accessibility of Ag+ cations for CO is given in fig.4. Data are from volumetric measurements and from i.r. measurements. The intensity of the stretching frequency of CO in the complex Ag+ . . . CO changes in proportion to the amount of CO chemisorbed. The CO/Ag+ ratio increases with the degree of dealumination. For highly aluminium deficient zeolites, the relative amount of accessible Ag+ ions is as high as 80 %. It seems, therefore, that dealumination gradually opens the side pockets of the structure, allowing more CO to enter in the hidden sites of the structure. 10 5 0 Al/unit cell FIG. 4.-Ratio of chemisorbed carbon monoxide to total Ag+ content for a series of dealuminated mordenites ; (0) from volumetric measurements ; (b) in arbitrary units from the intensity of vco at 2170 cm-'.CHEMISORBED HYDROGEN From previous work, it is known that hydrogen is chemisorbed at ambient temperature on silver mordenite [ref. (7), fig. 31. From the intensity of the Si-OD band at 2650 cm-I after deuterium sorption, it could be derived that reduction only started after a contact time of 9 x lo3 s. For each case considered in the following paragraphs, it was carefully checked that hydrogen reduction of silver ions could be excluded. Using the i.r. criterion, it was estimated that an uptake of hydrogen of 0.021 mol kg-l of zeolite causing reduction should be detectable. When hydrogen is admitted to silver mordenite, an amount is adsorbed almost immediately, while another quantity is more slowly chemisorbed. In table 1, pertinent data illustrating the process are shown.When the sample is pretreated in hydrogen, so as to reduce selectively the Ag+ ions in the main pores, hydrogen is only consumed during a slow process (sample 2). A completely reduced sample no longer chemisorbs hydrogen (sample 3), but upon reoxidation of any reduced sample, the initial two processes reappear and hydrogen is chemisorbed just as on the parent sample (samples 4 and 5). We thus conclude that chemisorption of hydrogen requires the presence of silver ions. The fast process needs Ag+ ions in exposed sites. The slow process is due to diffusion of hydrogen towards Ag+ in hidden sites in the " side pockets " of the structure. The ratio of the hydrogen molecules chemisorbed114 CHEMISORPTION ON AgNa MORDENITE to the number of Ag+ ions available is 1 : 4 and 1 : 3.3 for the exposed and hidden ions, respectively. This shows that in both parts of the structure, only a minor part of the cations are in a position to be able to chemisorb hydrogen.This is in contrast to CO chemisorption, which is an overall property of the exposed cations. The amount of hydrogen chemisorbed on AgNaZ,. 6-76 does not change with the outgassing temperature in the range 523-723 K. This was also true for CO chemi- sorption. As shown in fig. 5, the amount of fastly sorbed hydrogen changes with the degree of ion exchange just as the amount of carbon monoxide does. This TABLE ~.-CHEMISORPTION OF HYDROGEN AT 293 K ON AgNaZ7,6-76(673) amount hydrogen chemisorbed /moI kg-1 sample pretreatment atmosphere degree of in fast in slow number (temp./K)/(time/s) reduction total process process 1 - 0.00 0.463 0.300 0.163 2 H2/528/4000 0.65 0.161 O.OO0 0.161 4 Hz/528/4000 then 02/573/3600 0.00 0.462 0.298 0.164 5 H2/630/3000 then 02/573/3600 0.00 0.455 0.295 0.160 3 H2/630/3000 100.00 0.000 0.000 0.000 indicates that a fraction of the exposed Ag+ ions increasing in a way proportional to the degree of ion exchange is in such an environment as to be able to chemisorb hydrogen. The data for H2 chemisorption suggest that Ag+ ions in particular locations of the mordenite structure are able to chemisorb hydrogen. The difference in amount of CO and H2 chemisorbed is indicative of site heterogeneity in the main pores. The structural data available for K+ forms locate these cations in two sites (IV and VI).Three K+ occupy site IVY located in a 8-membered ring in the main pores. 0.9 K+ lie in site VI, a deformed 6-membered ring in the main pores, the bonding Ag+ exchange/ % FIG. 5.-Hydrogen chemisorption at 293 K during the fast process on AgNaZ7,6-(673) for different Ag+ contents of the sample.H. K. BEYER, P. A . JACOBS AND J . B . UYTTERHOEVEN 115 being strongly ~ne-sided.~ The ratio K+(IV)/K+(VI) also equals 3.3. Enough evi- dence has now been given for the similarity in cation location between the Ag+ and K+ systems. It therefore seems probable that hydrogen is quickly chemisorbed on site VI Ag+ ions. Chemisorption may be viewed as polarisation of hydrogen between Ag+ (coordinated to oxygen atoms at one side of the site) and a lattice oxygen in the 1 small channel 4 1- large channel .-I FIG.6.-Representation of the possible cation sites and hydrogen sorption site in Ag rnordenite. (a) Section through the mordenite structure perpendicular to the pores. (b) Projection of the atoms in the bc plane. The straight lines represent the diameter of lattice oxygens, the double lines inter- connecting 4-membered rings, and the dashed lines the coordination possibilities of the cations. [After ref. (lo)]. 0, Ag+ ions ; 8, H atoms. immediate vicinity. Four oxygens of a neighbouring 5-membered ring are suitable, or the oxygen ion sharing two neighbouring 5-membered rings. A diagrammatic representation of the site is shown in fig. 6. Already, the occupancy of this site by K+ ions is unusual, since all the ions can easily be accommodated in site IV.9 The occupancy of site VI is thought to allow " bonding to undersaturated oxygens from Al-centred tetrahedra ".116 CHEMISORPTION ON AgNa MORDENITE If such a site is occupied and binds hydrogen tightly, these ions are also expected to be most easily reduced.This was checked carefully and the results are given in fig. 7. It is shown that already around 18 % reduction the fast hydrogen sorption 0 50 100 rl I M A rl I M A 0 u 0 10 20 30 degree of reduction/ % FIG. 7.--Carbon monoxide (a) and hydrogen chemisorbed during the fast sorption (6) and slow process (c), at different degrees of reduction of AgNaZ7,6-76(673). has disappeared. The CO chemisorption disappeared at about 65 % reduction, while only then does the amount of slowly-sorbed H2 start to decline.These results support the hypothesis that the ability to retain hydrogen molecules in the main pores is due to the occupancy of a particular site by Ag+, in this case site VI. & 0 E . water sorbed/mol kgl time x 10a2/s FIG. &-(a) Replacement of chemisorbed hydrogen by water at 293 K from AgNaZ,~76(673). (b) Mutual replacement of chemisorbed CO and H1. Variation of the intensity of the vco band at 2170 cm-' of chemisorbed CO. ( 0 ) Admission of hydrogen to a sample containing chemisorbed CO ; (0) vice uersa.H. K . BEYER, P . A. JACOBS AND J. B . UYTTERHOEVEN 117 The ratio of slowly held hydrogen to the amount of hidden Ag+ ions, (0.30), indicates that heterogeneity also exists in the hidden sites. Structural information cannot help here to characterize more precisely the chemisorption site.Indeed, K+ ions are only found on site I1 (an 8-membered ring in the side pockets of the structure).g The results indicate that the site involved has to be very similar in nature to the one depicted for the main pores. COMPETITIVE CHEMISORPTION In order to collect further evidence for the nature of the proposed chemisorption sites, replacement experiments of hydrogen by carbon monoxide and water were carried out. TABLE 2.-REPLACEMENT OF CHEMISORBED HYDROGEN BY CARBON MONOXIDE ON AgNaZ,. 6- 76(463) AT 293 K time of CO amount CO amount Hz COsde. adsorption chemisorbed desorbed - I S /mol kg-1 lmol kg-1 Hzdes. 60 0.157 0.045 3.49 180 0.216 0.050 4.32 600 0.277 0.066 4.20 1200 0.321 0.080 4.01 1800 0.360 0.092 3.91 2400 0.380 0.099 3.90 average : 3.97k0.29 Fig.S(a) shows that chemisorbed hydrogen can be replaced by water at ambient temperature, at least when only small amounts of water are adsorbed. In the range covered, only four molecules of water are able to replace one molecule of hydrogen. In table 2, the replacement by carbon monoxide is given. Here too, only about 4 CQ molecules are able to replace one H2 molecule. In fig. 8(b), i.r. results clearly show that the replacement of hydrogen by carbon monoxide or vice versa, tend to form the same equilibrium composition : around 65 % of the exposed silver ions coordinated to one carbon monoxide molecule, the remaining Ag+ ions chemisorbing hydrogen. These results are consistent with the picture proposed for the nature of the adsorption site, in the case of separate adsorption of gases.CONCLUSIONS Each of the silver ions in the main pores of the mordenite structure chemisorbs one carbon monoxide molecule. Only about one quarter of these ions is able to chemisorb hydrogen. This ratio is consistent with the relative occupancy of sites IV and VI in the main pores for a K+ mordenite. Therefore, hydrogen is assumed to be adsorbed in a strongly polarised way between the Ag+ ions in site VI and a nearby lattice oxygen. The geometrical requirements for such a site seem to be fulfilled only for the mordenite structure in combination with silver ions. A similar site is proposed, although structural data do not allow us to propose a precise environ- ment for it. Also in the inner sites part of the silver ions chemisorb hydrogen.118 CHEMISORPTION ON AgNa MORDENITE P. A. Jacobs acknowledges a permanent research position as " Bevoegdverklaard Navorser " form N.F.W.O. (Belgium). Constructive comments from Dr. W. J. Mortier are highly appreciated. Financial support from the Belgian Government (Dienst Wetenschapsbeleid) is gratefully acknowledged. The technical assistance of Mrs. I. Szaniszl6 is also acknowledged. C. L. Angell and P. C. SchafTer, J. Phys. Chem., 1965, 69,3463. C . L. Angell and P. C. Schaffer, J. Phys. Chem., 1966,70,1413. Y . Y . Huang, J. Curulysis, 1973,30,187. H. Beyer, P. A, Jacobs and J. B. Uytterhoeven, J.C.S. Furaduy I, 1976,72,674. R. G. Herman, J. H. Lunsford, H. Beyer, P. A. Jacobs and J. B. Uytterhoeven, J. Phys. Chem., 1975,79,2388. P. A. Jacobs, J. B. Uytterhoeven and H. K. Beyer, J.C.S. Faraday Z, 1979,75, in press. ' H. K. Beyer and P. A. Jacobs, Molecular Sieves ZI, ed. J. Katzer, A.C.S. Symp. Ser., 1977, 40, 493. G. T. Ken, J. Phys. Chem., 1968,72,2594. W . J. Mortier, J. J. Pluth and J. V. Smith, Proc. Conf. Natural Zeolites, Tucson (Pergamon Press, 1977). lo W. J. Mortier, J. Phys. Chem., 1977, 81, 1334. (PAPER 8/692)

ISSN:0300-9599    

DOI:10.1039/F19797500109

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Metal-Ion Complexation Reactions in the Presence of Surfactants Part 2.-Mechanism of pH-dependent Reaction between Nickel(I1) and Murexide in Aqueous Solution and Application of the Reaction to Study of Micellar Phenomena BY MICHAEL FISCHFR AND WILHELM KNOCHE Max-Planck-Institut fur Biophysikalische Chemie, Gottingen, West Germany AND BRIAN H. ROBINSON* AND JOHN H. MACLAGAN WEDDERBURN Chemical Laboratory, University of Kent at Canterbury Received 12th April, 1978 The thermodynamics and kinetics of the reaction between Ni2+(aq) and the metal ion indicator murexide (Mu-) have been studied over the pH range 4.0-7.3 in aqueous solution. Rates and equilibrium concentrations are strongly pH-dependent. Rate constants were obtained using pressure- jump and stopped-flow methods and results from both techniques are in excellent agreement.All data are consistent with the reaction scheme : ki KH Ni2++ Mu- e (NiMu)+ + (NiMu)d, + H+. k-1 slow fast The reaction (involving charged reagents) is studied in the absence of added inert electrolyte and, therefore, under conditions of varying ionic strength. A general treatment for handling rate and equilibrium data in this situation is described. By the inclusion of appropriate activity co- efficients the following results (at 298.2 K) are obtained : Kl = kl/k-l = 3.8(+0.2) x lo3 dm3 mo1-1 ; kl = 7.8(f0.5) x lo3 dm3 mo1-1 s-1 ; KH = 1.8(+0.2) x 1P6 mol dm-3 k-l = 2.1 s-I. Such indicator reactions involving murexide are very convenient for the study of various aspects of micellisation and their application to the detection of micelles formed by anionic detergents is described.The chromophoric anion murexide (Mu-) shown in fig. 1 is a convenient ligand for the quantitative determination of metal ion concentrations in aqueous solution using visible spectrophotometry. The kinetics of metal-ligand complexation re- actions of this general type have been much studied in recent years; the Eigen mechanism 2* is generally invoked as an interpretation of the results. For the specific case of complexation of Ni”+(aq) with murexide as ligand, rates and equilibria are pH-dependent, and it is a main purpose of this paper to explain this effect in terms of a reaction scheme. Previously the kinetics of this reaction have been studied by G e i e ~ , ~ Lin and Bear and Jost,6 using the joule-heating temperature- jump method, and working at a high constant ionic strength and h e d pH.They explained their results in terms of the simple reaction scheme shown in fig. 1. For studies using the joule-heating temperature-jump method, the addition of a high concentration of supporting (inert) electrolyte (- 0.1 mol dm-3) is required. This necessary procedure has the advantage that activity coefficients of reactant ions are then essentially constant. However, the addition of electrolyte may not always 119120 METAL-ION COMPLEXATION KINETICS be desirable, as for example when the reaction is used to monitor aspects of micellar behaviour of detergents. The reaction between Ni2+ and murexide is well suited to study by the pressure- jump technique with spectrophotometric detection '* s since the reaction volume AVO is very large (23 cm3 mo1-1)6 and there is a pronounced ligand colour change from purple to red on complexation.With the pressure-jump technique no added electrolyte is required, but when the ionic strength of the medium is varied, activity coefficients are not constant, and this must be taken into account in the analysis of the rate and equilibrium data. A detailed mathematical analysis is given in the Appendix. FIG. 1.-Formula of Mu- and the simple reaction scheme. [The structure of the complex is taken from ref. (l)]. The complexation reaction between Ni2+ and Mu- provides a new and convenient method for the investigation of micellar behaviour of anionic surfactants. It is for this reason that the complexation reaction has been studied in detail in the absence of added electrolyte.Anionic micelles provide a dispersed negatively-charged surface in solution. As a consequence, the positively-charged nickel ions will partition out of the bulk aqueous phase into the surface region of the micelles. Since murexide ions are both hydrophilic and negatively-charged, they are located solely in the bulk aqueous phase. Therefore, as anionic micelles form in solution, Ni2+(aq) and murexide ions are effectively separated, and less complex formation will result, leading to an apparently reduced stability constant. The indicator reaction therefore suggests a simple experimental method for the precise detection of the surfactant concentration at which micelle formation occurs, which is generally considered to be the c.m.c.of the surfactant. EXPERIMENTAL MATERIALS A N D METHODS Nickel nitrate hexahydrate was a Merck Reagent, sodium dodecyl (lauryl) sulphate was B.D.H. specially pure grade, and murexide (ammonium purpurate) was obtained from Fisons. Murexide solutions were freshly prepared every 4 h since they decolorised slowly in the pH range used. (At pH values < 4, decolorisation occurred more rapidly). Ligand purity was checked spectrophotometrically (EM"- at ;Imax = 1 . 4 ~ lo4 dm3 mol-l cm-l). All measurements were performed at 25(fO.l)"C over the pH range 4.0 to 7.3. (At higher pH values, precipitation occurred.) Spectra were measured on either a Unicam SP 8000 or a Beckman Acta I11 instrument. The pressure-jump instrument with optical detection has been described previo~sly.~~ Solutions were carefully degassed before use, and data were analysed on-line after being processed by an analogue-to-digital converter.9 9 lo Relaxation times were independent of the monitoring wavelength. The murexide concentration was generally 5 x mol dm-3 and concentrations of Ni2+ up to 8 x Stopped-flow experiments were performed using a small-volume instrument with optical detection which has been described previously. Oscilloscope traces were photographed and analysed by means of semi-logarithmic plots. Concentrations of murexide after mixing mol dm-3 were employed.FISCHER, KNOCHE, ROBINSON AND WEDDERRURN 121 were 1 x mol dm-3 were used. The change in transmittance accompanying reaction was always < 5 %.Identical results were obtained from measurements at 450 and 520 nm. For all kinetic measurements, single exponential plots were obtained within experimental error. Various buffers were used including phosphate (pH > 6), acetate (pH - 5 ) and phthalate (pH - 4) buffers. mol d ~ n - ~ , and concentrations of Ni2+ up to RESULTS EQUILIBRIUM CONSTANTS Since the reaction involves charged species, and experiments have been performed in the absence of an excess of inert electrolyte, it is necessary to introduce activity coefficients in the calculation of equilibrium (and rate) constants. Activity co- efficients ( y i ) have been estimated by the use of the extended Debye-Huckel eqn (1) due to Davies l2 which is approximately valid for many salts for ionic strengths Z < 0.2 mol dm-3.where zi is the charge on ion i. (For the present work, all experiments have been restricted to I < 0.05 rnol dm-3). According to eqn (l), y i values depend only on ionic charge and ionic strength, so that the abbreviations yI and yII can be used for the activity coefficients of mono- valent and divalent ions respectively. Spectra showing the complexation equilibria at pH values of 5.0 and 6.0 are shown in fig. 2(a) and (b). An isosbestic point is obtained indicating a simple reaction. However, from fig. 2, it can be seen that the extent of complexation increases with pH. There is also a slight shift in the wavelength and absorbance at the isosbestic point. These observations suggest that the reaction involves (a) hydrogen ions and (b) more than two absorbing species.Since hydrolysis of Ni2+(aq) and of murexide only begins to interfere at pH values > 7.5,l the species involved in the acid ionisation equilibrium can only be NiMu+. A IikeIy reaction scheme (A) is therefore : log Yr = -0.5z)[If/(1 +Z')-O.31] (1) k i KH Ni2+ + Mu- + (NiMu)+ + (NiMu)dep + Hf (+I (-1 (1) (2) (HI (A) k- 1 in which (NiMu)deD represents a deprotonated complex, the proton being lost either from the bound ligand or from a solvating water molecule. The equilibrium is described by two constants : Kl = Wk-1 = clrl/(c+r+c-r-) = cl/(c+c-YII) and since KH = (C2Y2CHYH)/(ClYI) = (c2cH/cl) y- = y 1 = yH = yI ; y+ = yII ; and y z = 1 [see eqn (l)]. The hydrogen ion concentration is calculated from the measured pH as : The total concentrations of nickel ion ( M ) and murexide ion (L) are given by : and CH = 10-pHy,l.A4 = c++c1+c, L = c-+c,+cz.1 22 METAL-ION COMPLEXATION KINETICS To determine Kl and KH, values of the absorbance ( A ) of the various solutions have been measured at several wavelengths where the nickel ion does not absorb. Then : A/1 = E-C-fElC1 +EZCZ. = E-C-+&1,&1 + c 2 ) (7) (8) where E1,2 = ( E l + E2KHC; l)/( 1 +K,c, l). E-, E~ and g2 are the extinction coefficients of Mu-, (NiMu)+ and (NiMu)d,p respec- tively, and Zis the optical cell path length, 400 500 600 400 500 600 h / m FIG. 2.-Equilibrium spectrophotometric measurements at (a) pH = 5 and (b) pH = 6. L = 5 x mol dm-3 ; T = 25°C. Concentrations of NiZ+ are: 1, 0 ; 2, 5 x ; 3, 4.2 x 10-4 : 5.5 x ; 6, ; 7, 2 x ; 8 , 5 x mol dm-3.FISCHER, KNOCHE, ROBINSON AND WEDDERBURN 123 At low pH (pH 4 pKH), E ~ , ~ 3 el, and at high pH (pH % pK’), 81.2 -, 82. The spectra indicate that E~ - E ~ . We may, therefore, neglect the variation of C, with l i n eqn (8), and assume that E ~ , ~ is also constant at a given pH for pH - PKH. A Wang 2200 desk computer was used to calculate K1 and KH. Initially values of K1 and KH were estimated and values of c- and (cl +c2) were calculated using eqn (1) to (6) for experimental values of M and L. For each set of measurements at constant pH, has been calculated by a least squares fit of the measurements to eqn (7) (E- was obtained from the absorbance of murexide solutions). In the next stage of calculation, the standard deviation was determined between experimental and calculated values of A [eqn (7)].Then Kl and KH were systematically changed to minimise the standard deviation. This evaluation is performed at four different wavelengths at a given pH. Kl is mainly determined by measurements at low pH (pH < pKH) when c2 < cl. Measurements at pH > pKH yield values of Kl(l +KHcH-’.). From the “ best fit ” to the data over the pH range 4.0 to 7.3, the following equilibrium constants are obtained : Kl = (3.8k0.2) x lo3 dm3 mol-l KH = (1.8k0.3) x mol dm-3. No significant trends are found with pH or the wavelength used for data analysis. Equilibrium measurements have been made previously by Geier,4 Lin and Bear and Jost.‘j They described the equilibrium by [(NiMu)’ ] [Ni2+][Mu-] K‘ = which relates to Kl by the equation : (9) Geier worked at pH = 4, when c2 cl, so that K’ - K1yII.At 298.2 K and I = 0.1 mol dm-3, he obtained K’ = 1.4 x lo3 dm3 mol-l. Working at pH = 5, under the same conditions, Lin and Bear obtained K’ = 1.55 x lo3 dm3 mol-l and Jost obtained K’ = 1.9 x lo3 dm3 mol-l. Using eqn (1) and (9), the following values are obtained at I = 0 ; Kl = 3.7 x lo3 dm3 mol-1 (Geier), K1 = 4.1 x lo3 dm3 mol-1 (Lin and Bear), Kl = 5.0 x lo3 dm3 mol-l (Jost), Kl = 3.8 x lo3 dm3 mo1-1 (this work). Reasonable agreement is therefore obtained between all experi- ments. K’ = (C1-k c2)/(c+c-) = K~’)’II(~ +KHC~ ’). RATE CONSTANTS Two independent methods were used to follow the kinetics of the reaction between Ni2+(aq.) and murexide.A single relaxation time was observed over the time range 100 ps 3 5 s. If we assume that the protonation reaction is fast com- pared with metal-complex formation, the relaxation time for a reaction proceeding by scheme (A) can be expressed as : 2-l = klF (10) = LK1(l +KH/cH)l-l +YII(c+ +c-fl) for buffered solutions (cH constant) and for unbuffered solutions. p is defined by the equation fl = 1 + (d In yII/d In c+). (13)124 METAL-ION COMPLEXATION KINETICS Derivation of eqn (11)-(13) is given in the Appendix. The function F has been calculated for experimental solutions by inserting the values of Kl and KH derived from spectrophotometry. Then the rate constants kl and k-, (= k l / K , ) can be determined from each experimentally measured relaxation time by eqn (10).Since the value of k , is the rate constant corresponding to zero ionic strength, the same value should be found from all measurements at different reagent concentrations and pH. The results from pressure-jump experiments are given in table 1. For the pH range 4.7 to 7.0, the average value of kl is 8.05 (k0.45) x lo3 dm3 mol-1 s-l. It would appear that the value of kl is slightly higher at pH = 7.3, probably clue to the onset of an additional reaction step. Experiments carried out with a higher initial concentration of murexide (L = mol dm-3) gave the same value for kl over the pH range 5 to 7. TABLE 1.-PRESSURE-JUMP MEASUREMENTS : RELAXATION TIMES/10-3 S AND IN BRACKETS THE DERIVED RATE CONSTANT k1/103 dm3 mol-' s-l. M/mol dm-3 IS TOTAL NICKEL ION CONE CENTRATION : TOTAL MUREXIDE CONCENTRATION L = 5 x rnol dm-3.IN pH RANG- 6.0-7.3, 2X m01 dm-3 PHOSPHATE BUFFER WAS USED. M\PH 1 x 10-4 2~ 10-4 5~ 10-4 1 x 10-3 2~ 10-3 5 x 10-3 8 x 4.7 365 (7.7) 285 (8.1) 185 (8.2) 116 (8.5) 37 (8.2) 28 (7.6) 5.0 410 (7.1) 305 (7.8) 200 (7.8) 136 (7.3) 75 (8.0) 38 (8.0) 27 (8.0) 5.5 395 (7.7) 280 (8.7) 184 (8.5) 122 (8.2) 37 (8.2) 6.0 740 (7.4) 540 (7.5) 290 (7.6) 161 (7.8) 41 (8.0) 6.7 1290 (8 -4) 770 (8.2) 350 (7.7) 1 72 (8.1) 87 (8.5) 26 (8.9) T = 25°C. 7.0 7.3 1560 (9.0) 870 (8.4) 340 (8.5) 182 (8.0) 104 (7.3) 29 (8.0) 1640 (10.7) 850 (9.6) 334 (9.0) 161 (9.3) In order to confirm the activity coefficient analysis, experiments were performed in which the ionic strength was varied up to 5 x mol dm-3 by addition of sodium chloride or phosphate buffer.Relaxation times and derived values of kl [using eqn (10) to (12)] are shown in table 2. Again the same value for k , is obtained, independent of I. The result at pH = 7.0 corresponding to the higher buffer con- centration seems to be low, due to the formation of the complex NiHP04.13 A similar small effect is indicated from stopped-flow data. TABLE 2.-PRESSURE-JUMP MEASUREMENTS : DEPENDENCE OF RELAXATION TIMES AND kl ON INERT ELECTROLYTE AND BUFFER CONCENTRATION. ALL CONCENTRATIONS/l Ill01 dm-3. L = 5 x loe5 mol dm-3 ; T = 25°C. M 5 5 5 5 1 1 1 1 PH 4.70 4.70 4,70 4.70 7.00 7.00 7.00 7.00 [NaCll 0 2 10 50 0 0 0 0 [buffer] 0 0 0 0 0.6 2 6 20 71s 0.037 0.038 0.044 0.055 0.167 0.182 0.233 0.322 k 1 /dm3 m01-1 5-1 8 . 2 ~ 103 8.1 x 103 7 .6 ~ 103 7 . 7 ~ 103 8.1 x 103 8 . o ~ 103 7 . 2 ~ 103 6 . 6 ~ lo3FISCHER, KNOCHE, ROBINSON AND WEDDERBURN 125 Stopped-flow experiments were performed by mixing equal volumes of solutions containing nickel nitrate with murexide. Since pseudo-first order conditions were generally employed, [Ni2+] 9 [Mu] in both buffered and unbuffered solutions, and eqn (11) and (12) are applicable. Table 3 shows some typical data. The average TABLE 3.-sTOPPED-FLOW MEASUREMENTS SOME TYPICAL RELAXATION TIMES/10-3 S AND IN BRACKETS THE DERIVED RATE CONSTANT k1/103 dm3 mol-1 s-l FOR EXPERIMENTS IN BUFFERED (M = 10-4-7,5 x mol dm-3) AND UNBUFFERED (M = 10-3-10-2 mol dm-3) SOLUTIONS. L = mol dm-3 ; T = 25°C. M/mol dm-3\PH 1 x 10-4 2 . 5 ~ 10-4 5~ 10-4 7 . 5 ~ 10-4 M/mol dm-3\PH 1 x 10-3 2 .5 ~ 10-3 5~ 10-3 7.5 x 10-3 1 x LO - 30 - rl L 4.05 420 (6.8) 320 (6.8) 255 (6.6) 167 (7.2) 4.0 118 (8.1) 60 (8.3) 41 (7.3) 27 (8.2) 23 (7.9) 4.8 400 (7.8) 280 (8.4) 222 (7.4) 179 (7.1) 5.0 114 (8.7) 65 (7.9) 44 (6.9) 30 (7.5) 24.5 (7.4) / / / 5.7 670 (6.6) 400 (7.3) 265 (7.1) 202 (6.9) 6.0 151 (6.7) 69 (7.4) 40 (7.7) 32 (7.1) 24 (7.5) 6.6 1150 (7.8) 555 (7.9) 290 (8.3) 210 (8.0) 7.0 165 (6.0) 70 (7.3) 39 (7.7) 31 (7.2) 20 (9.0) 20 10 M/10-3mol dm-3 FIG. 3.-Plot of 7-l against total concentration of nickel. Pressure-jump data 0 ; Stopped-flow data A. -, Calculated line using eqn (10) and (12) ; - - -, calculated line assuming 711 = 1 (I = 0) ; . . ., calculated line assuming n1 = 0.38 (I = 0.1).126 METAL-ION COMPLEXATION KINETICS value of k , is 7.5( f0.65) x lo3 dm3 mol-' s-'.There is no systematic change of k , with pH, or nickel ion concentration. Values of k , obtained by the two independent methods are in good agreement. The mean value is 7.8 x lo3 dm3 mol-' s-I with uncertainty +5 %. Data obtained by both experimental techniques in unbuffered solutions at pH = 5 are shown in fig. 3. It can be seen that a good fit is obtained to the line calculated from our values of k,, K , and KH. The limiting line with slope k , which would be obtained for a hypothetical ideal solution (ylI = I ) is shown. The experimental points deviate significantly from this line, even at concentrations of A4 < mol dm-3. The predicted line for a constaiit ionic strength of 0.1 mol dm-3 is also shown. Under this condition, which was used in ref.(4)-(6), the plot will be linear but with a slope equal to yr1kl, and yIr = 0.38 from eqn (1). Our result for k , may be compared with that of Geier (k, = 3.5 x lo3 dm3 mol-' s-' at pH = 4), Lin and Bear ( k , = 1.8 x lo3 dm3 mol-1 s-' at pH = 5.0) and Jost ( k , = lo4 dm3 mol-1 s-' at pH = 5 ) all obtained at I = 0.1 mol dm-3 and 298.2 K. Applying eqn (1) and (10)-(12), we find k, = 9 . 2 ~ lo3 dm3 mol-' s-I (Geier), 5 x lo3 dm3 mol-' s-l (Lin and Bear) and 2.8 x lo4 dm3 mol-' s-l (Jost). Our mean value is in reasonably good agreement with that of Geier. DISCUSSION Scheme (A) is consistent with all our experimental observations. A value of k, According to the theory of EigenY2 the mechanism of ligand exchange is given for complexation (at Z = 0) of 7.8 (fO.5) x lo3 dm3 mol-' s-' is derived at 25°C.by scheme B : KO. kex Ni2++Mu- .- Ni2+(H20)Mu- + (NiMu)+ fast slow kl = Koske, when KO, < [Ni2+]-l. (14) KO, is the equilibrium constant for outer-sphere complex formation, and k,, is the rate constant for replacement of a water molecule by ligand. k,, has been found to be nearly independent of the nature of the incoming ligand; for Ni2+ it is of the order of lo4 s-l. KO, can be estimated by the Fuoss equation : KO, = 471Na3 exp (- z+z-e$/sakT) (1 5 ) where a = distance of closest approach in the outer-sphere-complex, z+ = charge on Ni2+, z- = charge on Mu- and E = permittivity. For z+z- = -2, KO, is nearly independent of the value assumed for a. The main uncertainty is in the effective charge (2-) on the murexide ion since this must be considerably delocalised.Assuming a formal charge of -1 on the ligand, KO, [from eqn (15)] is - 6 dm3 mol-l, and from eqn (14) we find a value of k,, of only 1.3 x lo3 s-l. On the other hand, assuming an effective ligand charge of zero, we can derive KO, - 0.3 dm3 mol-l and ke, - 3 x lo4 s-'. Since values of k,, - lo4 s-' are found for anionic ligands such as acetate,I4 we conclude that the kinetic data are consistent with the operation of the Eigen mechanism but with substantial charge delocalisation in the anion. It is of interest to speculate whether the proton is lost from a solvating water molecule bound to Ni2+ or from the ligand in the second step of scheme A, although our analysis provides no direct information on this question.There is only a slight change in the visible absorption spectrum on going from NiMu+ to (NiMu)dep.FISCHER, KNOCHE, ROBINSON A N D WEDDERBURN 127 However, when the four ionisable hydrogens on Mu- are replaced by CH:, groups, it has been found that the equilibrium constant is no longer pH-dependent.l There- fore, it may be concluded that in NiMu+ the proton is lost from the ligand rather than from a bound water molecule. Since the pK, of free murexide (Mu-) is N 9.2, the effect of complexation (fig. 1) must increase the acidity of an -NH group. The pH-dependence of the equilibrium appears to be a general observation for divalent metal-ion complexation with murexide-l The analysis shows that it is relatively straightforward to describe quantitatively the thermodynamics and kinetics of complexation involving charged species up to I = 0.1 rnol dm-3.The Ni2+/Mu- reaction has proved to be it very convenient test system for this type of analysis, and also, since IA,Y"( is large, the reaction can be used to evaluate the performance of the pressure-jump instrument with optical detection. I Xlm FIG. 4.-Equilibrium spectrophotometric measurements for the Ni2+ + Mu- system in the presence of SDS. M = 2 x mol dm-3 ; L = 5 x mol dm-3 ; T = 25°C. Concentration of [SDS] : 1 , O ; 2, 2 x ; 3 , 4 x ; 4, 6 x ; 5, 8 x ; 6, mol dm-3 at pH 6. As indicated in the introduction, the Ni2++Mu- complexation reaction can be used to detect micellisation. Fig. 4 shows spectra obtained for Ni2+/Mu- com- plexation as the concentration of sodium dodecylsulphate (SDS) is increased in the region close to the c.rn.c.When micelles form in solution, Ni2+(aq) is partitioned out of the bulk of the solution into the region of the charged micelle surface according to scheme C , in which subscript B denotes the bulk region and subscript s denotes the surface region of the micelle. Ms represents the micelle surface Ki KH (Ni2+)B + MU-)^ + (NiMu)B+ + (NiMu)dep + H+. (C) M s n t M s n t ( Ni2 +)s (NiMu)$ It is a reasonable assumption, over the SDS concentration range studied, that binding of NiMuf to the micelle surface may be ignored, since the NiMuf ion is hydrophilic and only singly-charged. From the spectra in fig. 4, Ni2+ surface binding128 METAL-ION COMPLEXATION KINETICS begins to occur at concentrations above [SDS] = 4 x mol dm-3, for M = 2 x mol dm-3.The spectra may be used to evaluate the equilibrium constant K,, eqn (2). c+ is taken to be equal to [(Ni2+)B] +[(Ni2+)s] ; for the purposes of calculation of ionic strength the surfactant is assumed to be completely dissociated at all concentrations. The extinction coefficients E- and E ~ , ~ are known at a given pH from measurements described earlier, and the concentrations c+, c- and c1 are calculated for each solution by eqn (3)-(7). 1 .o 1 G a 4 h d - 0.5 0 2 4 6 8 10 [SDS]/103 mol dm-3 FIG. %-Plot of (Kl)app/Kl against [SDS]. Experimental conditions as in fig. 3. Kj. is equal to its value obtained with no addition of SDS, provided there is no charged surface present in solution. The changes in the spectrum at concentrations below 4 x mol dm-3 SDS (spectra 1-3 in fig.4) are due to the changing ionic strength of the solution on addition of SDS. When activity coefficients are intro- duced (eqn 2), Kl is found to be constant below 4 x mol dm-3 SDS. However, if micelles (or pre-micellar aggregates) are formed, the Ni2+ ions will be attracted to them, and [(Ni2+)B] will be less than c+. Thereby the value of Kl is apparently reduced, and it should be called (K1)app which approximately is related to the true equilibrium constant by A plot of (Kl)app/K1 against SDS concentration is shown in fig. 5. The plot clearly indicates that micelle formation begins at SDS concentrations of the order of 4 to 5 x mol dm-3. (A similar influence on complex formation of nickel mur- exide has been observed when polyelectrolytes are added to the solutions).16 This indicator method gives a very sensitive indication of the first appearance of micelle surface in the solution (which may, however, be in the form of pre-micelle aggregates).Hence we can hope to obtain precise information on micellisationFISCHER, KNOCHE, ROBINSON AND WEDDERBURN 129 thermodynamics in the monomer-micelle transition region, and the effect of additives on micellisation. There is a significant difference between this and other indicator methods so far used for monitoring the presence of micelles. Indicator dyes, e.g., pinacyanol chloride l7 and acridine orange '9 are hydrophobic and are hence ad- sorbed or absorbed into micelles. There is a possibility that such dye additives can act as nuclei for surfactant aggregation and hence induce micellisation below the true c.m.c.(measured in the absence of dye). It has also been found l 8 that acridine dyes can considerably stabilise anionic micelles. In the present system, because the indicator is located in the bulk aqueous phase, it does not perturb the micellar system. The effect of added divalent metal ions is to lower the c.m.c. slightly. However, the study of the properties of micellar solutions in the presence of divalent metal ions is especially relevant in relation to our kinetic studies on metal ion reactivity at charged interfaces.l 9 9 2o The c.m.c. should be distinguished from the concentration of surfactant at which micelle surface first becomes apparent (as demonstrated by the break in the Kl against [SDS] curve). The c.m.c.is defined (in an arbitrary way) from experimental data and must depend to some extent on the experimental method used. It is also very sensitive to the presence of impurities. However, the sharpness of the transition in fig. 5 indicates that our method is particularly sensitive to the occurrence of micellar phenomena. The approach indicates an SDS concentration of 4 x mol dm-3 for the first appearance of micelles at a nickel concentration of 2 x lod4 mol dm-3. Further experiments indicate that as the concentration of Ni2+ is reduced, the transi- tion point shifts to higher concentrations of SDS, tending towards the value deter- mined for the c.m.c. at zero added ionic strength of - 8 x In a subsequent paper, we will discuss in detail the implications of our measure- ments for c.m.c.determinations and report results obtained for various dynamic processes occurring in micellar solutions in the presence of an indicator system. mol dm-3.17 We thank the S.R.C. for funds for the purchase of equipment associated with this work, and NATO for a travel grant (to B. H. R. and W. K.). APPENDIX The relaxation time expressions [eqn (10) to (13)] are derived as follows. The rate equation for the slow step of scheme B is : ( y * is the activity coefficient of the activated complex.) Since eqn (1) is used for the activity coefficients, several of them cancel in eqn (17), so that : -- - dc+ dt For a small displacement xi of the concentrations from equilibrium, we have : - xi = Ct-Ct (19) similarly 1-5130 METAL-ION COMPLEXATION KINETICS Neglecting squared terms, we obtain From the stoichiometry of the reaction with /3 defined by the expression : x- = x+: the relaxation time expression then becomes : From mass balance considerations : x++x1+x, = 0.Furthermore, the deprotonation reaction (1) $ (2) + H+ is very fast, and so it can be assumed that the deprotonation equilibrium is maintained during the com- plexation reaction. Then : If the solution is buffered, xH = 0, and from eqn (24)-(26) we obtain : On the other hand, when the solution is unbuffered, xH = x2, and 7-1 = kiylI(c+ + c-p) +k--icH(KH + cH)-l. 7-l = klyI,(c+ + c-p) + k-l(CH f c2)(KH + CH + c2)-'* I = 4(4c+ + CNOT + c - + CNH: + c1 + c,) + I i n e r t +Ibuffer. (27) (28) yrI and p can be calculated from the ionic strength of the solution using the equa- tion : (29) Iinert and Ibuffer allow for the inert electrolyte and buffer added respectively.With CNO, = 2M and cNH; = L, eqn (29) can be rearranged to give : It can also be shown that : I = ~ M + L - O . ~ ( C I + c,)[4+KH/(cH+KH)] +0.5CH$.Iinert +Ibuffer. (30) p = 1 -2.3c+(Zf(l -0.6) dZ/dc+. (31) For buffered solutions : dI/dc+ = 2.5-0.5(1 +KH/cH)-~ and for unbuffered solutions : dI/dc+ = 2.5-0.5(1 +KH/cH)-l +(cl +c~)KH(KH+cH)-~+K~(K~ +C~+C&'. (33) The term (c, + c,) is obtained from combining eqn (2)-(6), so that :FISCHER, KNOCHE, ROBINSON AND WEDDERBURN 131 Thus complete expressions can be derived for all conditions. Only a small perturbation is induced using the pressure-jump method so that the condition xf < cf always holds.For the stopped-flow measurements, M > L, and then the reaction represents a small perturbation on c+ so that the equations developed are still applic- able. Under certain conditions, the relaxation equations can be simplified. For pH < (PKH-~), KH/cH < 1, and we have (neglecting the formation of any de- protonated complex) : 2-l = k-1 +klyII(c+ + c-p). (35) For pH > (pKH + 1), KH/cH >> 1, and then for unbuffered solutions : For buffered solutions : 2-l = k-1Ki ' ( c H + c,) + k,yI,(c+ + c-P). (37) If the measurements are performed under the condition c- < c+, (as in the stopped- flow experiments), eqn (27) may be simplified as : At constant ionic strength, a plot of 7-l against A4 has a slope of k,y,, (inde- pendent of pH), whereas the intercept depends strongly on the pH of the solution. H. Hohl, Ph.D. Thesis (E.T.H. Zurich, Switzerland, 1973). M. Eigen and K. Tamm, 2. Elektrochem., 1962, 66,93. M. Eigen and R. G. Wilkins, Mechanisms of Inorganic Reactions, ed. R. F. Gould, Adv. Chem. Series, No. 49 ( h e r . Chem. SOC. Washington, D.C., 1965), p. 55. G. Geier, Ber. Bunsenges. phys. Chem., 1965, 69, 617. C. T. Lin and J. L. Bear, J. Phys. Chem., 1971, 75, 3705. A. Jost, Ber. Bunsenges. phys. Chem., 1975, 79, 850. W. Knoche and G. Wiese, Rev. Sci. Znstr., 1976, 47, 209. H. Strehlow and J. Jen, Chem. Instr., 1971, 3, 47. ' H.-J. Buschmann and W. Knoche, Ber. Bunsenges. phys. Chem., 1977, 81, 72. lo M. Krizan and H. Strehlow, Chem. Znstr., 1973, 5, 99. l 1 B. H. Robinson, N. C. White and C . Mateo, Adv. Mol. Relax. Processes, 1975, 7, 321. l2 C. W. Davies, Zon Association (Butterworths, London, 1962). l3 H. Sigel, K. Becker and D. B. McCormick, Biochim. Biophys. Acta, 1967, 148,655. l4 A. Bonsen, F. Eggers and W. Knoche, Inorg. Chem., 1976, 15, 1212. l5 B. H. Robinson and J. H. Maclagan Wedderburn, unpublished results. l 6 S. Kunigi and N. Ise, 2. phys. Chem. N.F., 1974,92, 69. l7 See P. Mukerjee and K. J. Mysels, Critical Micelle Concentrations of Aqueous Surfactant '' A. D. James and B. H. Robinson, Adv. Mol. Relax. Processes, 1976, 8, 287. l 9 J. Holzwarth, W. Knoche and B. H. Robinson, Ber. Bunsenges. phys. Chem., 1978,9,4049. 2o A. D. James, and B. H. Robinson, J.C.S. Faraday Z, 1978, 74, 10. Systems, N.S.R.DS-NBS-36, 1971. (PAPER 8/693)

