Standard Free Energy of Transfer of Ionic Surfactantsfrom Water to Water + Acetone Mixtures from VapourPressure MeasurementsB Y CLAUDE TREINER" AND A. LE BESNERAISLaboratoire d'Electrochimie, UniversitC P. et M. Curie,4, Place Jussieu, 75230 Paris Cedex 05, FranceReceived 13th May, 1976The standard free energy of transfer, AGi of sodium decylsulphate (SDS) and of decyltrimethyl-ammonium bromide (DTMABr) from pure water to mixtures of water and acetone (AC) have beendetermined by accurate vapour pressure measurements of dilute solutions at 298.15 K. Preciseconductance measurements were also made for the two ionic surfactants in water and in water + ACmixtures in the same solute concentration range. AC? was negative, went through a minimum andincreased in the AC rich mixtures for both ionic surfactants.These results are qualitatively similarto those for tetrabutylammonium bromide which forms no micelIes in the same solvents ; they arealso consistent with the results inferred from critical micelle concentration (c.m.c.) data on dodecyltri-methylammonium bromide in the same binary solvent system. Using an extrathermodynamicapproach for assignment of AG; single ion values, it is shown that these experimental findings canbe accounted for solely by the opposing behaviour of anion and cation towards the solvent molecules.Comparison of AG for SDS and DTMABr (which are almost equal over the whole AC concentrationrange) indicates that the contribution of the OSO; group is of the same sign (positive from waterto water+AC mixtures) and virtually equal to that of the bromide ion.It is well known that the variation of critical micelle concentration (c.m.c.) as afunction of chain length of surfactants in water is similarto the dependence of the solubility of n-alkanes (for example) in the same solvents.So, to a first approximation, the c.m.c.may be regarded as a " solubility " and thedriving force for micelle formation may be directly related to the properties of eachions of the surfactant. However, in the presence of organic additives, direct com-parison between c.m.c. and solubility data may be misleading: the high solubilityof many ionic surfactants in aqueous solutions compared with the low value of thec.m.c. precludes any attempt to separate excess and standard free energies in theformer case.Most information is thus derived from c.m.c. experiments alone.Interpretations of the variation of c.m.c. on addition of organic solvents are thusmost often based on assumed changes in the micelle i t ~ e l f , ~ ' ~ whether through itsdestruction or its penetration by the organic molecules, sometimes taking into accountthe change in the dielectric constant of the In particular, the possibilityof opposing behaviour of the anions and cations (preferential solvation) of thesurfactant towards the aqueous binary system is not generally disc~ssed,~ as thestandard partial molar free energies of the surfactant components are not known.We have recently lo* 'I determined the standard free energy of transfer AG," oftetrabutylammonium bromide (n-Bu,NBr) from water to water +acetone (AC)mixtures using a vapour pressure method.It was shown that the change of AG," withsolvent composition could be essentially accounted for assuming that the contributionof the organic cation could be calculated using the scaled-particle theory and that44or in salt solution 2 C . TREINER AND A . LE BESNERAIS 45of the anion ascribed to an electrostatic effect. The purpose of the present investiga-tion was to apply these ideas to ionic surfactants, which are chemically relatedcompounds, in the same solvent mixtures ; it was also thought interesting to compareAG," values obtained from c.m.c. data and by a vapour pressure method used atpre-micellar concentrations.As a consequence, the c.m.c. of the ionic surfactantschosen had to be high enough to avoid pre-micellar aggregation at the solute con-centration compatible with precise vapour pressure measurements, but not too highfor meaningful comparison with c.m.c. experiments ; for these reasons we have chosensodium decylsulphate (SDS) and decyltrimethylammonium