J . Chem. SOC., Furaday Trans. I , 1989, 85(1). 23--32 Ionic Contributions to the Viscosity B Coefficients of the Jones-Dole Equation Part 5.-Acetonitrile Kenneth G. Lawrence* Department of Chemistry, Birkbeck College, Malet Street, London WCl E 7HX Antonio Sacco and Angelo De Giglio Department of Chemistry, University of Bari, Via Amendola 173, 70126 Bari, Italy Angelo Dell'Atti Department of Physics, Uniuersitj, of Lecce, Via Arnesano, 73100 Lecce, Italy The B coefficients of the Jones-Dole viscosity equation are a measure of the size of the ions and of the interaction between the ions and the solvent. The B coefficients have been determined for the electrolytes Bu,NBu,B, Bu,NBr, Bu,NI, Ph,PBr, Ph,PI, NaI and NaPh,B, and for the homologous series from Et,NBr to Hept,NBr in acetonitrile at 25 and 35 "C.Ionic B values for the bromide and iodide ions have been calculated from the B coefficients for the tetra-alkylammonium solutions and are compared with those obtained from the tetraphenylphosphonium solutions. The transition-state treatment has been applied to the results, and the thermodynamic activation parameters for viscous flow have been calculated. These are compared with those found previously for solutions of dimethyl sulphoxide, hexa- methylphosphoric triamide and N,N-dimethylformamide, and are dis- cussed in terms of the new theory of B coefficients proposed by Feakins. For a number of years we have been studying the viscometric properties of non-aqueous solutions of electrolytes. Viscosity B coefficients of the Jones-Dole equation q r = I+AC;+BC (1) have been determined for each system studied, because these coefficients throw some light on the solute-solvent interactions.It is, however, more useful to be able to divide the B coefficients for the salts into ionic contributions, and our most recent work has focused attention on two of the methods of subdivision. One of these assumes that for salts like tetrabutylammonium tetrabutylborate (Bu,NBu,B) and the corresponding tetraphenylphosphonium salt (Ph,PPh,B) similar cation-solvent and anion-solvent interactions occur for each reference salt, and the contributions made to the viscosity of the solutions by the Bu,N+, Bu,B- and the Ph,P+, Ph,B- ions may be considered to be proportional to their van der Waals volumes, Vw. For example, the cationic B value from the tetrabutyl salt is obtained from the following: V,(Bu,B-) B( Bu,N+) = B( Bu,NBu,B) We have applied this method using both the tetrabutyl and tetraphenyl salts to a few solvent systems with remarkable suc~ess.l-~ In this paper we report viscosity and density measurements of Bu,NBu,B, Bu,NBr, 2324 Ionic Contributions to the Viscosity B Coeficients Bu,NI, Ph,PBr, Ph,PI, NaI and NaPh,B in ACN at 25 and 35 "C.Ph,PPh,B was insufficiently soluble, so a B value for this salt was obtained from (3) Although we would normally prefer to use bromide salts, which in our experience give more consistent results, we found that the Ph,PI was more soluble in ACN, and the B coefficients could then be determined with greater precision from measurements made over a wider concentration range.The tetrabutylammonium salts did not pose the same solubility problem. Additional measurements were made with Bu,NI and Ph,PBr for purposes of halide-ion comparison. In a previous paper we examined another method of determining ionic B values that had been reported in the literature. This involved plotting B coefficients of a series of