ISSN:0300-9599    

DOI:10.1039/F19797500119

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Characterisation of Water-containing Reversed Micelles by Viscosity and Dynamic Light Scattering Methods BY ROBERT A. DAY? AND BRIAN H. ROBINSON* Chemical Laboratory, University of Kent, Canterbury CT2 7NH AND JULIAN H. R. CLARKE AND JANE v. DOHERTY Chemistry Department, UMIST, Manchester M60 1 QD Received 31st May, 1978 The size and aggregation number of reversed micelles formed by the system aerosol-OT+H20+ organic solvent have been determined by viscosity and dynamic light scattering methods. For the viscosity method, a procedure for deriving values of the aggregation number from particles of variable density is described. Measurements were made in cyclohexane, toluene and chlorobenzene. The dynamic light scattering method, based on photon correlation spectroscopy, yields single exponential correlation functions from which values of the translational diffusion coefficient and the micelle radius can be derived.The droplet size was found to depend primarily on the ratio of surfactant to water concentrations, but was essentially independent of solvent and concentration at a fixed surfactant to water concentration ratio. Satisfactory agreement was obtained among the two methods discussed in this paper and one (sedimentation ultracentrifugation) described previously. Aerosol-OT (sodium bis-2-ethylhexylsulphosuccinate) or AOT (fig. 1) is an anionic surfactant capable of solubilising very large amounts of water in organic solvents. For example, in n-heptane, a 0.1 mol dm-3 solution of AOT can solubilize up to 10 % water. We have determined the size and aggregation number of the reversed micelles (or water-in-oil microemulsion droplets) formed by the three component system (fig.l), by the application of viscosity and dynamic light scattering methods. Such systems are of considerable topical interest, which, from our point of view, include the study of the properties of the heterogeneous water present in the aqueous core of the droplets and the mechanism of reversed micellar catalysis and of novel synthesis at interfaces. The nature of the water in reversed micelles has been recently investigated by n.m.r. spectroscopy.1° These studies indicate that when only small amounts of water are present, the solubilised water is highly immobilised. Bulk water properties are not observed until the water content of the system exceeds 1 %.As a prelude to the detailed study of the kinetics of reactions in reversed micellar media, it is necessary to determine the size and aggregation number of the droplets as a function of the concentrations of added AOT and water. Viscosity measure- ments have the advantage of being quick and easy to perform and the system is only mildly perturbed during measurement. Dynamic light scattering is a promising technique for measuring size parameters, and it has already been demonstrated ' 9 that by analysing scattered light intensity fluctuations using photon correlation spectroscopy (PCS) it is possible to study translational diffusive motions of macro- molecules and micelles suspended in aqueous s~lution.~ It is of interest, therefore, t Present Address : Department of Chemistry, University of Sheffield.132R . A . DAY, B . H . ROBINSON, J . H . R . CLARKE AND J . v. DOHERTY 133 to investigate whether the similar motions of reversed micelles could be measured using this technique. If the Stokes-Einstein equation is assumed to be valid for the reversed micelles, average micellar radii can then be derived from the measured diffusion coefficients. EXPERIMENTAL Using this device the kinematic viscosity is obtained, which is a measure of the volume fraction of solution taken up by the dispersed droplets. Considerable care is required when deriving values of the aggregation number from such data when the droplet has regions of different density. Measurements were made in cyclohexane, toluene and chlorobenzene over a range of R values (1-8) where R is defined as the molar concentration ratio (= [H,O]/[AOT]) in a given solvent.Measurements were performed at 293.3 K for cyclohexane and chloro- benzene and 294.7 K for toluene. Viscosity measurements were made by means of an Ubbelohde viscometer. ‘ZH5 I + / \ I \ / \ / 0 0 CH C H 2 CH3 C CH2 CH2 CH2 \ - -?-Y - - ” - 8 - - - - - - - - ‘rn ‘H20 I aerosol-OT structure of a reversed-micelle FIG. 1.-Formula of aerosol-OT (AOT) and postulated structure of a reversed micelle. The light scattering measurements were performed using a 24-channel digital clipped correlator (Precision Devices “ Malvern ” correlator) utilising 488 nm polarised radiation from an argon ion laser (Spectra-Physics Model 165). Samples of the microemulsions were contained in 1 cm2 cross-section clear glass cells.Each sample was centrifuged for x 18 h to remove suspended dust particles and finally allowed to stand for a further 24 h at which stage they were entirely clean and homogeneous. The optical aperture defining the scattering angle was located M 15 cm from the scattering source, and was 1 mm in diameter to minimise the coherence area.2 Scattered light further passed through a pinhole 8 cm behind the aperture and was detected by a photomultiplier (ITT FW130). Correlation functions were obtained for a series of angles with the scattering observed through either the front or side faces of the cells. Optical masks were used to minimise spurious light at the detector. It was necessary to make corrections for the large refractive index of the micro- emulsion to obtain the true angle of scattering.Aerosol-OT was a Fluka purum reagent ; reversed micelle solutions were prepared simply by adding water from a microsyringe to a solution of AOT in the organic solvent. An optically clear solution was formed after shaking for < 1 min. ANALYSIS OF VISCOSITY DATA We assume the droplets are spherical (as has been suggested previ~usIy)~ with a structure similar to that shown in fig. 1. In an ideal solution of non-interacting dispersed spheres the134 CHARACTERISATION OF REVERSED MICELLES volume fraction of the solution taken up by solute, 4, is related to the specific viscosity, qsp, by the Einstein equation : qsp = 2.54. (1) Cheng and Schachman ' tested the following extended empirical relationship (due to Guth and Simha)6 for values of q5 up to -0.10 and found it to hold well for dispersions of moderate concentration : qsp = 2.56+ 14.14'.(2) At the concentrations employed in our work it is necessary to use eqn (2). In the absence of added water it can easily be shown that if all the dispersant is associated in micellar form, 4 = (N[AOT]V&/(1000E) (3) where V, is the volume of a reversed micelle, 5 is the average aggregation number (number of AOT molecules per micelle) and N is Avogadro's number. 3 . 0 - 0 8 10 9 2 4 r, [H*Ol/[AOTl FIG. 2.-Dependence of 4 on [H20] for AOT in toluene from viscosity measurements T = 294.7 K ; [AOT] = 0.1 moldm-3. When water is added, the total micellar volume, Vm, is made up of a contribution from the water core ( VH~O) and the surfactant coat ( Vs).That is : Vm = VH,,+ V, and VHzo = SH20 iiR (4) where SH~O is the specific volume of a water molecule in the micelle. of the surfactant coat (fig. 1) : If rm is the total micellar radius, ~ H , O is the radius of the water core and I is the thickness Hence Values for SH~O and I (required for the calculation of 5 and YH~O) can be derived from experimental viscosity measurements by the following procedure. A plot of 4 against [H20] at constant AOT concentration has the form shown in fig. 2.R . A . DAY, B . H . ROBINSON, J . H . R . CLARKEAND J . v. DOHERTY 135 Above a certain value of R(#3), there is a linear dependence of 4 on [H20]. This suggests that : (i) the initially added water has a density which is apparently different from water added later.(ii) For R values >3, the density of the added water is found to be constant with respect to increasing water concentration. Furthermore, in cyclohexane and toluene, the slope of the line in fig. 2 is found to be 1.8 % mol-1 H2O indicating a water density of 1.0 kg dm-3 (i.e., as bulk water). A value for the surfactant contribution to the total solute volume, &, can be obtained from the extrapolated intercept on fig. 2. The high values of 4 at low R then suggest a more open or less dense structure of the aggregate. It is difficult to distinguish between effects due to surfactant or added water, for example there may be some restructuring of the surfactant region as the water content of the micelles increases and they become larger.However, if it is assumed that the surfactant density does not change, then derived values for the apparent densities of the water core for R < 3 are < 1.0 kg dm-3. is 1.1 nm, and the sulphonate head group is likely to be partially located in the water pool. An analysis of the intercept value of q5s suggests values for the density, pmic, of AOT of 1.3 kg dm-3 compared with a value of 1.14 kg dm3 obtained for the density (p) by direct pyknometry in the absence of added water in cyclohexane and ben~ene.~ If part of the AOT molecule is in contact with water in the core, Pmic/p N LIZ. In this way, values of 0.9 and 0.95 nm were derived in toluene and cyclohexane, respectively. By means of these values of SH20, I and 4 estimates for n' were computed using eqn (3), (4) and (6).From these, all the micelle size parameters were derived. A value for I of 0.9 nm can be estimated since the formal length (L) of the AOT molecule ANALYSIS OF LIGHT SCATTERING DATA In the PCS technique, the correlation function of the fluctuating photocurrent at the light detector (n(t)n(t+z)) is measured directly, where n(t) is the number of photodetections in a sample time interval from (t-At/2) to (t+A.t/2) and < . . .) indicates a statistical average over time origins. For signals with gaussian statistics it is sufficient (and more practical) to determine the single clipped correlation function (nq(t)n(t+z)) where q is a clipping level chosen to be close to the average number of photodetections in the sample time Ar.For a single-clipped correlator nq = 1 if n ( t ) > q and nq = 0 if n(t) < q. Under these conditions it can be shown that after taking N samples, the recorded correlation function is given by : where CE(Z) is the correlation function of the scattered electric field at the detector and Yq can be regarded as an empirically determined parameter. For scattering from particles executing translational diffusion CAT) is given by C&) cc exp (- &k2z) where k is the scattering wave vector and DT is the translational diffusion coefficient of the scattering species. The parameter k can be expressed in terms of the scattering angle 8, the incident light wave vector ko and the sample refractive index n, using the equation : k = 2nk0 sin (0/2).(9) For our particular case, the theory predicts that the correlation function is a single exponential, with a relaxation time ZD = (2&k2)-l, superimposed on a continuous back- ground, as given by eqn (7). Complications will arise if there is a range of independently diffusing species (arising from polydispersity) or if there are other dynamic processes coupled to diffusion. These may lead to non-exponential correlation functions and/or the inverse relaxation time may no longer be a simple linear function of k2. An additional problem encountered for suspensions in organic liquids such as toluene is the substantial intensity of Rayleigh scattering from the dispersing medium itself. (This136 CHARACTERISATION OF REVERSED MICELLES problem does not arise for aqueous suspensions due to the small scattering cross-section of water).Thus for a suspension 1 .O mol dm3 in H20 and 0.1 mol dm-3 in AOT the scattering intensity attributable to solvent was about the same as that originating from the suspended reversed micelles. Whilst relaxation processes involving the solvent occur at much shorter times and are assumed to be uncoupled to diffusion of micelles, this scattering contributed substantially to the background intensity and hence affected the statistical accuracy of the correlation functions. Satisfactory data were obtained, therefore, only for samples with R values >3. No correlation functions were observed for AOT solutions containing no added water. RESULTS Viscosity data obtained for pH o, ii and rH as a function of the water-to-surfactant ratio are shown in table 1, and the dependence of ii on the concentration of micelles at fixed R is shown in table 2.A typical correlation function and a plot of the reciprocal relaxation time against sin2 (0/2) are shown in fig. 3. Within the limits of statistical precision, the correlation functions could all be fitted to single exponentials, and it is seen that 76' shows a simple linear dependence on sin2 (0/2) (and hence k2). There was no evidence for the existence of substantial reversed micelle size fluctuations TABLE 1 .-SUMMARY OF RESULTS DERIVED FROM VISCOSITY MEASUREMENTS solvent ( E ) cyclohexane (2.02) toluene (2.38) chlorobenzene temp/K 293.3 294.7 (5.7 1)-293.3 N= [HzOl/[AOTl) P H ~ O ii r H 2 0 P E Z O n rE20 P E ~ O n rHZo 0.75 27 0.64 0.97 36 0.81 1.00 47 1.00 1.01 59 1.19 1.01 72 1.37 1.01 86 1.54 1.01 101 1.71 1.02 114 1.86 0.36 0.65 0.86 0.99 0.99 0.99 0.99 0.99 41 0.93 44 0.99 49 1.07 56 1.18 68 1.35 82 1.52 97 1.70 112 1.87 0.60 25 0.67 0.75 34 0.87 0.77 46 1.09 0.77 59 1.30 0.78 73 1.50 0.80 85 1.66 0.82 99 1.82 0.86 108 1.93 [AOT] = 0.10 mol dm-3 for all measurements.rH2O in nm, PH20 in kg dm-3. Likely error in E + &lo %. which should give rise to an additional k-independent scattering component. Such components might be manifest in non-exponential correlation functions and a non- zero intercept in the inverse time axis at zero scattering angle.2* However, such features are only observable if there is an appreciable permittivity change accompany- ing the size fluctuations.* The measured diffusion coefficients and mean micelle radii (calculated assuming the Stokes-Einstein relation DT = kT/6nyrm) are included in table 3.On subtracting the thickness of the surfactant coat (obtained from the viscosity data), rH20 is obtained. TABLE 2.-DEPENDENCE OF fi ON [AOT] IN TOLUENE AS SOLVENT AT 293.3 K. R = 5.4 [AOT]/mol dm-3 rHzo/nm ii 0.005 1.22 46 0.01 1.39 69 0.02 1.34 61 0.05 1.33 60 0.07 1.34 62 0.10 1.37 66R . A . DAY, B . H. ROBINSON, J . H . R . CLARKE AND J . v. DOHERTY 137 sin2 (8/2) FIG. 3.-Plot of inverse correlation time, T - ~ , against sin2 (8/2) obtained by photon correlation spectroscopy for micelle suspensions with R 21 10 in toluene at 20°C. 8 is the scattering angle (corrected for refractive index effects).Inset is a semi-log plot of a typical correlation function for R 2: 10, 8 = 88". TABLE 3 .-DERIVED VALUES FROM DYNAMIC LIGHT SCATTERING MEASUREMENTS IN TOLUENE AT 293 K (0 = STANDARD DEVIATION) R D~/lO-lo m2.s -1 a/10-11 rn2 s-1 rm/nm m20/nm 3.36 3.85 4.78 5.83 7.50 8.34 8.97 9.56 1.79 1.66 1.63 1.47 1.37 1.35 1.22 1.20 1.69 0.79 1.21 1.85 0.95 1.38 1.92 1.02 1.15 2.07 1.19 0.86 2.25 1.35 1.43 2.30 1.40 0.64 2.45 1.55 0.49 2.48 1.58 DISCUSSION Fig. 4 summarises results for the overall micelle diameter obtained by the two methods reported in this paper, together with data obtained by sedimentation ultracentrifugation for AOT-stabilised reversed micelles in heptane. Reasonable agreement is obtained using the three different methods. The data allow us to draw the following conclusions regarding the structure and stability of reversed micelles : (i) the average aggregation number increases rapidly as the [H,O]/[AOT] ratio increases.This is true for all solvents studied. (ii) The droplet size remains essentially constant when the concentration of AOT is varied at a fixed value of [H,O]/[AOT]. The primary factor which determines micellar stability in these systems is thus the ratio of water to surfactant rather than total concentrations or the solvent. (iii) The aggregation number (and hence m.w.) varies very little with the nature of the solvents used. (iv) The droplet systems are thermo- dynamically stable over long periods at room temperature. Although kinetic138 CHARACTERISATION OF REVERSED MICELLES evidence suggests that an inelastic collision process between droplets leads to the transient formation of dimer-type species, no evidence for such reactions was obtained by the dynamic light scattering method.(v) At high concentrations of added water, the water pool density is similar to that of bulk water, but for R values less than three, low apparent values are obtained. This probably indicates only partial occupancy of the core by added water ; possibly there is some " clustering " of solvated water molecules. (vi) The data in chlorobenzene indicate some differences in behaviour compared with the other solvents. Water solubilisation is more difficult in this solvent, and the maximum density of the water core is only 0.800 kg dm-3, indicating a more open structure.This is probably due to the reduced coulombic interactions 0.0 2.0 4.0 6.0 8.0 10.0 12.0 R = [H,O]/[AOT] FIG. 4.-Droplet diameter, dm, as a function of R. Open symbols are viscosity data for solvents A , toluene ; 0, chlorobenzene ; 0, cyclohexane ; + , ultracentrifuge data using n-heptane solvent, @, dynamic light scattering using toluene solvent. in chlorobenzene. It seems that the solubilising power of the different solvents is closely related to their permittivity values. (vii) The apparently simple form of the observed correlation functions does not necessarily indicate the absence of some polydispersity, only that the size distribution is rather small. For example, it is extremely difficult to resolve exponentials with relaxation times that differ by less than a factor of two even if the amplitudes are comparable.We can, therefore, only put an upper limit of x 50 % for the variance of the micelle size distribution. The light scattering and ultracentrifuge methods give excellent agreement in terms of weight-averaged values, but these are lower than those measured by the viscosity method. This difference may be significant in the interpretation of the results; e.g. it may give some indication of the extent of polydispersity. We especially thank Shell Research, Thornton for a CASE award (to R. A. D.) and the provision of the viscometer, and Mr. Peter Barlow of Shell for his guidance, encouragement, and interest in the work. We thank the S.R.C. for the provision of equipment associated with this project.R. A . DAY, B. H. ROBINSON, J . H. R . CLARKE AND J . v. DOHERTY 139 B. J. Berne and R. Pecora, Dynamic Light Scattering (Plenum, N.Y., 1975). Specialist Periodical Report, 1975), vol. 11. N. A. Mazer, G. B. Benedek and M. C. Carey, J. Phys. Chem., 1976, 80, 1075. M. B. Mathews and E. Hirschhorn, J. Colloid Sci., 1953, 8, 86. P. Y. Cheng and H. K. Schachman, J. Polymer Sci., 1955, 16, 19. E. Guth and R. Simha, KoZloidZ., 1936, 74,266. J. H. R. Clarke, G . J. Hills, C. J. Oliver and J. M. Vaughan, J. Chem. Phys., 1974, 61, 2810. B. H. Robinson, D. C. Steytler and R. D. Tack, J.C.S. Faraday I, 1979,75, in press. ’ P. N. Pusey and J. M. Vaughan, in Dielectric and Related Phenomena (Chemical Society ’ P. Eckwall, L. Mandell and K. Fontell, J. Colloid Interface Sci., 1970, 33, 215. lo M. Wong, J. K. Thomas and T. Nowak, J. Amer. Chem. SOC., 1977, 99,4730. (PAPER 8/1010)