bromide (DTMABr).The co-solvent is acetone (AC). Previous studies of single ion free energies oftransfer of simple 1 : 1 electrolytes have been made in water + AC mixtures,12 andsome c.m.c. experiments for ionic surfactants are known in these solvents.5* 9 - l3# l4Finally these compounds are well suited to vapour pressure measurements.THEORYGrunwald and Bacarella l5 have shown that the rate of change of the standardchemical potential Go of an electrolyte completely dissociated into free ions can beobtained (on the mole fraction scale) from the relationship(1)1000 a In (u,/u,) dlnY* %[ am 1, = & ~ + 2 ~ ~ ) m - 2 ~ ~ r ( ~ ) z l *al and a2 are the activities of each solvent, y* is the solute mean activity coefficient(yk + 1 when m + 0), rn its molality, Z1 the water mole fraction (Zl+Z2 = I),and r = (MI -M2)/M12, M l z = MIZl + MzZz where M1 and M2 are the molecularweight of each solvent.It has been shown 16* l7 that by measuring a G o / Z l forseveral values of Z1 and integrating the curve obtained, one can calculate the standardfree energy of transfer of a solute from a reference solvent (here water) to the differentsolvent mixtures.The method used to obtain BGo/dZl has been described previously in detail.16It has been shown that provided the solute is sufficiently diluted for y k to be calculatedby the Debye-Huckel equation, then the vapour phase composition y in equilibriumwith the solution can be calculated from the variation of the total pressure P withsolute concentration m using the Gibbs-Duhem equation.The activities a, and a2are then readily obtained assuming that the vapour behaves as an ideal gas(py and pg are the pure solvent vapour pressures). The introduction of the secondvirial coefficient of the gas mixture in the calculations results in a change of aGo/Z,well within experimental error.17* l 8 BGojaZl is finally calculated using eqn (1)again with the activity coefficient of the electrolyte obtained using the Debye-Huckelequation; the integration of BGo/8Zl with respect to 2, is performed analytically.EXPERIMENTALThe mixed solvent was degassed by freezing with liquid nitrogen, pumping and melting(5 cycles were necessary) in a 1 dm3 Pyrex flask; 5 cups containing the surfactant sampleswere added under vacuum to the solvent mixture using a cup dispensing device.The flaskwas thermostated at 25.000+0.003"C. The total pressure was measured on a TexasInstruments gauge with a sensitivity of 0.005 Torr46 AG," OF IONIC SURFACTANTSREAGENTSDTMABr (Eastman Kodak) was recrystallized three times from pure acetone and driedunder vacuum. SDS (Merck 99 %) was used without purification. Acetone (Merck,water content < 0.03 %) was used without purification; conductance water was used forthe acetone+ water mixtures.RESULTSIt was essential for our vapour pressure method that the highest surfactantconcentration be below the c.m.c.values. These are 0.0646 and 0.035 mol kg-1 forDTMABr and SDS respe~tive1y.l~ Both are known to increase initially with theaddition of acetone, so we never exceeded m = 0.02 mol kg-l in our experiments.Pre-micellar association of surfactants in water has been assumed by a numberof author^.^ The effect of such a phenomenon in our case could be accounted forby a correction term in the Debye-Hiickel activity coefficient law which is used ineqn (1). However, even if some association of like charges occurs (dimers or trimers)the degree of association has been found to be small for surfactants of the type wehave studied ;20* 21 moreover, as their c.m.c. increase with addition of acetone, thedegree of association (which is related to the hydrophobic interaction) should beeven smaller in the mixed solvent used.In order to test further the importance ofthe dimerization phenomenon in the solute concentration range studied, we havemade a number of precise conductance measurements both in water and in an80 wt % water+acetone mixture. The data were treated by the complete Fuoss-Onsager equation as previously described.22 Table 1 presents a sample of theresults obtained. Inspection of the standard deviations reveals no systematic trendor