tetra-alkylammonium halides in dimethyl-sulphoxide and hexamethylphophoric tri- amide as some function of the cation, and extrapolating the curve to obtain the B value of the halide ion, This was not very successful, but we thought it worthwhile to repeat this method in acetonitrile and so measurements were also made with tetraethyl- to tetraheptyl-ammonium bromides. B(Ph,PPh,B) = B(Ph,PI) + B(NaPh,B) - B(Na1). Experiment a1 Details of the purification of the salts and of the apparatus used have been given previo~sly.l-~ Bu,NI (Ega-Chemie), purity > 99 %, m.p. 147-148 "C, NaI (Merck Suprapur) and NaPh,B (Gold Label) purity > 9970, were vacuum-dried and used without further purification.Ph,PI was purified as reported in the literature. ACN (Fluka), purity > 99.8 YO, water content determined according to Karl Fischer < 0.008%0, was used without further purification. All the solutions were prepared in a dry box. Results and Calculations In table 1 are reported the experimental results for the salts examined at 25 and 35 "C. Table 2 shows calculated and experimental viscosity A coefficients. The constants used in the Falkenhagen-Vernon equation to calculate the A values at 25 "C were E = 35.95,4 and 21 = 0.3406 CP (this work), and limiting ionic conductances were taken from the literat~re.~ The experimental A values were obtained from a linear-regression least- squares fitting.The viscosity B coefficients were calculated by the method of orthogonal polynomials with theoretical A coefficients substituted in the statistical analysis. The values of the A coefficients used in the calculations at 25 "C were also used at 35 "C, a procedure we have used and discussed previously.' The B value for Bu,N+ was calculated using eqn (2). The value for Ph,P+ was obtained using eqn (3) and the appropriate form of eqn (2). The van der Waals volumes were taken from table 4 of ref. (1). Apparent molar volumes, #", of the solutions were calculated from the equation 1000(do-d) M CdO do +- q5v = (4) where d and do are the densities of the solution and solvent, respectively, A4 is the formula weight of the solute and c is the concentration.The partial molar volumes, #:, of the salts at infinite dilution were obtained by a least-squares fitting of the results to the Masson equation where S is an empirical constant. The values of q5: are reported in table 4. q5v = #:+sci ( 5 )K . G. Lawrence, A. Scicco, .4. Dc, Giglio and A . DelrAtti 25 Table 1. Data for the relative viscosity (q,.) and density (p,) at 25 and 35 "C 25 "C 35 "C Et,NBr 73 104 145 I63 227 305 382 486 107 157 215 265 314 383 437 505 1 I4 151 250 328 394 470 539 606 143 245 324 41 8 516 599 650 742 71 107 148 20 I 277 328 41 6 499 76 106 179 215 278 350 399 486 Pr ,N BR Bu,NBr Bu,NI Pe,NBr Hex,N Br 454 667 916 980 1354 I788 2270 2772 56 1 798 1126 1280 1772 227 1 3012 3 743 418 63 1 762 909 1303 I685 2310 2714 75 1 I3 150 179 237 305 402 503 569 810 1142 1298 1797 2303 3054 3795 814 1227 1705 2121 2525 31 I5 2429 3879 733 1071 I439 1750 2058 2494 2727 308 1 803 1210 1681 2092 2490 3073 3382 3816 792 1056 1452 1730 2027 2464 2667 3005 142 162 245 287 337 403 45 I 500 121 161 26 1 335 408 483 578 65 1 825 1100 1880 2426 3008 3568 4076 4645 855 1 1 1 1 1817 232 I 2825 3348 3803 430 1 813 1084 1854 2392 2966 3518 4020 4582 836 1090 I778 2259 2745 3252 3730 4212 728 1322 774 1290 1687 2123 3640 2992 328 1 3764 142 249 330 42 1 55 1 608 676 766 738 1341 181 1 231 1 2895 3314 3652 4209 778 