ISSN:0300-9599    

DOI:10.1039/F19797500132

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Rate Constants for Hydrogen+Oxygen System, and for H Atoms and OH Radicals+Alkanes BY ROY R. BALDWIN“ AND RAYMOND W. WALKER Chemistry Department, The University, Hull HU6 7RX Received 2nd June, 1978 Rate constants at 500°C for the elementary steps in the Hz+O2 reaction have been revised to take into account self-heating of the reaction mixtures, reaction of 0 atoms with HzOz, and other refinements in the mechanism. By combination with independent data at lower temperatures, Arrhenius parameters for the reactions have been obtained. Rate constants for OH + RH [reaction (21)] and H+ RH [reaction (22)] for C2-C5 alkanes have been revised to allow for self-heating, and for reaction of 0 atoms and HOz radicals with the additive. Combination with data at lower temperatures has given Arrhenius parameters for the reactions.The results indicate that, to a first approximation, rate constants for an unknown alkane can be obtained by the relationships kZ,/k, = 0.214np exp (1070/T)+0.173ns exp (1820/T)+0.273nt exp (2060/T) kZ2 = 2 . 2 ~ lO1OnP exp (-4715/T)+4.9 x 1O1OnS exp (-4005/T)+5.1 x 101*nt exp (-3030/T), where np, n, nt are the number of primary, secondary and tertiary C-H bonds, and kl is the rate constant for the reaction OH+H2 = HzO+H(l). Previous studies of the addition of small amounts (0.1 % or less) of C2H6,1* C3H8,3 n- and i-C4H10 and neopentane to slowly reacting mixtures of H2 + O2 have enabled rate constants at 480-500°C to be obtained for the reaction of H atoms and of OH radicals with the alkane (RH). The basic principle of the method, given el~ewhere,l-~ can be illustrated by assuming (a) a simplified mechanism for the H2 + O2 reaction, (b) that H2 is only removed by reaction (1) and (c) that RH is only removed by reactions (21) and (22).In this case the relative rate of consumption of RH and H2 is given by eqn (i).? k21CRHI + k22CRH1 dCRH”dCH21 = k1[H2] k,[O,][M] OH+RH = H20+R H+RH = HZ+R. Because of the difficulty in measuring accurately the initial slope of the [RH] against A P plot, the experimental parameter used initially 2* was AP2*, the pressure change corresponding to 20 % loss of RH. Integration of eqn (i), with [H2] effectively constant, gives eqn (ii). P,l[MI - k21C02l[Ml k22 - +- A[H2]20 0.223 kl[H2] 0.223 k,’ (ii) 7 Reaction numbers have been chosen to maintain consistency with previous papers.140R . R . BALDWIN AND R . W . WALKER 141 By measuring the consumption of RH gas-chromatographically, and by using the pressure change AP,, to obtain A[H2I2,, the rate constants k,,/kl and k22/k4 can be obtained by a suitable graphical treatment of results obtained over a wide range of mixture composition. To refine this treatment, allowance has to be made for the following additional factors. (1) The pressure change resulting from the formation of H202, and from the oxidation of the hydrocarbon and its oxidation products, which becomes even more important if the pressure change corresponding to 50 % consumption (AP5,) is used so as to increase the accuracy of measurement of AP. (2) In the full mechanism for the H2 + 0, reaction in aged boric-acid-coated vessels, reaction (1) is not the sole source of H,O; moreover, the ratio [H]/[OH] is not as simple as that implicit in expressions (i) and (ii). (3) The pressure change does not give an accurate measure of the water formation and hydrogen consumption unless allowance is made for the slight self-heating of the reaction mixture.(4) Attack on the hydrocarbon by 0 atoms and by H02 radicals, although relatively unimportant, does influence the final values obtained for k21/kl and k22/k4. The method of handling each of the factors is discussed below. PRESSURE CHANGES RESULTING FROM OXIDATION OF ALKANE For each of the alkanes studied,2* 6-12 detailed analyses of reaction products have been made for a certain number of mixtures up to an alkane consumption of over 60 %.Significant yields of carbon monoxide and other products are found, indicating substantial oxidation of the primary products. An overall oxidation equation of the form given by eqn (iii) can thus be written. (iii) The value of b is calculated so that the sum of the carbon atoms in the products is equal to n, and c is obtained by assuming that all the (2n +2) H atoms not found in CnH2n+2 + a 0 2 = b(carbon-containing products) + cH,O. TABLE 1 .-OVERALL EQUATIONS FOR HYDROCARBON OXIDATION AT 50 % CONSUMPTION TEMPERATURE 480°C (ETHANE 500°C) mixture H2 0 2 N2 RH a 0.85 0.91 1.21 140 70 285 5 b 1.24 1.54 2.01 c 1.23 1.16 1.37 a0.92 1.17 1.76 140 355 0 5 b 1.25 1.56 2.19 c 1.32 1.42 1.90 a 0.84 0.76 0.94 425 70 0 5 b 1.27 1.57 2.05 c 1.17 0.96 1.04 1.31 1.68 1.31 1.51 1.82 1.68 0.96 1.62 1.11 1.79 2.67 1.71 2.63 2.82 2.61 1.79 3.02 1.62 1.27 1.94 1.60 1.91 2.08 2.32 1.24 1.99 1.60 1.28 2.97 1.20 2.27 3.58 2.67 2.00 3.46 2.22 the carbon-containing products are present as H20.Values of a, b and c, for all the alkanes studied at 50 % consumption are given in table 1 for each of the three main H, + 0, + N2 mixtures used in the analysis of reaction products. The value of (b + c - a - 1) changes only slightly with mixture composition, so that by using these mixtures as a guide, the small pressure changes due to oxidation of the alkane and its products can be calculated with an accuracy such that the corrected1 42 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM pressure change is accurate to within 2 %.No correction is made for the pressure change due to H202 formation, as this is included in the computer program used to interpret the experimental results. ALLOWANCE FOR ALL REACTIONS REQUIRED I N THE MECHANISM OF H24-02 REACTION OH+RH = H2O+R (21) H+RH = H2+R (22) O+RH = OH+R (23) Previous papers 13* l4 have described a computer program which predicts the reaction profile for the full mechanism necessary to interpret the experimental features of the H2 + O2 reaction in aged boric-acid-coated vessels. Reactions (21)-(24) involving attack on RH by OH, H, 0 and HO, have been added to this scheme. Product analysis shows that the majority of alkyl radicals formed by this attack either undergoes reaction (25) to form the conjugate alkene and H02, or forms an oxygenated compound and OH by the overall reaction (26). Because of the very low concentrations of RH used, the occurrence of reactions (21)-(24), and (25) and (26) does not significantly alter the relative concentrations of OH, H, 0 and H02 from their values in the absence of RH; this is confirmed by the absence of any effect of RH at these low concentrations on either maximum rate, or the induction period (expressed as the time to one-half maximum rate).EFFECTS RESULTING FROM SELF-HEATING The temperature rise in an exothermic reaction is givsn 15* l 6 b y eqn (iv) : PC,(dT/dt) = R H - A;l(T- To)/d2 (iv) where p is the density, C, is the molar heat capacity, RH the rate of heat evolution. A is the constant in the equation h = (A;l/d2)V/S for the heat transfer coefficient, h, between the gas, volume V, and the vessel surface area, S.A is the thermal conductivity of the gas, d the vessel diameter, and To the initial temperature. Insertion of reason- able values shows that dT/dt is effectively zero within one second, so that with the rates involved in the present work, a stationary temperature rise AT = (T-To) given by dT/dt = 0 may be assumed. For H2 +O, +N, mixtures, the rate of heat evolution may be calculated either from the stoichiometric equations for the production of the stable products H 2 0 and H202, or by summing the heat produced by each elementary step. In the presence of alkane, the latter procedure has been adopted because of possible un- certainties in the mode of formation of a product, though the contribution from alkane reactions is, in any case, small.The conductivity 3, of the mixture was calculated using the Wassiljewa l7 equation for a two-component system, one component being H, and the other being a gas of conductivity equal to the weighted mean of the remaining components ; since the remaining components all have similar conductivities, this procedure is unlikely to introduce any appreciable error. From an analysis made by Tyler,18 based on a treatment by Boddington, Gray and Harvey,lg a value of A = 32 has been taken on the grounds that AT will be small,R . R . BALDWIN AND R . W. WALKER 143 rather than the value of A = 21.6 used by Foo and Yang.16 For the range of H2+O2+N2 mixtures used in previous studies, which gave reaction rates in the range 0.05-0.3 Torr s-l pressure change at 500"C, the calculated values of AT were in the range 0.5-2.5"C.Attempts were made to measure these rises in temperature experimentally, but although values of the correct order were obtained, the experi- mental fluctuation with different thermocouples suggested that the calculated values were more accurate than the measured values. EFFECT OF SELF-HEATING ON THE CONSTANTS OF Hz+Oz REACTION OH+H2 = HzO+H (1) H+O2 = OH+O (2) O+H, = OH+H (3) H+02+M = HOzSM (4) HzOz+M = 20H+M H+HO2 = 20H H+HO2 = Hz+02 H+HO2 = H2O+O HO2 + HOz = H2Oz + 0 2 HO2 +H2 = H202 + H O+H2Oz = H20+02 0 + H202 = OH + HO2 H+H202 = HzO+OH H+HzOz = H2+HOz OH + H202 = HZO + HO2. Previous papers 13* l4 have interpreted the induction period and maximum rate of the slow reaction, and the second explosion limit, in terms of a number of para- meters. The values of these parameters at 5OO0C, if no allowance is made for self- heating, are listed in the first line of table 2, together with the r.m.s.deviation between observed and calculated values for the induction period, the maximum rate, and the second limit. Of the parameters required, k , can be obtained from a direct study 1 4 9 2o of the decomposition of Hz02, k2/k4 from the second limit 21 in KC1-coated vessels, and the ratio k14a/k14 from studies 22 of the decomposition of H202 in the presence of H2. ks,, k13 and k13a were assumed to be zero in this treatment.l3' l4 Of the remaining parameters, the induction period is largely determined by k , /kto, which can thus be evaluated from measurements of induction periods over a wide range of mixture composition.The rate of the slow reaction is determined by k2/k,, k7, kll/k$o, k14/k2, k14a/k2 and k I 5 / k l , so that by measuring the rate as a function of mixture composition, the unknown parameters k14/k2 and k15/kl can be obtained. The remaining unknown parameter,:% kh/k2icf, can be evaluated from measurements of the second limit in aged B,O,-coated vessels over a wide range of mixture com- p0siti0n.l~ As shown by previous analysis,23 the maximum rate of the slow reaction is essentially the rate of decomposition of Hz02 which reaches a quasi-stationary concentration determined by reactions (14), (15) and (1 1). Self-heating increases * k8 and k8b are effectively indistinguishable kinetically and k: is used to denote k8 + ksb.144 RATE CONSTANTS FOR H , + O , + A L A K N E SYSTEM the reaction rate mainly because of the high value of E7 (w 190 kJ mol-l), thus reducing the values of k,4/k2 and k15/k1.The value of kll/kfo is obtained from the induction period, defined as the time to one-half maximum rate, and since the maximum rate is increased by self-heating, k, l/kto increases, as shown in line 2 of table 2. Since the original analysis,' 3 9 l4 an estimate of the rate constant for 0 + H202 has been given,24 and it has also been found possible 25 to evaluate the ratio ks,/kakto from second limit measurements, as well as kk/k2k;fo. Incorporation of reactions (8a) and (13) into the computer treatment affects slightly the values obtained for the other parameters, O+H202 having the greatest effect on k15/kl, and reaction @a) having the greatest effect on k;/k,kf,.Both reactions (8) and (8a) play only a minor role in the slow reaction. Lines 2 and 3 in table 2 show the effect of introducing reaction (13) with k13/k3 = 10.4 on the assumption that the measured 24 rate constant for 0 + H202 is k13. Line 4 gives the effect of introducing reaction (8a). Compari- son of lines 4 and 5 indicates the effect of replacing reaction (13) by (13a). Since a choice between these reactions is not feasible, possible errors are minimised in the last line by taking k13/k3 = k13a/k3 = 5.2. Although, except for kL/k2ki0, the changes from previously published values are almost within experimental error, the new figures given in line 6 now represent the most accurate values and supersede those given ea~1ier.l~ TABLE 2.-oPTIMUM PARAMETERS FOR Hz + 0 2 REACTION AT 500°C optimum values from slow reaction induction period rate optimum value from second limit self- -- r.m.s.r.m.s. r.m.s. heating k13/k3 kl3=/k3 k l l / k t o deviation/% k14/k2 k15/kl deviation/% keo/klk'2;, ks/kzkto deviation/% O+H202 no 0 0 0.0289 4.0 246 4.7 5.8 0 0.32 3.8 yes 0 0 0,0360 4.8 287 5.04 3.8 0 0.32 3.7 yes 10.4 0 0.0363 4.4 293 3.70 2.9 0 0.34 4.8 yes 10.4 0 0.0363 4.3 280 3.73 2.8 0.088 0.55 1.2 yes 0 10.4 0.0363 4.5 279 4.48 3.3 0.078 0.52 0.9 yes 5.2 5.2 0.0366 4.5 281 4.06 3.1 0.081 0.53 1 .o To evaluate kk, kga, kll, k14 and k15 from the ratios? in table 2, values of k , , k, and klo are required. The line drawn by Baulch et aLZ6 through the points for k, covering the temperature range 300-1200 K lies significantly above the point in the range 600-900 K.However, the results obtained by Greiner 27 (295-495 K), Eberius et al.28 (476-1150 K) and Westenberg and de Haas 2 9 (298-745 K) lie on a well defined curve. Points taken from this curve over the range 300-900 K are described by eqn (v) with a r.m.s. deviation of 3.0 %. This gives k , = (4.06If0.4) x lo8 dm3 rnol-1 s-, at 500°C. In view of recent accurate measurements 30 of k(H+C,H,) = 1.32 x 10" exp (-4715/T) = 2.96 x lo8 at 500"C, it is considered that combination of this value with k(H+C,H,)/k, = 33.7, given later, provides a more accurate estimate of k, = 7.65 x lo6 at 500°C than the value of 3.95 x 10, obtained from the expression recommended 26 by Baulch et al.A number of determinations 3 1 9 32 have given klo = 2.0 x lo9, independent of temperature. From these values, ks, = 2.8 x lolo, kg = 1.81 x lo',, k , , = 1 . 6 4 ~ lo3, k,, = 2.15 x lo9, k14a = 2.6 x lo8, k15 = 1.65 x lo9 at 500°C. k , = 1.28 x lo5 T s exp (- 1480/T). (v) t All rate constants and ratios are given in dm3 mol s units.R . R . BALDWIN AND R . W . WALKER 145 The change in the values of kk and k8, from those given in an earlier paper,25 is almost entirely due to the new value taken for k2. No new measurements at other temperatures have been reported. Combination of the new values of (k, +k,b) and k8, with values 24 at lower temperatures, as in an earlier paper,25 gives A8 = 5.4 x mol-l. With as assumed activation energy of 90 kJ mol-l, the value of kll gives A l = 1.97 x lo9 dm3 mol-1 s-I.The value of k15 = 1.65 x lo9 at 500°C may be combined with earlier estimates over the range 300-460 K 3 3 and 298-666 K 34 to give A15 = 3 . 7 ~ lo9, E15 = 4.8+ 0.6 kJ mol-l. lo1', E8 = 7.6 kJ mO1-l, Asa = 2.8 x lo1', = 0, A g b = 5.5 X lo'', E8b = 7.6 kJ 1000 KIT FIG. 1.-Variation with temperature of rate constant for H+H202. 0, k14, present work ; x , k14a, present work; A, (k14+k14a), from Klemm et aZ;35 -, lines using data of Albers et aZ;24 - - -, lines using data of Klemm et aE.35 In a previous paper,25 the ratio k14a/k14 at 44O-48O0C, obtained from studies of the H2+H202 system, was combined with a value obtained by Albers et aZ.24 for k14aD/k14D, the corresponding ratio for D atoms reacting with H202, to give (E14- El&) and A14/A14a on the assumption that k14a/k14 = k14aD/lf14D. A better estimate is obtained by the use of k14a/k14 = 0.143 at 450°C,22 which gives (E14- E14J = 17.5 kJ mol-l, A14/A14, = 128 on the assumption that the ratio k14,D/ k14D = 10 given by Albers et al.refers to the lowest temperature used. (If their ratio refers to the mean temperature, A14 then becomes unreasonably high). Albers et aZ.24 give E14aD = 17.6 kJ mol-l, and a reasonable estimate 3 5 of (E14,- is 3.0 kJ mol-I, so that E14, = 20.6 kJ mol-1 and E14 = 38.1 kJ mol-l. With these activation energies, the experimental value of k14 = 2.1 x lo9 at 500°C gives A14 = 8.0 x 1O1I and hence A14a = 6.3 x lo9. However, a recent paper 3 5 has given values for (k14+k14,) in the temperature range 283-353 K higher, by a factor of ~ 1 0 , than those obtained by Albers etaZ.24146 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM These results are shown in fig. 1, which also gives the lines corresponding to the above expressions for k14 and for J ~ 1 4 ~ , and which are derived by use of the low temperature results of Albers et al.Klemm et aL3' give reasons why the method used by Albers et al. might give low values for k14 and k14a. If their own results are accepted, their points can be linked to the high temperature values of k14 and k14a with almost equal scatter. The former case would give A14 = 3 . 6 ~ 1O1O, EI4 = 18.1 kJ mol-'. Klemm et al. (fig. 5 of their paper) adopt this view and suggest a much higher value of E14a = 40 kJ mol-1 based on our own studies of the H, + H202 system, but we do not believe the accuracy of those results is sufficient to justify this decision.Combination of the results of Klemm et al. with the value of k14a at 500°C gives E14a = 8.9 kJ mol-l, A14a = 1.05 x lo9, and EI4 would then have to be greater than E14a. There seems no way of resolving the discrepancies in the low temperature results. Use of the results of Albers et al. gives parameters consistent with those obtained for reactions (8) and @a), as discussed earlier,25 but further work is required. EFFECT OF ATTACK BY 0 AND BY HO, ON RATE CONSTANTS H+RH AND OH + RH By adding reactions (21)-(24) to the mechanism already used for the slow reaction of H, + 0, +N2 mixtures, a computer program can be written to construct the relationship between the alkane consumption and the pressure change, including allowance for the effect of self-heating both on the rate constants and on the pressure change.By interpolation, the pressure change corresponding to 50 % consumption of alkane can be calculated, and the r.m.s. deviation between observed and calculated values obtained. By incorporating an optimisation procedure, the parameters k , / k , and k22/k2 can be adjusted so as to give minimum r.m.s. deviation for a wide range of mixture composition* with [H2]/[0,] ratios ranging from 12 to 0.075. To operate the program, values of k23/k3 and k24/k$o must be supplied, but since reactions (23) and (24) play a relatively minor part in the consumption of alkane, approximate estimations of their value are sufficient.Values of kZ3 for the various alkanes were obtained using the expressions given by Heron and Huie 37 for attack at individual C--H bonds ; the value of k3 = 1.74 x 1O1O exp (-4755/T) was used.26 The values used for k23/k3 at 480°C for the alkanes c2H6, C3Hs, n-C4H1,, i-C4H10, neopentane, n-CSHI2 and 2,2,3,3-tetramethylbutane (TMB) were 9.4 (5OO"C), 61, 103, 87, 37, 629 and 52, respectively. The values of k,,/kfo were based on the preliminary estimates? of k24/k24f of 0.028, 0.080 and 0.13, for C2HG, C3Hs and i-C4H10 respectively at 440-500"C, obtained from a study of the addition of these hydrocarbons to HCHO +- 0, mixtures in KG1-coated vessels. From the value at 500°C of k24fjkfo = 22.7 (dm3 mol-1 s-l)*, (18.9 at 488OC) and on the assumption of additivity of attack at the different types of C--H bond, values of k24/klo at 480°C for the above hydro- carbons, except TMB, were estimated as 0.70 (5OO0C), 1.8, 2.9, 2.8, 1.1 and 3.8, respectively. For TMB, an experimental determination 3 9 at 440°C was used, with a suitable activation energy to give k24/kt0 = 0.67 at 480°C.Preliminary experi- ments 40 with C2HG added to TMB+02 mixtures confirm the similar values for C2H6 and TMB. HOZ + HCMO HZOL -t-HCO. (24 f 1 * The experimental data for most of the alkanes discussed here are given in ref. (2), (3), (10)- p The original estimates 38 have been reduced slightly in view of the contribution from OH attack (12) and (36). on the RH, which preliminary calculations indicate to be of some significance.R .R. BALDWIN AND R . W . WALKER 1 47 RATE CONSTANTS FOR H+RH AND OH+RH The effects of the various corrections discussed are illustrated in table 3 for two hydrocarbons, C3H8 and i-C4Hlo. The original correction to the pressure change caused by reactions of the hydrocarbon was 3A[RH], based on the overall reaction given below for the formation of the main primary products, namely conjugate alkenes. The effect of the improved correction, based on product analysis, can be seen in lines 1 and 2 of table 3 for C3H8, and in lines 6 and 7 for i-C4Hlo ; k21/kl is reduced by * 10 % and k,,/k, by x 5 %. The effect is most marked for hydrocarbons with the highest values of k,,/k,, kZ2/k2, since AP50 is small. CnHZn+2 4-40, = CnH2n + H20.TABLE 3.-EFFECT OF CORRECTIONS ON VALUES OF k21/kl AND k22/k2 optimum values of correction r.m.s. % RH to A P A k23/k3 k24/kto kzl/kl k22/k2 deviation 1 C3H8 2 3 4 5 6 n-C4Hlo 7 8 9 10 11 “HI 12 analysis analysis analysis analysis analysis analysis analysis analysis analysis “HI12 0 0 0.0835 0.0835 0.0835 0 0 0.0835 0.0835 0.0835 0.0835 0 0 0 54 54 0 0 0 92 92 92 0 18.2 145 0 17.8 144 0 15.9 140 0 13.4 143 1.8 9.9 125 0 30.0 264 0 27.7 255 0 24.1 242 0 19.9 245 2.9 13.2 217 3.5 12.0 211 4.2 4.5 4.3 5.8 4.1 8.1 9.9 8.5 10.0 7.2 6.6 Comparison of lines 2, 3 for C3H8 and lines 7, 8 for i-C4H10 shows that the introduction of self-heating reduces k21/kl by = 10-15 % and has a smaller effect (< 5 ”/o) on kZ2/k2. The effect will be significantly less for C2H6 because the values of AP50 are much larger.Comparison of lines 3, 4 and 8, 9 shows that introduction of 0 + RH reduces the value obtained for the kinetically equivalent OH + RH, the ratio k, / k , decreasing by *15 % for all hydrocarbons as expected. Comparison of lines 4, 5 for C3H8, and lines 9, 10 for n-C4Hl0 shows that introduction of HO, +RH reduces k2,/kl by =25-35 % and k2Jk2 by z 10-15 %, the effects being most marked for those hydrocarbons with the highest value of k24/kf0. Comparison of lines 10, 11 for n-C4Hlo shows that a small uncertainty in the value of k24/kto has some effect on k,,/k, but much less effect on k,,/k,. Table 3 shows that the effect of all the corrections is to reduce the value of kZ1/kl TABLE 4.-RATE CONSTANT RATIOS AT 480°C FOR H+RH AND OH+RH 2,2,3,3- hydrocarbon C2H6 t C3Hs n-C4Hl0 ~ - C ~ H I O neo-CsHl2 n-CsH12 tetramethylbutane k2 1 lkl 5.7 9.9 13.2 12.6 10.2 18.1 8.0 k2 2 lk2 39 125 217 223 52 309 112 number of mixtures used 28 27 27 29 17 13 12 r.ni.s.% deviation 3.5 4.1 7.2 7.6 5.4 7.3 8.2 t Value at 500°C.148 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM by a total factor of nearly 2, and that each correction makes a significant contribution. In contrast, the effect on k2,/k2 is much less marked. The optimum values of k2,/kl and k22/k2 for all the hyd,rocarbons studied are shown in table 4. RATE CONSTANTS FOR OH+RH Absolute values of the rate constants k,, for each hydrocarbon can be obtained if the value of k , is known. For comparison with Greiner's values 41 for these hydrocarbons, however, it seems more logical to compare the present ratios of k,,/k, 2.L 2.c 1.6 n s s, --- cl N 0 9 1.2 - d 0.L 1 I 1.2 1.6 2.0 2.L 2.8 3.2 1000 KIT FIG.2.-Variation of kzl/kl per CH bond with temperature. CzHs neo-C5Hlz TMB (CH3)3CH Greiner 41 0 A v present work 0 A v (a) Tertiary C-H, (6) primary C-H for CzHs, CSH12, (c) primary C-H for TMB. with those obtained by Greiner using his values both for OH + RH 41 and his expres- sion k , = 4.07 x lo9 exp (-2023/T) for OH +H2,27 since in this way small experi- mental errors in Greiner's work, such as the calibration for OH concentration, may cancel out. A number of workers 379 41-43 have suggested that a reasonably accurate rate constant for the total radical attack on an alkane can be obtained by assuming additivity of attack at the three different types of bond, primary, secondary and tertiary, in the molecule.Fig. 2 shows a composite plot of k8'/kl per C-H bond* * As in previous papers, subscripts e, p, nb, ib, pe, np and tb are used to indicate rate constants for CzH6, C3H8, n-C4Hlo, i-C4H10, n-C5Hl2, neopentane and 2,2,3,3-tetramethylbutane, respectively. Superscripts p, s and t are used to denote attack at primary, secondary and tertiary C-H bonds, respectively.R . R. BALDWIN AND R. W. WALKER 1 49 for hydrocarbons containing only primary C-H bonds over the range 0-5OO0C, obtained by combining the present results with those of Greir~er.~, In view of the experimental scatter, particularly apparent in Greiner’s data, the results for CzH6 and neo-C5H12 are considered to lie on a common line giving k$,/k, = 0.214exp (1070/T).Although Greiner, from his data alone, considered that neo-C5HI2 and tetramethylbutane lay on a common line with C2H6 having a different gradient, the high temperature point suggests that a separate line can be drawn through the points for tetramethylbutane giving k$,/k, = 0.062 exp (1520/T) per C-H bond. 1.8 1.L n r. s I N W * M 2 1.0 - 0.6 I 1 I 1 I 1.2 1.6 2.0 2.1 2.0 3.2 3.5 0.2 1000 KIT FIG. 3.-Variation of k i , / k , per CH bond with temperature. C3Hs n-C4Hlo n-C5HI2 n-CsHls 0 - Greiner 41 0 A present work 0 A X Fig. 3 shows the plot for secondary C-H bonds. Using the mean value of k;, for C2H6 and neo-C5H12 at each temperature from fig. 2, the value for 6 primary C-H bonds has been subtracted from the values of k2,/k, for C,H,, n-C,Hlo, n-C,H,, (present results only) and n-CsHls (Greiner’s results only).The values per C-H bond again give a common plot with no significant trends, and the best straight line gives k”,,lk, = 0.173 exp (1820/T). Fig. 2 also shows the plot for a tertiary C-H bond, obtained by subtracting the value for 9 primary C-H bonds from the total rate constant ratio for i-C4Hlo. The straight line gives the expression k‘,,/kl = 0.273 exp (2060/T). The overall rate constant k,, can thus be expressed by eqn (vi), k , , / k , = 0.21411, exp (1070/T) +0.173nS exp (1820/T) +0.273nt exp (2060/T) (vi) where pi,, n, and nt are the number of primary, secondary and tertiary C-H bonds. Although this equation provides the most useful general method of calculating the150 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM relative proportions of the various radicals formed by OH attack on an alkane, its accuracy may be limited in specific special cases.The only independent work appears to be that of Booth, Hucknall and S a m p ~ o n , ~ ~ who produced OH radicals in a mixture of two hydrocarbons by thermal decompo- sition of H202 and measured the yields of alkene produced. They obtained the rate constant ratios at 653 K given in table 5, which are in close agreement with the rate constant ratios given by eqn (vi) at 653 K. It would be useful to add the data obtained by Booth et to fig. 2 and 3 to reinforce the higher temperature values, but this would require an accurate knowledge of k(OH+RH)/k, for one of the hydrocarbons, preferably C3H8.The uncertainty in this ratio is at least as great as the small discrepancies between the ratios obtained by Booth and those given by eqn (vi). The ratios given by Booth et al. for C2H6/C3H8 and for (n-C4H10/C3HS) require k21s/k211, = 3.5 at 653 K as compared with 2.5 from the plots in fig. 2 and 3. However, a line drawn through the experimental point for C2H6 in fig. 2 would reduce k21s/k21p below 2.5. The slightly higher selectivity required by the data of Booth et al. is within the experimental accuracy of their data, but may also be caused by some attack by the more selective HO, radical which, according to calculations given in their paper, will occur to some extent. TABLE 5.-RATE CONSTANTS FOR OH ATTACK ON ALKANES AT 653 K 6.72 0.54 0.46+ 0 05 n-C4H10 1.12 2.80 - 17.72 1.45 1.54+ 0.1 3 i-C4H1 ,, 1.12 - 6.55 16.63 1.35 1.28+_ 0.07 1.12 - - C2H6 C3Hs 1.12 2.80 - 12.32 (1 .w (1 .OO) Although only ratios of k2 , / k l have been given, absolute values of k2 for primary, secondary, and tertiary bonds, and for the overall values for individual hydrocarbons, can be obtained by combining these ratios with the recommended expression (v) for k, over the range 300-900 K.RATE CONSTANTS FOR H+RH With (E2-E22e) = 31 kJ mol-l, the ratio kZ2Jk2 = 38.7 at 500°C would become 44.0 at 480°C. From the expression 30 given earlier for k22e, k2 = 5.73 x lo6 at 480°C. The absolute values of k(H+RH) at 480°C can then be calculated from the data in table 4. The ratios k22/k2 for CzH6, neo-C,M,, and 2,2,3,3-tetramethylbutane give values of k,P,/k2 per primary C-H bond of 7.3, 4.4 and 6.2, respectively, at 480°C.The discrepancy for neo-C,H, , is well outside experimental error. A possible explanation of these results and the corresponding values for OH attack is that the C-H bond strength in neo-C,H,, is rather higher than in the other two hydrocarbons (which would affect H attack more than OH attack), but that steric hindrance is greater with 2,2,3,3-tetramethylbutane in the case of OH attack. Subtracting an average value of 7.0 per primary C-H bond from the ratios for C3Hs, n-C4Hlo and n-C,H12 gives values of 41.5, 43.5 and 44.5 for k”,,lk, per secondary C-H bond at 480”C, respectively. From the ratio for i-C4Hlo, ki2/k2 = 160 per tertiary C-H bond. A reasonable estimate of the ratio k2,/k2 for any alkane at 480°C is thus given by eqn (vii) (vii) k22 Jk2 = 7.011, + 43n, + 160n,.R.R. BALDWIN AND R. W. WALKER 151 Absolute values of k22 can be obtained by use of the value of k, = 5.73 x lo6 given above. Surprisingly, no new measurements of k,, for hydrocarbons other than C2H6 have appeared45 since our earlier paper.46 Two types of study at lower temperatures were then available. (a) Kazmi, Diefendorf and Le Roy 47 produced H atoms by dissociation of H, on a heated tungsten wire. Recent discussion 30 indicates the difficulty of determining the stoichiometry in such a system, though evidence for a ratio (H atoms consumed)/ (RH consumed) of 6 for C3H8 has been given.47 9.0 8.0 h 3 ?, rl 1 1 i3 “E 7.0 z. s b;; 0 0 6.0 -.I 1 .o 1 .L 1.8 2.2 2.6 3.0 3.1, 1000 K / T FIG.4.-Variation with temperature of rate constant for H+ C3Hs. present work Kazmi et aL4’ Darwent and Roberts 48 k(t0tal) - - - 0 A kfor s-CH2 - 0 n El (b) Darwent and Roberts 48 produced D atoms by the photolysis of D2S, and determined the ratio k(D + RH)/k(D + D2S) over the temperature range 300-750 K. In earlier papers,49* so k22 was evaluated from their ratios using their ratio of k(D + H2)/k(D + D2S) and Shavitt’s 51 evaluation of k(D + H,) ; it was assumed that k(D + RH) = k(H + RH). If the reliability of the recent figure for H + C& is accepted, a more direct evaluation from Darwent and Roberts’ data may be made using their ratios for k(D + C2H6)/k(D + D2S) to eliminate D + D2S, the only asswmp- tion being that k(D + RH)/k(D + C2H6) = k(H + RH)/k(H + C2H6).Fig. 4 shows the values for H+C3H8 obtained in this way from Darwent and Roberts’ data, and from the revised treatment of Kazmi, Diefendorf and Le Roy.47 The plot gives A22p = 1.93 x 10l1 and an overall activation energy E22p = 34.9 kJ rnol-l, identical with the previously published value. The plot also shows the data for the secondary CH, group, obtained by subtracting the rate constant for C2H6 from that for C3H8, on the assumption of bond additivity. The corresponding parameters are = 4.80 x 1O1O dm3 mol-1 s-l per second- ary C-H bond. = 33.4 kJ mol-l,I52 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM Combinations of Darwent and Roberts’ data 48 for n-C,H,,, treated as for C3Hs, with the present value at 480°C give &2nb = 34.1 kJ mol-l, k f 2 2 n b = 2.85 x l o l l and Ai2nb = 2.00 X loll, or 5.0 x 10’’ per secondary C-H bond, Ei2nb = 33.2 kJ mo1-l.Corresponding treatment for i-C4H10 gives E221b = 27.1 kJ rnol-l, E i 2 i b = 25.2 kJ mol-l. Unfortunately, the difference (E22e -Ez2J = 5.9 kJ mol-1 is not consistent with the estimate of E$’2p-Ei2P = 8.4k0.8 kJ mol-l obtained by Campbell, Strauss and I I 1 r Y 0 1 2 3 1000 KIT 2.0 1 FIG. 5.-Plot of log (kpZzp/kB,,p) against 1/T for C3H8. A Present work; 0, Campbell et al.,52 low intensity static system ; x Campbell et al.y52 high intensity circulating system. Gunning 5 2 by measurement of the yield of isomeric hexanes obtained by the attack of H atoms, produced by Hg-photosensitisation of Ha, on C3H8 over the temperature range 300-450 K.If a value at 480°C is obtained by assuming that attack on the primary C-H bonds in C3H8 has the same value as for C2H6, the activation energy difference (fig. 5) increases to 10.8 kJ mol-l. If the data of Campbell, Strauss and Gunning are extrapolated to 480°C to obtain k$,,/k”,,,, the resultant value of kiZ1, reduces slightly the value of obtained from fig. 3, so that the discrepancy remains. TABLE 6.-ARRHENIUS PARAMETERS FOR H+ RH using results of Campbell et aZ.52 recommended - type of bond E/kJ mol-1 A per C-H bond E/kJ mol-1 A per C-H bond primary 39.2 2.2x 1O’O 39.2 2.2x 1O’O secondary 29.6 2 . 7 ~ 10’’ 33.3 4.9x 1 O ’ O tertiary 21.4 2.75 x 10’’ 25.2 5.1 x 1Olo None of the estimates are free from criticism. Kazmi, Diefendorf and Le Roy 47 give the ratio k22nb/k22p, which decreases from 2.3 at 340 K to 1.6 at 450 K corres- ponding to E22p-E22nb = 4.5 kJ mo1-l.In contrast, our measurements at 480°C give k22nb/k22p = 1.74 suggesting negligible variation with temperature over the range 340-753 K, as would be expected since secondary C-H abstraction dominates even at 753 K. Darwent 53 suggests that photolysis of H,S gives “ hot ” H atoms, and there is also the assumption that the relative rates of abstraction by D and by H are the same for different hydrocarbons. The existence of “ h o t ” atoms mightR . R . BALDWIN AND R . W . WALKER 153 reduce the higher activation energy E22e more than E&, so that the difference (E22e - Ei2p) is reduced. Use of the results of Campbell, Gunning and Strauss 5 2 gives a mean value of (EZp2p-E;2p) = 9.6& 1.2 kJ mol-l.Acceptance of this value implies that use of the Darwent and Roberts' 48 points gives Ei2 (for the CH2 group both in C3H8 and n-C4Hl,) about 3.8 kJ mo1-1 too high, and would suggest a reasonable estimate of Ei2 = 25.2-3.8 = 21.4 kJ mol-l. Use of the values of ki2, ki2 at 480°C then gives the Arrhenius parameters shown in table 6. However, although it is difficult to suggest any reason why the value obtained by Campbell, Gunning and Strauss 5 2 should be in error, the activation energy differences in table 6 are rather higher than would be expected from the differences in bond strength, and the earlier values for Ez2s, Ei2 are thus preferred, with the corresponding A factor obtained from ki2, k i 2 at 480°C.The greater part of this work was supported by the Air Force Office of Scientific Research, United States Air Force (AFOSR). R. R. Baldwin, C. J. Everett, D. E. Hopkins and R. W. Walker, Adv. Chem. Ser., 1968,76,124. R. R. Baldwin, D. E. Hopkins and R. W. Walker, Trans. Faraduy SOC., 1970, 66, 189. R R. Baker, R. R. Baldwin and R. W. Walker, Trans. F'raday SOC., 1970, 66,2812. R. R. Baker, R. R. Baldwin and R. W. Walker, Combustion and Flume, 1976, 27, 147. R. R. Baker, R. R. Baldwin and R. W. Walker, 13th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1971), p. 251. R. R. Baker, R. R. Baldwin and R. W. Walker, Trans. Furaduy SOC., 1970,66,3016. R. R. Baker, R. R. Baldwin, A. R. Fuller and R. W. Walker, J.C.S. Furaduy I, 1975,71,736. R.R. Baker, R. R, Baldwin, C. J. Everett and R. W. Walker, Combustion and Flame, 1975, 25,285. R. R. Baker, R. R. Baldwin and R. W. Walker, Combustion and Flame, 1976, 27, 147. * R. R. Baker, R. R. Baldwin and R. W. Walker, J.C.S. Faruduy Z, 1975, 71, 756. I 1 R. R. Baldwin, J. P. Bennett and R. W. Walker, unpublished work. l2 R. R. Baldwin, R. W. Walker and R. W. Walker, J. C. S. Faraday I, 1979,75, in press. I3 R. R. Baldwin, D. Jackson, R. W. Walker and S. J. Webster, Trans. Faraday SOC., 1967, 63, l4 R. R. Baldwin, D. Jackson, R. W. Walker and S. J. Webster, Trans. Faraday SOC., 1967, 63, l5 B. J. Tyler and T. A. B. Wesley, 11th Int. Symp, Combustion (The Combustion Institute, 1665. 1676. Pittsburgh, 1967), p. 1115. K. K. Foo and C. H. Yang, Combustion and Flume, 1971, 17,223.A. Wassiljewa, Phys. Z., 1904, 5, 737. B. J. Tyler, personal communication. l 9 P. Gray, T. Boddington and D. I. Harvey, Phil. Trans. A., 1971, 270,467. 2o R. R. Baldwin and D. Brattan, 8th Int. Symp. Combustion (Williams and Wilkins, Baltimore, 1962), p. 110. B. Lewis and G. von Elbe, Combustion, Flame and Explosions in Gases, (Academic Press London, 1961). 22 R. R. Baldwin, D. Brattan, B. Tunnicliffe, R. W. Walker and S. J. Webster, Combustion and Flume, 1970, 15, 133. 23 R. R. Baldwin and L. Mayor, Trans. Faruduy SOC., 1960,56, 80, 103. 24 E. A. Albers, K. Hoyermann, H. Gg. Wagner and J. Wolfrum, 13th Znt. Symp. Combustion 2 5 R. R. Baldwin, Mrs. M. E. Fuller, J. H. Hillman, D. Jackson and R. W. Walker, J.C.S. Faraday 26 D. L. Baulch, D. D. Drysdale, D. G.Horne and A. C . Lloyd, Evaluated Kinetic Datafor High 27 N. R. Greiner, J. Chem. Phys., 1969, 51, 5049. 28 K. H. Eberius, K. Hoyermann and H. Gg. Wagner, 13th Znt. Symp. Combustion (The Combus- 29 A. Westenberg and N. de Haas, J. Chem. Phys., 1973,58,4061. (The Combustion Institute, 1971), p. 81. I, 1974, 70, 635. Temperature Reactions (Butterworth, London, 1972), vol. 1. tion Institute, Pittsburgh, 1971), p. 713.154 RATE CONSTANTS FOR H,+O,+ALKANE SYSTEM 30 P. Camilleri, R. M. Marshall and J. H. Purnell, J.C.S. Faruday I, 1974, 70, 1434. 31 T. T. Paukert and H. S. Johnston, J. Chem. Phys., 1972,56,2824. 32 J. Troe, Ber. Bunsenges. phys. Chem., 1969, 73, 946. 33 N. R. Greiner, J. Phys. Chem., 1968,72,406. 34 W. Hack, K. Hoyermann and H. Gg. Wagner, Int. J. Chem. Kinetics Symposium, 1975,1,329. 35 R. B. Klemm, W. A. Payne and L. J. Stief, Int. J. Chem. Kinetics Symposium, 1975, 1, p. 61. 36 R. R. Baker, R. R. Baldwin and R. W. Walker, Combustion and Flume, 1976,27,147. 31 J. T. Herron and R. E. Huie, J. Phys. Chem., 1969, 73,3227. 38 R. R. Baldwin, D. H. Langford, M. J. Matchan, R. W. Walker and D. A. Yorke, 13th Int. 39 G. M. Atri, R. R. Baldwin, G. A. Evans and R. W. Walker, J.C.S. Furudzy I, 1978, 74, 366. 40 R. R. Baldwin, G. A. Evans and R. W. Walker, unpublished work. 41 N. R. Greiner, J. Chem. Phys., 1970,53, 1070. 42 J. H. Knox and R. L. Nelson, Trans. Furuday SOC., 1959,55, 937. 43 M. H. J. Wijnen, C. C. Kelly and W. H. S. Yu, Cunud. J. Chem., 1970,48,603. 44 D. Booth, D. J. Hucknall and R. J. Sampson, Int. J. Chem. Kinetics Symposium, 1975, no. 1, 45 W. E. Jones, S. D. Macknight and L. Ten, Chem. Rev., 1973,73,409. 46 R. R. Baker, R. R. Baldwin and R. W. Walker, Trans. Furduy SOC., 1970, 66, 2812. 47 H. A. Kazmi, R. J. Diefendorf and D. J. Le Roy, Cunud. J. Chem., 1963,41, 690. 48 B. de B. Darwent and R. Roberts, Disc. Furuduy SOC., 1953, 14, 55. 49 R. R. Baldwin, Trans. Faruduy SOC., 1964, 60, 527. 51 J. Shavitt, J. Chem. Phys., 1959, 31, 1359. 5 2 J. M. Campbell, 0. P. Strauss and H. E. Gunning, Cunad. J. Chem., 1969, 47, 3759. 53 B. de B. Darwent, 13th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1971), Symp. Combustion (The Combustion Institute, Pittsburgh, 1971), p. 251. p. 301. R. R. Baldwin and R. W. Walker, Trans. Furuduy Soc., 1964,60, 1236. p. 713. (PAPER 8/1033)

ISSN:0300-9599    

DOI:10.1039/F19797500140

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Chronocoulometric Measurements of Azobenzene Adsorption on Mercury from Water+Ethanol Mixtures of Different Composition BY MARIA LUISA FORESTI, FRANCESCO PERGOLA AND ROLANDO GUIDELLI* Institute of Analytical Chemistry, the University, Via Gin0 Capponi 9, 50121 Florence, Italy Received 24th November, 1977 Chronocoulometric measurements of azobenzene adsorption on mercury at - 0.430 V/s.c.e. from water + ethanol mixtures are reported. Having assumed that, at ethanol concentrations Cx > 4 mol dm-3, water adsorption at the chosen potential is negligible, we interpreted the adsorp- tion data by using the adsorption isotherm KC:/C:n = €I1 e/nae'(l -€Il)., where C: and O1 are the bulk concentration and the surface coverage by azobenzene, n is the number of adsorbed ethanol molecules displaced by one azobenzene molecule, K is an adsorption coefficient and CL is an interaction factor.The possibility of varying both C: and C,* allows the configurational effect, due to a n value equal to 3, to be distinguished from the effect of adsorbate-adsorbate interactions, due to a nonzero cc value. A statistical mechanical derivation of the isotherm employed is provided. In a previous note by Pezzatini and Guidelli the changes in shape and half-wave potential of the polarographic waves for azobenzene reduction and hydrazobenzene oxidation, following an increase in reactant concentration,2 were quantitatively interpreted as due to azobenzene adsorption. In particular, on assuming langmuirian adsorption of azobenzene, an adsorption coefficient Kl = 2.8 x lo3 dm3 mol-1 was derived from polarographic measurements in a pH 9, 90 % (v/v) ethanol+water mixture.The present note deals with a chronocoulometric investigation of azobenzene adsorption on mercury from pH 9 water + ethanol mixtures of different composition. The aim of this investigation is to show how the measurement of the adsorption of a given surfactant from mixtures of two solvents, one of which is only negligibly adsorbed, may provide valuable information as to the competition between the adsorbed solvent and the surfactant for adsorption sites. EXPERIMENTAL APPARATUS Potential-step chronocoulometric measurements were carried out with a computerized system analogous to that described by Lauer et aL3 Thus the current was electronically integrated and the charge-time data acquired and analysed with the aid of a Data General 1220 digital computer.The potentiostat was an Amel Mod. 551 with positive feedback for IR compensation. A special hanging mercury drop electrode which could be submitted to a forced laminar flow of solution lasting for 15 ms under computer control, was used throughout. This electrode was used in connection with the cell described by Cozzi et aL5 In most cases an electrode area of 0.035 cm2 was used. REAGENTS Merck reagent-grade azobenzene was used without further purification. All solutions were prepared from triply distilled water treated with active charcoal. Mercury was 155156 ADSORPTION OF AZOBENZENE purified by a wet process followed by three distillations. The pH 9 buffer contained about 0.2 mol dm-3 NH3 and 0.2 mol dm-3 NH4CI.For further details, see ref. (1). PROCEDURE All solutions were deaerated with a stream of prepurified nitrogen, previously passed through two washing bottles containing the same solution as the electrolysis cell, to avoid a decrease in the ethanol and ammonia content during measurements. All test solutions were thermostatted at 25+ 0.2"C. A platinum wire was used as the counter-electrode. The reference electrode consisted of a saturated calomel electrode, to which all potentials herein reported are referred. At pH 9 azobenzene and hydrazobenzene are both electroinactive over a narrow potential range straddling - 0.430 V.l Azobenzene adsorption was determined by stepping the applied potential from the initial value Ei = - 0.430 V to the final value Ef = - 1.40 V, at which azobenzene is reduced under diffusion limiting conditions from the first milliseconds of electrolysis.The resulting values of the charge Q(t) against time t, averaged over 10 successive drops, were then analysed, via the computerized system, fitting them by least squares to a linear Q(t) against t 3 plot to obtain an intercept Qi+f on the charge axis. In all cases standard deviations for the slopes and the intercepts were no greater than 0.1 %. In a majority of the experimental runs the charge Q(t) was sampled at 1 ms intervals for a period z of 100 ms from t = 0 of the potential jump Ei -+ Ef. To separate the faradaic component of the intercept Qi+f, due to instantaneous reduction of the adsorbed azobenzene molecules, from the corresponding double-layer charging component, the latter was estimated by stepping the applied potential backward from Ef to Ei at time t = z.The charge Qf+i involved in the backward potential jump is exclusively capacitive. To achieve a fast equilibration of the double layer with respect to the bulk solution at Ei, just after the back- ward jump the mercury drop was submitted to a forced laminar flow of solution lasting 15 ms. The quantity Qf+i was estimated by subtracting the charge passed at time t = (z+ 15 ms), namely just after cessation of the forced convection, from the charge Q(z) passed immediately before the backward potential jump Ef-+ Ei. In any case, both with and without forced convection the capacitive charge Qf+i varied by no more than 1 pC cmU2 when varying the azobenzene concentration from 10-5-1.3 x mol dm-3, thus indicating that the charge density on the metal at Ei is only slightly affected by azobenzene adsorption.The surface concentration rl of azobenzene at Ei was calculated through the equation The polarographic behaviour of the azobenzene+ hydrazobenzene system indicates that hydrazobenzene adsorption is entirely negligible. No direct chronocoulometric measure- ment of hydrazobenzene adsorption could be carried out at pH 9, since the jump from the potential Ei = -0.430 V, at which both azo- and hydrazo-benzene are electroinactive, to the most positive potential at which mercury is not yet oxidized, does not allow diffusion- limiting conditions to be attained within a few ms.To achieve the latter result chrono- coulometric measurements of hydrazobenzene adsorption were carried out at higher pH values, taking advantage of the fact that the formal potential of the azobenzene-hydrazo- benzene couple shifts towards more negative values with increasing pH. Thus, the narrow potential range over which azo- and hydrazobenzene are both electroinactive lies at W - 0.63 V in a pH 11 phosphate buffer and at % -0.77 V in a 0.2 mol dm-3 KOH solution. Con- sequently in these media anodic potential jumps of -0.5 V, high enough to attain diffusion limiting conditions, could be performed, Under these conditions saturated solutions of hydrazobenzene in ethanol+ water mixtures of different composition yielded differences between the absolute values of the anodic intercept Qi+f and of the cathodic capacitive charge Qf+i which were no greater than 1 pC cm-2.This confirms the very low adsorptivity of hydrazobenzene. After having ascertained that azobenzene adsorptivity varies only slightly when passing from 0.2 mol dm-3 KOH solutions to pH 9 ammonia buffer solutions of equal ethanol content, we carried out chronocoulometric measurements of at the latter pH. In factM. L. FORESTI, F . PERGOLA AND R . GUIDELLI 157 in the neighbourhood of pH 9 the standard rate constant for azobenzene reduction to hydrazobenzene is a minimum, thus permitting a less critical choice of the initial potential Ei. Measurements of the charge density qM on the metal as a function of the applied potential in the absence of the reactant were carried out at a dropping mercury electrode by the same procedure described by Lauer and Osteryoung.6 RESULTS AND DISCUSSION Fig.1 shows the surface concentration rl of azobenzene, measured at Ei = - 0.430 V as described in the experimental section, against the corresponding bulk concentration Cf for different ethanol concentrations C,* in the ethanol + water mixture. In all these curves rl seems to approach asymptotically a maximum limiting value. This apparent limiting value, however, increases continuously as C,* 40 30 l-i I !z 1 Y k" k *O w 10 I I C: x 103/m01 dm-3 FIG. 1.-Plots of 2Fr1 against C: at -0.430 V in a pH 9 ammonia buffer. Ethanol concentration C,* = 15.65 (a), 8.7 (b), 6.07 mol dm-3 (c). Left-hand scale refers to curves (6) and (c) ; right-hand scale refers to curve (a).is decreased and hence is by no means related to the attainment of full coverage of the electrode surface by azobenzene. Such a conclusion is confirmed by the curves of rl against C,* at constant Cf in fig. 2. Incidentally, if the " apparent " limiting value of rl in curve (a) of fig. 1 is estimated at 6 yC ~ m - ~ / 2 F = 0.31 x 10-l' mol cm-2 and is formally equated to the maximum surface concentration then curve (a) turns out to satisfy a Frumkin isotherm with an apparent adsorption coefficient K1 = 1.8 x lo3 dm3 mol-l ; this value compares favourably with 2.8 x lo3 dm3158 ADSORPTION OF AZOBENZENE mol-l, that estimated from the half-wave potential shift of the azobenzene wave in the same medium,l as produced by an increase in Cf.However, a rl,m value of 0.31 x 10-lo mol cm-2 is decidedly too low to have any physical significance. This emphasises the limitations of the polarographic method for estimating reactant adsorption. In fact this " indirect " method is sensitive to deviations from the Henry-isotherm behaviour,' but not to the magnitude of Tm. I I * 1 1 I I I I 50' ! 40 - CI I E Sj- 30- 2 3 - 26 - 10- L I I I 1 1 I I 2 4 6 0 10 12 14 C:/mol dm-3 C: = (a), 2 x (b), 6 x (c), 7 x loh4 (d), mol dm-3 (e). FIG. 2.-Plots of 2Fr, against C,* at -0.430 V in a pH 9 ammonia buffer. Azobenzene concentration The true value can be regarded as equal to the height, x50 pC cm-2/ 21; = 2.6 x 10-lo mol cm-2, of the step exhibited by the rl against C,* curves of fig. 2 at low C,* values. The preceding Tl,m value matches the maximum surface con- centration, 2.55 x mol cm-2, as calculated from the area, x65 A2, projected by a Leybold space-filling model of the azobenzene molecule, placed with the two benzene rings flat on the electrode surface.The further increase in 2Pr1 beyond 50 pC cm-2, as shown by some of the curves in fig. 2, is probably to be ascribed to a closer packing of the azobenzene molecules, e.g. with the plane of the benzene rings perpendicular to the electrode surface.M. L. FORESTI, F. PERGOLA AND R. GUIDELLI 159 The gradual decrease of I?, as the ethanol content is increased is expiained by competitive adsorption of azobenzene and ethanol for adsorption sites. Experimental data will be interpreted on the basis of the rather general adsorption isotherms * * K,Cr = 8,[nl(l -8, -8,)ni]-1 exp (n, all 8, +nl a,, 0,) K,c,* = 8,[n2(1 -8, -e,)nz]-l exp (n, a,, 8, +n2 a12 0,) (1) (2) which account both for adsorbate-adsorbate interactions and for any differences in the size of the various adsorbed molecules.In eqn (1) and (2) K l , K2 are the adsorp- tion coefficients of azobenzene and ethanol, 8,, 8, are the corresponding surface coverages, and n l , n, are the numbers of water molecules displaced by one molecule to 0 6 pl -10 -20 V1s.c.e. FIG. 3.-Plots of the charge density qm against the applied potential E for different water+ethanol mixtures containing 0.2 mol dm-3 NH3 + 0.2 mol dm-3 NH4Cl. Ethanol concentration C: = 0. (solid curve), 0.87 (C), 1.73 (a), 3.47 (a), 5.21 (H), 8.68 rnol dm-3 (A). of azobenzene and of ethanol, respectively.Moreover, all, and a,, are inter- action factors of azobenzene molecules between themselves, of ethanol molecules between themselves, and of azobenzene with ethanol molecules. In practice, at ethanol concentrations which are not too low, water molecules are almost completely displaced from the adsorbed monolayer in direct contact with the electrode by ethanol and azobenzene molecules. Thus Arevalo et al., lo from polarographic measurements of the capacitive current of water + ethanol mixtures containing 0.1 mol dm-3 KCl, concluded that at C; 2 5.2 mol dm-3 surface saturation by ethanol molecules is attained over a wide potential range. For a further confirmation, we have measured the charge density 4m on the metal in different water+ethanol mixtures containing160 ADSORPTION OF AZOBENZENE 0.2 mol dm-3 NH3 +0.2 mol dm-3 NH,Cl (see fig.3). For C,* >/ 5.2 mol dm-3 the charge density 4m attains a limiting value between x -0.4 and = - 1.5 V, thus indicating that the compact layer does not change appreciably as the ethanol concentration is increased beyond 5 mol dm-3. Over the potential range from = -0.4- = -0.6 V the limiting value of qm is already attained at Cg = 3.47 mol d ~ n - ~ . We may therefore conclude that at the chosen potential Ei = -0.430 V water n * r ( I- L, 8 QPOO 0 I 1 I I I I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 61 FIG. 4.-Plots of {In (e1/C:)-n In [(l-O1)/C;)} against el = r1/(2.6x 10-lo mol cm-2) for C; = 6.07 (0) and 8.7 mol dm-3 (0) and variable C; ,as well as for C: = (a), 2 x (m), 6 x (A), 7 x (A), mol dm-3 (0) and variable C;.(a) n = 1, (b) n = 2, (c) n = 3, (d) n = 4 and (e) n = 5.M . L . FORESTI, F . PERGOLA AND R . GUIDELLI 161 molecules are almost absent from the adsorbed monolayer in direct contact with the electrode at C,* > 3.47 mol dm-3. Under these conditions, dividing eqn (1) by eqn (2) raised to the nl/n2 power and setting 8, + O2 z 1 yields with a = n1(all+a22-2a12); n = n,/n2. The parameter n is the number of ethanol molecules displaced by one molecule of azobenzene. Eqn (3) is substantially a Frumkin isotherm accounting for the different size of solvent and surfactant molecules, and is also expected to apply to adsorption of a single surfactant from a single solvent.g* l 1 9 l2 Eqn (3) has been derived in a piecemeal fashion from eqn (1) and (2), which in their turn were derived in a similar fashion 8 * by combining the Frumkin isotherm with the Flory-Huggins statistics.We therefore found it useful to derive eqn (3) directly from first principles via a generalization of the statistical derivation of the Frumkin isotherm l 3 (see Appendix). In the present investigation we are in the favourable condition to test eqn (3) by varying not only CT but also C;. This was accomplished by plotting {ln(O,/Cf) - n ln[(l -8,)/C~]) against 8, (see fig. 4) using the data of fig. 1 and 2. To this end Tl,m was equated to 2.6 x 10-lo mol cm-2 and n was alternatively equated to 1,2, 3, 4 and 5. The area projected by a molecular model of ethanol with the hydrocarbon chain normal to the electrode is ~ 2 0 A2 ;14 hence the n value which should comply best with the experimental value, 65A2, of the area covered by an azobenzene molecule at full coverage is 3.The scattering of experimental data in fig. 4 is indeed less for n = 3 than for n = 1 or n = 2. A still lower scattering is observed for n = 4 and 5, but the plots corresponding to these n values show an appreciable curvature at 8, > 0.6. At any rate the n values 4 and 5 are not physically significant. If the data relative to n = 3 are fitted to a straight line by least squares, a In K value of 13.7 and an a value of -3.58 are obtained. This implies that, on average, inter- actions between adsorbed molecules are attractive. The difficulty shown by 8, in approaching unity with increasing C,* must therefore be ascribed not to repulsive adsorbate-adsorbate interactions, but rather to a configurational effect due to the different size of azobenzene and ethanol molecules.The points in fig. 4 corresponding to n = 3 which show greater deviations from the average are those relative to C$ = 6.08 mol dm-3 and to 8, < 0.2. This residual data scattering is probably because at this relatively low ethanol concentration the surface coverage by water is not completely negligible, especially at low 8, values, thus partly invalidating the assumption (8, + 8,) = 1. In conclusion we note that measurements of adsorption of a solute from a single solvent are often insufficient to distinguish and separate the effect of a configurational term involving an n value greater than unity from the effect of a nonzero Frumkin interaction factor a.This result is more convenienty achieved by measuring adsorption of a solute from a mixture of two solvents, one of which is not detectably adsorbed. In fact in this case a given composition of the adsorbed monolayer in direct contact with the electrode at a given applied potential can be attained for different compositions of the bulk solution phase. K = Klnl(K2n2)-" exp [-n1(a12 -a22)] = (C~/C:)O,(l -el)-. exp (a€),) (3) APPENDIX Following Flory,16 assume that the surfactant Al consists of a linear sequence of n segments, any one of which may replace a solvent molecule S2 from the adsorbed monolayer in direct contact with the electrode. Let B be the number of adsorption 1-6162 ADSORPTION OF AZOBENZENE sites on the electrode, as created by the adsorbed solvent molecules prior to the adsorption of Al, and let N , be the number of A , molecules distributed among the B sites (B 2 nN,), one per n contiguous sites.The partition function for the present system is R Q(N,, B, T ) = qylq$B-nN1) exp (-EJRT). (Al) i = l In eqn (Al) q1 and q2 are the single-molecule partition functions without interactions relative to the surfactant A , and to the solvent S,, Ei is the total nearest-neighbour energy of interaction for the ith configuration, and fi is the total number of configura- tions. Assume that the n segments of any A , molecule are perfectly equivalent, as regards both their interchangeability with the solvent molecules and the magnitude of their interaction energies with adjacent solvent molecules or with adjacent segments of other A , molecules. Let ull, u22 and u12 denote the interaction energy between two adjacent segments of two different Al molecules, that between two adjacent solvent molecules, and that of a segment of an A , molecule with an adjacent solvent molecule. Eqn (Al) can then be written in the form U12N12 +u22N22)lkTI.(A21 In eqn (A2) N i l , NZ2, N,, are the numbers of pairs of adjacent adsorption sites occupied by segments of two different A , molecules, by two solvent molecules and by an A , segment and a solvent molecule, respectively. In addition, g(N,, By N i l ) is the number of configurations having Nil pairs of sites occupied by segments of two different A , molecules when there are N1 molecules of Al and B sites.Denoting the number of nearest neighbours for any given adsorption site by r, from elementary statistical considerations 179 where N 1 , is the number of nearest-neighbour pairs of sites occupied by two A l segments, independent of whether they belong to the same or to different A , molecules. Let us assume as a first approximation that all configurations of N, molecules of A l on B sites have the same weight as they would have if u,,, u12 and u22 were null.,'. l 8 With this assumption the canonical partition function of eqn (A2) is written it follows that, for B -+ co, rnN, = 2 N l 1 + N l 2 ; r(B-nNl) = 2N2,+NI2 (A31 where u l l ~ i l , u12N12 and uZ2iV2, are average interaction energies for molecules distributed randomly among the sites.nil is readily estimated by noting that, for a random distribution, an intermediate segment of an A molecule has (r - 2)(nN1 / B ) nearest-neighbour sites occupied by segments of different A , molecules. On the other hand a terminal segment of an A , molecule has (Y - l)(nN, / B ) nearest-neighbour sites occupied by segments of different A , molecules. Noting that the total number of intermediate segments is (n-2)N1 whereas that of terminal segments is 2N1, we have = [(n-2)(r-2)nNf/B+2(r- l)nNf/B]/2 = nqNf/2B (A51 with q -= nr-2n+2M . L . PORESTI, F . PERGOLA AND R . GUIDELLI 163 where the 1 / 2 factor prevents the counting of each pair of contiguous segments twice. Naturally, the value N, , assumed by N , for a random distribution equals PI 1 plus the number, (n- l)N1, of nearest-neighbour pairs occupied by segments of the same A , molecule The expression for the summation Nl = nqNf/2B+ (n + l)N1.(A6) g(N1, B, Nil) is provided by the Flory statistics l6 n; 1 C g(N1, B, iVi 1) = [(r - I)/B]("- ' ~ 1 n""[(B/n)!/(B/n - N1)!]"/2"N1 ! n; 1 (A71 where the 2" factor must be replaced by unity in the trivial case of n = 1. Upon combining eqn (A4), (A5) and (A7) and making use of the Isl2 and N22 values as derived from eqn (A3) and (A6), the following expression for the chemical potential p, of A , in the adsorbed state is readily obtained p l / k T = -(a In Q/i2V,),,, = In [2q",lql(r- 1)"-1]+[qu12-(m-n+ l)u2,]/kT+ where 8, E nNl/B is the fractional surface coverage by A , .In deriving eqn (A8) Stirling's approximation for factorials was adopted. In general the chemical potential bpl of A , in the bulk solution will have an analogous form, with different values of the various interaction energies. Under usual conditions, however, the analogue, = n VVJbB, of 8, for the bulk solution phase is much less then unity, so that the term proportional to in the expression for can be neglected. We may therefore write concisely where CT and Cs are the bulk concentrations of A , and of the solvent S2. At equilibrium p, is equal to bpi. Hence, from eqn (A8) and (A9), the following adsorption isotherm is obtained with and In [el/n(l -~1)"1+!?(u11 +u22 +2u12)(31lkT (A81 ",/kT = bpi/kT+h [b81/n(l -b81)n] = bpy'/kT+ln ( C f / C f . ) (A9) KCT/C$" = 8, exp (a 8,)/n(l-0,)n (fw K = ql(r- l)"-' exp ([bpi'+(rn-n+ l ) ~ ~ ~ - q u ~ 2 1 ) / 2 q ~ a = ~ ( U ~ ~ + U ~ ~ - ~ U ~ ~ ) / ~ T .The preceding adsorption isotherm holds even if A , is adsorbed from a mixture of the solvent S2 previously considered and of a further solvent S3, provided that only S2 and A , are adsorbed at the interphase. In fact, in this case, within the closed system consisting of the interphase and of the solution phase, the desorption of an A , molecule will only occur by replacement of this adsorbed molecule with n molecules of S2 from the solution phase. Assume that the solution phase consists of n bN1 + bN2 +&N3 = bB+ bN, cells containing bN, polymer molecules of A , , bN2 monomer molecules of S, and bN3 monomer molecules of S,.In estimating the total number bg(bN,, bN3, bB) of possible configurations within the solution phase, Flory's process l6 of successive addition of the bN1 polymer molecules of A , to the three- dimensional lattice must now be performed not with the lattice initially empty, but rather with a lattice already containing the bN3 molecules of S3 ; in fact these molecules are not available for replacement by segments of the polymer A l . The number of distinguishable arrangements of the biV, molecules within the initially empty lattice equals (bB+bN3)!/(bB!bN3!). For each of these arrangements there is a number W164 ADSORPTION OF AZOBENZENE of different arrangements of the bN1 molecules of A , in the remaining cells, which can be calculated as follows.After ' N , polymer molecules of A , have been added, the probability that one of the two terminal segments of the next A l molecule will enter the lattice equals (bB -n bN1). With Flory's assumptions l6 the probability that the segment adjacent to the terminal segment just added will find an empty cell amounts to br(bB- n bN,)/(bB+ bN3), whereas the analogous probability for each of the remaining (n -2) segments equals (%- l)(bB- n bNl)/(bB+ bN3). Incidentally, is the coordination number for the solution lattice. Following Flory's procedure,16 Zbg(bN,, bN3, bB) will therefore be given by - (bB+bN,)!( %- 1 ) ( f l - l ) b N 1 ( n" bN1 )[ (bB/n)! 1" bB!bN3 ! bB+ bN3 2bN1bN1! (bB/n-bN,)! It is readily seen that upon differentiating the logarithm of the preceding function with respect to bN1 at constant bB and bN3 an expression of of the form of eqn (A9) is again obtained. Analogous conclusions hold if the S3 molecule consists of more than one segment. G. Pezzatini and R. Guidelli, J.C.S. Faraduy I, 1973, 69, 794. B. NygArd, Arkiv. Kemi, 1962,20, 163 ; 1966, 26,167. G. Lauer, R. Abel and F. C. Anson, Analyt. Chem., 1967,39,765. M. L. Foresti, G. Pezzatini, G. Piccardi and R. Guidelli, unpublished results. D. Cozzi, G. Raspi and L. Nucci, J. Electroanalyt. Chem., 1966, 12, 36. G. Lauer and R. A. Osteryoung, Analyt. Chem., 1967, 39, 1886. R. Guidelli, J. Phys. Chem., 1970, 74, 95. J. M. Parry and R. Parsons, J. Electrochem. SOC., 1966, 113, 992. B. B. Damaskin, 0. A, Petrii and V. V. Batrakov, Adsorption of Organic Compounds at Electrodes (Plenum Press, New York, 1971). lo A. Arevalo, S. Gonzalez and E. Fatas, Anales de Quim., 1975, 71, 273. l 1 R. Parsons, J. Electroanalyt. Chem., 1964, 8,93. l2 B. B. Damaskin, Elektrokhimiya, 1965, 1, 63. l3 R. Fowler and E. A. Guggenheim, Statistical Thermodynamics (University Press, Cambridge, 1939), p. 431. l4 B. B. Damaskin, A. A. Survila and L. E. Rybalka, Elektrokhimiya, 1967, 3, 146. H. P. Dhar, B. E. Conway and K. M. Joshi, Electrochim. Acta, 1973, 18, 789. l6 P. J. Flory, J. Chem. Phys., 1942, 10, 51. l7 A. Clark, Theory of Adsorption and Catalysis (Academic Press, New York, 1970). l8 1. Prigogine, A. Bellemans and V. Mathot, Molecular Theory of Solutions (North-Holland, Amsterdam, 1957). (PAPER 7/2069)