anomalies : the solutes seem to behave as ordinary 1 : 1 electrolytes.We havethus assumed that no correction due to any aggregation of like charges has to bemade in the calculation of aG,/Z,.It has been shown previously lo that in the solute concentration range studied,the total pressure and vapour phase composition change with molality can beiepresented within experimental error by the linear relationshipsP =p,+kmy = yo+k'm (3)where po and yo are, respectively, the total pressure and mole fraction vapour phaseof AC with no solute. Tables 2 and 3 present the results obtained together with thestandard deviations (least-square curve fitting).The d G o / Z l values are the average of 3 or 4 experimental determinations. Thedata were treated assuming no short range ion-ion interactions (KA = 0) since whenthe ions are associated into ion pairs, eqn (1) may be written aswhere y$ is the mean activity coefficient of the free ions and a the degree of association.The derivative of a with respect to Z1 cannot be obtained experimentally with a highdegree of accuracy, especially when the association constants are rather small, soany attempt to take this effect into account results in a lower precision in aG,/aZ,in the present case.The error introduced by ignoring the association phenomenacan be evaluated by comparison with the careful study of de Ligny et al. on thesolubility of 1 : 1 electrolytes in hydro-organic mixtures,23 who take into account thedegree of dissociation of the ions in their calculation. The accuracy of AG," for thC .TREINER AND A . LE BESNERAIS 47TABLE 1 .-CONDUCTANCE OF SURFACTANTS IN AQUEOUS SOLUTIONS AT 298.15 KSDS n-DTMABrwater a 104c/mol-l dm-3 AlQ-1 cmz dm-3 lO4c/mol--1 dm-3 A/f2-1 cm* dm-3302.622 63.781229.5 56 65.022139.347 66.83786.035 68.30534.216 70.404A, = 74.55f0.03 SZ-'KA = 0GA = 0.015145.606 91.153117.414 92.32493.027 93.29753.165 95.70035.014 97.01421.781 98.196A, = 102.46+_0.02 i 2 - IKA = 2.7f0.3~TA = 0.02580 % AC lO4c/mol-1 dm-3 A/Q-1 cmz dm-3 lO4c/mol-1 dm-3 AjQ-1 cm2 dm-3109.665 50.62964.874 54.48441.866 57.54429.556 59.73019.666 62.1231 1.753 64.469A. = 73.3k0.3 C2-lKA = 51f2OA = 0.06611 1.872 59.72595.709 61.20343.582 67.42127.894 70.44515.01 7 73.812A, = 83.950.1 i2-'KA = 40fr2OA = 0.043a D = 78.54, q = 0.008 903 P ; b D = 29.6, q = 0.006 26 P ; C OA is the standard deviation of a run.TABLE 2.-cHARACTERISTIC PARAMETERS FOR VAPOUR-LIQUID EQUILIBRIUM a DECYLTRIMETEIYL-AMMONIUM BROMIDE IN WATER+ ACETONE MIXTURES AT 298.15 K--AGO/Z1 PolTorr Yo - k C -k'X102C k3 mol-1 J mol-11 .o0.98480.97460.96660.92790.82830.68330.44550.3658-51.6261.9972.03110.15159.02183.083 99.85205.80-0.52170.61330.67540.80600.86890.89010.90750.9082-4.5k0.314.8 f 0.118.7k0.941.5kO.126.6fr 0.19.7 f 0.9-9.3k1.1- 9.3 f 0.8I2.6k0.48.2f0.17.7k 0.47.3 k0.51.9kO. 1 o.o+ 0.0- 3.2f0.2- 3.4k0.1-12.2 k 0.544.3 f 0.648.8+ 1.751.8k 1.317.5 k 0.6- 3.1 fr 0.4- 23.3 & 0.6-26.8k 1.00953 5078521006555749040652685The values of dielectric constant D of the water + acetone mixtures necessary for the calculationof the activity coefficient were taken from ref.(23) ; b see ref. (10) ; C coefficients for eqn (3).TABLE 3 .-CHARACTERISTIC PARAMETERS FOR VAPOUR-LIQUID EQUILIBRIUM : a SODIUM DECYL-SULPHATE IN WATER + ACETONE MIXTURES AT 298.1 5 K- k C --0 - - - - - 1 .o0.9834 50.41 0.5217 6.0+ 0.1 4.1 0.1 20.4k0.2 1700.9294 108.66 0.8054 35.5+ 3.0 6.1 f 0.5 50.2fr1.3 24000.8301 161.33 0.8688 37-25 1.6 3.050.2 26.25 1.0 62500.6854 186.36 0.8901 10.1 k0.4 O.O+ 0.0 - 2.6f 0.2 75700.4489 200.88 0.9075 - 12.5k0.7 - 3.0f0.1 -24.9k0.4 43100.3650 204.58 0.9082 - 17.650.9 -4.7fr0.2 -35.2+ 1.0 1690a b C See footnotes to table 248 AGP OF IONIC SURFACTANTS2 surfactants is then estimated to be of the order of f 50 J mol-l in the water-richregion and increases up to about +400 J mol-I in an 85 wt % water+AC mixture.DISCUSSIONThe main characteristics of our experimental results may be summarized asfollows : (a) AG," from water to water +AC mixtures is negative, passes through aminimum and increases in the AC-rich mixtures for the 2 ionic surfactants.Inaddition, an inflection point appears in the water-rich region, which corresponds tothe maximum in the variation of 8Go/8Zl with Z1 (see tables 2 and 3). The samebehaviour was found for tetrabutylammonium bromide which does not form micellesin these solvents (see fig. 1) lo and also in water+tetrahydrofuran and water+acetonitrile mixtures.ll So, from the view point of standard free energies, there isno qualitative difference between the 2 surfactants and the tetra-alkylammonium salt.