1316 1734 2170 2675 3062 3344 3833 1786 2278 2856 3268 3602 4151 514 723 1074 1507 2017 23 74 3070 3708 608 755 1 I95 I669 2172 2610 3285 3877 83 99 151 209 280 3 30 434 526 52 I 733 I089 1528 2046 2408 31 12 3760 600 803 1247 1675 2376 2750 3404 4019 719 968 1349 1857 243 1 301 I 3485 4229 77 107 159 229 306 386 428 51 1 539 76 1 1111 1830 2027 2469 290 1 349 1 739 1004 1412 1905 2498 308 I 3520 4208 53 1 750 1095 1509 1999 2435 286 1 344326 Ionic Contributions to the Viscosity B Coeficients Table 1 (cont.) 25 "C 35 "C c / ~ O - ~ mol dm-3 105(qr- 1) lo5@,- 1) c / ~ O - ~ mol dmP3 105(qr- 1) lo5@,- 1) - 532 780 1113 1534 1993 2432 2973 800 1306 1814 2377 2900 3436 3974 4407 423 596 750 942 1171 1342 1499 1678 359 524 732 974 1123 1204 1372 1583 788 1146 1513 1960 2325 2705 301 1 342 1 804 1130 1583 2000 2273 28 14 3089 820 1235 1742 2265 2885 3494 423 1 995 1573 21 17 2739 331 1 3919 4434 5000 67 1 914 1109 1368 1686 1918 21 19 2377 353 51 1 664 876 989 1066 1197 1366 1034 1472 1909 2425 2860 3292 3658 4128 1031 1428 1952 2443 2756 3379 3726 Hept,NBr 76 525 109 769 206 1097 212 1513 280 1965 345 2398 42 1 2932 Bu,NBu,B 36 68 78 101 119 143 160 179 76 116 141 170 214 244 270 298 68 99 130 179 20 1 223 25 1 287 203 293 406 505 60 1 689 774 868 242 344 478 607 68 1 84 1 937 NaPh,B NaI Ph,PBr Ph,PI 789 1288 1789 2344 2860 3389 3920 4346 417 588 740 929 1154 1324 1478 1655 354 538 72 1 960 1107 1188 1360 1521 777 1130 1492 1933 2293 2668 2969 3374 793 1115 1561 1972 2242 2775 3047 817 1630 171 1 2203 2819 3498 4206 965 1536 2067 2667 3215 3782 4303 4840 667 900 1105 1325 1667 1903 2077 2275 337 479 657 830 949 01 1 189 335 006 438 1828 2344 2794 3207 3545 4024 1022 1388 1901 2374 2699 3279 3630 94 112 184 223 297 360 438 38 82 85 123 138 155 180 20 1 79 121 173 183 232 320 288 313 61 98 113 159 190 204 205 274 189 275 368 486 60 1 687 76 1 8 70 243 339 475 602 686 848 948K .G. Lawrence, A . Sacco, A . De Giglio and A . Dell'Atti 27 Table 2. Viscosity A/dmg mol-; coefficients at 25 "C Et,NBr Pr,NBr Bu,NBr Pe,NBr Hex,NBr Hept,NBr Bu,NBu,B Bu,NI Ph,PI NaPh,B NaI Ph,PBr theoretical 0.0 158 0.0 172 0.0 I84 0.0191 0.0 199 0.0205 0.0236 0.0 182 0.0 187 0.02 18 0.0 164 0.0 190 ~~ ~ experimental" 0.0108 & 0.0030 0.01 89 & 0.0009 0.0 I 70 & 0.0007 0.0070 0.0059 0.0 18 1 & 0.0022 0.0234 f 0.0052 0.01 83 f 0.0022 0.0203 & 0.0009 0.01 53 & 0.001 1 0.021 8 & 0.0016 0.0150+ 0.0016 0.01 87 f 0.0007 a With standard error.Table 3. B/dm3 mol-' coefficient differences for salts with a common ion __ -~ ~ ~~ _ ~ _ _ _ ~ ~ ~~ T/ "C Bu,NBr - Bu,NI Ph,PBr - Ph,PI Ph,PBr - Bu,NBr Ph,PI - Bu,NI 25 0.018 0.0 I6 0.265 0.267 35 0.014 0.013 0.256 0.257 Discussion A Coefficients It is not uncommon to find that, for non-aqueous systems possessing large B coefficients, the agreement between the experimental and theoretical A coefficients is not as close as that found for aqueous systems. If ion pairing is occurring to any great extent experimental A values are found to be consistently higher than the theoretical values,' but this was not the case here.Since the theoretical A values were used in the orthogonal polynomials program from which the B coefficients were obtained, the program was re- run with the experimental values substituted, but the resulting B values were not sufficiently changed to warrant reporting them. In any case, the purpose of this work is to investigate our ideas about splitting the B coefficients into ionic contributions, and for