ISSN:0300-9599    

DOI:10.1039/F19797500155

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Magnetic Determination of Metallic Nickel Particles Dispersed on X and Y Zeolite Structures BY M. F. GUILLEUX ANDD. DELAFOSSE* ER 133 " Reactivite de Surface et Structure ", Laboratoire de Chimie des Solides, UniversitC P. et M. Curie, 4 Place Jussieu, 75230 Paris Cedex 05 G. A. MARTIN AND J. A. DALMON Institut de Recherche sur la Catalyse, 69000 Villeurbanne, France AND Received 9th January, 1978 A magnetic study of metallic nickel particles by the reduction of Nix and NiY zeolites in the presence of a second cation shows that, not only the reducibility of Ni'f ions, but also the dispersion of the Nio particles formed, depend on which second cation is przsent. Recently the reduction of transition metal ions supported on zeolites has been the subject of numerous with the aim of obtaining highly dispersed metallic particles of homogeneous size.In studies involving Ni2+ ions on X and Y zeolites, it was observed in all cases that the metallic particles formed migrated towards the external surface and that these particles rapidly increased in size with reduction temperature. Work in this field is now, therefore, concerned primarily with the possibility of stabilizing the metallic particles formed inside the rigid cavities of the zeolite, by varying different factors such as : pretreatment conditions which influence the initial location of the ions to be reduced; introduction of an additional cation likely either to modify the environment of the Ni2+ ions or to affect the reduction process itself; the reduction conditions, whether static or dynamic.In this work, following a kinetic study of the reduction by hydrogen of Ni2+ ions exchanged in X and Y zeolites in the presence of different cation~,~-ll we have endeavoured to characterize, by magnetic methods, the size of the Nio particles obtained on these different zeolites. EXPERIMENTAL MATERIALS The samples were prepared by exchanging X and Y sodium zeolites (Union Carbide) with 0.1 mol dm-3 solutions of Ni2+ and Ce3+ nitrates, and with ammoniacal solutions of Pt(NH3)i+ and Pd(NH3)i+ ions. The sample composition was determined by chemical analysis (table 1). PRETREATMENT OF SAMPLES All samples were pretreated for 16 h under vacuum at Torr and at 773 K. In this work, we considered mainly the case of static reductions. Reduction was carried out in a classic volumetric apparatus at constant hydrogen pressure (50 Torr) and at various temperatures.For each sample, reduction-desorption cycles were performed at different temperatures and, during the desorption cycles, the amount of gas desorbed was measured by a MacLeod gauge and analysed by mass spectroscopy. 165166 MAGNETIC DETERMINATION OF NICKEL ON ZEOLITES EXPERIMENTAL METHOD The extent of reduction a of the samples was determined, first, from the hydrogen uptake in a given reduction time (25 b) and, secondly, from the saturation magnetization as of the sample considered. The magnetization was measured by the Weiss extraction method,12 either in an electro- magnet giving 21 kOe (measurements at 300 and 77 K) or in a superconductive coil reaching 70 kOe (measurements at 4.2 K).Generally, magnetization, 6, against field, H, curves give information on the metallic nickel content of the sample and on the size of the Ni parti~1es.l~ TABLE 1 .-CHEMICAL COMPOSITION OF ZEOLITES samples degree of exchange/ % Na+ H+ Niz+ Ce3+ Pt2+ Pd2+ NieNaX 74 7 18 NiS1NaX 28 0 72 Ni2&!e6X 21 2 56 21 Ni14Pd6X 17 37 32 14 Ni17Pto.SX 46 13 39 1 Ni13NaY 48 5 46 Ni, oNaY 29 0 71 The metallic nickel content was obtained from the ratio of the saturation magnetization observed for the sample to that of the specific magnetization of the bulk nickel. The assumption that the specific magnetization of finely divided Ni particles is the same as that of bulk nickel was made. The experimental determination of the saturation magnetization of the samples studied raises difficulties.First, the magnetization-field curves were corrected for the diamagnetism of the zeolitic support as well as for the paramagnetism of the residual Ni2+ ions. In the latter case, we calculated the quantity of residual Ni2+ from the extent of reduction measured I- t? \ b 10 20 0.8 - 0.6 - 0.4 . n 32 A _*_----- HlkOe 1.0: 2 1.2: 3 1-60 4 2.0; 5, 3.0nm. FIG. 1.Theoretical curves ./us against H at 77 K for different values of particle diameter : 1,M . F . GUILLEUX, D . DELAFOSSE, G . A . MARTIN AND J . A . DALMON 167 volumetrically and have assumed that the specific magnetic properties of the residual Ni2+ ions were not changed by the hydrogen treatment. We then extrapolated magnetization against 1 / H to obtain the saturation magnetization.This method is justified for nickel particles > ~ 2 . 5 and 1.5 nm, when the magnetization measurements are carried out at temperatures of 300 and 77 K, respectively, in a field of 21 kOe. If the measurements are performed on heterogeneously dispersed samples the extrapolation only accounts for nickel grains greater than the critical diameter ; smaller particles are not saturated under these conditions. Fig. 1 , representing the theoretical curves calculated from the Langevin equation : B pH kT 6 s kT pH for different values of particle diameter and for a given temperature (77 K), shows clearly the linearity of this function below a certain diameter. The saturation magnetization can be calculated by extrapolation to zero field of the linear part of the curves Q = f ( H ) at high field.This method supposes that the metallic particles saturation is attained, otherwise the value calculated will be inferior to the real one. For measurements at 4.2 K and 70 kOe, it can be considered that the smallest nickel particles are saturated ( D < 0.5 nm) and that the saturation magnetization can be obtained by extrapolation to zero field. When the samples are ~uperparamagnetic,~~~ l4 it is possible to calculate the average surface diameter DS of the nickel particles, by Langevin low field (LLF) and high field (LHF) methods. When the samples show a remanent magnetization, we have also used the Nee1 remanence (NR) method 13* - = coth - -- to estimate the size of the nickel particles. RESULTS We will consider the reduction of Ni2+ ions first in the presence of Na+ in the X and Y structure and then in the presence of other cations in X zeolites.IN THE PRESENCE OF Na+ Kinetic studies 9* lo have shown that the static reduction of Ni2+ ions is easier in X zeolites than in Y and that, for the same structure, it is easiest in samples least exchanged with Ni2+ ions. However, in all cases complete reduction is very difficult. The results obtained by magnetic measurements at 77 and 300 K on X zeolites show that : (a) for reduction temperatures below or equal to 523 K (a < 0.1) the samples do not show remanence and are superparamagnetic. Fig. 2 shows typical curves of the magnetization of the samples as a function of applied field at 300 and 77 K. The metallic nickel content estimated by extrapolation to zero field is always much less than the value calculated volumetrically (table 2).It has been shown by e.p.r. that under these reduction conditions little Ni+ is formed. These observations therefore indicate the presence of Nio particles not saturated at 77 K and probably smaller than 1.5 nm. Owing to the very large contribution of the paramagnetism of the Ni2+ ions to these low degrees of reduction, it is not possible to determine, from measurements at 4.2 K, the contribution of the smaller Nio particles nor their size. The mean size of the larger particles measured at 300 and 77 K is 6.0 nm. These particles are probably located on the outside of the zeolite surface. Reduction-desorption cycles were carried out on these samples, at the reduction temperature.Simultaneous with the loss of hydrogen in the desorption cycle, a decrease in the magnetization of the sample was observed. This can reasonably be attributed to partial reversal of Ni2+ ion reduction, according to the reaction : Nio + 2H+ + Ni2+ + H2.I68 MAGNETIC DETERMINATION OF NICKEL ON ZEOLITES v) U .- El HlkOe FIG. 2,-Typical curves of the magnetization u of a NisX sample reduced below 523 K as a function of applied field at 300 (curve 1) and 77 K (curve 2). (b) At higher reduction temperatures (7' 2 573 K) the mean particle diameter increases rapidly with reduction temperature and reaches values >25 nm (table 2). Under these conditions, reduction is no longer reversible. In the Y structure, Ni2+ ions are more difficult to reduce than in the X.Con- sequently, for the same degree of reduction but obtained at a higher temperature, the mean particle size found is greater (table 2). TABLE 2.-PARTICLE DIAMETER & OF SAMPLES AS A FUNCTION OF DEGREE OF REDUCTION reduction degree of reduction particle diameter DS 1W Ni,NaX 523 0.1 0.07 6.0 samples temperature1K C L H ~ aaS 573 0.38 0.38 10 (with 20 % 2 25) 673 0.80 0.80 15 (with 30 % 2 25) Nil ,Nay 573 0.07 0.06 12.0 673 0.19 0.19 13 (with 20 % 2 15) 748 0.36 0.36 15 (with 35 % 2 25) a~~ is determined by hydrogen uptake and aus is calculated from the value of the saturation magnetization us estimated at 77 K. I N THE PRESENCE OF PdO AND PtO Before any reduction of Ni2+ ions, the Pt2+ and Pd2+ ions are reduced at 373 K. The metal particles thus obtained are expected to be located within the zeolite cavities in a homogeneous dispersed ~tate.l"~ Note that the magnetic measurements of Nio are not affected by the presence of these two elements in the cases where there is alloy formation.In fact, the presence of very small amounts of Pto does not modify the magnetic moment p of the Nio, and in the case of zeolite NiI4Pd6X where the amount of PdO is not negligible, the moment p of Nio varies little inthe Ni-Pd alloys. For these reasons, we cannot determine whether or not alloys are formed after Ni2+ reduct ion.M. F . GUILLEUX, D. DELAFOSSE, G . A . MARTIN AND J . A . DALMON 169 (a) In the case of Ni14Pd6X zeolite, a kinetic study showed that the reduction of Ni2+ ions in the presence of Pd" is activated by this metal in the temperature ranges where the Pd" particles remain localized inside the zeolitic cavities.I1 Magnetic measurements on samples reduced at different temperatures between 473 and 673 K showed that the particle size is very homogeneous (2.5, 3.0 nm) and does not depend on the reduction temperature (table 3).Furthermore, by carrying out reduction-desorption cycles on a given sample between 523-663 K, it is possible to attain almost complete reduction and to obtain Nio particles of uniform size, about 3 nm. During the desorption cycles, the OH groups or water molecules formed, which seem to be reduction inhibitors, are eliminated by dehydroxylation. The Nio particles are not affected by these desorption treatments. TABLE 3.-PARTICLE DIAMETER Ds OF SAMPLES AS A FUNCTION OF DEGREE OF REDUCTION reduction degree of reduction particle diameter Ds samples temperature/K -2 ads Im Ni 14Pd 6X 523 0.16 0.16 3.0 573 0.60 0.60 3 .O Ni17Pt o.5X 523 0.13 0.13 2.5 573 0.28 0.28 2.5 at 593 K 1 2.5 dynamic reduction Ni&e 6X 508 0.1 0.012 573 0.3 0.08 { 2.5 673 0.43 0.2 dynamic reduction 85 % 0.7 at 593 K 0.85 { 15 % 3 .O a H Z is determined by hydrogen uptake and aus is calculated from the value of the saturation magnetization as estimated at 77 IS. (b) The effect of platinum on the Ni2+ reduction is similar to that of PdO. The Nio particle size obtained is about 2.5 nm and does not vary with the extent of reduction, depending on the temperature (table 3). Preliminary results of the study using dynamic reduction methods show that total reduction of the Ni2+ ions can be attained at temperatures below 623 K.The Nio particles are homogeneously distributed but their sizes appear to depend on the pretreatment conditions, their diameters varying from 5 to < 1.5 nm. I N THE PRESENCE OF Ce3+ Kinetic measurements have shown that for reduction temperatures below 523 K, the extent of Ni2+ reduction in the presence of Ce3+ is greater than for NiNaX zeolites. The reduction-desorption cycles do not involve the loss of hydrogen. In all cases, they increase the reduction rate. Magnetic measurements on samples reduced between 473 and 673 K show that : (a) the degree of reduction a determined by saturation magnetization at 77 K is always very much less (10-40 %) than that measured by hydrogen uptake (table 3).This suggests that there are very small Nio particles not saturated at this temperature. The mean size of particles saturated at 77 and 300 K is 2.5 nm; (6) when the NiCeX zeolite is pretreated under oxidizing conditions, static reduction leads to Nio particles which are homogeneously distributed but much larger than before (Ds > 15.0 nm) ;170 MAGNETIC DETERMINATION OF NICKEL ON ZEOLITES (c) dynamic reduction at 593 K of a sample pretreated at 773 K is almost complete (80 %). Since the paramagnetic contribution of the Ni2+ ion is very small in this case, we have been able to study the magnetization of the sample in the super- conductive coil at 4.2 K. After various corrections for the diamagnetism of the support and the paramagnetism of the Ce3+ ions were made, it was calculated that 85 % of the particles formed were x0.7 nm in diameter and 15 % were 3 nm.DISCUSSION These results show clearly that not only the reducibility of Ni2+ ions exchanged in zeolites but also the dispersion of the Nio particles formed, depend on the cation or metal present in its environment. With no element other than Na+, reduction is more difficult in the Y than in the X structure, but leads in both cases to the same result. At a low degree of reduction, there are both very small particles occluded in the zeolitic cavities and larger particles of 6-10 nm, probably located on the outside of the surface. In this range, the reduction is partially reversible by desorption. The redox equilibria have already been mentioned in the literat~re.~ They are no longer observed for more extensive reduction where the larger particles grow at the expense of the smaller ones.In these zeolites, it is therefore difficult to obtain total reduction and a homogeneous distribution of metallic particles. The introduction of a cation such as Ce3+ or a metal (Pto or PdO) modifies completely the behaviour of Ni2+ ions with respect to their reduction. The introduction of small amounts of Pd or Pt activates the reduction of Ni0.20 In our case, these two elements increase the reducibility of Ni2+ ions but also stabilize the metal particles formed in small aggregates of regular size (2.5, 3.0 nm). The presence of Ce3+ in the environment of Ni2+ ion also leads to easier reduction of the ion but particularly, it stabilizes a highly dispersed state of the metal in the zeolitic lattice.On the whole, the diffusion rate of atomic species during their formation and the migration of crystallites are greatly reduced when there are strong metal-support interactions.21 Consequently, the size of the crystallites decreases and their stability increases. The diameter and the stability of metal particles obtained during reduction depend on several factors: (a) the acidity or the basicity of the support; (6) the eventual existence of redox mechanisms which interact with the energeties of the kinetic processes : thus, for example, the more or less oxidizing properties of the support can influence the morphology of the metal particles; (c) the thermostability of the OH groups formed during the reduction which depends on the cation or cations present on the support; ( d ) the presence of a “modifying” element which can interact strongly with the support and also with the metal crystallites, which thus decreases the mobility of these crystallites. For the zeolites studied in this work, we see that the above factors are all involved to different degrees.In the NaNiX and NaNiY zeolites, there are two dominant and interdependent factors: the acidity of the support and the existence of redox equilibria. The introduction of bivalent cations leads to the formation of Brernsted acid centres which, upon dehydroxylation at 773 K, become Lewis acid centres. These acid centres can behave like oxidizing centres which will therefore favour the redox equilibria commonly observed in the case of nickel.In this situation, the reduction of Ni2+ ions is difficult and requires fairly high activation energies. Also, thisM . F. GUILLEUX, D. DELAFOSSE, G. A . MARTIN AND J. A . DALMON 171 reduction leads to irregular dispersion and to the growth of the larger particles at the expense of the smaller ones. Trials on the reduction of Ni2+ in zeolites decation- ized prior to Ni2+ exchange, i.e. zeolites which contain a larger number of acid sites, exhibit considerable inhibition to reduction and, consequently, the formation of large particles. In the presence of PdO or PtO, several factors may be involved: these metal particles, probably dispersed inside the cavities of the zeolite, interact strongly with the lattice and are also active in the Ni2+ reduction process by providing an atomic hydrogen effect.These strong interactions both with the support and the Nio crystallites during their formation will inhibit the diffusion of crystallites. Also, more extensive reduction and more homogeneous crystallites distribution are obtained. Thus, a more highly dispersed metallic state is observed in the polycationic form2' In the presence of Ce3+, the reduction of Ni2+ ions leads to a highly dispersed metallic state. The role of the Ce3+ ion in this reduction process has not yet been elucidated. Ce3+ ions could have an important effect upon the thermostability of the OH groups formed during the reduction and on the acidity of the support. Up to now, we have observed first that the degree of Ce3+ exchange and secondly that the oxidation state of the cerium cation prior to Ni2+ reduction has great influence on the state of dispersion of the Nio particles obtained.These different factors should be studied in detail. In conclusion, it has been shown that it is possible to obtain a highly dispersed state of metallic nickel on zeolitic supports with particle size < 3 nm. l D. J. C. Yates, J. Phys. Chem., 1965, 69, 1676. J. A. Rabo, C. L. Angell, P. H. Kasai and V. Schoemaker, Disc. Faraday SOC., 1966,41, 328. L. Riekert, Ber. Bunsenges. phys. Chem., 1969,73, 331. J. T. Richardson, J. Catalysis, 1971, 21, 122. W. Romanowski, Roczniki Chemie Ann. Soc. Chim. Polonium, 1971,45,427. C. S . Brooks and G. L. M. Christopher, J. Catalysis, 1968, 10, 211. ' W. G. Reman, A. H. Ali and G. C. A. Schuit, J. Catalysis, 1971, 20, 374. * K. H. Bager, F. Vogt and H. Bremer, Proc. 4th Int. Conf. Molecular Sieves (A.C.S. Symposium Series, Chicago, 1973, p. 528. M. Kermarec, M. Briend-Faure and D. Delafosse, J.C.S. Chem. Comm., 1975,272. M. F. Guilleux, M. Kermarec and D. Delafosse, J.C.S. Chem. Comm., 1977, 102. lo M. Briend-Faure, J. Jeanjean, M. Kermarec and D. Delafosse, J. C. S. Faraday I, 1978,74,1538. l2 P. Weiss and R. Forrer, Ann. Phys. (Paris), 1926, 5, 153. l3 P. W. Selwood, Chemisorption and Magnetization (Academic Press, N.Y., 1975). l4 M. Primet, J. A. Dalmon and G. A. Martin, J. Catalysis, 1977,46,25. l5 L. Neel, Ann. Geophys., 1949, 5, 99. l6 D. Olivier, M. Che and M. Richard, to be published. l7 P. Gallezot, A. Alaroon Diaz, J. A. Dalmon, A. J. Renouprez and B. Imelik, J. Catalysis, l8 P. Gallezot and B. Imelik,Proc. 3rd Int. Con$ Molecular Sieves (A.C.S. Symposium series, l9 M. Che, J. F. Dutel, P. Gallezot and M. M e t , J. Phys. Chem., 1976, 80, 2371. '* E. J. Nowak and R. M. Koros, J, Catalysis, 1967, 7, 50. 21 E. Ruckenstein and B. Pulvermacker, J. CataZysis, 1973,29,224. zz Kh. Minachev, G. V. Antoshin, E. S. Shpiro and Yu. A. Yusifov, 6th Int. Congr. Catalysis, 1975, 39, 334. Ziirich, 1973), p. 66. (London, 1976), B2. (PAPER 81034)