(b) AG," is almost equal numerically for the 2 surfactants in the whole AC concentrationrange studied.These 2 points will now be considered in relation to the variation ofthe c.m.c. of surfactants with organic additives.I1.0 0.8 0.6 0.4FIG. l.-AGi (on mole fraction scale) as a function of mole fraction of water for n-Bu4NBr andn-DTMABr in water + acetone mixtures, from vapour pressure measurements. Upper curve,n-Bu4NBr ; lower curve, n-DTMABr.RELATION BETWEEN AG; AND c.m.c. CASE OF DTMABrThe results presented in tables 2 and 3 make use of the reasonable assumptionthat there is no pre-micellar aggregate at the surfactant concentration used in ourexperiments.The standard free energy of transfer of ionic surfactants may, inprinciple, be deduced from the variation of their c.m.c. on addition of organicmolecules. If it is assumed that the chemical potential of the surfactant in themicelle phase is equal to the chemical potential of the surfactant in the bulk phaseC . TREINER AND A . LE BESNERAIS 49and that the standard chemical potential of the surfactant in the micelle is independentof solvent composition, then eqn (5) may be applied ' 9 24c.m.c., fwc.m.c., fs AGP = 2RT In - +2RT In -where c.m.c.,, fw, c.m.c., and fs refer respectively to the c.m.c. and the activitycoefficient of the surfactant in water and in the mixed solvents.f w and fs can becalculated using the Debye-Huckel equation.We wanted to compare AG," obtained fr0m.c.m.c. and vapour pressure measure-ments. Unfortunately there are no c.m.c. data for the surfactants we have studied inwater + AC mixtures, so we have used instead for comparison with our results, those ofMiyagishi on dodecyltrimethylammonium chloride (DOTMACl) who apparentlycould observe a c.m.c. in the same solvents at 35°C up to a mole fraction of AC ofZ, =0.3. The c.m.c. of this surfactant in water was too low to permit precise vapour pres-sure measurements, but, as the change of the ratio c.m.c.,/c.m.c., with temperature, -.E-4 tI \\\\0.0 0 1 0.2 0.3Iz2FIG.2.-Comparison of A G values (on molarity scale) in water + acetone mixtures for n-DTMACI(as obtained from our vapour pressure method at 25°C) and n-DOTMACl [as obtained from c.m.c.data at 35°C using eqn (5)]. -, n-DTMACl ; - - - , n-DOTMACI.is rather ~ r n a l l , ~ we believe that the comparison between AG," as obtained from the2 methods will be significant, the only difference between the 2 surfactants being twoCH, groups. Using the experimental results of Miyagishi, AG," was calculated usingeqn (5). To make a more direct comparison between the c.m.c. and vapour pressuredata we have transformed our results on DTMABr into DTMACl using the additivityrule and the standard e.m.f. results of Bax et at.25 on HCI and HBr in water+ACmixtures. Fig. 2 presents thevariation of AG," with AC mole fraction for the 2 ionic surfactants, obtained fromvapour pressure and c.m.c.experiments. There is a clear parallelism between the2 curves. As expected AG," is more negative for DOTMACl, with two more CH2Finally, these were recalculated on the molar scale50 AG," OF IONIC SURFACTANTSgroups, than for DTMACl. A minimum is observed for both surfactants. Theminimum of the AG," function corresponds to the maximum of the AGO functioncorresponds to the maximum observed for the variation of c.m.c. with solventcomposition in the case of DOTMAC1.14 Because of the temperature differencebetween the 2 sets of data, comparison of the respective positions of the minima forAG: is not significant ; also, the value of 2, for which the minimum occurs dependson the concentration scale chosen for the calculation of AG,".When changing frommole fraction (table 2) to molarity scale (fig. 2) this value is shifted to lower 2,values [see ref. (26) for a discussion on the " cratic " factor].The similarity between the curves presented in fig. 2 for the 2 ionic surfactants isinteresting as it suggests that we do not need to consider the influence of the organicadditive on the micelles in order to explain the essential characteristics of the variationof c.m.c. with AC concentration. In particular, the fact that AG," goes through aminimum can easily be interpreted in a manner analogous to that proposed previouslyfor n-Bu4NBr.l0. l1 Bax et a l l 2 using an extrathermodynamic approach haveshown that the standard free energy of transfer of Br- (or Cl-) is positive from waterto water + AC mixtures (preferential solvation by water molecules).This behaviouris very common for the transfer of inorganic anions from water to aqueous binarymixtures. 27-3 *It follows that AG,"(+) for the individual organic cation is negative from waterto water +AC mixtures ; this behaviour is characteristic of aliphatic groups in thesemedia and has been attributed, in part, to the difference in the work of cavity formationin water and in the mixed solvents, as can be calculated, for example, by the scaled-particle theory.ll As the variation of AGF with solvent composition for each ion isgenerally not linear, the minimum observed in fig. 2 can be looked upon simply as aconsequence of the opposing behaviours of the anion and cation.The same obser-vation has been made for n-Bu4NBr in the same water+AC solutions.AG," is more negative for n-DTMABr than for n-Bu4NBr in the AC concentrationrange studied (fig. l), although there are three more CH2 groups in the former case thanin the latter. This may be interpreted as evidence for a larger cavity effect for a linearaliphatic chain than for a spherical solute with (nearly) the same number of CH2groups. Alternatively, one could argue that the van der Waals forces between theorganic ion and the AC molecules should be larger in the case of an aliphatic chainwhere all the CH2 groups are exposed to the solvent than in the case of a morespherical solute where some of the CH, groups are shielded.This ambiguity isinevitable in any theory which considers the effect of a solute in a solvent as made upof a cavity (volume) term and a specific interaction term : it is one of the weaknessesof the theory, especially when applied to non-spherical molecules (solute or solventmolecules). After the minimum value of AG," has been reached, a new trend isobserved. AG," increases for both electrolytes as the effect of the bromide ion becomespredominant, but the increase is faster for the surfactant than for n-Bu,NBr. Thisnew trend must be the consequence of ahead-group effect of the surfactant.The coulombic effect predicts a positive contribution to AGF from water towater + AC mixtures according to the equationwhere D, and Do are, respectively, the dielectric constant of the solvent mixture andpure water and the other symbols have their usual meaning.This contribution isopposite to that of the cavity effect : it is larger for the tri-methylammonium group,which has a smaller r+ radius than the tetrabutylammonium ion, and must be addeC . TREINER A N D A . LE BESNERAIS 51to the same electrostatic contribution due to the bromide ion. Thus AG,"(+, for thesurfactant tends to level off while that of the tetrabutylammonium ion decreases.Ralston and Hoerr 31 have measured the solubility of hexyl- and decylammoniumchloride in aqueous ethanol. They found a maximum solubility (minimum AG,) forthe dodecyl salt, which forms micelles in these solutions, but no maximum for thehexyl salt which forms no micelles.They concluded that the maximum observed[which is also found for sodium dodecylsulphate (SDOS) in water + dioxan mixturesfor example] is related to micelle formation. This interpretation is not necesserilycorrect. In order to get a minimum for AG," at a particular 2, value, contributionsfrom the anion and cation of the same order of magnitude are required. If theabsolute value of AG," for one ion of the electrolyte is very different from the other,than