this we require internally consistent B values (see below). Confidence in the wider interpretation of the B values will then depend on the relative magnitudes of the experimental errors, which are reported in tables 4 and 5. B Coefficients The internal consistency of the results may be checked by calculating the differences between the B coefficients of two salts with a common ion.Satisfactory agreement for pairs of bromide-iodide and tetraphenyl-tetrabutyl salts at both temperatures can be seen in table 3. Direct comparisons of our results with those available in the literature can be made in table 4. We have shown' that Bu,NPh,B should not be used as a reference salt for28 Ionic Contributions to the Viscosity B Coejicients Table 4. Viscosity B/dm3 mol-' coefficients and partial molar volumes q5:/cm3 mol-' B K 25 "C 35 "C 25 "C 25°C 35°C Et,NBr Pr,NBr Bu,NBr Pe,NBr Hex,NBr Hept,NBr Bu,NBu,B Bu,NI NaI Ph,PBr Ph,PI NaPh,B Bu,NPh,B 0.650 f 0.005 0.706 f 0.001 0.839 f 0.001 0.984 f 0.008 1.100 f 0.004 1.309 f 0.008 1.002 f 0.003 0.821 f 0.001 0.73 1 f 0.003 1.104 f 0.00 1 1.088 f 0.001 1.240 f 0.002 0.640 f 0.014 0.704 f 0.005 0.829 f 0.002 0.952 f 0.007 1.091 f 0.008 1.313f0.008 0.982 f 0.002 0.8 1 5 f 0.00 1 0.699 f 0.005 1.085 f 0.002 1.072 f 0.002 1.237 f 0.006 0.69" 0.71" 0.93" 276f 10 268f 11 574f4 578f4 0.87" 283f 10 327f 18 293f12 303f4 1.26 f 0.02b 262 f 8 254 f 27 1.35" and 1.32 f 0.02b a Ref.(8). and 95 % confidence limits on the fitted apparent molar volumes. Ref. (7). The error limits for this work are standard errors on the fitted B coefficients, Table 5. Ionic viscosity B/dm3 mol-' values in acetonitrile at 25 "C this work Criss" Krumgalzb Gill" Na+ Et,N+ Pr,N+ Bu,N+ Pen,N+ Hex,N+ Hept,N+ Ph,P+ Br- I- Bu,B- Ph,B- 0.453 f 0.004 0.44 0.33 0.32 0.39 0.39 0.37 0.48 0.500+ 0.002 0.56 0.62 0.59 f 0.06 0.67 0.78 0.99 0.8 10 f 0.003 0.32 f 0.03 0.37 0.31 0.30 f 0.03 0.34 0.25 0.502 f 0.002 0.787 f 0.003 0.87 0.735 0.73 f 0.06 a Ref.(14). Ref. (13). " Ref. (7). splitting viscosity B coefficients into ionic contributions, so we did not include it in our measurements, but a value may be calculated assuming the principle of additivity of B coefficients from our values for Bu,NI, NaPh,B and NaI. From these a value of 1.33 is obtained, which is in close agreement with that of Gill.' With the exception of Pr,NBr, the coefficients of FUOSS~ appear to be rather high. When eqn (2) is used to calculate ionic B values from Bu,NBu,B, Bu,NBr and Bu,NI, values of 0.339 for Br- and 0.321 for I- are obtained, whereas the corresponding bromide and iodide values obtained from the tetraphenyl salts are 0.294 and 0.278, each with a standard error of k0.003 dm3 mol-l.This is the first aprotic solvent that we haveK . G. Lawrence, A . Sacco, A. De Giglio and A . DelVAtti 29 studied for which there are notable differences between the halide ion B values from the two reference salt systems. These differences may arise from specific interactions between solvent molecules and the Ph,P+ and Ph,B- ions as proposed by Coetzee and Sharpeg for a number of nonaqueous solvents including ACN. Their spectroscopic results led them to suggest that anions interact directly with the methyl hydrogens of ACN, and that the anion bonding was weaker than for the cations because of the nature of the charge distribution on the solvent molecule.'o However, no firm conclusion was reached other than that ACN discriminated between Ph,P+ and Ph,B- and that the