ISSN:0300-9599    

DOI:10.1039/F19797500165

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Effect of Pressure and Temperature on some Kinetic and Thermodynamic Parameters of Non-ionic Reactions Volume Changes on Activation and Reaction BY BORIS S. EL’YANOV* AND ELENA M. GONIKBERG N. D. Zelinsky Institute of Organic Chemistry of the Academy of Sciences of the U.S.S.R., Leninsky Prosp., 47, Moscow, U.S.S.R. Received 21st February, 1978 The formulae currently used to calculate volume changes on activation, A V,f and reaction, A V,, are shown to be unsuitable even at pressures of m 1 kbar, and calculations are shown to be sensitive to errors, owing to empirical coefficients present in the formulae. The A V’ = A V,[1 -a In (1 + ,6”)] relationship is substantiated and its validity in a broad pressure range shown, as exemplified by 23 non-ionic reactions of various types.The dependence of equili- brium constants on pressure is described by the formula RTln (K’IK,) = -AVo[(l +a)p-(a/ /3)(1+ /3p) In (1 + fip)], where, as a first approximation, CL = 0.170 and /3 = 3.91 x bar-’. A second approximation can be obtained with the help of the linear free energy relationship. The validity of these formulae for kinetic values is confirmed. The accuracy of A Yof and A & calculations can be increased with the help of both these formulae and some criteria of the value of the computa- tional procedure used. The method of calculation is illustrated by 56 Diels-Alder reactions ; the values obtained are a = 0.170 and j3 = 4 . 9 4 ~ As exemplified by 34 reactions of eight types, a linear dependence of A Von temperature has been shown to exist in the range of temperature variation up to 90°C.The values of K = @A V/W)p/A Y are very close for all the reactions. We have formulated the rule that a 1°C increase in temperature results in ]A VI being increased by (0.5+0.1)% (at temperatures close to room temperature). The widespread nature of the compensation effect has been demonstrated, as well as the determining role of the entropy in the change of free energy with pressure. Formulae have been obtained to compute the enthalpies and entropies of reaction or activation under pressure from limited data. bar-l. Investigation of the dependence of reaction rate constant on pressure makes it, in principle, possible to determine the value of A“”, the volume of activation, using the formula of Evans and Polanyi :l (1) Here k is the reaction rate constant expressed in concentration units independent of pressure.Like activation energy and entropy, A V # is a fundamental value character- izing the reaction mechanism and the transition state properties. With the expanding range of problems whose solution makes it necessary to use numerical values of AY#, the requirements on the accuracy of its determination increase. In so far as the Ink = f(p) relationship is not linear, and no sufficiently well- grounded formula for the f ( p ) function has as yet been proposed, serious problems arise in determining the (a In kldp), derivative. Using a comparatively narrow pressure range to determine A V# (by graphical or analytical differentiation) has the disadvantage of the result being highly sensitive to random errors.Attempts to expand the pressure range by using insufficiently well-grounded empirical formulae may result in unpredictable systematic errors. This apprehension is shown to be justified. AV# = -RT@ In klap),. 172B . s. EL’YANOV AND E . M. GONIKBERG 173 The accuracy in determining A V f may be increased as follows, apart from reducing the experimental errors : (1) finding theoretically and experimentally substantiated formulae for f(p) ; (2) decreasing the number of empirical coefficients inf(p), based on the generalization of experimental data or theoretical considerations ; (3) elaborating and applying tests of goodness of fit of the formulae used. In this work an attempt has been made to carry out this programme for non-ionic reactions.Although the emphasis is placed on determining AV#, this is closely related to the solution of the direct problem of describing quantitatively the effect of pressure on the reaction rate constant and other quasithermodynamic activation parameters. The other objective of this work was to investigate the temperature dependence of volumes of activation. Its regularities and quantitative characteristics have not been ascertained up to the present, because of the insufficient accuracy in calculating AV’ and the laboriousness of experiments. Apart from its intrinsic value, this information is needed to solve certain practical problems : calculating the kinetic effects of pressure at different temperatures and comparing the AV# values of several reactions studied at different temperatures. Such information also allows quantitative assessments and calculations of pressure effects on the activation enthalpy and entropy .1. EFFECT OF PRESSURE ON VOLUME CHANGES OF ACTIVATION AND REACTION AND ON RATE AND EQUILIBRIUM CONSTANTS A. FORMULA FOR VOLUME CHANGES Integration of eqn (1) yields RTInk, = RTlnko- rAV’dp. 0 Here subscript 0 refers to the atmospheric pressure.* To find the form of the AV# = [ ( p ) function we shall assume the compressibility of initial reagents as well as that of transition state to adhere to the Tait equation At present this equation is regarded as the best one to describe the effect of high pressure (reaching in some cases 20 kbar) on the compressibility of water and aqueous solutions,2* organic dense gases and even solids7 First obtained empirically, eqn (3) has been subjected to theoretical examination,4u* and has been shown 8b to be close to the theoretically better-grounded equation of Moelwyn- hug he^.^ The assumption that eqn (3) is applicable to the compressibility of the transition state is a serious one.It was first made by Benson and Berson ;5b but doubts as to its validity have been expressed.’O Deviations due to the “abnormal ” compressibility of the transition state, as compared with that of stable molecules, were explained by a shift of the transition state along the reaction coordinate associated with the con- tribution of the pAV term at high pressures,1o and the abnormal compressibility of weak b0nds.l’ In our opinion, however, a possible “ abnormal ” compressibility of the transition state does not necessarily mean that the Tait equation is inapplicable. Moreover, assessments made 1 1 * l 2 indicate the insignificance of the effects in question.* Here and later we disregard the differences in the magnitudes of all values at p = 0 and at atmospheric perssure.174 VOLUME CHANGES ON ACTIVATION A N D REACTION In the subsequent discussion we omit superscript (#), since the required expression We write eqn (3) for the i-th component of reaction in the following form : for [ ( p ) must be equally valid for volume changes on reaction, AV. Vi = V,,[l -ai In (1 +Pip)]. (4) Here ai = AJln 10, and Pi = l/Bp Differentiation of eqn (4) with respect t o p yields Let us now introduce the coefficient P (without a subscript) whose meaning will become clear from subsequent discussion.Adding to and subtracting from the right hand side of eqn (5) the term aiVOiPi/(l +Pp), we get Using eqn (6) we find dAV/dp = Here vi is the stoichiometric coefficient (for equilibria) or the order of reaction with respect to the ith component (for kinetics) taken as positive for reaction products or transition state and negative for reagents : vi(aV,/ap). 1 f 7) or Here Let P = C viaiVoiPi/F viaiVoi* (10) Then y is equal to zero at p = 0, at p p l/Pi * and at any p in the case of the Pi being equal to one another. Therefore, in many cases, especially when the differences between the pi values are not too high, the following relationship will hold true From eqn (8) and (11) it then follows that i IYl @ 1.(1 1) Integration of eqn (12) yields the required relationship, AV = [ ( p ) Here AV' = AVo[l -a In (1 +Pp)J. (13) a = C viaiVoi/?i/AVoP. 1 * pi N" (0.6-6) x bar-' (see below).B. s. EL'YANOV AND E. M. GONIKBERG 175 B. VERIFICATION OF EXISTING EMPIRICAL RELATIONSHIPS AND FORMULA (13) The following relationships are at present most frequently used for calculating AV; Ink, = In ko+ap+bp2 In kp = In ko+ap+bp1-523 In kp = In ko +up/( 1 + bp). (14)10~, 1 3 (15)5b (16)14 Here a = -AVg/RT. Calculations are either performed by the least-squares method (1.s.m.) or, for eqn (14) and (15), by the plotting straight lines of In (kp/ko)/p against p and In (k,/k,)/p against p0.523. The practice of using these relationships has not yet made it possible to either reject or prefer conclusively any one of them.l 3-1 We felt it to be difficult to raise the accuracy of verification using direct kinetic data.It is possible to increase the sensitivity of verification of the goodness of fit of a certain functional dependence by examining a corresponding derivative. We therefore decided to check the following relationships corresponding to eqn (14)-(16) AVp = AVO-b'p (17) AV, = AVo-b'p0*523 (18) AVp = AVo/(l+bp)2. For this purpose, using the values of density and compressibility of liquids at different pressures, taken from literature,16 we calculated their molar volumes, V, and from these the AV of reactions (both real and hypothetical). The list of reactions is given in table 1. Graphical verification of eqn (17) and (19) showed deviations from the straight lines in corresponding coordinates to occur even in the pressure range below 1 kbar.Eqn (18) is better satisfied, but above 1.5 kbar it also no longer holds true. The next stage in the investigation was to verify eqn (13). Calculations were made using a computer. The optimum a, p and AVO(calc.) parameters corresponded to the minimum sum of squares of errors, ZA2 = $(a, p, AVO). Minimization included two stages: ( 1 ) the minimum value of $ at fixed p values was determined by the standard 1.s.m. procedure ; (2) the @ values obtained were minimized by varying 8. Comparison of the " experimental " AVO values and those calculated by this procedure, presented in table 1, showed their excellent agreement ; the standard error for AV does not exceed 0.8 % of the AVO value.Table 2 illustrates the validity of eqn (13) throughout the whole pressure range up to 12 kbar ; a similarly good agreement between the calculated and the experi- mental values was obtained in all the reactions studied. For the above reactions, the a and p values vary within 0.14 < a < 0.27 and 1.2 < p x lo3 bar-' < 7.8 ; the averaged values are a = 0.187+0.033 and p x lo3 = 3.84 + 1.66 bar-' (standard deviations are given). We now compare a and p with the corresponding characteristics of liquids, al and pl. The data presented by Benson and Berson 5 b make it possible to estimate the approximate range of al and p1 values : 0.08 < al < 0.11 and 0.6 < x lo3 < 6. The ranges of p1 and #I values are thus approximately the same.The values of a, as well as those of a,, vary within a comparatively narrow range, although the a values are about twice as high as those of al. Examples of such graphs are shown in fig. 1.reaction b TABLE AN ANALYSIS OF APPLICABILITY OF EQN (13) AND A Yo CALCULATIONS a eqn (1 3 ) ~ eqn (1 3)d eqn (17)e P ~ X number -A VO(exptl lkbar of points /cm3 mol- (i) isoprene dimerization 12 7 (ii) pentene + pentane 3 decane 3 4 (iii) pentene + heptane 3 dodecane 1.5 4 (iv) pentene+ propanol -+ octan-3-01 4 7 (v) pentene+ propanol -+ 2-methylheptan-3-01 5 8 (vi) pentene + propanol -+ 2-methylheptan-5-01 5 8 (vii) pentene + propano1 -+ 3-methylheptan-1-01 5 8 (viii) pentene + propanol -+ 3-methylheptan-4-01 5 8 (ix) pentene+ pentanol -+ diamyl ether 5 11 (x) acetone condensation into mesitylene 3 7 (xi) pentene + water -+ pentanol 5 11 (xii) octenefwater + octan-3-01 4 7 (xiii) octene + water -+ 2-methylheptan-3-01 5 8 (xiv) octene+ water -+ 2-methylheptan-5-01 5 8 (xv) octene+ water -+ 3-methylheptan-1-01 5 8 (xvi) octene+ water -+ 3-methylheptan-4-01 5 8 (xviii) acetone+ pentane 3 octan-3-01 4 5 (xvii) acetaldehyde condensation into ethyl acetate 1.5 5 (xix) acetone + pentane 3 2-methylheptan-3-01 5 6 (xx) acetone + pentane + 2-methylheptan-5-01 5 6 (xxi) acetone+pentane 4 3-methylheptan-1-01 5 6 (xxii) acetone + pentane 4 3-methylheptan-4-01 5 6 (xxiii) ally1 aIcohol+ pentane + octan-3-01 3 4 37.88 29.79 28.66 25.04 25.49 24.45 26.73 26.87 15.59 26.78 19.31 14.42 14.87 13.83 16.11 16.25 14.74 29.26 29.71 29.42 30.95 31.09 24.20 -A Vo(ca1c) /cm3 mol-1 37.89 29.79 28.65 25.07 25.52 24.46 26.76 26.90 15.60 26.72 19.31 14.42 14.87 13.80 16.11 16.25 14.74 29.26 29.72 29.43 30.96 31.10 24.20 a 0.148 0.169 0.251 0.157 0.154 0.160 0.161 0.159 0.144 0.242 0.154 0.195 0.196 0.21 5 0.200 0.204 0.265 0.191 0.186 0.191 0.190 0.190 0.187 ~ ~ 1 0 3 s 4.40 0.19 7.77 0.12 2.87 0.13 5.25 0.16 4.76 0.14 4.64 0.07 4.96 0.14 4.43 0.15 7.09 0.12 1.72 0.17 3.91 0.04 2.47 0.02 1.96 0.07 1.75 0.08 2.40 0.05 1.90 0.03 1.25 0.01 4.16 0.11 4.02 0.17 3.74 0.10 4.20 0.14 3.79 0.12 4.85 0.02 /bar- 1 /cm3 mol- 1 -A Vo(ca~c) 39.39 27.21 27.15 24.70 25.72 24.42 26.36 27.07 15.23 27.19 20.22 14.79 15.79 14.49 16.43 17.14 15.42 27.66 28.44 28.10 29.06 29.77 22.78 /cm3 mol-1 a/ % 4.0 - 8.7 - 5.3 - 1.4 0.9 -0.1 - 1.4 0.7 - 2.3 1.5 4.7 2.6 6.2 4.8 2.0 5.5 4.6 - 5.5 -4.3 - 4.5 - 6.1 - 4.2 - 5.9 -A J’o(cslc) /cm3 mol-1 35.17 27.25 27.55 21.96 22.61 21.62 23.86 23.50 13.46 25.06 17.32 13.10 13.75 12.76 14.64 14.99 14.43 26.34 26.93 26.69 27.91 28.20 22.44 s/ % - 7.2 - 8.5 - 3.9 - 12.3 -11.3 -11.6 -11.2 - 12.1 - 13.7 - 6.4 - 10.3 - 9.2 - 7.5 - 7.7 -9.1 - 7.7 -2.1 - 10.0 - 9.4 - 9.3 - 9.8 - 9.3 - 7.3 0 r d 5 n X 9 Vl 0 Z 9 0 4 9 0 Z 9 =! 2 z tl 9 0 0 Z 2 * L.s.m.-calculations ; S is the standard deviation, S = (A V&alc)-A Vo(,,pt)>/A Vo(e,pt) ; b all the reagents are of normal structure, the double bond or the functional group are in position 1 ; C results of optimization ; d a = 0.170, t3 = 3.91 x bar-’ ; epma, not exceeding 4 kbar.B .S .EL’YANOV A N D E . M . GONIKBERG 177 Benson and B e r s ~ n , ~ ~ when deriving eqn (18), also proceeded from the Tait equation. With the help of an appropriate approximation to the initially complex expression for the AVZ = c(p) function they obtained eqn (18). These authors believed that this formula should be valid within the pressure range of 1-16 kbar. However, it follows from our results that this conclusion is unwarranted, and formula (18) cannot be considered satisfactory. p/kbar 52 3 /barO * 52 3 FIG. 1.178 VOLUME CHANGES ON ACTIVATION AND REACTION 1.0 + I I I I I I 0 1 2 3 2 5 Plkbar FIG. 1.-Verification of eqn (17)-(19) for the reactions (0) (i), (a) (v) and (A) (xi) from table 1; (4 eqn (13, eqn (181, (4 eqn (19). TABLE CO COMPARISON OF CALCULATED a AND EXPERIMENTAL AV VALUES FOR REACTION (i) plkbar 0 0.49 0.98 2.94 5.83 9.81 11.77 -A Vlcm3 mol-1 expt.calc. 37.88 37.89 31.52 31.45 28.49 28.52 22.91 23.10 19.61 19.42 16.79 16.62 15.42 15.62 a Eqn (13), a = 0.148, /3 = 4.40 x bar-'. c. FORMULA FOR THE CONSTANTS. CALCULATION OF VOLUMES OF ACTIVATION FROM KINETIC DATA Using eqn (13) we get from eqn (2) the formula describing the dependence of reaction rate constant on pressure Although formula (20) must conform with experimental results better than eqn (14)- (16), it contains one extra empirical parameter, which increases the sensitivity of AV,f values to random errors. In addition, it prevents the use of the simple 1.s.m. procedure. As a first approximation, we therefore took the " averaged " values of a = 0.170 and p = 3.91 x bar-l, found by optimizing all the data for the reactions presented in table 1 with the help of eqn (21) RTln k, = RTln ko-AV,f[(l +a)p-(a/fi)(l+fip) In (1 +fip)].(20)" W = (AVO-AVp)/AVo = a In (l+/3p). (21) * For equilibrium constants, K, one obtains an expression similar to eqn (20) (with K substituted for k and A Yo for A Vof ) by using, instead of eqn (l), its thermodynamic analogue, Planck's equation : A V = - RT(a In K l a p ) ~ .B . s. EL'YANOV AND E . M. GONIKBERG 179 The optimization procedure is similar to that for eqn (13). The AVO values determined to this approximation with the help of 1.s.m. from eqn (13) and the errors, 6, are given in table 1. Their examination shows that, even under the assumptions made, the value of AVO can in most cases be determined with good accuracy (the [Sl mean value is equal to 3.8 % and the maximum deviation does not exceed 8.7 %).For comparison the same table shows these values calculated using eqn (17). In this case, despite the pressure range decreasing to 4 kbar, for most of the reactions the errors in determining AVO are substantially higher and, more important, are all negative. A second approximation for the a and p values can be obtained by proceeding from the linear free energy relationship : l7 Here @ is a function of pressure, universal for reactions of the same type. The form of the @ function can be found by juxtaposing eqn (20) and (22) : It follows that reactions of the same type have the same a and p values. They can be found by proceeding from the exact data for a standard reaction or by processing statistically the data for a large number of reactions.An example of such an optimization is given below. An important problem is that of tests of goodness of fit of a certain equation for A Vg calculation and the indices characterizing the calculation. This question was previously touched upon by El'yanov et al. ;14c it was, however, not discussed with sufficient comprehensiveness and clarity. In this paper a more detailed and precise examination of the problem is presented, a distinction between tests and indices is introduced and a new test formulated.* The test of goodness of fit of an equation is a characteristic having the properties of the necessary or sufficient condition, as distinct from the index of goodness of calculation, which does not have such a categorical property although in some cases it can be used for the same purpose.Tests based on statistical assessments are, however, of a probabilistic nature. The following tests and indices can be formulated. @ = [(l +a)p-(a//I)(l +pp) In (1 +pp)]/R In 10. (23) TEST AND INDEX OF ACCURACY If the accuracy of experimental log k values is characterized by a standard error, Sexp., and the standard error of calculation performed with the help of agiven equation, by Scale., one can then, using the statistical test of verification of hypotheses,' * regard the equation as not contradicting the experimental data if s&p./%!alc. F0.05 (24) where Fo,05 is Fisher's test at the significance level of 0.05.A doubtful case can be characterized by the relationship : and at S&,JS&,. > FoSol the equation verified can be regarded as not satisfying the requirements placed upon a strict functional dependence. To evaluate the data from literature which do not contain any information on Scxp. we have proposed 14c the index of accuracy based on the following classification * The symbols have also been changed.180 VOLUME CHANGES ON ACTIVATION AND REACTION of the accuracy of kinetic data : excellent accuracy : the maximum deviation of the calculated and the experimental values of the rate constant does not exceed 5 %; good accuracy : 10 % ; satisfactory : 20 %. For reactions where deviations exceed 20 % the accuracy will be regarded as low. In this case we get the following ratings of accuracy : accuracy excellent good satisfactory low S (for log k ) GO.011 G0.022 < 0.044 > 0.044.A low accuracy can be caused both by the equation being incongruous with the experimental data and by the poor quality of the data themselves. TEST OF LINEARITY If the dependence of log k on pressure is presented in the form of eqn (22), this dependence for correct @ values will be graphically expressed as a straight line by plotting log k against a. If the experimental log k values fall on a curve they will be better described by eqn (25) Here b is an empirical coefficient; ko, AV,f and b are determined by 1.s.m. As a test of linearity, indicating the insignificance of the differences between eqn (22) and (25), we can take the relationship Here S,, and S25 are standard errors which result from using eqn (22) and (25).s;2/si5 G F0.05* (26) A doubtful case will be characterized by the relationship : F0.05 < s?2/S:5 I ; b . O 1 7 and at Si2/S,”5 > F0.,, we shall regard eqn (22) as not being satisfied. We thugsee that the test of linearity is a necessary but not sufficient condition to decide on the goodness of fit of eqn (22). TEST OF RANDOMNESS OF ERRORS In the case when great numbers of data are available for reactions of the same type, it becomes possible to verify the goodness of fit of the equation used with the help of a test that can be conventionally defined as the test of error random- ness, as follows. If we process experimental data using eqn (25), then, provided eqn (22) is valid, the deviation of b from zero, with the chosen @ functions, results from random causes. Reactions with b > 0 and with b < 0 must then be equipro- bable.This is also equivalent to the equiprobability of cases satisfying the conditions of (AV,f>,, > (AVg)25 and (AV;),, < (AVz)2s. Here and (AVof)25 are AV; values calculated from eqn (22) and (25), respectively. The confidence interval for j3, the probability of the appearance of b < 0, can be determined by proceeding from the frequency of this condition being fulfilled, 0, in n tests :l Here u1--p0~2 is the quantile of the normal distribution at the significance level of po. For po = 0.05 (assumed in this work), z.iO.975 = 1.96. The test of error random- ness is the falling of the p = 0.5 point within the confidence interval of eqn (27).The fulfilment of this test is a necessary but not sufficient condition to decide on the goodness of fit of the equation verified.B. s. EL'YANOV AND E . M . GONIKBERG 181 INDICES OF ACCURACY OF AvZ The standard error for AV:, which we designate as Sv, can serve as the index of accuracy of its calculation. When the equation used for calculation has the form of eqn (22), Sy is found from formula sv = ST[C Q,Z-(C ~ ~ y 1 ~ 1 - 0 . 5 . (28) i i Here S is the standard error of the function, Tis the temperature, and n is the number of points. If the @ function has been chosen correctly, one can then determine with the help of Sv the confidence interval (at probability p) within which lies the true AVZ value, using the formula where t is Student's coefficient found from tables.18 If, however, the function is incorrect, the true value of AV;, as a result of the systematic error, may lie outside the confidence interval.(gAv,z)m,x. = kSVt(P, n) (29) TABLE 3.-EFFECT OF UPPER PRESSURE LIMIT ON CALCULATION ' OF Avg (REACTION OF ISOPRENE WITH MALEIC ANHYDRIDE IN ETHYL ACETATE AT 35"@ - A V ~ icm3 mol-1 highest plbar 51 7 689 1013 1379 2068 3102 41 36 5169 6204 number of points used in fit 4 5 6 7 8 3 10 11 12 eqn (14) eqn (16)~ eqn (20)d 36.1 37.5 38.1 37.4 35.5 33.3 32.4 31.6 30.3 36.9 36.3 35.2 34.4 33.9 34.0 34.2 34.3 34.8 (1) 39.6 39.5 39.0 38.5 38.2 38.4 38.1 37.8 37.7 (2) 38.1 37.7 38.6 38.2 39.8 42.2 39.6 38.1 40.1 (3) 40.5 40.5 40.2 39.9 39.9 40.2 40.1 40.0 40.0 vd.)inst /cm3 mol-l 7.8 3 .O 1.9 4.5 0.6 a Least squares method ; b ref. (19) ; C b = 9 . 2 0 ~ bar-l [ref. (14c)l; d (1) 01 = 0.170, /3 = 3.91 x bar-l, (2) optimization of all the parameters, (3) a = 0.170, /3 = 4 . 9 4 ~ b a r i . Apart from Sy, another index of the goodness of fit of the AVO calculation can be used. As noted by E ~ k e r t , ~ ~ ~ the AV; value can vary significantly if we vary the number of points, obtained in the same measurement series, used in a fitting. By way of illustration table 3 shows the results of Eckert's calculations,13c expanded by us for a broader pressure range, using eqn (14), as well as the calculations of the same data using eqn (16)14c (at b = 9.20 x bar-I) and eqn (20) [procedures (1)-(3)]. It is seen from the table that, when eqn (14) is used, the difference in AV,f can reach 7.8 cm3 mol-l.This difference, designated as (6AV&st., can be defined as the index of instability. It reflects the effect exerted upon the AV,f calculation both by the random experimental errors and the systematic errors resulting from an inexact formula being used. Generally, the value of (6AVZ)inst. must increase with the increasing number of empirical coefficients in the calculation formula. This can be illustrated by comparing the results of calculations performed with the help of eqn (20) using procedures (2)182 VOLUME CHANGES ON ACTIVATION AND REACTION and (3) (further details will be given in the following section). With procedure (2), as distinct from procedure (3), the a and p parameters are optimized in the course of calculation, and, consequently, the value of (6A Vz)jnst.is substantially higher. Despite the relative nature of the index of instability, its application, together with the other tests and indices, can be useful in characterizing the accuracy of the A V$ values obtained and comparing different calculation procedures. Calculation by eqn (20) [procedure (l)] thus, shows good stability, exceeding that of the calculations by eqn (14) and (16). This result is an additional argument in favour of the recommendations formulated above. The application of the above tests and indices makes it possible to judge with greater confidence whether a certain equation is applicable for calculation. With their help one can eliminate equations not suited to describe experimental data or to identify the data which, for some reason or other, are not described by the given equation.D. APPLICATION TO DIELS-ALDER REACTIONS When sufficiently accurate kinetic data are available, one can attempt to carry out the optimization of all the parameters in eqn (20) using 1.s.m. As seen from table 3, [procedure (2)], the values of AVg obtained by optimizing the data for the cited reaction, have good stability despite the great number of parameters being optimized. For the entire pressure range, S = 0.0074 is an excellent index of accuracy with such a broad interval. These results confirm the high accuracy of the initial data and also the validity of eqn (20) for kinetic values within a broad pressure range. Despite the great number of parameters optimized in this case, (C~AV&~.is smaller than when the optimization is performed using a quadratic equation [eqn (14)]. The constants obtained by optimization in the entire pressure range (a = 0.170 and p = 4.94 x bar-l) proved to be quite close to the " averaged " values previously found for non-kinetic data. The high AV,Z stability obtained in calcula- tions with these constants (table 3, last column) makes it possible to use them with sufficient reliability. Let us now consider the possibility of calculating the volume of activation for a broad variety of Diels-Alder reactions. The first attempt 14c was made to apply an equation similar to eqn (22) to these reactions using the @(p) function found for electrolyte ionization reactions.2o In this case eqn (22) acquires the form of eqn (16) with b = 9.20 x bar-l.Verification of this relationship has shown that out of 34 reactions only one does not satisfy the linearity test and 2 reactions are regarded as doubtful. The equation was satisfied with good indices of AV: accuracy and stability. From this the relationship was concluded to be valid. The test of error randomness was, however, not applied. The calculation of fi from eqn (27) for these reactions gives the interval of 0.179 5 5 0.497. The = 0.5 point, although close to this interval, still does not fall within it. For the verification to be more reliable we increased the number of reactions to 56, using some additional data.2f Calculations gave the interval 0.115 < jj < 0.332, which is now seen to be sufficiently removed from the jj = 0.5 point.The test of randomness of errors is, thus, not fulfilled, and the @(p) function has to be further specified. The next stage consisted of verifying the goodness of fit of eqn (23) at a = 0.170 and #I = 4.94 x bar-l. 3 reactions did not satisfy the test of linearity and 4 fell into the category of doubtful reactions, with 13 reactions (23 %) being characterized as excellent, 22 (39 %) as good, 12 (21 %) as satisfactory and 9 (16 %) as of lowB . s. EL'YANOV AND E. M. GONIKBERG 183 accuracy. For j we obtained the value of @ = 0.41 +0.13, which does not differ significantly from 0.5. Eqn (23) with the constants in question is, thus, with some exceptions, consistent with the tests of goodness of fit, and is satisfied with a good index of accuracy for a large number of reactions.Let us consider the indices of accuracy for AVZ. In the last calculation the values of (C~AV&,~~. for 85 % of the reactions proved to be lower than with the calculation by eqn (14). Comparison of the results for only 35 reactions, studied by Eckert and 21b* 22 in which the maximum pressure range did not exceed 1380 bar, gave almost the same result : 81 % (with the minimum number of points equal to 4). Given below are the rneanvaluesof (SAV~)in,,., SYand(GAV$)max, for these reactions ; the error indicated is the standard deviation : accuracy excellent good satisfactory number of reactions 12 15 8 (SAVt )inst. 1.5k0.7 2.85 1.2 4.852.8 SJ'/cm3 rno1-I 0.6k0.1 l . l k 0 . 2 1.9k0.3 !ciAJqlmax.1.550.3 2.8k0.5 4.9k0.8. These figures give an indication of the accuracy of the AV; calculation. Both indices, Sy and (C5AVgZ)inst.y are not contradictory, since (6AV,+),n,,. does not fall beyond the limits of the confidence interval, equal to ~ ( C ~ A V : ) ~ ~ ~ . In this case the value Of (dA Vgf)inst. equals exactly half the confidence interval at any grade of accuracy. TABLE 4 . 4 VALUES AT VARIOUS a AND /3 VALUES IN EQN (23) a = 0.236 a = 0.170 a = 0.170 /3 =:4.94x 10-3 bar1 = 2 . 5 2 ~ 10-3 bar1 /3 = 3.91 x 10-3 bar1 plkbar @,t/cm-3 K cP/cm-3K @/cm-3K dl%a 0.1 0.5 1 .o 1.5 2.0 3.0 4.0 5 -0 7.5 10.0 0.503 2.279 4.209 5.947 7.554 10.48 13.13 15.56 20.94 25.60 0.508 2.326 4.289 6.026 7.598 10.38 12.79 14.92 19.31 22.70 1 .o 2.1 1.9 1.3 0.6 - 1.0 - 2.6 -4.1 - 7.8 - 11.3 0.507 2.328 4.337 6.163 7.861 10.98 13.82 16.45 22.33 27.49 0.8 2.2 3.0 3.6 4.1 4.8 5.2 5.7 6.7 7.4 Another, independent procedure was used to determine the a and p constants in eqn (23).It consisted of optimizing the data for all the reactions. The optimization procedure was as follows. First, the data of each reaction were optimized in accordance with eqn (20) for all 4 parameters by 1.s.m. In so far as, in most cases, a and p varied within unreasonable limits (3-4 orders of exponent), which resulted in abnormally high A V,f deviations from their reasonable values, a restricted interval of j? values was introduced : 0.6 < p x lo3 bar-l < 15. From the values found for AV; we then calculated the @ values for all pressures, using eqn (22).The next stage consisted of optimizing the a and p values in eqn (22) for the whole array of values for all reactions at all pressures. The values obtained were : a = 0.236 and /3 = 2 . 5 2 ~ bar-l. Table 4 gives a comparison of values, calculated by proceeding from different a and /3 values. Their examination shows that up to 4 kbar the values of @ in the first two columns are quite similar and differ only slightly from those in the third column. At higher pressures the difference begins to increase184 VOLUME CHANGES ON ACTIVATION AND REACTION rapidly. Taking into account that out of 56 reactions only 7 have been studied at pressures above 4 kbar, a small discrepancy between the optimization data and the data for a standard reaction at these pressures is not surprising.The excellent coincidence of @ values obtained by two independent procedures for Diels-Alder reactions and their closeness to the values obtained by a third procedure indicate their reliability at least up to 4 kbar. Even this small difference in <D values above 4 kbar in columns 1 and 2 of table 4 results in the standard reaction not satisfying the test of linearity when its computation is attempted with a = 0.236 and /3 = 2.52 x bar-l in the pressure range of up to 6 kbar. Eqn (20) with a = 0.170 and /3 = 4.94 x bar-l can thus be recom- mended for use in the pressure range of up to 4 kbar. 2. TEMPERATURE DEPENDENCE OF VOLUME CHANGES ON ACTIVATION AND REACTION A. QUANTITATIVE CHARACTERISTICS The starting point of our investigation was an important result obtained by Marani and Talamir~i.~~ Proceeding from quasithermodynamic relationships these authors showed that, within limits of applicability of the Arrhenius equation, a linear dependence of A V on T must hold true.Extensive verification of this dependence for A P values and its quantitative assessment appears at present to be 35 H I '3 30 E s I 25 20 3 d 15 PPI 0 20 40 60 80 T/"C and A, (Gl) (table 5). FIG. 2.-Temperature dependence of volume changes on the reactions x , (A4) ; 0, (A5) ; 0, (E2) practically impossible for the reasons described in the introduction. We assumed that the temperature dependence of AVf can be simulated by a corresponding dependence of A V. This offers possibilities of performing necessary calculations, since the numerous data on the densities of compounds at different temperatures, available in literature, can be used to calculate AV of various reactions.We have€3. S. EL'YANOV AND E . M. GONIKBERG 185 TABLE 5.-TEMPERATURE DEPENDENCE OF VOLUME CHANGE ON REACTION reaction a (1) pentene-2+ pentane (2) pentene-2+ hexane (3) pentene-2+ heptane (4) dodecene+ octane (5) dodecene+ nonane -AVd temperature /cm3 mol-1 rangePC (A) alkylation of alkanes with olefins 28.1 1 60 27.48 40 34.39 40 28.64 90 24.65 60 (B) C-alkylation of alcohols with olefins (1) hexene+ethanol 26.10 30 (2) heptene C+ methanol 19.61 30 (3) heptene C+ propanol 24.04 10 (4) heptene C+ propan-2-01 25.79 10 (5) hexene+ butanol 24.95 10 (6) hexene+ 2-methylpropan-1-01 25.82 10 (7) octenef ethanol 23.65 10 (C) unsaturated alcohol+ alkane + alcohol (1) allyl alcohol+ pentane 26.30 30 (2) allyl alcohol+ 2methylbutane 27.68 30 @> C-alkylation of acetone with alkanes (1) pentane+ acetone (2) heptane+ acetone (1) CH31+ hexene (2) CH31+ heptene (3) C2H5Br+ hexene 28.65 30 28.39 10 (E) addition of alkylhalides to olefins 23.30 30 18.00 30 26.02 30 (F) olefin dimerization (1) hexene + dodecene 28.10 10 (2) heptene -+ tetradecene 27.14 10 (3) octene 3 hexadecene 26.60 10 (4) octene+ heptene 4 pentadecene 26.84 10 (5) octene+ hexene +.tetradecene 27.37 10 (6) hexene+ heptene -+ tridecene 27.62 10 (1) into mesitylene 27.15 35 (G) acetone condensation (2) into 1,2,3-trirnethylbenzene 32.10 15 (H) Tischchenko condensation (1) 2 CH3COH + ethyl acetate 15.41 20 (2) 2 C2HsCOH 4 propyl propionate 13.95 30 (3) 2 CzHsCOH + ethyl butyrate 13.60 30 (4) 2 C2HSCOH + butyl acetate 13.95 30 (5) 2 C3H7COH +.heptyl formate 15.75 30 (6) 2 C3H7COH -+ hexyl acetate 14.79 30 (7) 2 C3H7COH 3 methyl oenanthate 16.10 30 -8AV - ~ T F 0.144- 0.126 0.130 0.125 0.123 0.107 0.080 0.097 0.105 0.107 0.109 0.095 0.110 0.128 0.153 0.129 0.098 0.080 0.121 0.140 0.130 0.109 0.118 0.126 0.130 0.168 0.163 0.060 0.054 0.054 0.059 0.069 0.061 0.066 1 / A V (aA V/aT)p x 103/1(-1 5.12 4.59 3.78 4.36 4.98 4.10 4.08 4.03 4.07 4.29 4.22 4.02 4.18 4.64 4.85 4.54 4.13 4.44 4.66 4.98 4.79 4.10 4.41 4.60 4.73 6.17 5.06 3.89 3.87 3.95 4.23 4.38 4.12 4.07 a Unless otherwise stated, the reagents and products are of normal structure, the double bond or the reaction product is 3-ethyloctadecane ; C 3-ethylpent-2- the functional group are in position 1 ; ene ; d at 20°C.186 VOLUME CHANGES ON ACTIVATION AND REACTION carried out such calculations for 34 reactions (real and hypothetical) presented in table 5, using the data from ref.[16(b)]. In no case have we noted any substantial deviations from a straight line, some of which are shown in fig. 2. With each type of reaction, characterized by different AV and (dAV/aT), values, the values of IC = (aAV/aT),/AV for 20°C show remarkable constancy. The mean value of E~~ thus equals (4.43 f 0.48) x “C-l. The calculated standard error of only 11 % of the mean value is taken as the measure of deviation. The results obtained make it possible to formulate a simple rule : a 1°C increase of temperature results in a (0.5f0.1) % increase of IAV] (at temperatures close to room temperature).Let us derive formulae suitable for A Y and IC calculations at different temperatures, We shall present the linear dependence of AV on T as AV, = AVO +( aAv T),o-TO). Here subscript 0 refers to a certain standard temperature. Equality (30) can be presented as AVT = AVo[l+ KO(T-T*)] which is suitable for the change-over from standard A V values to their values at another temperature and vice versa. Dividing both parts of equality (30) by (aA V/dT), we get 1IICT = l/rco+fT-To). (32) Eqn (32) is more convenient for use as It is appropriate to examine some possible methods of assessing the IC value in a certain reaction, apart from direct calculations based on densities or dilatometric measurements.(1) As a first approximation we can take the mean value of E20 obtained by us, which is equal to 4.4 x deg-I. (2) A very narrow range of K fluctuations for different reactions gives us grounds to assume that IC is constant for the same type of similar reactions. As a more precise IC value we can thus take its mean value for a given type of reaction, or if it is not available, K: for an individual reaction belonging to this type. (3) It can probably be assumed that IC# i2i IC,,,, where IC* is a value characterizing the activation process and K , ~ , is a corresponding equilibrium value for the same reaction. Assessments of this kind will be presented in the following section. B. SOME COROLLARIES: EFFECT OF PRESSURE O N ENTHALPY AND ENTROPY When a great number of bimolecular reactions were being investigated it was noted 24 that the general increase of reaction rate under pressure (AV” < 0) is accompanied by the growth of the pre-exponential factor [(aAS”/dp)T > O].* Laidler 26 arrived at the conclusion that in a series of heterolytic reactions AV” and (aAS* lap), must not only have an opposite sign but also vary in opposite direc- tions.This conclusion follows from consideration of the thermodynamic relationship 8AV’ dASf (2T), = -( dp), * CX, however, ref. (25). (35)B . s. EL'YANOV AND E. M. GONIKBERG 187 and the conclusion of Fajans and Johnson 27 on the approximately linear dependence (with a positive slope) between the partial molar volumes of ions in water solutions and their temperature coefficients. A similar conclusion for non-ionic reactions, based on the assumption that the values of AVX,, and (aAYFfree/aT) run parallel to each other in a series of reactions, was made by G~nikberg.~~ Using the results obtained in the previous section we can estimate the effect of pressure on reaction or activation enthalpy and make some quantitative assessments.Using the notation of the preceding section r$)p = KAV. Taking into account the thermodynamic equality AV = rz) T where AG is the Gibbs free energy, and eqn (35) and (36) we get ( Y ) T = In so far as K > 0, derivatives in both which is in agreement with experiment. Let us denote (37) parts of equality (38) have different signs, and from eqn (38), (39) and (41) Since from eqn (38)-(40) we obtain (39) Let us assess the value of By the meaning of which is that of isokinetic (isoequili- brium) temperature.For this purpose from eqn (41) and (32) we first get J = T O - l / K o . (43) Taking the mean value of go = 4.4 x deg-' obtained by us as corresponding to To = 293 K, we shall get for non-ionic reactions the most probable value of fl = 65 K. Using the extreme values of K from table 5 we get 30 < fl < 130 K. The possible boundary values of fl are seen to differ from the probable value by a factor of ~52. The value of fl is positive, i.e., according to eqn (39), the changes of AH and AS with pressure run parallel to each other and exert an opposite (compensating) effect on the reaction free energy (or rate), which is observed experimentally.From eqn (39) it also follows that the value of (aAH/ap), is from 0.1 to 0.5 of the T(aAS/ap), value at temperatures close to room temperature.188 VOLUME CHANGES ON ACTIVATION AND REACTION This analysis, which does not contain any assumptions and is based on the generalization of many experimental data, thus demonstrates the widespread nature of the compensation effect, as well as the determining role of the entropy component in the change of free energy under the effect of pressure. Further possibilities for quantitative computations are offered by the linear relationships between the enthalpy and the entropy (AH against AS linear relation- ships) with changing pressure. Previously l7 we showed that these relationships must hold true for a certain type of similar reactions, if the CD parameter does not depend on temperature.Up to now this dependence has not been observed. A good agreement for the log k against rP linear relationship was noted 2o for the ioniza- tion of acetic acid in the temperature range 25-225°C at pressures of up to 3 kbar ; with the iD values for ionization reactions having been obtained at 25°C. One can, therefore, expect the AH against A S linear relationship to hold true, at least for some types of reactions. In the case under consideration the AH against A S linear relationship means that p in eqn (39) is not dependent on pressure. From eqn (41) it then follows that K is not dependent on pressure either. In this case integration of eqn (38) and (42) yields linear relations hips (AS,- AS,) = - K(AG,- AGO) (44) (AH,-AHO) = (1 -xT)(AG,--AGO). (45) Having estimated in some way the values of K [e.g., with the help of approximations examined in section 2(A)], one can then, using the values of (AG,-AGO), calculate (AS, -ASo) and (AHp - AHo).We shall illustrate dependences (44) and (45) and K # calculations using as an example the kinetic parameters of two Diels-Alder reactions : isoprene and cyclo- pentadiene dimerizations. The first reaction was studied by Rimmelin and Jenner 21a at pressures of up to 8 kbar in the temperature range of 4O-7O0C, and the second, by Walling and Schugar,28 at pressures of up to 3 kbar and temperatures of 0-40°C. In fig. 3(a) and (b) experimental points corresponding to 40°C are plotted and straight lines are drawn by 1.s.m.in accordance with eqn (44) and (45). Calculated IC# values are presented below. For the first reaction it also proved possible to calculate the IC,,, value for the entire reaction, since the values of AV,,, measured by Rimmelin and Jenner at four temperatures fitted the straight line remarkably well. Finally, the same table also contains the value of E40. Comparison of the IC' values of both reactions shows their closeness, just as we expected for reactions of the same type. The differences between K,, and E40 values on the one hand, and K' on the other shown here are close to the experimental error, in so far as the accuracy of AS' reagent K + ~ ~ 0 3 = K r r n ~ 1 0 3 b 6 / % c ?i40x103' s / % c isoprene 5.84 4.68 20 31 4'04 27 cyclopentadiene 5.50 - Q From experimental data with the help of 1.s.m.; b from the linear dependence of AVr,, on T; determination, as indicated by Rimmelin and Jenner,21a is equal to f 4 cal "C-' mob1, which amounts to 21 % of the maximum (ASp-ASo) value. These results bear witness to the feasibility of quantitative estimates and more precise calculations of enthalpies and entropies for reactions under pressure from a limited number of initial data. When experimental AG, values are not available, the calculation can be performed if the AGO and Qi, values for a given reaction are - C deviation from K+ ; d calculated for 40°C by eqn (33) from &O = 4.4 x OC-'.B. s. EL’YANOV AND E . M . GONIKBERG . .28 29 30 31 32 44 I I I 189 I I I I I 24 25 26 27 AGZ /kcal mol-I 23 2 2 21 20 19 10 AG# /kcal moV FIG.3.- -Linear dependences of (a) A S against AG and (6) AH against AG for the isoprene (0) and cyclopentadiene (0) dimerizations at 40°C.190 VOLUME CHANGES ON ACTIVATION AND REACTION known. As has been previously shown,17 given a linear relationship between AH and AS, the following linear dependences will hold true : ASp = ASo-m@ (46) AHp = AHo +n@. (47) Here m = R In 10 x (aAV0/aT), n = R In 10 x [AVO - T(BAV0/BT),]. The last two equalities are easily transformed into m = R In 10 x AV,K n = R In 10 x AVo(l -TIC). (483 (49) (50) (51) In this case, the calculation of ASp and AHp can thus be carried out from eqn (46) and (47) using eqn (50) and (51). ADDENDUM After the manuscript of this paper had been prepared for publication, the work of Orszagh et aL2’ became known to us.In it formula (13) was also proposed, based on the assumptions that the Tait equation holds true and the ai and pi constants for the reagents and the transition state have similar values. The formula was verified with 4 reactions by straight-line plots of (a In klap), against In (1 +Qp) coordinates, where k is the rate constant. The (a In k/Bp), values were found by graphical differentiation, and those of Q constants by approximate estimation. The authors came to the conclusion that, in all the reactions examined, experimental data cannot be described by one equation valid within the entire pressure range. According to their explanation, there exists a critical pressure at which the mechanical properties of the transition state undergo sharp changes and, therefore, its compressibility before and szfter the critical pressure is described by different Tait equations.Consequently, the change of AV# with pressure is also described by two equations similar to eqn (13).* Another explanation can be offered, uiz., the simplified initial assumptions of the authors are not verified and, therefore, eqn (14) is, in principle, not valid within the entire pressure range, even when the Tait equation holds true for every component. We believe, however, that the conclusion obtained by Orszagh et al., is wrong. It is not corroborated by our data on volume changes both for reaction [section l(B)] and for activation [section l(D)], and sharply contradicts our conclusion on the applicability of eqn (13) within a broad pressure range.This result can be explained by gross, poorly controllable errors which appear during the plotting of a smooth Ink = f ( p ) curve and the graphical differentiation and, at the same time, by the extreme sensitivity of the calculated p values to errors ; it illustrates the unsuitability of this method for the verification of eqn (13). Bearing in mind the work of Orszagh et al. we are, nevertheless, convinced that our work on the substantiation and verification of eqn (13) is useful and, therefore, stand by the conclusions drawn in this paper. * The critical point is approximately in the middle of the pressure range, irrespective of its magni- tude. E.g., even in the reaction of isoprene with maleic anhydride in dichloromethane, studied in a narrow pressure range of 1-1380 bar, the critical pressure is 600 bar.B .s. EL'YANOV AND E. M . GONIKBERG 191 M. G. Evans and M. Polanyi, Trans. Faraday Soc., 1935,31, 875. P. G. Tait, Physics and Chemistry of the Voyage of H.M.S. Challeager (H.M.S.O., London, 1 888), part IV. J. 0. Hirschfelder, Ch. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley and Sons, New York, 1954). (a) R. E. Gibson and 0. H. Loeffler, Ann. N. Y. Acad. Sci., 1949, 51, 727 ; (b) R. E. Gibson, J. Amer. Chem. SOC., 1934, 56, 4. (a) €1. Carl, 2. phys. Chem., 1922, 101, 238; (b) S. W. Benson and J. A. Berson, J. Amer. Chem. SOC., 1962, 84, 152. D. S. Tsiklis, Dense Gases (Khimia, Moscow, 1977). ' R. Ginell and T. J. Quigley, J. Phys. Chem. Solids, 1965, 26, 1 157 ; 1966, 27, 1173.* (a) R. Ginell, J. Chem. Phys., 1961,34,1249 ; (b) G. A. Neece and D. R. Squire, J. Chem. Phys., 1968, 72, 128 ; (c) D. S. Tsiklis, U. Ya. Maslennikova and V. A. Abolsky, Doklady Akad. Nauk S.S.S.R., 1977,233,816. E. A. Moelwyn-Hughes, J. Phys. Chem., 1951, 55, 1246 ; E. A. Moelwyn-Hughes, Physical Chemistry (Pergamon Press, London, 1961). lo (a) C. Walling and D. D. Tanner, J. Amer. Chem. SOC., 1963, 85, 612; (b) S. D. Hamann, Ann. Rev. Phys. Chem., 1964,15,349. l1 S. W. Benson and J. A. Berson, J. Amer. Chem. SOC., 1964,86,259. l2 W. J. Le Noble, A. R. Miller and S. D. Hamam, J. Org. Chem., 1977, 42, 338. l3 (a) H. S. Golinkin, W. G. Laidlow and J. B. Hyne, C a d . J. Chem., 1966, 44, 2193 ; (6) S. J. Dickson and J. B. Hyne, Canad. J. Chem., 1971, 49,2394; (c) C. A. Eckert, Ann. Reu. Phys. Chem., 1972,23,239. l4 (a) H. Heydtmann and H. Stieger, Ber. Bunsenges.phys. Chem., 1966,70,1095 ; (b) B. T. Baliga and E. Whalley, Canad. J. Chem., 1970, 48, 528 ; (c) B. S. El'yanov, S. K. Shakhova and G. A. Rubtsov, Izvest. Akad. Nauk S.S.S.R., Ser. khim., 1975, 2678. l5 D. Buttner and H. Heydtmann, Ber. Bunsenges. phys. Chem., 1969, 73, 640. l6 (a) P. W. Bridgman, Proc. Amer. Acad. Arts Sci., 1931, 66, 185; 1932, 67, 1 ; 1933, 68, 1 ; 1948, 77, 129 ; P. W. Bridgman, Physics of High Pressure (Bell and Sons, London, 1949) ; P. M. Chaudhury, R. A. Stager and G. R. Mathur, J. Chem. Eng. Data, 1968, 13, 9 ; Inter- national Critical Tables (McGraw-Hill, New York, 1928), vol. I11 ; (b) J. Timmermans, Physico-Chemical Constants of Pure Organic Compounds (Elsevier, New York, 1950), vol. I ; G. Egloff, Physical Constunts of Hydrocarbons (Reinhold, New York, 1939), vol. I. H. Cramkr, Mathematical Methods of Statistics (Princeton University Press, 1946). l7 B. S. El'yanov, Austral. J. Chem., 1975, 28,933. l9 R. A. Grieger and C. A. Eckert, Amer. Inst. Chem. Eag. J., 1970, 16,766. 2o B. S. El'yanov and S. D. Hamam, Austral. J. Chem., 1975,28,945. 21 J. Rimmelin and G. Jenner, Tetrahedron, 1974, 30, 3081 ; J. R. McCabe and C. A. Eckert, Ind. and Ew. Chem. (Fundamentals), 1974,13,168. 22 R. A. Grieger and C. A. Eckert, Trans. Faraday Soc., 1970, 66, 2579 ; J. Amer. Chem. SOC., 1970, 92,7149; Ind. and Ens. Chem. (Fundamentals), 1971, 10, 369; B. E. Poling and C. A. Eckert, I d . and Eng. Chem. (Fundamentals), 1972,11,451. 23 A. Marani and G. Talamini, High Temp. High Press., 1973,4, 183, 24 M. G. Gonikberg, L'&uilibre Chimique et les Vitesses des Rbactions sous Haute Pression 25 K. E. Weale, Disc. Furahy Soc., 1956, 22, 122. 26 K. J. LaidIer, Disc. Farahy SOC., 1956, 22, 88. 27 K. Fajans and 0. Johnson, J. Arner. Chem. Soc., 1942,64,668, 28 C. Walling and H. J. Schugar, J. Amer. Chem. SOC., 1963,85,607. 29 J. Orszagh, M. Barigand and J. J. Tondeur, Bull. SOC. chim. France, 1976, 1685. (Mir, Moscow, 1974). (PAPER 8/307)

ISSN:0300-9599    

DOI:10.1039/F19797500172

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

y-Radiolysis of Methane Adsorbed on y-Alumina Part 3.l. 2-Influence of Additives on Product Desorption BY DAVID J. NORFOLK* and TIMOTHY SWAN Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire Received 20th March, 1978 Previous studies showed that methane adsorbed on y-alumina undergoes radiolysis to form chemisorbed precursor species. These decompose when heated to give C1-C3 alkane and alkene products together with hydrogen. The present study uses nitric oxide, nitrous oxide, sulphur hexafluoride, oxygen and carbon dioxide as additives to interfere with product formation, and so allows probable structures to be deduced for each precursor. Both alkane and alkene precursors involve alkylaluminium groups which decompose by homolytic fission of the Al-C bond.The alkane precursor has an accessible hydroxide ion from which a hydrogen atom can be extracted during desorption, whereas the alkene precursor does not. Earlier parts of this study '* showed that y-alumina surfaces outgassed above 570K contain exposed ion sites at which methane becomes chemisorbed during y-irradiation at 77 K. All this hydrocarbon material is recovered as C1-C3 alkanes and alkenes, together with hydrogen? when the y-alumina is reheated to the original outgassing temperature. The rate of methane consumption is determined by the rate at which excited charge carriers arrive at the surface and activate chemisorption sites, but the ratios between each product depend chiefly on the site configurations formed during outgassing. The present paper describes the effect of chemical additives on the formation and desorption of these products, with the aim of elucida- ting the structure and decomposition reaction of each product precursor.Additives chosen include scavengers previously used in radiolysis of homogeneous phases as well as poisons known to interfere with hydrocarbon reactions on oxide surfaces. Nitric oxide has frequently been used to scavenge free radicals in hydrocarbon radi~lysis.~ It is readily adsorbed at exposed aluminium ion sites on y-al~mina,~ including those at which but- 1 -ene undergoes isomerisation. Oxygen also scavenges radicals in homogeneous phase radi~lysis.~ It is adsorbed by y-alumina slightly in the absence and readily in the presence 5 * 6 of radiation to give -0; and -0- ions at exposed aluminium ion sites.Many adsorbed hydrocarbons react with oxygen when irradiated.' Sulphur hexafluoride and nitrous oxide both scavenge electrons in homogeneous phase radiolysis. Nitrous oxide decomposes on y-alumina at high temperatures or under irradiation,1° and as on other oxides the products probably include e 0 - ions. Carbon dioxide is readily adsorbed by y-alumina l2 and efficiently poisons the sites which cause isotopic exchange between normal and deuterated hydrocarbons or deuterium. Under irradiation extra carbon dioxide is adsorbed but very little Alkenes irradiated on y-alumina in the presence of carbon dioxide polymerise to long chain carboxylic acids. As in earlier papers, " physisorbed " products are arbitrarily defined as those desorbed at up to 313 K, and " chemisorbed " products as those desorbed at higher temperatures.The following definitions are also continued : total product carbon (TPC) = chemisorbed CH4+2(C2H4 + C2Hs) + 3(C3H6 + C3H8) 192 carbon balance (CB) = CH4 added - physisorbed CH4 - TPC.D . J . NORFOLK A N D T . SWAN 193 EXPERIMENTAL All experiments used Camag N1 y-alumina outgassed at 723 K. Nitric oxide (B.D.H. 99 % NO), sulphur hexafluoride (B.D.H. 99.8 % SF6) and carbon dioxide (Distillers’ Company, reactor grade) were purified by repeated trap-to-trap sublimation. Oxygen and nitrous oxide (both B.O.C. X grade) were used as received. Most of the procedures followed have already been described.‘ Each adsorbate was added at 77 K and allowed to equilibrate at room temperature for - 10 min before further adsorbate additions.The standard methane coverage was 1 . 7 2 ~ 10l6 molecules m-2 (0.3 % B.E.T.), and as the effect of nitric oxide on alkene yields (see below) saturated at a coverage of 1 1 . 4 ~ 10l6 molecules ma2 (“2 % B.E.T.), this was used as the standard additive coverage. Each sample was irradiated to 4.5 Mrad at 1.10 Mrad h-l, radiation doses and G-value yields both being calculated on the dose to A1203. RESULTS NITRIC OXIDE In a first series of experiments y-alumina samples were dosed with methane and irradiated as previously described.l Nitric oxide (NO) was then added as soon as possible ( - 15 min after irradiation ended) and without allowing the temperature to rise above 77 K. Fig. 1 and 2 compare the product desorption curves from an unscavenged experiment (the “ blank ”) with those after NO additions of 5.71 x 10l6 and 11.4 x 10l6 molecules m-2 (- 1 and 2 % B.E.T.).n 9, desorption temperature/K FIG. 1.-Desorption curves of (a) TPC, (6) hydrogen. NO additions, (0) 2 % before irradiation, ( a) 1 % after irradiation before warm-up, (D) 2 % after irradiation before warm-up, (0) 2 % after warm-up, ( x ) blank. NO addition clearly reduced the total product carbon (TPC) yield. Calculation of the carbon balance (CB) showed that much of this material had been scavenged, i.e. did not reappear as any identified product (table 1). NO was given off throughout the usual hydrocarbon desorption temperature range up to 570 K, and as the quantity of NO consumed always exceeded the CB it seems likely that the scavenged product had reacted with NO before or during desorption. The effect on different types of product was markedly dissimilar.Alkene and hydrogen yields were completely eliminated by -2 % B.E.T. NO. Even after a 1-7194 7-RADIOLYSIS OF METHANE O N ALUMIKA s description temperat ure/K FIG. 2.--Desorption curves of (a) ethane, (b) ethene. Legend as fig. 1. N 1 % addition the only traces of these products observed were obtained above 570 IS, where little NO was available. Alkane yields on the other hand were only partly suppressed, and although much less chemisorbed alkane (desorbed above 313 K) was obtained, yields of physisorbed alkane (desorbed up to 313 K) were higher than in the blank. This was substantiated by warming an irradiated y-alumina sample to 313 K to desorb the physisorbed products before adding NO.As anticipated, product yields at this temperature were similar to those in the blank. When NO was added, however, extra alkane was desorbed at the same temperature (fig. 1 and 2). Product yields thereafter followed the scavenged pattern described above. TABLE 1 .-CARBON BALANCE AFTER NO ADDITIONS quantity of NO added % B.E.T. carbon balance / % of methane addedt blank -3k10 2 % before irradiation 94 1 % after irradiation, before warm-up 27 2 % after irradiation, before warm-up 51 2 % after irradiation, after warm-up 41 t The quantity of methane added was 1.18 x mol = 0.3 % B.E.T. In a second series of experiments both methane and NO were added before irradiation.NO was again given off throughout the usual hydrocarbon desorption temperature range, and the effect on product yields (fig. 1 and 2, and table 1) was in most respects similar to, though more severe than, that in the first series. However physisorbed alkanes, including methane, were eliminated. It was previously concluded that most physisorbed methane is unreacted starting material, so the NO must have scavenged material which would not normally have reacted.D. J . NORFOLK AND T. SWAN 195 NITROUS OXIDE In a first experiment, nitrous oxide (N,O) was added after irradiation but before warming from 77 K. Most of the N20 was recovered unchanged at the first desorp- tion temperature, 313 K, but - 1.7 x 10l6 molecules m-2 were lost. Meanwhile nitrogen and oxygen yields rose by -0.9 x 10l6 molecules m-2, suggesting that at least half the loss of N20 resulted from its decomposition.The effect on hydrocarbon 500 700 desorption temperature/K FIG. 3.-Desorption curves of (a) methane, (b) TPC. Scavenger additions, (0) 2 % NzO before irradiation, (D) 2 % N20 after irradiation before warm-up, (0) 2 % O2 after irradiation before warm-up, ( x ) blank. product yields is shown in fig. 3 and 4. About 0.4 x 10l6 C atoms m-2 of TPC were lost, this being much less than the quantity of N,O not recovered. The products lost were almost entirely alkanes, though not physisorbed methane. However whilst overall alkene and hydrogen yields were only slightly lower than in the blank, the temperature required to desorb these products rose by - 100 K.n W desorption temperature/K FIG. 4.-I&sorptioncurves of (a) ethene. (bl ethane and tc) hydrogen. Lcgtmd as fig. 3.I96 7-RADIOLYSIS OF METHANE ON ALUMINA In a second experiment both N,O and methane were added before irradiation. Less N,O and more nitrogen and oxygen were desorbed than before, while the TPC (fig. 3) fell to - 10 % of the blank yield. This was almost entirely due to reductions in alkane yields, including in this case physisorbed methane. Alkene and hydrogen yields were little lower than in the blank, but were again desorbed - 100 K higher than usual. 300 500 700 desorp tion temperature /I( FIG. 5.-Desorption curves of (a) hydrogen, (6) C 0 2 and (c) ethane. CO, additions, (0) 2 % before irradiation, (A) 2 % after irradiation before warm-up, ( x ) blank.CARBON DIOXIDE In two different experiments carbon dioxide (CO,) was added to methane-dosed y-alumina before and after irradiation. Yields of carbon monoxide and oxygen were very small even in the former case, corresponding to G(-C02) ~0.05, and almost identical CO, desorption curves were obtained in both experiments (fig. 5). The effects on products derived from methane were also similar (fig. 5 and 6). Scavenging n 2 T j LI n O 1 I I I X I - 8 50 I Y U I3 2 300 500 700 d esorp t ion temperature/K FIG. 6.-Desorption curves of (a) methane, (b) TPC. Legend as fig. 5.D . J . NORFOLK A N D T . SWAN 197 of alkanes (excluding physisorbed methane) reduced the TPC by half, while alkene yields showed no systematic change. OXYGEN Oxygen (0,) was added after irradiation but before warming from 77 K.Its effect on hydrocarbon yields and desorption temperatures was qualitatively the same as that of N20 (see above), though scavenging was more extensive. However, unlike N20 added after irradiation, 0, scavenged much of the physisorbed methane (fig. 3). SULPHUR HEXAFLUORIDE Sulphur hexafluoride added after irradiation but before warm-up was all recovered at the first desorption temperature, and had a negligible effect on the products derived from methane. DISCUSSION SF6 and N20 both behave as electron scavengers in gas phase radiolysis. The present results show, however, that their effects in adsorbed phase radiolysis differ greatly and it is clear that this reflects differences in the way they interact with the y-alumina surface.The nature of the surface reaction undergone by each additive must therefore be assessed before its influence on hydrocarbon product yields can be discussed. REACTIONS OF ADDITIVES AT 7-ALUMINA SURFACE The loosely associated species formed by NO at exposed aluminium ion sites readily decomposes when evacuated at room temperature and cannot therefore be responsible for the observed release of NO to above 570K. This is much more likely to be due to the decomposition of surface anions such as NOT and NOT. Surface -0- ions are known to be present during and after i r r a d i a t i ~ n , ~ ? ~ ~ and since NO rather than NO, is the major decomposition product NO; is the more likely ion [reaction (l)] *O-+NO +NOT. (1) Nitrite ions are quite likely to be capable of reacting with radiolytic intermediates, such as radicals, derived from methane.They are unlikely, however, to be mobile across the y-alumina surface. Since the radiolytic hydrocarbon intermediates are also apparently immobile,2 direct reaction with nitrite is unlikely and the effects of NO addition on methane radiolysis are therefore attributed to NO itself. N20 does not appear to form reversibly chemisorbed species. Instead its effect on hydrocarbon product yields follows the quantity of N,O decomposed, both being much greater when N,O is added before rather than after irradiation. In view of its electrophilic nature it probably decomposes by reacting with electrons at the y-alumina surface [reaction (2)] N20 + e- + N2 + *O-. (2) O2 also reacts with electrons to give 00- ions and has a scavenging effect qualitatively very similar to that of N,O.However, many of these ions are formed when y-alumina is irradiated alone 5 * l6 so scavenging cannot be attributed solely to their presence : indeed the proposed methane chemisorption mechanism 1 * implies198 y-RADIOLYSIS OF METHANE ON ALUMINA that -0- ions only react at particular site configurations. Some other species must be involved. An analysis of the electronic equilibria in y-alumina) suggests that electron withdrawal by N20 or O2 rapidly increases the concentration of 0 atoms at the surface. Moreover, 0 atoms are known to react with hydrocarbons such as methane [reaction (3)] whilst alkylaluminium compounds are readily oxidised to alkoxide l 8 It therefore seems likely that the scavenging effects of both N20 and O2 can be attributed to 0 atoms.SF, might be expected to withdraw electrons from y-alumina in the same way as N20. However very little does so and there is almost no effect on hydrocarbon product yields. This may be because the sites at which electrons are available do not stabilise the SF, anion or its decomposition products, e.g. because they are of the wrong size or polarisibility. By contrast the -0- ions formed from N20 and O2 are well stabilised. Almost all the C 0 2 added becomes chemisorbed, but the desorption curves obtained are independent of whether it is added before or after irradiation. Chemi- sorption therefore probably results not from radiolytic processes, but from the O+CH4 + (*OH+*CH,) 4 CHSOH.(3) t The concentrations of mobile electrons e-, mobile holes h+ and oxide species in y-alumina are related by the equilibria A1203 + A1203 + e- + h+, equilibrium constant Kl 02-+h+ + -0- KZ *O-+h+ + 0 K3. Any adsorbate which reacts with electrons thereby injects holes into the lattice, driving these equilibria to the right and increasing the oxygen atom concentration (0 The size of the increase is determined by the change in [h+] brought about when the scavenger is adsorbed. In the absence of scavengers [h+] has two components ; intrinsic holes formed by thermal excita- tion of electrons across the gap between the valence band (almost full) and the conduction band (almost empty), and extrinsic holes due to impurities. The concentration of intrinsic holes depends on the value of Ki.This follows a Boltzmann temperature dependence, and when no extrinsic charge carriers are present [O] = K3[h+][*O-] = KZK3[h+]'[O2-]. - [e-1 = [ h+] = dKl E [e-]" exp (-%)a (ii) Here [e-1, is the concentration of electrons in the valence band ; if each oxide ion contributes 8 electrons, [e-]" = 1.4 x loz3 g-l. The activation energy Ea is ideally half the band gap,27 which in y-alumina is 7.2-9.5 eV wide 28 (1 eV = 1.602~ Reliable experimental values are not available for this material, but in or-alumina, which has a similar band gap, the values observed are in the range 3-5 eV.29 Substitution of the lowest plausible value, 3 eV, in eqn (ii) gives Kl - 10-372g-2 at 77K. This extremely low value means that the concentration of intrinsic holes is vanishingly small. The concentration of extrinsic holes depends on the impurity content and the exact stoichiometry of the yalumina lattice.This must clearly vary with the batch of the material and the outgassing treatment used. Nevertheless the behaviour of T-alumina,28 which is structurally very similar, indicates that very few extrinsic carriers are present either. This is consistent with the absence of colour and the high electrical resistivity of y-alumina. molecules N20 g-I decomposed. If each molecule reacted with one electron and so injected one mobile hole, [h+] would have changed by 1 . 4 ~ l O ~ * g - ~ . Application of eqn (i) then shows that if [h+] before N20 addition had been (6.5 x 1017 g-l, the oxygen atom concentration would have been increased at least tenfold.In view of the very low expected concentrations both of intrinsic and extrinsic holes, this condition is likely to have been met. Thus addition of N20 or any other electron scavenger would be expected to produce a significant change in the surface concentration of oxygen atoms. J). The results in the text suggest that about 1.4 xD. J . NORFOLK AND T . SWAN 199 formation of surface bicarbonate and carbonate ions; the former are known to predominate l2 on y-alumina outgassed at 723 K [reaction (4)] CO,+OH- + HCOT. (4) C02 added before methane does not prevent methane radiolysis, so the radiolytically active sites are clearly not blocked by reaction with CO,. Furthermore, CO, anions are not thought to be mobile across the surface and so (like nitrite ions, see above) are unlikely to react directly with radiolytic hydrocarbon intermediates.Free C02 by contrast is sufficiently reactive to become attached to growing polyethene chains during irradiation of ethene on y-a1umina.l The effects of CO, addition on methane radiolysis are therefore attributed to CO, itself. The bicarbonate and carbonate ions act as reservoirs ensuring that an appreciable surface concentration of C02 is maintained throughout the desorption temperature range. Having arrived at the most probable scavenging species in each case, the present results are now used to establish structures for the product precursors formed in methane radiolysis. This is done in two stages for each type of precursor. In the first a tentative structure is inferred from previous work.In the second stage this structure is tested by deducing how it would be affected by each scavenging species and then comparing this with experiment. DESORPTION OF ALKENES It was noted in an earlier paper that the alkene products in methane radiolysis are desorbed in the same temperature range as the type I1 chemisorbed ethene described by Amenomiya,20 suggesting that both have the same adsorbed precursors. The hydrogenation behaviour 20* 21 of type I1 adsorbed ethene is consistent with its being either an alkyl or a vinyl group, and the absence of products containing oxygen when it is desorbed implies that it is attached by an A1-C bond.' Type I1 ethene polymerises in the presence of excess gas phase ethene.22 The sole initial products are type I1 n-butenes, which suggests that in each propagation step an ethene molecule adds to the Can homalogue of type I1 ethene and forms the C2n+2 homologue.If this is so, however, the following argument demonstrates that the alkyl structure is more plausible than the vinyl. Consider an adsorbed vinyl group which must react with ethene to give n-butene homologues and no other product [reaction (5); S represents a surface aluminium ion] CHS-CH2-CH=CH-S CH2=CH-S + C,H,< CH,-CH=C( CH3)-S. ( 5 ) Mechanisms which require more than two bonds to be broken at the same time are unlikely because they wouId need too much activation energy. Under this restriction reaction (5) can only proceed if ethene inserts into one of the vinylic C-H bonds.However, there are only three such bonds per molecule and homologues higher than c8 therefore require ethene to insert into a C-C bond instead. This is much less probable and would in any case be expected to produce a discontinuity in yields between products of up to and beyond c8. No such discontinuity has been reported.22* 23 With an adsorbed alkyl group by contrast all the requirements above are met if ethene inserts into the bond to the surface [reaction (ti)] CH3--CH2--S+CzH, + CHj--(CH-Jj-S. (6)200 Y-RADIOLYSIS OF METHANE ON ALUMINA Furthermore, although alkylaluminium compounds are not entirely analogous to the surface groups postulated here they do polymerise by ethene insertion into the AI-C bond [reaction (7)]. They also desorb alkene when heated to above 470 K [reaction (S)].This corresponds closely to the alkene desorption temperature range in the present study (> 420 to N 570 K) CHS-CH2-AlR2 + C2H4 + CH3-(CH2)3-A1R2 CH3-CH2-AIR2 + HAAIR;! + C2H4. (7) (8) A The structure proposed for the alkene precursor is therefore an alkyl group attached to a surface aluminium ion. Since ethene insertion during polymerisation on y-alumina is thought to occur by a radical mechanism 19* 23 it is likely that the Al-C bond also breaks homolytically during desorption of the alkene, forming a transient alkyl radical intermediate [reaction (9)] SCAVENGING OF ALKENES NO is an efficient radical scavenger. It should therefore intercept the transient alkyl radical in reaction (9) and so eliminate alkene products.This behaviour is indeed observed. Oxygen readily oxidises alkylaluminium compounds to the corresponding alkoxides,18 and 0 atoms produced by the addition of N20 or O2 are likely to have a similar effect on surface alkylaluminium groups [reaction (lo)] Alkoxides of this /*I\ HA'\ type are also formed by alkanols adsorbed on y - a l ~ m i n a . ~ ~ When heated they desorb as ethers if excess alkanol is available 2 5 (unlikely in the present study); otherwise they decompose in two ways. The first yields alkene,25 which because of its different precursor and desorption reaction (11) is unlikely to be produced in the same temperature range as that from unscavenged methane radiolysis. The second "QC", <-* 0 , A ' y A ' \ (1 1) '2 OH 0- I I 4- C2H4 A! I - 0 \*0"\ I involves the oxidation of the alkoxide to carboxylate and the desorption of an equivalent quantity of hydrogen.24 Although the mechanism of this is unclear, the carboxylates are known to be stable to above the highest desorption temperature used (723 K), so alkoxide groups which decompose in this way are lost from the TPC.The anticipated effect of N20 or O2 is therefore first to reduce the alkene yields,D . J . NORFOLK A N D T . SWAN 20 1 and second to change the temperature at which that remaining is desorbed. The latter change is well marked and provides strong support for the structure proposed. Overall alkene yields are, however, only slightly reduced. The reason for this is discussed below. The ability of CO, to convert ethene polymerising on y-alumina into long-chain carboxylic acids suggests that it too can insert into the A1-C bond [reaction (12) ; cf. reaction (6)] The resulting surface carboxylates are known to be stable throughout the desorption temperature range.24 CO, addition should therefore reduce alkene yields and increase the CB.The latter effect is certainly observed, but as with N20 or 0, the drop in alkene yields is less than expected (see below). CH3-CH2-S + C02 4 CH3-CH2-CO-0-S. (12) DESORPTION OF ALKANES A structure for the alkane precursors was put forward in an earlier paper.l This differs from the alkene precursor discussed above in having an accessible hydroxide ion adjacent to the alkylaluminium group [reaction (1 3)] Alkanes are desorbed over a much greater temperature range than are alkenes 1 v ( < 300 to - 570 K, compared with > 420 to - 570 K), implying that alkane desorption requires a wider range of activation energies.The probable cause of this heterogeneity is the orientation of the hydroxide ion with respect to the alkylaluminium group. Orientations which allow part of the bonding energy between the alkyl and hydrogen fragments to be released before the 0-H and Al-C bonds are completely broken must have a lower activation energy than those where this is not possible. Moreover, the Al-C bond in a surface alkylaluminium group is thought to break homolytically {see above) so it is probable that alkanes desorbed at high temperatures, i.e. chemisorbed alkanes, are produced through alkyl radical intermediates [reaction (1 3a)l while physisorbed alkanes are desorbed in a more concerted manner [reaction (1 3b)lf -f In order to portray the correct alkyl radical intermediate these reactions are written as though an excess electron is left at the aluminium ion and an excess hole at the oxide ion.However, the electronic structure of y-alumina is continuous between these ions, and it is probable that the electron and hole recombine during or shortly after product desorption to leave the solid in the electronic ground state.202 7-RADIOLYSIS OF METHANE O N ALUMINA SCAVENGING OF ALKANES NO is an efficient radical scavenger and so would be expected to intercept the transient alkyl radical in reaction (13a) before it attacks the adjacent hydroxide ion. Chemisorbed alkanes should therefore be scavenged by NO and physisorbed alkanes should not, as is observed.NO is also thought to react with surface -0- ions [reaction (l)] to form relatively stable nitrite ions. If this occurred at the sites carrying physisorbed alkane [reaction (14)] the energy required to desorb the alkane would be reduced by the N-0 bond energy, while the availability of an unpaired electron on NO would allow desorption to proceed without the AI-C bond having to undergo spontaneous homolytic fission ON.> ti -k '2"6 (14) O'd CH2-CH3 NO2 1 A.1 12 - I Al /A'\O/ \ \ The reaction would therefore be aided both thermodynamically and kinetically, and NO addition should stimulate desorption of extra physisorbed alkane. This too is observed, supporting the distinction drawn in the previous section between the desorption mechanisms for chemisorbed and physisorbed alkanes, respectively.0 atoms from N20 or O2 should oxidise the alkylaluminium groups in the alkane precursors in the same way as suggested for the alkenes [reaction (lo)]. These additives do indeed reduce alkane yields. However the alkoxides so formed must decompose in the same way as those derived from alkene precursors, i.e. to stable carboxylates together with alkenes. The conversion of scavenged alkane to desorbed alkene which this entails probably accounts for the unexpectedly high alkene yields when N20 or 0, is added (see above). C02 should also scavenge alkanes and alkenes by the same mechanism, in this case by insertion into the Al-C bond [reaction (12)]. Much of the alkane product is indeed scavenged.Furthermore, CO, is known l 2 to react with hydroxide ions [reaction (4)], and comparison of the proposed precursor structures shows that this must tend to convert alkane precursors into those of alkenes. The extra alkene produced by this means probably compensates for that scavenged and so accounts for the lack of a systematic effect of COz on alkene yields (see above). DESORPTION A N D SCAVENGING OF HYDROGEN NO added after irradiation but before warm-up eliminates hydrogen yields, so no molecular hydrogen can be present at this time. E.s.r. spectra 26 show that few free hydrogen atoms are present, while hydrogen bonded to oxide ions (i.e. hydroxide ions) desorbs from y-alumina as water,' not hydrogen. The hydrogen yields from methane radiolysis are probably therefore due to hydrogen attached to surface aluminium ions, like that left by the proposed alkene desorption reaction (9).The fact that this can be scavenged by NO implies that the Al-H bond, like the Al--C bond, breaks homolytically on heating. Hydrogen desorption therefore appears analogous to that of chemisorbed alkane [reaction (15); cf. reaction (13a)l. Con-D . J . NORFOLK AND T . SWAN 203 timing the analogy between the Al-H and alkylaluminium groups, O2 or N20 would be expected to oxidise the hydrogen to hydroxide ion (though some hydrogen will still be obtained from the decomposition of alkoxide ions, see above), while COz should insert into the Al-H bond to give stable formate ions. The changes in hydrogen yield are consistent with each of these reactions.REACTIONS DURING IRRADIATION The preceding discussion has shown that the effects of each additive are in full agreement with the proposed set of precursor structures and desorption mechanisms. In view of the substantial differences between the anticipated behaviour of physisorbed alkanes, chemisorbed alkanes and alkenes, this gives considerable support to the mechanisms proposed. It is also clear, however, that the product yield changes caused by each additive are in general different when it is added before rather than after irradiation. In part this must be due to interference with the reactions which take place during irradiation and in which methane is converted to the product precursors. Thus NO added before irradiation eliminates physisorbed alkanes even though when added after irradiation it stimulates desorption of these products.This implies that NO prevents formation of the alkane precursors, and so suggests that these species are normally formed by a radical mechanism. However, several additives when present during irradiation eliminate physisorbed methane. This is thought to consist largely of unreacted starting material, so the additive in these cases is clearly reacting other than as a pure scavenger. In view of this complication the present results do not allow further conclusions to be reached on the mechanism of the reactions during irradiation. CONCLUSION Both alkane and alkene products come from precursors involving alkylaluminium groups. These contain the carbon skeleton of the product and when heated decompose by homolytic fission of the Al-C bond.The alkane precursors differ from those of the alkenes by including an accessible hydroxide ion from which an atom of hydrogen can be extracted as the product is desorbed. These structures are shown to be consistent with the effect on product yields of each of the additives used. This paper is published by permission of the Central Electricity Generating Board. D. J. Norfolk and T. Swan, J.C.S. Faraday I, 1977, 73, 1454. D. J. Norfolk and T. Swan, J.C.S. Faraday I, 1978,74,1676. P. Ausloos and S. G. Lias, in Actions Chimiques et Biologiques des Radiations, ed. M. Haissinsky (Masson, Paris, 1967), vol. 11, chap. 1. J. H. Lunsford, J. Catalysis, 1969,14,379 ; J. H. Lunsford, L.W. Zingery and M. P. Rosynek, J. Catalysis, 1975, 38, 179. D. D. Eley and M. A. Zammitt, J. Catalysis, 1971, 21, 366. R. Coekelbergs, A. Crucq, J. Decot, L. Degols, M. Randoux and L. Timmermann, J. Phys. and Chem. Solids, 1965, 26, 1983. ' H. W. Kohn, J. Phys. Chem., 1964,68,3129. * G. G. Meisels, in Fundamental Processes in Radiation Chemistry, ed. P. Ausloos (Interscience, lo R. Coekelbergs, A. Crucq and A. Frennet, Adu. Catalysis, 1962,13,55 ; D. V. Glebov, Yu. A. l1 A. J. Tench, T. Lawson and J. F. J. Kibblewhite, Truns. Faraduy SOC., 1972, 68, 1169; R. J. l2 N. D. Parkyns, J. Chem. SUC. (A), 1969,410. New York, 1968), chap. 6. E. R. S. Winter, J. Catalysis, 1970, 19, 32. Kolbanovskii and A. S. Chernysheva, Khim. vysok. Energii, 1974, 8,444. Breakspere, L. A.R. Hassan and D. K. Roberts, J.C.S. Faraday I, 1975,71,2251.204 7-RADIOLYSIS OF METHANE O N ALUMINA l3 J, G. Larson and W. K. Hall, J. Phys. Chem., 1965, 69, 3080; M. P. Rosynek and J. W. Hightower, in Proc. 5th Int. Congress on Catalysis, 1973, p. 851. l4 R. Coekelbergs, A. Crucq, A. Frennet, J. Decot and L. Timmermann, J. Chim. phys., 1963, 60, 891 ; R. N. Dietz, Ju Chin Chu and M. Steinberg, Trans. Amer. Nuclear SOC., 1964, 7, 314; Yu. A. Kolbanovskii and V. I. Shaburkina, Khim. vysok. Energii, 1967, 1, 583. l5 L. S. Polak and S. Ya. Pshezhetsky, Pure Appl. Chem., 1965, 10,441 ; Yu. A. Kolbanovskii, L. S. Polak and V. I. Shaburkina, Neftekhimiya, 1968, 8,276. G. C. Allen, D. J. Norfolk and T. Swan, J. Nuclear Materials, 1976, 60, 132. l7 A. Hori, S. Takamuru and H. Sakurai, J. Org. Chem., 1977,42,2318. * G. E. Coates, Organometallic Compounds (Methuen, London, 1960). l9 Yu. A. Kolbanovskii, L. S. Polak and V. I. Shaburkina, Neftekhimiya, 1968, 8,276. 'O Y. Amenomiya, J. H. B. Chenier and R. J. Cvetanovic, J. Catalysis, 1967, 9, 28. 21 Y. Amenomiya, J. H. B. Chenier and R. J. Cvetanovic, J. Phys. Chem., 1964, 68, 52; Y. 22 Y. Amenomiya, J. H. B. Chenier and R. J. Cvetanovic, in Proc. 3rd Int. Congress on Catalysis 23 C. Mechelynck-David and F. Provoost, Int. J. Appl. Radiation Isotopes, 1961, 10, 1191. 24 R. G. Greenler, J. Chem. Phys., 1962,37, 2094; R. 0. Kagel, J. Phys. Chem., 1967,71, 844. 25 H. Knozinger, H. Biihl and E. Ress, J. Catalysis, 1968, 12, 121. '' G. C. Allen, D. J. Norfolk and T. Swan, J. Nuclear Materials, 1976, 60, 132. " C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1962), chap. 13. 28 S. Khoobiar, J. L, Carter and P. J. Lucchesi, J. Phys. Chem., 1968, 72, 1682; E. Harari and B. S. H. Royce, Appl. Phys. Letters, 1973,22, 106. P. Kofstad, Nonstoichiometry, Diflusion and Electrical Conductivity in Binary Metal Oxides (Wiley, New York, 1972). Amenomiya, J. Catalysis, 1968, 12, 198. (Amsterdam, 1965), vol. 2, p. 1135. (PAPER 8/523)