tetra-alkyl- substituted reference salt should be preferable to its tetraphenyl counterpart.Gas-phase studies of the solvation of alkali-metal and halide ions by acetonitrile also indicated unequal solvation of cations and anions.ll Our division into ionic values assumes the validity of eqn (2) and an analogous equation for the tetraphenyl salt system. When we calculate B(Ph,P+) it is clear that if we allow an additional contribution to V,(Ph,P+) on the grounds of unequal cation-solvent and anion-solvent interactions, the resulting B values for the halide ions derived from the tetraphenyl salt will be even smaller than those reported above. Examination of the single-ion conductances in ACN obtained from transference- number measurements by Kay et a[.'' shows that there would be no improvement if we chose volume ratios based on Stokes radii for the division into ionic B values, as used by Krurngal~'~ and Gill.' Thus although one might look more favourably upon the values derived from the tetra-alkyl salt, there does not seem to be any convincing reason for choosing one set of values in preference to the other, so we have reported the mean values for the halide ions from both reference salts in table 5.The error limits shown for the reference ions are calculated from the standard errors on the fitted B coefficients for these salts, whereas for the halide ions we show the resulting standard deviation from the mean of the pairs. The derived ionic values shown in table 5 are therefore only reported to two decimal places.The B values for Bu,N+ and Bu,B- are considerably smaller than the values for Ph,P+ and Ph,B-, and table 4 shows that the partial molar volume of Bu,NBr is of comparable magnitude to the corresponding tetraphenyl salt. Similar results have been seen in all of our studies with these reference salts, and have been explained in terms of the differing flow patterns around the long-chain tetra-alkyl ions and the propeller-like tetraphenyl ions. Also shown in table 5 are Criss's ionic B values,', which must be regarded as speculative, since he used the experimental results of FUOSS' and chose, without giving a reason, a value of 0.25 for the Me,N+ ion. Krumgalz also used Fuoss's values. We have previously tested another method of obtaining ionic B values that involves measuring the B coefficients for an homologous series of tetra-alkylammonium salts with a common anion, and plotting the B coefficients of these salts as a function of the formula weight or van der Waals volumes of the ~ a t i 0 n s .l ~ Extrapolation of the independent variable, e.g. to V,(R,N+) = 0, should give the B(X-) as intercept. This method assumes that the B coefficients are a linear function of this variable, and the contribution of the chosen cationic variable to the B value should vanish at zero. Fig. 1 shows that the assumption of linearity of B coefficients with V, is true only for tetrapropyl to tetrahexyl ; the circles approximately correspond to 95 % confidence limits.Extrapolation for these four salts produced the value at V,(R,N+) = 0 of B(Br-) = 0.26f0.02 at 25 OC, and this does not compare well with the reference-salt value. A similar situation was found for both DMSO' and HMPT2 solutions published previously. Krumgalzl' also tried extrapolating B coefficients against the cube of Stokes radii for the tetra-alkylammonium ions; the radii were values averaged from literature sources of ionic conductances. Using his radii a value of