ISSN:0300-9599    

DOI:10.1039/F19797500192

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Quantum Theory of Kinetic Isotope Effects in Proton Transfer Reactions B Y NINA BRUNICHE-OLSEN AND JENS ULSTRUP" Chemistry Departments A and B, Buildings 207 and 301, The Technical University of Denmark, 2800 Lyngby, Denmark Received 10th April, 1978 Within the framework of multiphonon electron and atom group transfer theory we have calculated the kinetic isotope effect of proton transfer reactions in homogenous solutions using both harmonic and anharmonic potentials for the proton. The calculations can reproduce all the important features of the isotope effect, such as the maximum for the zero free energy change, and the higher activation energy and Arrhenius pre-exponential factor for the heavier isotope. Quantitative agreement with several experimental data relating to the dependence of the isotope effect on the free energy of reaction and the temperature is furthermore obtained for plausible values of the two parameters required, i.e., the solvent reorganization energy and the proton transfer distance. 1.INTRODUCTION A fundamental result of the theory of electron and atom group transfer processes is that nuclear tunnelling is expected when sufficiently high vibration frequencies are associated with the nuclear modes undergoing reorganization.'. However, unambiguous evidence for nuclear tunnelling is usually difficult to obtain, i.e., the majority of experimental results concerning the kinetics of elementary processes in condensed phases can be explained both by the elaborate quantum theory of chemical processes and by much simpler semiclassical approaches.Nuclear tunnel effects in chemical processes are, however, manifested in low- temperature proce~ses,~-~ in strongly exothermic processes and in particular in homogeneous and heterogeneous proton transfer reactions. '-' Evidence for proton tunnelling is thus usually based on : (a) " unusually " large absolute values of the kinetic isotope effect, kH/k,, where kH and k,, are the rate constants for proton and deuteron transfer, respectively ; (b) different activation energy for proton and deuteron transfer (i.e., a larger difference than the difference in initial state vibrational zero- point energies) ; (c) pre-exponential Arrhenius factors which are smaller for the proton transfer and ( d ) a temperature dependent apparent activation energy for the rate constant or the isotope effect.In the semiclassical theory of proton transfer reactions, with tunnel corrections, major attention is given to motion of the proton along a stretching coordinate. This motion is assumed to provide both the activation energy and the tunnel corrections by proton tunnelling near the barrier tops* In contrast, the key results of the quantum theory of multiphonon proton transfer reactions are that the activation energy is provided by excitation of a multitude of low-frequency intramolecular and solvent modes, whereas the proton in general proceeds from its initial to its final state ground vibrational level by tunne1ling.l A considerable amount of evidence for the latter view has recently been provided by studies of the electrochemical hydrogen evolution reaction on mercury and other metal electrodes of low hydrogen adsorption energy.This evidence can be summarized as follows :lo 205206 THEORY OF PROTON TRANSFER REACTIONS (A) The transmission coefficient is also low when the reaction proceeds under barrierless conditions, i.e. when the transfer coefficient, a, is unity. (B) The second step in the overall process, i.e., the electrochemical desorption, also displays a substantial isotope effect when this step is activationless, i.e., when a -+ 0. Both of these effects are incompatible with the semiclassical view, but not with the quantum theory of proton transfer reactions. (C) The pre-exponential factor of the electrochemical rate constant decreases with increasing adsorption energy of the hydrogen atom at the metal electrode.This effect is understandable on the basis of quantum theory, whereas the semiclassical theory would predict the inverse relationship. (D) Comparison of the activation parameters of the hydrogen evolution reaction in water and acetonitrile shows that the solvent exerts a pronounced effect on the activation energy of the process, whereas the nature of the depolarizer ( i e . , H30+ or CH3CNH+) largely determines the value of the pre-exponential factor. Studies of kinetic isotope effects in homogeneous and heterogeneous proton transfer reactions have thus provided the most comprehensive evidence for nuclear tunnelling. In the following we shall present a quantitative application of the formalism of multiphonon atom group transfer theory to kinetic isotope effects in such p r o c e ~ s e s .~ ~ - ~ ~ In particular we shall extend previous results based on a harmonic oscillator representation of the proton 12* l3 by the application of Franck- Condon nuclear overlap factors also for Morse and squared hyperbolic tangent potentials, these being more realistic representations of the progon stretching and bending modes, respectively. 2. SUMMARY OF MULTIPHONON ATOM GROUP TRANSFER THEORY The rate constant of the elementary atom group transfer process is usually expressed in the nonadiabatic limit and by the time evolution of zero-order Born-Oppenheimer vibronic states corresponding to the atom group being localized on the donor and acceptor. 1s Moreover, the high-frequency modes associated with the transferring atom group are essentially deconvoluted from all other intramolecular and (low- frequency) medium modes.The latter may be strongly or weakly coupled to the reaction centre. If the coupling furthermore is linear, the resulting rate expression shows a gaussian or lorentzian free energy dependence, respectively,16 where we shall apply the former limit only, which is appropriate for most proton transfer reactions in condensed media. Finally, for reasons discussed previously,l* 11* l 5 we shall consider proton transfer between immobile donor and acceptor fragments, the relative distance and orientation of which are characterized by a vector, R, i.e., we shall assume that the mass of the proton is so much smaller than the masses of the fragments that the latter remain stationary during the proton transfer.We shall thus basically apply the following expression for the rate constant k 1 9 ' 9 l1 to k = Q(R)W(R) dR RdU where W(R) = [ V(R)12(n/kTA2Es)*Z-1 exp (-PQ x v w E, is here the reorganization energy of the medium and all other low-frequency modes, AE the free energy of reaction [the energy gap, equal to -kTln (KA/KB), where KA and KB are the acid dissociation constants of the proton donor and acceptor,N. BRUNICHE-OLSEN AND J . ULSTRUP 207 respectively], EY and E? the proton vibrational energy levels in the initial and final state, respectively, corresponding to the vibrational quantum numbers v and w, Z the statistical sum of the transferring proton modes in the initial state, and p = kT, where k is Boltzmann's constant and T the absolute temperature.Furthermore, Sv,,v = [(@'14u)lz is the Franck-Condon nuclear overlap factor of the total proton (stretching and bending) nuclear wave functions in the initial (4;) and final ($r) state, V(R) the electronic exchange integral, and the function @(R) expresses the probability that the particular configuration characterized by R is achieved. a@) is the quantum statistical distribution function of the reactants. However, for the sake of simplicity we shall introduce the plausible assumption that the motion of the reactants as a whole is classical, at least up to the value of R = Rmi,, and that O(R) can therefore be represented by the form @(R) = exp [-PU(R)I (3) where U(R) is the potential energy of interaction between the reactants.We shall furthermore assume that U(R) is the same in the initial and final states. We noticed previously l5 that most proton transfer reactions are likely to belong to the category of partially adiabatic processes.'* l7 The electronic interaction between donor and acceptor fragments is sufficiently strong that only the lowest (electronically) adiabatic potential energy surface needs to be invoked. On the other hand, the probability of proton transfer is low, i.e., the proton must penetrate a large barrier, even when the system has acquired sufficient energy to reach the saddle point of the reaction hypersurface with respect to the classical (medium) modes. All fundamental implications of the nonadiabatic scheme represented by eqn (1)-(3) then remain valid, but it is convenient to rewrite the equations in a form which no longer involves the electronic factor,l* l7 i.e.Weff W(R) = 1 -Su,w(R) exp (-BE!) exp [-/~(E,+AE+E,"-EY)~/~E,] (4) 0 w 2x where uCff is the effective frequency of the whole classical (medium) system.18t Eqn (4) essentially constitutes a semiclassical formulation of the rate expression for proton transfer reacti0ns.l it contains an activation factor predominantly determined by the medium and other low-frequency modes, and a gre-exponential factor consisting of the medium frequency and the Franck- Condoii nuclear overlap (tunnel) factor of the transferring proton or deuteron. Strictly speaking, the nonadiabatic activation energy of eqn (4) should be diminished by the resonance splitting energy at the reaction hypersurface.l* l7 However, since our basic conclusions below would not be qualitatively affected by this correction, and in view of our lack of quantitative information about its magnitude, we shall not include it in subsequent analysis.U(R) is a repulsive potential and @(R) therefore decreases with decreasing R. On the other hand, W(R) strongly decreases with increasing R, largely due to the decreasing barrier for proton tunnelling, since the other factors in eqn (4) are weakly dependent functions of R, and since we have ignored the electronic factor. The integrand of eqn (1) therefore has a sharp maximum at some value R* which depends t Strictly, within the partially adiabatic approach the electrons and the proton constitute the total quantum system.In semiclassical terms this means that I V(R)I 2Su,w(R) in eqn (2) is replaced by (AEu,w/2)2, where AEu,w is the splitting of the proton levels v and w. Since this quantity is approximately proportional to both Su,w and fin, our conclusions about the ApK and temperature dependence of the isotope effect are not affected, whereas the absolute values may be affected by a constant factor. As noted previously,l~208 THEORY OF PROTON TRANSFER REACTIONS on the concrete form of the proton potential (e.g., harmonic or Morse) and the repulsive potential U(R). We can thus replace eqn (1) by the equation 1* 2* where AR is the R-interval which effectively contributes to k. k = O(R*) W(R*) AR (5) R* is determined approximately by the equation pU'(R*) = [ W(R*)]-l d W(R)/dRR = n*.(6) of harmonic proton potentials for the ground levels only, i.e., So,o - - In order to see the physical meaning of this equation more clearly, we shall insert a parabolic repulsive potential of the form U(R) = +y(R- I)' and the Franck-Condon factor exp (- aR2).13 y characterizes the curvature of the repulsion potential and I its range, and a is a parameter which depends on the proton vibration frequencies in the initial and final states and on possible mixing coefficients ;12* 13* a is thus different for proton and deuteron transfer, i.e., a, # aH. Eqn (6) then takes the form Eqn (6) and (7) have the following implications : (a) for a sufficiently rapidly rising repulsion potential (with decreasing R) R* is independent of the characteristics of the tunnel barrier.In the analysis of kinetic isotope effects this implies in particular that the proton and heavier isotopes are transferred over the same distance when they tunnel between the ground vibrational levels.12* l 3 (b) When the potential does not rise sufficiently rapidly, i.e., when a/y is not much smaller than unity, the proton and its heavier isotopes tunnel over different distances. Since a,, > aH, the distance is smaller the heavier the isotope.12* l 3 ( c ) One implication of (b) is that the pre- exponential factor in the Arrhenius rate expression is smaller for the proton than for the heavier isotopes and that the activation energy is smaller due to a smaller repu1sion.l29 l3 However, we shall see below that for the majority of experimental results where such effects are observed, a slight thermal excitation of the heavier isotope, in contrast to the proton, provides a more convenient rationalization of the data.We conclude this section by introducing the Franck-Condon factors for the transferring proton, necessary for our subsequent quantitative analysis of experi- mental data. In general the proton transfer may proceed along a three-dimensional path involving mixing of modes.' 9 9 2o Although in principle this can be incorporated in the theoretical analysis, we shall take the simpler approach of representing the proton transfer by motion along a single mode only. However, we shall not restrict the description of this mode to the harmonic approximation,' '-l4 which is not expected adequately to represent the substantial proton transfer distances in question.Thus, we shall represent the proton or heavier isotope motion by Morse potentials, where the final state potential curve is inverted relative to the initial state curve, or by the symmetric squared hyperbolic tangent potential. These two potentials are more realistic representations of atom group motion along a stretching and a bending mode, respectively. Moreover, we shall incorporate, although only numerically, the possibility of large frequency shifts corresponding to the situation where the proton leaves the donor along a stretching mode and enters the acceptor along a bending mode or vice versa. The Franck-Condon factors of harmonic oscillators undergoing both coordinate and frequency shifts have been reported on several occasions.1* 2 - In the present work we have found it most convenient to calculate these factors directly by numerical integration of products of harmonic oscillator wavefunctions of the form R* x 1/(1+2a/y). (7) 4[f(Qi,,> = ( Z 3 / 2 j .0% ~ X P ( - Q&)Hj(Qi,f) (8)N . BRUNICHE-OLSEN AND J. ULSTRUP 209 j = v, w ; Qi = Q, Qf = Q-A, where A is the equilibrium coordinate shift, Hj(QiJ is the Hermite polynomial of degreej, and Q denotes the normal coordinate associated with the proton stretching or bending mode. On the other hand, for Morse potentials in the initial [h(Q)] and final [ff(Q)] state of the form .fi(Q) = D[1 -exp (-aQ)I2 ( 9 4 f X Q > = D i 1 - e ~ ~ [a(Q-A)l>’ ( 9 4 where D is the dissociation energy and a the anharmonicity constant [a = (hG/2D)+, where R is the proton frequency], the Franck-Condon factor is l5 X (P - 2 4 ( P - 2W)(P + r ( u + i)r(P + 1 - v)r(w + i)r(p + 1 - w) Su,w = ( ~ + 1 ) - “ + ~ ’ exp {-aA[p-(1+k)l/2)KI,_,,C(p+1) exp(-aA/2)] .(10) We shall apply the limiting r Kv(z) is the modified Bessel function of the third kind.21 asymptotic form valid for large argument, i.e.,21 and furthermore keep only the first term in this expansion. The corresponding vibrational energy levels are 2 2 E~ = Qh(j++)-+hQa2(j++)’. (1 2) It was shown previously l 5 that squared hyperbolic tangent potentials of the form 2 3 L(Q> = D th2 (aQ) h<Q> = Dth2 [a(Q-NI (1 3 4 (1 3 4 where the symbols have the same meaning as before, adequately incorporate the main features expected for atom group transfer along bending modes.In this case the Franck-Condon factors l5 and energy levels l 5 9 23 take the form F[+y-w+l, +p-$v-+w, p-v-w+k+Z; l-exp(2aA)I where B is the beta function, F the hypergeometric function 24 and respectively . c j = tiQ(j+$)-$kQa2(j++)’ -#iQa2,210 THEORY OF PROTON TRANSFER REACTIONS We notice finally that eqn (10) and (14) are valid when the proton transfer mode undergoes equilibrium coordinate shift only. If, in addition, frequency shift occurs, the Franck-Condon factors are calculated by direct numerical integration using wavefunctions of the form 229 23 4bf = N j exp (zi,f)z!pf-2j)/2Lp-2Ti(z P - J i,f ) where L is the Laguerre polynomial, zi = (p+l)exp(-aQ); zf = (p+l)exp[-a(A-Q)] Nj = [a(p - 2j)/r( j + l)r(p + 1 - j)]* ; p = 2a-2 - 1 and F [ - j , p + 1 - j , $ p + 1 - j ; +( 1 + th Zi.31 for Morse and squared hyperbolic tangent potentials, respectively.3. RESULTS OF MODEL CALCULATIONS We have performed numerical calculations of both the absolute values of kinetic isotope effects for proton and deuteron transfer reactions, { = kH/kD, and the dependence of on several important parameters, in particular A E and T. The isotope effect primarily arises from differences in Sv,w, EY and ~1." in eqn (4) when the proton is substituted by heavier isotopes. Thus, E&>, R& > E&), whereas SEW > SEW. In addition, the value of the remaining parameters, E,, AE and coeff, in principle undergo small changes when the isotope is substituted.Thus, first, the shift of AE = pK,--pK, generally amounts to 0.02-0.04 eV (ix., the acid containing the lighter isotope is the stronger) when the proton is substituted by a deuteron. Secondly, the long-range (coulomb) contribution to E, depends largely on the proton transfer distance and the geometry of the collision complex. If the deuteron transfer distance is smaller than the proton transfer distance (cf. section 2) the corresponding value of E, is therefore also smaller. Finally, both the short-range part of E,, weff, and the free energy of formation of the collision complex from the separated reactants [not included in eqn (4)] all depend on a variety of different molecular interactions and vibrational modes such as hindered translation and rotation of medium molecules as a whole, deformations of hydrogen bonds etc., which are also in principle isotope dependent.However, these effects are expected to be small; their absolute values are largely unknown. We shall, therefore, consider only the dominating effects of the isotope substitution, i.e., the effects reflected in the vibrational energy and Franck- Condon nuclear overlap factors associated with the proton transfer modes. We have chosen various values for E, and the proton transfer distance, AR, in the range 0.1-1 eV and 0.3-0.6 A, respectively ; in general the transfer distance is taken to be the same for all isotopes (implying that AH < AD), i.e., the repulsion potential is assumed to be a sufficiently strongly varying function of R. In a few cases (see section 4) this assumption has to be relaxed in order to obtain quantatitive agreement with experimental data.Proton stretching and bending frequencies are typical values of these modes known from spectroscopic data,g* 2 5 and the corres- ponding deuteron frequencies were obtained by multiplying these values by 2-*. Fig. 1-4 show the dependence of 5 on A E for various values of the important parameters E,, A and f2 for harmonic proton potentials. A maximum is always observed, in agreement with both predictions of classical theories of proton transfer and many experimental observation^.^ Moreover, the maximum is located at AE = 0N . BRUNICHE-OLSEN AND J . ULSTRUP 21 1 Y m Ii T I A i- I I -l.-- -1.0 -0.5 0.G 0.5 1.0 1.5 I AEIeV FIG. l.-tfplotted against A E for various values of Es.(a) ! 2 ~ = 3000 cm-I and AR = 0.37 8, (transfer along stretching modes), (b) ! 2 ~ = 1500 cm-' and AR = 0.62 A (transfer along bending modes), and the AE-scale of the latter is shifted by 3.0 eV. Values of Es are 0.25, 0.50, 1.0, 1.5 and 2.0 eV, and the larger &, the broader the curves. Harmonic potentials. I I I I I I . , I , -1.2 -a.a -0.4 0.0 0.4 0.8 1.2 - AE/eV FIG. 2 . 4 plotted against A E for various frequency values. l& = 1 eV, AR = 0.50A. Harmonic potentials. Roman numerals refer to the following frequency values : I : 1500 ; I1 : 2OOO; 111: 2500; IV: 3000; V: 3500cm-'.212 THEORY OF PROTON TRANSFER REACTIONS 56 La LO 32 n 3 2L * 16 a 0.C J I I I I I I * .2 -0.8 -0.4 0.0 0.4 0.8 1.2 AE/eV FIG. 3.--Kinetic isotope effect, 5, plotted against A E for various AR.Transfer along stretching modes (a, = 3000cm-'), and Es = 1 eV. Roman numerals I-V correspond to AR = 0.27, 0.32, 0.37, 0.42 and 0.47 A, respectively. Harmonic potentials. 15 12 n -Y % 9 Y K m II I -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0 8 1.0 AEIeV FIG. 4 . 4 plotted against A E for transfer along a stretching mode involving frequency shift. Es = l.OeV, AR = 0.37A. Roman numerals correspond to the following couples of frequency values (cm-') in the initial and final states (G, QL) : I : (2600, 3000) ; I1 : (2800,3000) ; I11 : (3000, 3000) ; IV : (3200, 3000) ; V : (3400, 3000). Harmonic potentials.N. BRUNICHE-OLSEN AND J . ULSTRUP 213 when the proton transfer is not accompanied by frequency shifts, whereas it is shifted to finite values of AE when such shifts do occur.This effect has also been observed e~perimentally.~~ 26 We notice furthermore the following features of fig. 1-4 : (a) c increases approximately exponentially with A2 as expected. For E, = 1 eV and Q = 3000cm-l the absolute value thus increases from 4 to 56, i.e., the range of most experimentally observed values, when the proton transfer distance increases from 0.27 to 0.47A (fig. 1). (b) The value of AR for " typical " c-values at the maximum (z 10) is x0.35 A. In view of the fact that this would be the proton transfer distance between the strongly hydrogen-bonded donor and acceptor water molecules in ice 27 this value seems low. On the other hand, this result is changed to larger values when Morse potentials are applied.(c) 5 also increases approximately exponentially, as expected, with increasing frequency. Such considerations are appropriate for proton frequencies in the range 1500-3000 cm-l, this being the n s X -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AEIeV FIG. 5.-Plots of 5 against AE showing the effect of anharmonicity. E, = 1.0 eV. Curves to the left have Morse proton potentials, AR = 0.41 8, and D = 1, 4 and 7 eV with I lower the lower the value of D. Curves to the right (shifted 3.0 eV along the AEaxis) have squared hyperbolic tangent proton potentials, AR = 0.65 8,, QH = 1500 cm-l, and the same D values. The top curve in both families corresponds to harmonic potentials. approximate range of frequencies for stretching and bending modes along which the proton may be transferred.A consequence of this effect is that for a given value of 5, the value of AR is higher the lower the value of Q. Proton transfer along bending modes therefore proceeds over longer distances than for stretching modes (fig. 3). (d) The absolute value of 5 is largely determined by A and R, whereas the width of the maximum depends strongly on E,. This provides a possibility of obtaining the value of this important parameter in cases where it cannot be calculated from the curvature of the Brarnsted plot. In addition we notice that for sufficiently small values of EJhR > (2ESkT)%] the plot of 5 against AE displays an oscillating structure analogous to the one predicted both in free energy relationships for elementary The maximum is shifted to positive or negative values of AE when the process is accompanied by a decrease or increase, respectively, of the proton frequency.Fig. 5 shows similar plots when the Morse and squared hyperbolic tangent potentials of anharmonicity constants in the range 0.1-0.4 (dissociation energies in = 3000 cm-'. chemical processes and in vibrational structure of optical transition^.^' (4214 THEORY OF PROTON TRANSFER REACTIONS the range 1-7 eV) are applied. For the latter potential we have only shown data for a typical bending frequency, and for comparison the results for harmonic potentials are also shown. We notice that c decreases strongly with increasing anharmonicity for both potentials or the proton transfer distance resulting in a given value of c, increases.This is due to the smaller proton tunnelling barrier for the anharmonic potentials compared with the harmonic ones. Thus, for proton transfer along a stretching mode corresponding to a maximum isotope effect of 12 the proton transfer distance is 0.39, 0.40 and 0.46 A for a = 0.16, 0.22 and 0.43, respectively, or D = 7, 4 and 1 eV, respectively. We finally notice that for both stretching and bending modes the apparent activation energy, EA = d In W/d/3, for deuteron transfer is higher than for proton transfer, whereas the ‘‘ pre-exponential factor ”, A , is typically lower. For maximum values around 10 (Es = 1 eV) the differences are : for stretching modes Ei-Ef = 0.3 kcal and A D / A H = 0.13, for bending modes : EZ-E: = 1.7 kcal and A D / A H = 0.69 (AR is 0.4 and 0.65, respectively and D = 4 eV).This effect is often observed experimentally.8* In our present formalism it is due to a thermal excitation of the deuteron mode, even though the dominating contribution to the sum of eqn (4) is still provided by the ground vibrational levels. As expected, the effect is larger for larger values of IAEl, for lower values of the frequency (e.g., corresponding to bending modes), and for increasing anharmonicity. The reason for the higher excitation in the latter potentials is that the distance between the energy levels of the “ barrier spectrum ” is lower for the anharmonic potentials than for harmonic potentia1s.l. 4. APPLICATION TO EXPERIMENTAL DATA We shall now apply the theoretical framework outlined above to several sets of experimental data on the relationship between the primary kinetic isotope effect and the two fundamental physical parameters which characterize this quantity, viz.the free energy of reaction and the temperature. Thus, distinct maxima in the plots of < against AE appearing approximately at AE = 0 have been observed for the deproto- nation of nitroalkanes 9-31 and phenylalkane~,~~* 33 the deprotonation of a-carbon hydrogen in carbonyl compounds,26* 34* 35 the bromination of 3-nitro-( +)-camphor,3s the dehydrochlorination of 2,2,2-trichloro- 1,l -bis-(p-chlorophenyl)ethane, 37 for the acid catalysed hydrolysis of substituted vinyl ethers 38 and for the base catalysed hydrogen exchange of a z ~ l e n e s . ~ ~ Studies of the temperature dependence of 5 have been reported for the ionization of nitroalkanes by pyridine b a ~ e s , ~ O - ~ ~ the ionization of 2-carbethoxycyclopentanone 44* 45 and other carbonyl several base- induced elimination reactions, * 47-50 the deprotonation of 4-nitrobenzylcyanide by ethoxide ions 51 and the deprotonation of 4-nitrophenylnitromethane by several nitrogen Throughout our analysis we shall take the view that the primary kinetic isotope effect can be identified with the observed effects.This is justified in view of the small magnitude and relatively weak free energy dependence of secondary and solvent isotope effects,g* 33 and the fact that the systems considered involve proton or deuteron transfer to or from a carbon atom which does not exchange rapidly with the solvent.FREE ENERGY DEPENDENCE OF ISOTOPE EFFECT In several cases experimental investigations of the Brlansted relationship for the same system as those considered for the isotope effect analysis have been reported.N. BRUNICHE-OLSEN AND J . ULSTRUP 21 5 This would offer a possibility of an independent estimate of the important parameter E8. Thus, when the proton is transferred along a stretching mode, eqn (3) and (4) take the simpler form k M SfARS(R*) exp [ - fiU(R*) - B(Es + AE)2/4E,] (18) 2n: for all practical purposes, i.e., the dominant contribution in the sum is provided by u = w = 0. E, can therefore be determined by a least squares analysis of the curvature of the experimental relationship between k and ApK, i.e., where A = In ( o , ~ ~ / ~ ~ S ) - B U ( R * ) - B E , / ~ , B = 1.15 and C = (2.3)2/4fiEs.This analysis is not valid for proton transfer along bending modes nor for deuteron transfer since, due to the smaller frequencies, in both cases excited vibrational levels in the initial or final state contribute significantly even for small values of jApKI. Moreover, the experimental Brarnsted relationship frequently displays either a substantial scatter or a curvature which is too small for an accurate determination of E,. In these cases we have to fit a value to the experimental data for C(AE) the width of which is determined primarily by E,. In k = A +BApK+ C(pK)2 (19) IONIZATION OF NITROALKANES Systematic studies of kinetic isotope effects for reactions involving proton transfer from several nitroalkanes to both 0- and N-bases have been reported by Bell and G ~ o d a l l , ~ ~ Bell and Cox 30 and by Dixon and B r ~ i c e .~ ~ Fig. 6 shows a combined plot of the results of the two former. < shows a maximum where, however, the ascending branch is largely determined by variations in ApK resulting from changes in the (water+dimethylsuIphoxide) solvent. Since this is also expected to give rise to changes in E,, less attention should be given to these points. On the other hand, the remaining part, including the maximum, shows a sufficiently small scatter that a theoretical plot can be fitted reasonably accurately, even for different substrates (nitroalkanes) and acceptor bases (water, OH-, acetate, chloroacetate and pyridines). An exception is the base 2,6-lutidine which has an isotope effect much larger than indicated by the plot, presumably due to the larger proton transfer distance.g* 29 Although a Brarnsted plot is a~ailable,~’. 30 it shows too much scatter and too little curvature for an estimate of E,.On the other hand, the “ width ’’ of the plot of fig. 6 suggests a value of 0.7 eV using the harmonic approximation for the proton and 0.85 eV using the Morse potential (D = 4 eV). Moreover, appropriate typical values for the C--H stretching and bending frequencies are 2900 and 1400 cm-’, respectively and 3300 and 1700 cm-l for the 0-H stretching and bending modes, re~pectively.~~ Using these values the experimental data, including the shift of the maximum to slightly negative values of AE, can be reproduced if we assume that the proton and deuteron are transferred either along a stretching or along a bending mode, and for a transfer distance, AR, which is independent of the isotope.The experimental data, however, do not allow a distinction between these two alternative modes of proton transfer. The resulting values of E, and AR summarized in table 1 illustrate our previous conclusion, i.e., the lower the frequency and the higher the anharmonicity, the larger is the proton transfer distance which fits a given value of 5. The data by Dixon and Bruice 31 referring to aliphatic ammine bases are too scattered to justify an analysis, although a maximum in the isotope effect at ApK x 0 can be recognized. However, the data of Keefe and Munderloh 32 for ionization of phenylnitromethane by a variety of 0- and N-bases and the data of216 THEORY OF PROTON TRANSFER REACTIONS Bordwell and Boyle for ionization of 1 -phenylnitroethane and several m-substituted derivatives by piperidine, diethylammine and piperazine are shown in fig.7 and 8, respectively. The former data show a clear maximum in the isotope effect for ApK x 0 and, although a fair amount of scatter is displayed, the bases which show the largest discrepancy from the general trend are those which are also structurally 9 n 8 . s. x 7 ' 6 - 5 - 4 - 3 - 2 - -tz t 11 to 9 - 8 - 7 - 6 - 5 - L - 3 - - - 1 ' 1 I 1 I 1 - -1.0 - 0.6 - 0.2 0.2 0.6 1.0 AEIeV FIG. 6.-Plot of k ~ / k ~ against A E for ionization of nitroalkanes. 0 Experimental data of ref. (29) ; (.D ref. (30) for different solvent compositions.The curve corresponds to Es = 0.80eV, AR = 0.39 A, and transfer along stretching modes for which 52L = 2900 cm-' and i2& = 3300 cm-', and D = 4eV. 12 i 0 0 0 I ' I L 1 - -0.8 -0.4 0.0 0.5 0.8 A E FIG. 7.-Plot of k ~ / k ~ against A E for ionization of phenylnitromethane. The points are the experimental data of ref. (32), and the line is the best theoretical fit (Es = 0.6 eV, AR = 0.62A, transfer along bending modes ; Oh = 1400 cm-' ; SZL = 1700 cm-').N. BRUNICHE-OLSEN AND J. ULSTRUP 217 1 11 - 10 - 9 - 8 - 4 7 - 3 6 - * * 5 - 4 - 3 - 2 - I I a - -1.0 -0.6 -0.2 0.2 0.6 1.0 AEIeV FIG. &-Plot of k ~ / k ~ against A E for ionization of substituted phenylethanes. Points are from ref. (33) and the line is the best theoretical fit (Es = 0.7 eV, AR = 0.61 A, transfer along bending modes ; QL = 1400 cm-I ; Q& = 1700 cm-l).TABLE 1 .-BEST PARAMETER VALUES FOR FITTING EQN (4), (B), (lo), (16) AND (17) TO VARIOUS SETS OF EXPERIMENTAL DATA stretch nitro alk. phenyl-n. meth. phenyl-n. eth. 3-nit-( + )-camph . Et-n.-acet- Na-pr-2-one-sulph. Me, Et-ac. acet. ._ . _ _ harm Morse AR1 AR2 G--H N-H 0-H EL AR Es 0.7 0.37 0.85 0.39 0.42 2900 3300 0.5 0.36 0.5 0.38 2900 2700 3100 0.26 0.34 0.26 0.36 2900 2700 0.5 0.36 0.5 0.39 2900 3000 3000 0.9 0.36 0.9 0.36 2900 3000 3000 0.9 0.36 0.9 0.36 2900 3000 3000 bend nitro alk. phenyl-n. meth. phenyl-n. eth. h i t - ( + )-camph. Et-n.-acet- Na-pr-2-one-sulph. Me, Et-ac. acet. harm th2 ES AR EB AR1 AR2 C-H N-H 0-H 1.0 0.61 1.0 0.63 0.67 1400 1 700 0.6 0.61 0.6 0.63 1400 1600 0.7 0.60 0.7 0.61 1400 1700 0.26 0.54 0.26 0.56 2000 1700 0.5 0.59 0.5 0.60 1400 1700 1700 0.9 0.59 0.9 0.60 1400 1700 1700 1.4 0.59 1.4 0.60 1400 1700 1700 Es in eV, AR in A, and C-H, N-H and 0-H refer to the appropriate frequencies in cm-'.Furthermore, " harm ", " Morse ", and " th2 " indicate that the corresponding proton potentials have been applied, " stretch " and " bend " that the proton is transferred along stretching and bending modes, respectively, and AR, and ARz that the dissociation energy is 4 and 1 eV, respectively.21 8 THEORY OF PROTON TRANSFER REACTIONS most dissimilar to the bulk of the substances. We should also notice that the ascending and descending branches (with increasing AE) are largely constituted by N- and 0-bases, respectively.Following the same procedure as before we find quite good agreement between the experimental and theoretical results when bending frequencies (shown in fig. 7) and hyperbolic tangent potentials represent the proton, whereas the agreement is substantially poorer when high-frequency stretching modes in the harmonic or Morse approximation are applied. The resulting parameter values are given in table 1. The data of Bordwell and Boyle 33 (fig. 8) show less scatter, which is most likely due to the much greater structural similarity of the members of the series considered. The results are compatible with proton transfer along both stretching and bending modes ; the appropriate parameters are collected in table 1. 7 - 6 - 5 - A - 3 - BROMINATION OF 3-NITRO-( +)-CAMPHOR In this reaction bromine is used as a scavenger for the intermediate in the mutarotation of the The rate of reaction is, therefore, independent of the bromine concentration and determined by the base catalysed formation of the intermediate from the initial endo form, i.e., a proton transfer reaction.The dependence of the kinetic isotope effect on AE for proton transfer to various 0-bases is shown in fig. 9. The best fit to the experimental data is obtained here for proton A t n * X * \ 2t------ -0.3 -0.1 0.1 0.3 AEIeV FIG. 9.-Plot of kH/kD against AE for bromination of 3-nitro-( +)-camphor. Points from ref. (36) and the line the best theoretical fit (Es = 0.26 eV, AR = 0.44 A, transfer along bending modes ; QL = 2000cm-'; SZL = 1700cm-l). transfer along a stretching mode giving the parameters shown in table 1.We notice that E, values determined from the Brarnsted plot [which can be constructed from the data in ref. (35)] and from the " width " of the plot of the isotope effect practically coincide. This agreement is satisfactory, since the former only displays a fairly small mount of scatter. However, the frequency change necessary for the reproduction of the experimental data is opposite to the direction observed in most other cases for proton transfer from C- to 0-donor and acceptor fragments. IONIZATION OF CARBONYL COMPOUNDS The AE-dependence of the isotope effect of the proton transfer reactions between the carbonyl derivatives ethylnitroa~etate,~~ 26 ethyl- and methyl-acetoacetates, 9* 26* 35N .BRUNICHE-OLSEN AND J . ULSTRUP 21 9 sodiumpropane-2-one sulphonate 9* 34 and several 0- and N-bases has also been reported (fig. 10). For the ionization of ethylnitroacetate E, can be determined independently from the Brransted relationship using the data of ref. (26). Thus, including all bases investigated (H,O, OH-, CH2ClC00-, 2- and 4-picoline, 2,6-lutidineY phenoxide and 2-chlorophenoxide) a value of E, = 0.60 eV is found. If water is excluded the value 0.46 eV is found, whereas E, cannot be determined if both H20 and OH- are excluded. If we use the data of Bell and Spencer,56 where six carboxyl acids and 10 9. 8 - 7 - ' 6 - s 2 5 - 4 - 3 - - 2 - AEIeV FIG. 10.-Plot of k ~ / k ~ against AE for ionization of carbonyl compounds. 0 ref. (26) on ethyl- nitroacetate ; 0 ref.(26) on ethyl- and methyl-nitroacetates ; @ ref. (34). The lines are the best theoretical fits using stretching frequencies. Es = 0.5, 0.6 and 0.9 eV. AR = 0.39 8, ; RL = 2900 cm-I ; Q& = 3000 cm-'. I 1 I I 1 c two pyridine bases were investigated we find that E, is 0.46 and 0.52 eV, respectively, when the two pyridine bases are included and when they are not. These values are all reasonably consistent but differ from the value of 2.3 eV estimated by Cohen and The experimental data can be reproduced almost equally well by Morse and hyperbolic tangent potentials for the proton, and the corresponding best para- meter values are given in table 1. Much less comprehensive data are available for the other two systems, and as shown in fig. 10, only the descending branch of the isotope effect dependence on AE is available.The figure shows the best calculated plots, and table 1 gives the corresponding parameter values. DECOMPOSITION OF DIAZO-COMPOUNDS Both the Brsnsted relation and the dependence of the kinetic isotope effect on AE for the acid catalysed decomposition of several diazo-compounds have been r e p ~ r t e d . ~ ~ - ~ O While the smooth Brransted plot 5 8 9 6o for the decomposition of diazoethylacetate catalysed by several trialkylammonium salts permits a fairly unambiguous determination of E,, only the descending part of the plot of the isotope effect i s available. Moreover, the pK of the substrate can only be estimated within the limits of -5 and -2.59 For these reasons we do not show a figure relating220 THEORY OF PROTON TRANSFER REACTIONS to this system.The best fit for proton transfer is obtained if we assume that the proton is transferred from a bending N-H mode (1400 cm-l) to a stretching C-H mode (2900 cm-I), and for AR = 0.74A. ACID CATALYSIS OF 3-HYDROGEN EXCHANGE I N INDOLES The reaction scheme for these processes involves a rate-determining proton transfer from the acid catalyst to the indole followed by liberation of the proton or deuteron from the same carbon atom.61 The isotope effect for the deuterium-tritium exchange is almost constant (CD-T z 2) for a series of substituted indoles and different 0-acid catalysts corresponding to a free energy interval 0.1 2 AE 2 -0.6 eV. These observations are compatible with the theory outlined, if E, = 1-1.5 eV, A R = 0.6 A and the proton is transferred along bending modes.If stretching frequencies are applied, a more distinct maximum than the one observed experimentally is obtained. TEMPERATURE EFFECTS Evidence for nuclear tunnelling in chemical processes also rises from the study of the temperature dependence of the kinetic isotope effect in proton transfer and is manifested in the effects listed above. According to the present theory these effects must be ascribed to thermal excitation of either deuteron modes or proton bending modes, since the proton stretching modes are already frozen at room temperature. TABLE 2.-APPARENT ACTIVATION ENERGIES AND PRE-EXPONENTIAL ARRHENIUS FACTORS FOR DIFFERENT VALUES OF Es, AR AND PROTON VIBRATION FREQUENCIES QR = 1500 cm-1; D = 4 eV; AE = 0 Es 4.6 11.5 23 4.6 11.5 23 4.6 11.5 23 AR 0.58 0.68 0.75 AH/AD 0.80 0.73 0.76 0.56 0.57 0.61 0.42 0.45 0.50 AH/AT 0.40 0.39 0.38 0.19 0.22 0.22 0.11 0.14 0.14 EAH 1.23 3.19 6.19 1.46 3.46 6.48 1.66 3.69 6.72 A&-H 1.44 1.36 1.35 2.07 1.92 1.88 2.56 2.37 2.32 AET-H 2.56 2.42 2.36 3.57 3.36 3.29 4.36 4.12 4.03 DH = 3000cm-1; D = 4 e V ; A E - 0 ES 4.6 11.5 23 4.6 11.5 23 4.6 11.5 23 AR 0.35 0.42 0.52 AH/AD 6.9 5.7 4.9 13.8 10.5 8.2 47 23 20 AH/AT 20.8 12.3 9.2 49 25 17 151 62 38 EAH 0.86 2.6 5.5 0.86 2.6 5.5 0.86 2.6 5.5 AED-H 0.04 0.1 0.2 0.08 0.2 0.3 0.2 0.4 0.6 AET-H 0.3 0.5 0.7 0.5 0.9 1.0 1.3 1.7 1.8 Anharmonic potentials and a dissociation energy of 4 eV.Energy quantities in kcal, AR in A. In most cases the quantum effects are, however, weakly manifested in the tempera- ture dependence of EH-D or <.Thus, the appropriate activation energy difference, E:--EF, usually amounts to less than a single vibration quantum.s* Such effects are expected from the present theory, as seen from table 2 which shows the apparent activation energies and pre-exponential factors for proton and deuteron transfer reactions for representative values of E, and AR. The largest differences in activationN. BRUNICHE-OLSEN AND J . ULSTRUP 22 1 energy are clearly expected when transfer along bending modes occurs. If this is not plausible from the molecular structure of the reactants the possibility of different transfer distances for the proton and the heavier isotopes must be invoked [cJ eqn (7) and below].In the following we shall, therefore, only consider a few cases which either display " abnormally " large effects 5 8 or for which additional checks of the calculated parameter values can be obtained, by comparison between rate parameters for transfer of both proton, deuteron and triton. With reference to these criteria we shall thus, in turn, consider (Q) the ionization of 2-~arbethoxycyclopentanone,~~~ 45 (b) the ionization of nitroalkanes 40-43 and (c) the proton and deuteron transfer from 4-nitrophenylnitromethane to different N - b a s e ~ . ~ ~ ' ~ I ON1 Z AT1 ON OF 2-C A RBE THOXY C Y C LOP ENTA NON E The proton, deuteron and triton transfer between this substrate and D20, CH,C1000- and F- show both large isotope effects and considerable activation energy differences.Thus, table 3 gives the experimental values 4 4 9 45 for both the activation energies, EA, and the Arrhenius pre-exponential factor, A , for the various isotopes. Following the previous procedure, using literature values for ApK44g 45 and the appropriate vibration frequencie~,~ and assuming transfer along stretching modes, the best fit to the experimental data for the reaction with CH,ClC00- is obtained for Es = I .O eV, and AR = ARH = ARD = ART = 0.3 which give Ez = 11.0 kcal, AED-H = 0.3 kcal, AET-H = 0.7 kcal, kH/kD = 3.8 and kH/kT = 9.1, i.e., no satisfactory agreement for the activation energies. Fitting E, and AR to the latter gives isotope effects which are much larger than the experimental values. TABLE 3.-EXPERIMENTAL DATA ON ABSOLUTE VALUES OF k ~ / k ~ AND k ~ / k ~ AND ACTIVATION PARAMETERS FOR VARIOUS ISOTOPE TRANSFER REACTIONS system logAH E? logAD EZ 1ogAT E;f AED-H ~ O ~ A D I A H AET-a: I o g A r l A ~ k d k D k d k r 1 3.94 11.9 4.25 13.0 4.89 14.3 1.1 0.36 2.1 0.45 3.4 2 6.70 11.0 7.12 12.4 7.83 13.9 1.4 0.46 3.2 0.93 3.7 11.4 3 9.24 14.6 10.61 17.0 10.65 17.2 2.4 1.38 2.8 1.41 2.7 3.4 4 14.4 17.4 3.0 0.83 24 79 5 6.6 4.0 9.0 9.4 5.4 1.94 33 The system numbers 1-5 refer to the deprotonation of 2-carbethoxycyclopentanone by DzO, CH2C1C00- and F-, the deprotonation of 2-nitropropane by 2,4,6-trimethylpyridine and the deprotonation of 4-nitrophenylnitromethane by tetramethylguanidine, respectively.The activation energies are given in kcal mol-l. Application of typical bending frequencies gives similarly E z = 11.0 kcal, AED-H = 0.7 kcal, AET-H = 1.3 kcal, kH/kD = 3.8 and kH/kT = 8.6 for E, = 0.6 eV and AR = 0.59 A.When F- is the acceptor, the values E f = 14.6 kcal, AED-M = 0.1 kcal, AET-H = 0.3 kcal, kH/kD = 2.7 and kH/kT = 5.5 for E, = 1.5 eV and AR = 0.28 A and transfer along stretching modes, whereas Ef = 14.6 kcal, AED-H = 0.3 kcal, AET-H = 0.8 kcal, kH/kD = 2.67 and kH/kT = 6.0 are found for Es = 1 .OO eV, AR = 0.58 A and transfer from a bending to a stretching mode. Although the consistency of the theoretical data for bending modes is not bad and could be improved by inclusion of the isotope effect in some of the parameters where it has been ignored so far (e.g. the reaction volume or secondary isotope effects), we believe that the major cause of the discrepancy is the fact that the repulsion potential for the proton at small distances does not rise sufficiently rapidly with222 THEORY OF PROTON TRANSFER REACTIONS decreasing distance to ensure the effective equality of ARH, ARD and ART.Part of the differences in activation energy for kH, kD and kT therefore originates from the different repulsion energy, and the fact that ARH > ARD > ART [cf. eqn (7)]. In order to obtain an estimate of this effect we adopt the view that the repulsion potential can be satisfactorily represented empirically by a sufficiently simple function, e.g., harmonic or exponential and that the experimental activation energy for the proton transfer, E t , approximately represents contributions other than repulsion [the latter assumption can be relaxed if an estimate of U(R*) for the proton is avail- able].The difference in repulsion energy for the deuteron, AUD, then gives a contribution exp (AUD/kT) to the isotope effect. Using AUD as a parameter we can find the contribution ttun = to 5 arising solely from tunnelling, and from the activation energy of the deuteron transfer, (E2)tun = AUD, Stun and E z we can determine ARH, ARD and E,. Subsequently we can repeat this procedure for the triton transfer. If we ignore the small isotope effects on E,, however, it is more appropriate to use the value of E, already estimated. Together with the experimental values of AET-H and kH/kT this allows a determination of ART and AUT. Following the latter procedure we can reproduce the experimental data for the proton transfer to chloroacetate by the following set of parameters : E, = 0.9 eV, 0.9 kcal mol-' ; ART = 0.34 A, AUT = 2.2 kcal mol-l, i.e., we observe a monotonous dependence of the parameter values on the isotope mass as expected.When fluoride is the acceptor, the following values are found : E, = 1.6 eV, f2c--H = 2900 cm-', CH+ = 3450 cm-l ; ARH = 0.5 A ; ARD = 0.35 A, AUD = 2.3 kcal mol-' ; ART = 0.33 A, AUT = 2.2 kcal mol-l. The approximate equality between ARD and ART can be partly associated here with the relatively small difference between the reduced masses of DF and TF. C2c-H = 2900 cm-l; C2-H = 2700 cm-l; ARH = 0.49 A ; ARD = 0.41 A, AUD = IONIZATION OF NITROALKANES The proton transfer reaction between 2-nitropropane and the sterically hindered 2,4,6-trimethylpyridine shows both an " abnormally " large isotope effect, 9* an activation energy for this quantity which is substantially higher than the vibrational zero-point energy difference 41* 42 (see table 3), and a divergence from the general trend in the free energy relationship.Again using literature values for ApK29* 41. 42 and the vibration frequencies, the values of E, = 2-2.3 eV, ARH = ARD = ART = 0.77 A and typical bending frequencies can reproduce the experimental values of BE, kH/kD and AD/AH. This gives, however, kH/kT = 125, i.e., higher than the experimental value. Using stretching modes, the agreement is poorer, viz. E z = 11.3 kcal, AED-H = 0.7 kcal, kH/kD = 24 and kH/kT = 195 for E, = 2.0 eV and AR = 0.48 A. On the other hand, if we ascribe this discrepancy to the same effects as for the ionization of 2-carbethoxycyclopentanone, all the experimental data can be reproduced, if we choose E, = 2.4 eV, C2c--H = 2900 cm-l, = 2700 cm-l ; ARH = 0.7 A ; ARD = 0.57 A, AUD = 2.1 kcal rnol-l ; ART = 0.54A, AUT = 2.2 kcal mol-l.However, since no experimental data on E l are available, the choice of the last two parameter values cannot be made unambiguously. I ON1 Z A T I 0 N OF 4-NITRO PHENY LNI TROMET HAN E The proton and deuteron transfer from this compound to tetramethylguanidine, N,N'-diethylbenzamidine, tributylammine and triethylammine in several different solvents has been extensively studied recently. 52-5 These reactions generally showN . BRUNICHE-OLSEN AND J . ULSTRUP 223 large isotope effects ( k H / k D = 11-50), AI5D-H (1.5-5.4 kcal), A D / A H (1-30) and small AH and AD (log AH z 5-7, log AD x 6-91? which are all strongly indicative of proton and deuteron tunnelling.The most pronounced effect is observed when tetramethyl- guanidine is the base and cyclohexene the solvent; for this reason the appropriate data for this reaction are shown in table 3. Table 2 shows that effects of this magnitude cannot easily be associated solely with proton and deuteron transfer over fixed transfer distances. On the other hand, following the procedure outlined above the following parameter values are compatible with the experimental data (table 3) for the 4-nitrophenyl- nitromethane-tetramethylguanidine reactions : E, = 0.9 eV, Qzc-H = 2900 cm-I, = 2700 cm-l, D = 4 eV; A R H = 0.69 A; ARD = 0.53 A, A U D = 3.56 kcal mol-l.We also notice the relatively large value of ARH for both this and the previous reaction compared with most of the data discussed above. We notice finally that very large isotope effects (kH/kD > lo3) and an activation energy, Bz, which decreases strongly with decreasing temperature in the interval 77-120K has been observed for hydrogen and deuterium atom transfer from deuterated methanol and from acetonitrile, respectively, to methyl radicals in solid glasses.62* 63 While the former effect is compatible with the theory outlined above, the latter requires a modification of the formalism to incorporate the increasing quantization of medium modes with decreasing temperature at the low temperatures in question.Such an analysis is possible provided that the frequency spectrum of the medium is l6 However, since at least one additional parameter would then be introduced? and since the temperature interval investigated is not sufficiently wide to distinguish the role of the medium and the intramolecular modes, we shall not perform such an analysis here. 5. DISCUSSION We have shown that the quantum theory of elementary processes in condensed media provides an adequate description of all the important features of deuterium and tritium isotope effects of proton transfer reactions in homogeneous solution. This approach is fundamentally different from both the semiclassical approaches usually applied, which ascribe the isotope effect to loss of zero point energy when going from the initial to the transition state along the proton coordinate, and from the theory of Cohen and Marcus 63 according to which the isotope effect originates from differences in the ‘‘ intrinsic ” activation energies for the proton and deuteron transfer. The semiclassical approach cannot easily explain the qualitative dependence of t$ on AE and Tunless additional assumptions about the force constants of the transition state and the possibility of proton tunnelling are involved.In contrast, the formalism outlined and applied in the present work is based on the fundamental theoretical result that the proton and the solvent (including other classical modes) are repre- sented by separate (although possibly coupled) modes, and both sets exert important but different roles in the activation process. In addition, the rate expressions contain parameters of initial and final states only, i.e., information which is in principle experimentally available ; difficult estimates of transition state Parameters are thereby avoided.Finally, the theory represents an extension of previous applications incorporating anharmonicity effects for the proton potentials and by inclusion of all excited vibrational states in quantitative estimates of the various parameters. Our results can be summarized in the following way : of multiphonon electron and atom group transfer theory to isotope effects 12* l3 b Y224 THEORY OF PROTON TRANSFER REACTIONS (A) the presence of an isotope effect is ascribed to the fact that the proton and deuteron are generally transferred by tunnelling and that the tunnelling is easier the lighter the isotope.However, in most cases the barrier for tunnelling only contributes a small fraction of the activation energy. The dominant contribution to the fatter is provided by the solvent and other classical modes, i.e., nuclear motion along coordinates which do not refer to the proton. (B) For proton transfer along stretching modes and in cases where the Brarnsted coefficient is ~ 0 . 5 , only the ground vibrational level of the proton contributes significantly. For the deuteron a small but significant contribution is also provided by the first excited level, either in the initial or in the final state. This effect increases with increasing IApKl and is much more pronounced for transfer along bending modes, in which case excited states of the proton also contribute.Moreover, the effect is the fundamental cause of the dependence of on both AE and T. This conclusion differs from that of previous applications of the theory to kinetic isotope effects which ascribe the temperature dependence of 5 largely to different transfer distances for the proton and the deuteron and consequently to different values of the repulsion potential . (C) The experimental dependence of 5 on AE is always quantitatively reproduced by the theory for reasonable values of E, and AR = ARH = ARD. These two important parameters can furthermore be determined independently, from the Brarnsted relationship or the width of [(AE), and from the absolute value of 5 at the maximum, respectively.(D) The dependence of [ on AE is not strongly affected by possible differences in ARH and ARD, and in no case is it necessary to invoke such an assumption. (E) On the other hand, in a number of cases the experimental data on the dependence of 5 on T imply that AR decreases with increasing mass of the isotope, i.e., the repulsion potential between donor and acceptor varies less rapidly with R than the transmission coefficient. (F) Anharmonic proton potentials give smaller isotope effects or larger isotope transfer distances for a given value of the isotope effect compared with harmonic potentials. For Morse and squared hyperbolic tangent potentials the latter effect amounts to approximately 10 % for representative parameter values.However, the " resonance " splitting in the region of the reaction hypersurface may increase the " effective " anharmonicity of the proton potentials, and the effect may, therefore, be larger than estimated in the present work. We notice finally that transfer along stretching and bending modes can often equally well account for the observed effects. This means that a more involved path implying a mixing of initial and final state modes would also do so. This is also considered in semi-classical theories of proton transfer. In principle, such a path can be quantitatively incorporated in our calculations as well l2 when either the geometry or the total three-dimensional interaction potentials are known. Note added in proof: Recent calculations on the kinetic isotope effect, published after submission of the present work, has provided concIusions similar to ours concerning the dependence of k ~ / k ~ on ApK and Es.64 We would like to thank Prof.J. P. Dahl, Chemistry Department B, Lyngby, and Drs. E. D. German and A. M. Kuznetsov, Institute of Electrochemistry of the Academy of Sciences, Moscow, for helpful discussions. (a) R. R. Dogonadze and A. M. Kuznetsov, Physical Chemistry, Kinetics (VINITI, Moscow, 1973) ; (b) Progr. Surface Sci., 1975, 6, 1. N. R. Kestner, J. Logan and J. Jortner, J . Phys. Chem., 1974, 78, 2148.N. BRUNICHE-OLSEN AND J . ULSTRUP 225 B. Chance and D. DeVault, Biophys. J., 1966,6,825. R. H. Austin, K. W. Beeson, L. Eisenstein, H. Frauenfelder and T. M. Nordlund, Science, 1976,192,1002.J. Jortner, J. Chem. Phys., 1976,64,4860. A. M. Kuznetsov, N. C. SsndergZlrd and J. Ulstrup, Chem. Phys., in press. E. F. Caldin, Chem. Rev., 1969, 69, 135. R. P. Bell, The Proton in Chemistry (Chapman and Hall, London, 2nd edn, 1973). ’ J. Ulstrup and J. Jortner, J. Chem. Phys., 1975, 63,4358. lo R. R. Dogonadze and L. I. Krishtalik, Uspekhi Khim., 1975,44,1987. l1 V. G. Levich, R. R. Dogonadze, E. D. German, A. M. Kunetsov and Yu. I. Kharkats, 12E. D. German, R. R. Dogonadze, A. M. Kumetsov, V. G. Levich and Yu. I. Kharkats, l3 E. D. German and Yu. I. Kharkats, Izvest. Akud. Nuuk S.S.S.R., Ser. khim., 1572, 5, 1031. l4 M. I. Gverdtseli, E. D. German and R. R. Dogonadze, Izvest. Akad. Nuuk S.S.S.R., Ser. Electrochim. Actu, 1970, 15, 353. Elektrokhimiya, 1970, 6, 350.khim., 1975, 10, 1029. N. Briiniche-Olsen and J. Ulstrup, submitted for publication. Chem., 1977,75,315. Ser. Fiz. khim., 1973, 209, 1135. l6 R. R. Dogonadze, A. M. Kuznetsov, M. A. Vorotyntsev and M. G. Zakaraya, J. Electroanalyt. l7 M. A. Vorotyntsev, R. R. Dogonadze and A. M. Kuznetsov, Dokludy Akad. Nuuk S.S.S.R., l 8 R. R. Dogonadze and Z. D. Urushadze, J. Electroanalyt. Chem., 1971,32,235. l9 M. M. Berndfeld, M. I. Gverdtseli, E. D. German and R. R. Dogonadze, Izvest. Akud. Nuuk 2o R. R. Dogonadze, Yu. I. Kharkats and J. Ulstrup, inProc. 3rd Int. Summer School on Quantum 21 A. ErdClyi, W. Magnus, F. Oberhettinger and F. Trkomi, Higher Transcendental Functions 22 P. Morse, Phys. Rev I 1929, 34, 57. 23 N. Rosen and P. Morse, Phys. Reu., 1932,42,210.24 M. Abramowitz and I. A. Stegun, Hundbook of Mathemutical Functions (Dover, New York, 2 5 L. J. Bellamy, The Infra-Red Spectra of Complex Molecules (Methuen, London, 2nd edn, 1958). 26 D. J. Barnes and R. P. Bell, Proc. Roy. SOC. A, 1970,318,421. ’’ D. Eisenberg and W. Kauunann, The Structure andProperties of Water (The Clarendon Press, 28 M. D. Sturge, Phys. Rev. B, 1973, 8, 6. 29 R. P. Bell and D. M. Goodall, Proc. Roy. Soc. A, 1966,294,273. 30 R. P. Bell and B. G. Cox, J.C.S. Perkin II, 1971, 783. 31 J. E, Dixon and T. C. Bruice, J. Amer. Chem. SOC., 1970,92,915. 32 J. R. Keefe and N. H. Munderloh, J.C.S. Chem. Comm., 1974, 17. 33 F. G. Bordwell and W. J. Boyle, Jr., J. Amer. Chem. SOC., 1976, 97, 3447. 34 R. P. Bell and G. A. Wright, Truns. Faraduy SOC., 1961,57,1386. 35 R. P. Bell and J. E. Crooks, Proc. Roy. SOC. A, 1965,286,285. 36 R. P. Bell and S. Grainger, J.C.S. Perkin II, 1976, 1060. 37 D. J. McLennon, J. C.S. Perkin 11, 1976,932. 38 A. J. Kresge, D. S. Sagatys and H. L. Chen, J. Amer. Chem. SOC., 1968,90,4174. 39 J. E. Longridge and F. A. Long, J. Amer. Chem. SOC., 1967,89,1232. 40 E. S. Lewis and J. D. Allen, J. Amer. Chem. SOC., 1964,86,2022. 41 L. Funderburk and E. S. Lewis, J. Amer. Chem. SOC., 1964,86,2531. 42 E. S. Lewis and L. Funderburk, J. Amer. Chem. Sac., 1967,89,2322. 43 E. S. Lewis and J. K. Robinson, J. Amer. Chem. SOC., 1968,90,4337. 44 R. P. Bell, J. R. Hulett and J. Fendley, Proc. Roy. SOC. A, 1956, 235, 453. 45 (a) J. R. Jones, Trans. Furuday SOC., 1969, 65, 2430; (6) 1965, 61, 95. 46 J. R. Jones, R. E. Marks and S. C. Subba Rao, Truns. Furaduy SOC., 1967, 89, 111,993. 47 V. J. Shiner and B. Martin, Pure Appl. Chem., 1964, 8, 371. 48 E. L. Macker and C. McLean, Pure Appl. Chem., 1964,8,393. 49 A. V. Willi, J. Phys. Chem., 1966, 70, 2705. 50 D. Bethel1 and A. F. Cockerill, J. Chem. SOC. B, 1966,917. 52 E. F. Caldin and S. Mateo, J.C.S. Faraduy I, 1975, 71, 1876. 53 E. F. Caldin and S . Mateo, J.C.S. Faruday I, 1976,72, 112. S.S.S.R., Ser. khim., 1976, 12,2825. Mech. Asp. Electrochemistry, ed. P. Kirkov (Skopje University, Skopje, 1974). (McGraw-Hill, New York, 1963), vol. 1. 5th edn, 1970). Oxford, 1969). E. F. Caldin and G. Tomalin, Trans. Furuday SOC., 1968, 64,2814. 1-8226 THEORY OF PROTON TRANSFER REACTIONS 54 E. F. Caldin, D. M. Parbhoo, F. A. Walker and C. J. Wilson,f.C.S. Furuduy I, l976,72,185C. 5 5 E. F. Caldin, D. M. Parbhoo and C. J. WiIson, J.C.S. Faraday I, 1976, 72,2645. 56 R. P. Bell and T. Spencer, Proc. Roy. SOC. A, 1959, 251,41. 57 A. 0. Cohen and R. A. Marcus, J. Phys. Chem., 1968,72,4249. 58 M. M. Kreevoy and D. E. Konasewich, Adv. Chem. Phys., 1971,21,243. 5 9 W. J. Albery, A. N. Campbell-Crawford and J. S. Curran, J.C.S. Perkin II, 1972, 2206. 6o M. M. Kreevoy and S.-W. Oh, J. Arner. Chem. SOC., 1973,95,4805. 61 B. C. Challis and E. M. Miller, J.C.S. Perkin ZI, 1972, 1618. J.-T. Wang and F. Williams, J. Arner. Chem. SOC., 1972, 94, 2930. 63 A. Campion and F. William, J. Arner. Chem. SOC., 1972,94,7433. 64 E. D. German, Izuest. Akad. Nauk S.S.S.R., Ser. khim., 1977,2802 ; 1978, 959. (PAPER 81670)