B(Br-) = 0.48f0.03 was obtained. This further confirms our view that extrapolation methods should be viewed with caution.30 Ionic Contributions to the Viscosity B Coeflcients 0 Et,N+ Pr,N* Bu,N+ Pe4N+ Hex4N+ Hept,N+ 100 150 200 2 50 300 v, /an3 mol- I I I I I Fig. 1. Plot of B(R,NBr) us. Vw(R,N+) at 25 "C.Transition-state Treatment The detail of the viscous flow process as it pertains to B coefficients has recently been re- examined in terms of the transition-state treatment.17 This new theory suggests that the magnitude of the ionic molar contribution to the activation energy, A&*, depends only on differences in ion-solvent interactions between the ground and transition states. The movement of an ion into the transition state may be considered to involve the breaking of ion-solvent bonds to create a cavity ahead of the moving ion, and the re-making of ion-solvent bonds in the transition state. For highly structured solvents the coordination of the ion in the ground state may be incomplete, but the viscous flow process disrupts more of the solvent structure, so in the transition state the coordination of the ion is likely to increase.For less well structured solvents an ion's ground-state coordination may even diminish in the transition state. Consequent changes that may occur in the solvent-solvent interactions are reflected in the enthalpies and entropies of activation only, and do not contribute to Api*. We have calculated the activation parameters for the salts involved in this work and divided them into cationic and anionic contributions using the same technique as that used to divide the B coefficients. These are shown in table 6, along with values calculated from the work presented in previous papers for comparison. Values for the bromide ion in the various solvents are the mean values obtained from Bu,NBr and Ph,PBr.Examination of this table reveals that the results for the tetrabutyl and tetraphenyl ions in ACN are unusual; the TAS,O* values are negative, their AH,"* values are smaller than in the other solvents, and their A&* values are considerably larger than the corresponding AH;* values. Of the three solvents DMSO, HMPT and DMF, DMSO is believed to possess the most structure through dipoledipole interactions to form small chains ; nevertheless the molecular association is probably not strong enough to prevent complete coordination of an ion by DMSO molecules in the ground state, so in the transition state a reduction in the coordination is most likely. Thus ion-solvent and solvent-solvent bond-breaking contributes to the large positive values of the enthalpies and entropies of activation for the reference ions in DMSO.HMPT and DMF are less structured than DMSO, and this results in a similar pattern but smaller numerical values for AH;* and TAS,"* for these ions.Table 6. Ionic thermodynamic activation parameters for viscous flow at 25 "C AH,"+/kJ mol-' DMSO" Bu,N+ Ph,P+ Bu,B- Ph,B- Br- I- Na' solvents 42.5 78.3 43 .O 76.1 44.6 39.1 32.9 13.7 HMPTb DMF' 38.3 38.7 65.5 42.5 38.7 39.2 64.1 41.3 32.5 29.8 - - - - 14.4 8.3 ACNd DMSO HMPT DMF 31.6 29.6" 31.8 28.6" 29.5 32.0 37.9 8.8 11.6 32.2 11.9 31.3 21.2 16.6 14.3 - 0.9 12.5 6.3 12.8 6.6 26.5 - 1.5 14.3 12.0 26.8 - 1.5 -3.6 -4.2 ACN - 8.9 - 25.0' - 8.9 - 24.5" 11.2 14.6 12.5 - 0.6 DMSO 30.9 46.1 31.1 44.8 23.4 22.8 18.5 14.57 Api*/kJ mol-' HMPT DMF 25.8 32.4 38.7 44.0 25.9 32.6 37.6 42.8 18.2 17.8 - ~ - - - 17.99 12.49 ACN 40.5 54.6e 40.7 53.1" 18.3 17.4 24.5 9.44 a , b Table 7, ref. (2). Calculated from ref. (3). This work. " From Ph,PI +NaPh,B-NaI. b b b cp w c)32 Ionic Contributions to the Viscosity B Coeficients ACN molecules have a strong tendency to form dimers by association.l' The dissociation energy of the dimers is estimated to be 16-30 kJ mol-l, with 96 YO of the CN groups associating in pairs at 30 "C. For a given temperature the degree of solvation of an ion in the ground state will depend on whether the ion-solvent interactions are strong enough to open the solvent dimers. In the transition state there will be more molecules freed from dimer association by the viscous flow process allowing an increase in the solvation of the ions.The concomitant bond-making results in negative entropies of activation, and a negative contribution to the enthalpies of activation that lowers their numerical values (see table 6). As mentioned above, changes in the ion-solvent interactions from ground to transition state are effectively measured by A&*, and we see that the largest values occur for the reference ions in ACN. NaI in DMSO and ACN makes an interesting comparison with the reference salts. A strong interaction between Na+ and I- ions and solvent molecules will occur in the ground state, and formation of the transition state will be accompanied by some ion-solvent bond-breaking (?!-'AS: * positive) and a reduction in the solvation of these ions in both solvents.The Influence of Temperature Table 4 can be used to show the change in the B coefficients with rise in temperature, AB/A T. A comparison with results reported for the salts in solvent systems previously studied in this series of papers shows that the values for ABIAT for ACN are unusually small. A full discussion of this aspect of the work will be reported in a subsequent paper. References 1 K. G. Lawrence and A. Sacco, J. Chem. Soc., Faraday Trans. 1, 1983, 79, 615. 2 A. Sacco, M. D. Monica, A. De Giblio and K. G. Lawrence, J. Chem. SOC., Faraday Trans. I , 1983,79, 3 A. Sacco, A. De Giglio, A. Dell'Atti and K. G. Lawrence, 2. Phys. Chem. N.F., 1983, 136, 145. 4 G. P. Cunningham, G. A. Vidulich and R. L. Kay, J. Chem. Eng. Data, 1967, 12, 336. 5 G. J. Janz and R. P. T. Tomkins, Nonaqueous Electrolytes Handbook (Academic Press, New York, 1972); A. K. Covington and T. Dickinson, Physical Chemistry of Organic Solvent Systems (Plenum Press, London, 1973). 6 J. Crudden, G. M. Delaney, D. Feakins, P. J. O'Reilly, W. E. Waghorne and K. G. Lawrence, J. Chem. SOC., Faraday Trans. 1, 1986, 82, 2195. 7 D. S. Gill, M. S. Chauhan and M. B. Sekhri, J. Chem. SOC., Faraday Trans. 1, 1982, 78, 3461. 8 D. F. Tuan and R. M. Fuoss, J. Phys. Chem., 1963, 67, 1347. 9 J. F. Coetzee and W. R. Sharpe, J. Phys. Chem., 1971, 75, 3141. 10 J. A. Pople and M. Gordon, J. Am. Chem. SOC., 1967, 89,4253. 11 W. R. Davidson and P. Kebarle, J. Am. Chem. SOC., 1976, 98, 6125. 12 C. H. Springer, J. F. Coetzee and R. L. Kay, J. Phys. Chem., 1969, 73,471. 13 B. S. Krumgalz, Russ. J. Phys. Chem., 1973,47, 956. 14 C. M. Criss and M. J. Mastroianni, J. Phys. Chem., 1971, 75, 2532. 15 K. G. Lawrence, R. T. M. Bicknell, A. Sacco and A. Dell'Atti, J. Chem. Soc., Faraday Trans. 1, 1985, 16 B. S. Krumgalz, J. Chem. SOC., Faraday Trans. I , 1980, 76, 1275. 17 D. Feakins, W. E. Waghorne and K. G. Lawrence, J. Chem. SOC., Faraday Trans. I , 1986, 82, 563. 18 A. M. Saum, J. Polym. Sci., 1960, 42, 57. 263 1. 81, 1133. Paper 8/0022OG; Received 18th January, 1988