ISSN:0300-9599    

DOI:10.1039/F19797500205

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Thermodynamic Properties for Transfer of Cations from PropyIene Carbonate to Dimethylsulphoxide and to Propylene Carbonate + Dimethylsulphoxide Mixtures BY BRIAN G. Cox* Department of Chemistry, The University of Stirling, Stirling FK9 4LA, Scotland AND W. EARLE WAGHORNE* AND CHARLES K. PIGOTT Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland Received 24th April, 1978 The free energies, AGtr, enthalpies, AH,, and entropies, AS,,, of transfer of Li+, Na+ and Ag+ from propylene carbonate to dimethylsulphoxide and to their mixtures, have been estimated from electrochemical and calorimetric measurements. The free energies and enthalpies of transfer decrease monotonically with increasing dimethylsulphoxide concentration, the decrease being most pronounced in the neighbourhood of pure propylene carbonate.The entropies of transfer pass through a sharp minimum upon the addition of the first few per cent of dimethylsulphoxide. These results are compared with those calculated upon the assumption that the changes in the thermodynamic parameters arise solely from changes in the coordination of the ions by the solvent components . The agreement for AGtr is practically quantitative in all cases. The values of AH*, and AS,, including the minima in AS, which is identified with the unfavourable entropy effects arising from preferential inclusion of dimethylsulphoxide in the ionic coordination sphere, agree qualitatively with the calculated values but show systematic deviations with increasing dimethylsulphoxide concentration. These, presumably, arise from changes in the bulk solvent properties.The values of AGtr appear to be influenced less by changes in bulk solvent properties than AH, and AS,, as effects on the last two are largely compensating. The treatment of ionic solvation data can be simplified by making an arbitrary distinction between effects arising from interactions of an ion with its first shell of solvent molecules and those arising from interactions of this ‘‘ complex ion ” with the surrounding medium. The latter group of effects reflect changes in the bulk dielectric constant of the medium, differences in soIvent-solvent interactions, and changes in interactions between coordinated solvent molecules and those in the bulk solvent. The advantage of such a distinction lies in the fact that the effects arising from changes in the coordination sphere of the ion can be treated relatively simply in terms of coordination equilibria between the ion and solvent molecules.It is also clear, from studies of the interaction between ions and common solvent molecules in the gas phase,l that the interactions between ions and the solvent molecules in the coordination sphere may contribute a major fraction of the total solvation energy of an ion. The free energies of transfer of electrolytes between pure and mixed solvents could be satisfactorily accounted for solely from considerations of changes in the interactions between the ions and their nearest neighbour solvent molecules, except where strong 221228 CATIONS IN PROPYLENE CARBONATE AND DIMETHYLSULPHOXIDE specific interactions between the component solvent molecules occur (e.9.dimethyl- sulphoxide and water).2* In several cases, involving binary mixtures of dipolar aprotic solvents, agreement between experimentally estimated values of the free energies of transfer of cations, AG,,(M+), and those calculated from an idealized coordination model of ionic solvation were within experimental error over the entire range of solvent compositions. It was decided to extend this investigation to include the enthalpies and entropies of transfer of ions. Entropies and enthalpies of solution and transfer are frequently far more sensitive to changes in ion-solvent and solvent-solvent interactions than the corresponding free energies. Thus they constitute a more severe test for any model of ionic solvation, and at the same time may provide much more detailed information about solvation phenomena.In this paper experimentally estimated free energies, AGt,, enthalpies, AH,,, and entropies, AStr of transfer of Na+, Li+ and Ag+ from propylene carbonate (PC) to dimethylsulphoxide (DMSO) and to PC + DMSO mixtures are reported. These are compared with values calculated via a simple coordination model of ionic solvation. This solvent system was chosen because the effects arising from changes in the composition of the first solvation shell were expected to dominate the changes in AGtr, AH,, and AStr. EXPERIMENTAL AND RESULTS CHEMICALS Analytical grade NaC104 and LiClO, were recrystallized from distilled water Tetraphenylarsonium perchlorate was prepared by the dropwise addition of an The resulting precipitate was filtered, recrystallized twice from methanol and Sodium tetraphenylborate was recrystallized from toluene and dried at 60°C Silver perchlorate (B.D.H., Laboratory Reagent) was dried at 60°C under reduced Dimethylsulphoxide and propylene carbonate were dried and distilled under and dried under reduced pressure at 120°C prior to use.aqueous solution of NaC10, to a warmed, stirred, aqueous solution of PbAsC1. dried at 40°C under reduced pressure. under reduced pressure. pressure. reduced pressure as described previously.2 EQUILIBRIUM PRODUCTS OF DIMETHYLSULPHOXIDE COMPLEXES Equilibrium products, pi, for Li+ complexes with DMSO in PC as solvent, were calculated in the usual way 3 3 5 * from the results of potentiometric titrations of a 0.01 mol dm-3 solution of LiC104 in PC with dilute solutions of DMSO in PC.They are reported in table 1, along with the values for the equivalent complexes of Na+ and Ag+. As for Na+ and Ag+, the potentiometric data were consistent with TABLE 1 .-EQUILIBRIUM PRODUCTS * FOR COMPLEX FORMATION BY DIMETHYLSULPHOXIDE IN PROPYLENE CARBONATE AT 298.15 K ion log81 log82 log83 log 8 4 Na+& 0.74 0.92 0.9 0.8 L F C 1 S 3 2.Z7 2.44 2.& Ag+b 2.2 3.6 4.4 4.8 /3i = [Li (DMSO)i+]/[Li+]DMSO]i. G. Clune, W. E. Waghorne and B. G. Cox, J.C.S. Furuduy I, 1976, 72, 1294. C Experimental uncertainty? 0.02 in log pj.B . G . COX, W . E . WAGHORNE AND C . I<. PIGOTT 229 a coordination number of 4 for the Li+ cation.Recent studies for the coordination of acetonitrile to alkali metal ions in the gas phase have also shown that the stability constants for the addition of the first four acetonitrile molecules are considerably higher than those for the addition of subsequent molecules. A Corning monovalent cation sensitive electrode was used to monitor changes in Li+ activity, both in the determination of the pi. values and the free energies of tran~fer.~. FREE ENERGIES OF TRANSFER, AGtr The values of AG,, for Lif from PC to DMSO or to PC+DMSO mixtures were estimated by assuming negligible liquid junction potentials in cell C, where TEA Pic is tetraethylammonium picrate, solvent S is DMSO or a PC+DMSO mixture and Li+-sens was a Corning monovalent cation selective glass electrode (no.476220). This assumption has been Ag I AgClO, (0.01 mol dm-3 in PC) I TEA Pic (0.1 mol dm-3 in PC) I LiC104 (0.01 mol dm-3 in PC or solvent S) I Li+-sens (C) shown to give values of AG,, which are comparable with those estimated via the assumption that the free energies of transfer of the tetraphenyl arsonium cation and tetraphenylborate anion are equal and is far simpler to use for the estimation of single ion AGt, values. TABLE 2.-FREE ENERGIES OF TRANSFER OF Li+ INTO DMSO+PC MIXTURES ~ D M S O 0.01 0.02 0.048 0.11 0.20 0.41 0.50 1 .oo AGk(Li+)a -1.4 -2.3 -3.9 -5.4 -6.8 -8.4 -8.8 -10.9 a Values at 25"C, expressed in kcal mol-I (1 cal = 4.184 J), experimental uncertaintiesk0.1 kcal mol-I. Using this assumption, values of AGtr(Li+) were calculated from eqn (l), where F is Faraday's constant and the factor 4.184-1 converts the results to calories (from joules) .- I ; 4.184 AGt,(Li') = -(EpC-ES). In eqn (1) Epc is the potential of cell C when the Li+ half cell contains PC as solvent and Es is the potential of cell when the Lif half cell contains DMSO or a PC + DMSO mixture as the solvent S. For this work no corrections were made to the e.m.f. measurements for Debye- Hiickel effects, but as these corrections are commonly of the order of 0.1 to 0.3 kcal mol-l for dilute solutions in solvents having high dielectric constants,* and largely cancel when values are compared, no significant change in the results would arise from such corrections. In determining the AG,,(Li+) values it has been assumed that LiC104 is completely dissociated.No measurements of relevant association constant data in the solvent mixtures are available, however LiC10, has been shown to be completely dissociated in PC and a variety of electrolytes, including NaC10, were found to be strong electrolytes in DMS0.l' The values of AGt, are reported in table 2. ENTHALPIES OF TRANSFER, AH,", The rate of dissolution of electrolytes in non-aqueous solvent systems is commonly very slow, making the measurement of heats of solution difficult in these media.230 CATIONS IN PROPYLENE CARBONATE AND DIMETHYLSULPHOXIDE To overcome this, an alternative procedure was adopted whereby successive aliquots of a concentrated solution of the electrolyte in PC were introduced into the solvent being studied and the resulting heat change measured.This heat change contains three terms: the heat of dilution of the injected electrolyte solution, the enthalpy of adding the propylene carbonate to the solvent, and the enthalpy of transfer of the electrolyte from PC to the solvent. The first two of these terms can be measured independently, and so the enthalpy of transfer can be obtained. All of the values used were those extrapolated to infinite dilution from measurements for a series of additions, so that no change in the solvent composition is involved. Final electrolyte concentrations used were in the range 5 x to 2 x lo-, for NaB(C,H,), and As(C6H6)4C104 and 3 x to 2 x for the others. TABLE 3 .-ENTHALPIES OF TRANSFER OF ELECTROLYTES, AH,",, FROM PROPYLENE CARBONATE a ~ D M S O AgC104 LiC104 NaC104 NaB(C&)4 (C6H~)&sC104 0.00 0.01 0.02 0.05 0.10 0.20 0.40 1 .oo 0.0 - 8.1 - 9.6 - 10.7 - 11.8 - 11.4 - 11.7 - 12.2 0.0 - 5.2 - 6.2 - 7.5 - 8.3 -- 8.4 - 8.8 (- 7.7$ 0.0 - 1.6 - 2.0 - 3.4 - 3.9 - 4.2 -4.8 - 5.0 (- 4-85)' 0.0 - 0.5 - 1.2 - 2.5 - 3.7 - 4.3 - 4.6 (- 3.53)" 0.0 0.0 0.0 - 0.3 -0.5 - 0.5 - 0.6 (- 0.04)C a Values at 298.15 K, expressed in kcal mol-' (1 cal = 4.184 J) ; experimental uncertainties k 0.2 kcal mol-1 except (C6H&AsC1O4 to +DMSO = 1, 0.5 kcal mol-l.$DMSO is the volume fraction of dimethylsulphoxide. CC. V. Krishnan and H. L. Friedman, J. Phys. Chem., 1969, 73, 3984. The method and calorimeter used have been described in detail e1sewhere.l l-l In mixed aqueous + organic solvent systems this method has been shown to give values in good agreement with those obtained directly from enthalpy of solution measure- ments.A difficulty arises with this procedure when the heat change associated with the addition of the carrier solvent becomes large compared to the heat change due to the transfer of the electrolyte. Thus the experimental uncertainties increase with increasing DMSO concentration in the solvent, and with decreasing concentration of the electrolyte solution added. This latter effect was particularly evident in measurements for sodium tetraphenylborate and tetraphenylarsonium perchlorate, where the available concentrations were limited by the low solubilities of the electrolytes. The measured standard state enthalpies of transfer of the electrolytes LiClO,, NaClO,, AgClO,, Ph,AsC10, and NaBPh, are reported in table 3.The enthalpies of transfer of Ag+, Li+ and Na+ ions were estimated by application of the assumption that AH,", Ph4A, = AH,", BPhc to the data in table 3.14 ENTROPIES OF TRANSFER, Astr The entropies of transfer for the ions were obtained from the values of AGtr and AHtr above, using eqn (2) AG = AH-TAS. (2)B . G . COX, W . E. WAGHORNE AND C. K . PIGOTT 23 1 DISCUSSION FREE ENERGIES OF TRANSFER, AG,,(M+) It has been shown previously,2 that if the interactions of an ion Mf with solvent molecules beyond its first coordination sphere are constant, AGtr(M+) from solvent A to a second solvent B is given by eqn (3), and from solvent A to mixtures of A and B by eqn (4). In eqn (3) and (4) n is the coordination number of M+ (four in all AG,,(M+) = -RT In (3) cases studied), +A and +B are the volume fractions of A and B, and are the suc- cessive equilibrium products for the complexing of M by B in solvent A, expressed in terms of the volume fraction concentration scale.Assuming the ideal volume fraction, /?[ are related to the pi expressed in the molar concentration scale (table 1) by eqn (5), where pB and MB are the density and molecular weight of component B Qualitatively, eqn (3) and (4) predict a monotonic decrease in AG,,(M+) from its value in the poorer solvent, A, to that in B. The decrease is most pronounced in the neighbourhood of +B = 0, and becomes progressively less steep as #B is increased. This behaviour has been discussed in detail elsewhere and it is sufficient to note that it reflects the preferential inclusion of the better solvent, or ligand, B in the ionic coordination sphere, with the attendant increase in the interaction energy of the ion with its nearest neighbour solvent molecules.ENTROPIES OF TRANSFER, AStr(M+) When an ion is dissolved in a pure solvent, there will be entropy changes resulting from the restriction of the motion of solvent molecules bound to the ion (primarily translational entropy), and from changes that may occur in the bulk structure of the solvent. In a mixed solvent, whenever the ion interacts preferentially with one of the solvent components, where will be an additional entropy loss resulting from differences between the composition of the solvent molecules surrounding the ion, and that of the bulk solvent.Thus the entropy of transfer of an ion from a pure to a mixed solvent will contain a negative term, ASc, resulting from the selection of the solvent molecules to form the coordination sphere. If the ion is transferred to a binary solvent mixture containing mole fractions x, and xB of A and B, and the resulting coordination sphere contains nA and nB moles of A and B, the entropy change associated with the rearrangement of solvent molecules, ASc, is given by eqn (6) where nA/n and n,/n are the fractions of A and B are in the inner coordination sphere of the ions (n = n,+ng). The right hand side of eqn (6) is simply the difference between the entropy of mixing n A and ng moles of A and B to form the coordination sphere, and the entropy of adding nA and Itg moles of A and B to the bulk solvent.ASc clearly approaches zero as X, or x, approach unity (i.e. in pure A or B), or as nA/ttB approaches xA/xS in a solvent mixture.232 CATIONS I N PROPYLENE CARBONATE AND DIMETHYLSULPHOXIDE Thus, according to the present model in which changes occurring outside the coordination sphere are assumed to be constant, the entropy of transfer of M from A to a mixture of A and B will be given by eqn (6), which on rearrangement gives eqn (7). Thus values of AS,,(M+) nA AS,,(M+) = - nAR In - +nBR In { nxA (7) can then be calculated from a knowledge of nA and nB at varying values of x,. It has been shown previously that the composition of the coordination sphere of an ion can be calculated from measured stability constants pi via eqn (8), where the symbols have the meanings defined above.Thus, using eqn (7) and (8) it is possible to calculate AStr from a knowledge of the appropriate p; values and the composition of the solvent system. Analysis of eqn (7) and (8) shows that AStr between pure solvents is zero ; transfer to solvent mixtures from a pure solvent is negative and passes through a minimum, if one of the solvent components interacts more strongly with the ion than the other does, and it is always zero when the interactions are equal. The unfavourable entropy of transfer in the former case results from the preferential inclusion of the more strongly interacting component in the coordination sphere of the ion, which is clearly entropically unfavourable. Furthermore, as the difference in the strengths of ion-solvent interactions for the two component solvents increases (i.e.as the pi values increase), the minimum in AStr increases in magnitude and moves to lower concentrations of the better solvent. ENTHALPIES OF TRANSFER, AHg(M+) The enthalpy of transfer of an ion from one solvent to another is given by eqn (9), at any temperature T Values of AH,,(M+) for transfer from A to mixtures of A and B may be obtained from eqn (9), by substitution of values for AG,, and AS,,, calculated as described above from eqn (3), (4) and (7). The values show a monotonic decrease from the value in the poorer solvent. However, this decrease is much more rapid than that of AG,,, since the latter contains an unfavourable AS,, term. Since, in the absence of effects arising from beyond the coordination sphere, AStr from one pure solvent to another is zero, AH,,(M+) from pure A to pure B should equal AGtr.AH,, = AGtr+ TAStr. (9) COMPARISON OF EXPERIMENTAL AND CALCULATED RESULTS Fig. I show the experimentally estimated values of AGt,, AH,, and -TASt, for Ag+, Li+ and Na+, along with those calculated from the equilibrium products in table 1, via eqn (3), (4), (7) and (9). The general agreement with the experimentally estimated values gives considerable support to the idea that changes in solvation parameters in these solvent systems are dominated by changes in the coordination of the ions by the component solvents. Particularly striking in this regard is the presence of the predicted humps in -TAS,, (corresponding to minimum in AStr), and the almost quantitative agreement in the AGtr values.It is also of interest to note the magnitude of the maxima in -TAS,,B . G . COX, W . E. WAGHORNE AND C. K . PIGOTT 233 ( N 1.5 kcal mol-1 for Na+ to 5.0 kcal mol-1 for Agf), showing that preferential solvation may lead to very large decreases in the entropies of transfer of ions from pure to mixed solvents. It can be seen from the figures that the good agreement for AGtr values results from the fact that the deviations between calculated and experimental AHtr and -TAS,, values are almost exactly compensating. As the calculated values do not include effects arising from beyond the first coordination shell, it is reasonable to 0.5 volume fraction of DMSO 1 .o U X -10- -A% 0 FIG.1234 CATIONS IN PROPYLENE CARBONATE AND DIMETHYLSULPHOXIDE +5 0 -5 0 -.. X -10 3 FIG. 1.-Comparison of empirical free energies (AG,, O), enthalpies (AH,",, x ) and entropies, as -298AStr (- TAStr, 0) with those calculated uia eqn (3), (4), (7) and (9), (solid lines) for (a) Ag+, (6) Li+ and (c) Na+. Thermodynamic vaIues are in kcal mol-1 (1 cal = 4.184 J) and solvent composition is expressed as volume fraction of DMSO. Empirical values of AG&a+) from ref. (3) and AGt,(Ag+) from ref. (2). identify these deviations with changes in the surrounding medium. For example, the partial molar enthalpy of DMSO in the mixtures decreases with increasing DMSO concentration.15 This means that AH,",(M+) should be less negative than that expected purely on the basis of changing coordination.However, the stronger solvent-solvent interactions experienced by DMSO, should also reduce its trans- lational entropy, which should decrease the entropy loss resulting from coordination by the ion. CONCLUSION The variations in the AGt,, AH,", and AStr values of cations in the DMSOfPC solvent system, and, by implication, other similar solvent systemsY2* can be satisfactorily accounted for in terms of changes in the coordination of the ions by the component solvents. Changes in the bulk solvent properties appear to influence AGt, less than AH,, and ASt, as effects on the last two tend to be compensating. We thank the S.R.C. for a research grant. W. R. Davidson and P. Kebarle, J. Amer. Chem. Soc., 1976,98, 6125, 6133. B. G. Cox, A. J. Parker and W. E. Waghorne, J. Phys. Chem., 1974,78, 1731. G. Clune, W. E. Waghorne and B. G. Cox, J.C.S. Furaduy I, 1976,72, 1294. G. G. Cox, G. R. Hedwig, A. J. Parker and D. W. Watts, Austral. J. Chem., 1974, 27, 477. K. Tzeetzu, T. Nomurce, T. Nakamura, H. Kazama and S . Nakajimo, Bull. Chem. SOC. Japan, 1974, 47,1657. F. J. C. Rossotti and H. Rossotti, The Determination of Stability Constants (McGraw-Hill, New York, 1961). ' M. K. Chantooni and D. M. Kolthoff, J. Phys. Chem., 1973,77, 1.B . G . COX, W . E. WAGHORNE AND C . K . PIGOTT 235 R. Alexander, A. J. Parker, J. H. Sharp and W. E. Waghorne, J. Amer. Chem. Soc., 1972, 94, 1148. M. L. Jansen and H. L. Yeager, J. Phys. Chern., 1973,77, 3089. lo M. J. Wootten, Electrochemistry (Spec. Period. Rep., Chem. SOC., London, 1973), vol. 3, p. 20. l1 E. de Valera, Thermodynamics Properties of Electrolytes in Mixed Solvents (University College l2 D. Feakins, E. de Valera and W. E. Waghorne, in preparation. l 3 Y. Pointud, J.-P. Marcel and J. Juillard, J. Phys. Chem., 1976, 80,2381. l4 B. G. Cox and A. J. Parker, J. A m . Chem. SOC., 1973,95,402. Is J. Courtot-Coupez and M. C. Madec, Compt. rend., 1973, 277, 15. Dublin, 1976). (PAPER 8/765)

ISSN:0300-9599    

DOI:10.1039/F19797500227

出版商:RSC    

年代:1979

数据来源: RSC