the minimum disappears. For example AG," for tetramethylammonium bromide(Me,NBr) is positive from water to water+AC mixtures l 2 withwhereas a minimum is found for n-Bu4NBr for whichIAG, (n-Me,N+)I < lAG,"(Br-)lIAGt(n-Bu,N+)I = lAG:(Br-)l.Qualitatively the same situation may occur for the hexyl- and dodecylammoniumchlorides. We know from extrathermodynamic assumptions that the free energy oftransfer is positive for the chloride ion from water to water +ethanol mixtures.28* 30The effect of this ion must be predominant in the whole ethanol concentration range(the solubility decreases from pure water to pure ethanol) for the salt with the smallestaliphatic hydrocarbon tail; it should be of the same order of magnitude for theanion and cation in the case of the dodecylammonium salt, the contribution of CH,groups to AGP for the transfer from water to ethanol being negative.32COMPARISON BETWEEN DTMABr AND SDS I N WATER+AC MIXTURESThe AG," values are very similar for DTMABr and SDS over the whole ACconcentration range.Emerson and Holtzer made the same observation for thec.m.c. of DOTMABr and SDOS in dilute AC solutions (Z2 < 0.08). We proposethe following explanation: each ionic surfactant might be considered, to a firstapproximation, as a 3 component electrolyte having a hydrocarbon tail, a positiveion and a negative ion. Then for our 2 surfactantsAG,"(DTMABr) = AG,"(Me,N+) + AG,"[(CH,>,] + AG,"(Br-)AG,"(SDS) = AG,"[CH,(CH,),] + AGtO(OS0;) + AG:(Na+).We have no single ion values for the Na+ ion but we have the data of Bax et a2.l2for the K+ ion; the behaviour of these 2 ions is very similar in aqueous systems.It can be seen then l 2 that the single ion values for Me,N+ and K+ are both positiveand almost equal from water to pure AC.Further, we can safely assume that thecontributions of the hydrocarbon tails of both surfactants having (nearly) the samenumber of carbon atoms are of the same order of magnitude. It follows that thecontribution to AG," of the OSO, group of SDS and the Br- contribution of DTMABrmust be of the same sign and numerically similar. This seems reasonable whencompared with the similar behaviour of inorganic anions such as the perchlorate ionin the same solvents. Fig. 3 compares the single ion free energies of transfer ofsome of the electrolytes discussed in this study.In conclusion the minimum in AG,O observed for SDS in water+AC mixtures isa consequence of the opposing behaviour towards the solvent of the 3 different part52 AG," OF IONIC SURFACTANTSof the surfactant. The hydrocarbon tail and the positive ion (Na+) contributionsare both negative because of a cavity effect for the aliphatic groups, as can be shownby Pierrotti's scaled particle theory,33 and a preferential solvation effect for Na+ bythe AC molecules ; these 2 effects dominate in the water-rich region [AG,"(CH3(CH2)J< 0, AGf(Na+) < 01.The contribution of the OSOY group to AG," [AG,"(OSO,) > 0must dominate in the AC-rich mixtures. The sum of these 2 opposing contributionsis again responsible for the minimum in the AGF function. In the case of solubilityor c.m.c. experiments a maximum would then be observed, as indeed is the case forthe solubility of SDOS in water + dioxane or dodecylammonium chloride in water +ethanol mixtures.0 0 2 0 4 0 62 2FIG.3.-Single ion AG; values in water + acetone mixtures (mole fraction scale) using the extra-thennodyanmic approach of Bax e f a1.12 (a) Br-; (b) n-Me4N+; (c) n-Bu4N+; ( d ) n-DTMA+.The main conclusion of this study is that the variation of the c.m.c. of ionicsurfactants with organic additives could be evaluated from a knowledge of thestandard free energies of the constituents of the surfactant. The interpretationwe have proposed for the variation of c.m.c. on addition of a typical organic additivesuch as acetone should apply to all organic additives which initially increase thec.m.c. of ionic surfactants. The case where the additive decreases the c.m.c. throughan assumed penetration of the micelle, as in the case of alcohol additives, will bediscussed in a forthcoming paper.C.Tanford, The Hydrophobic Bond (Wiley, New York, 1973), p. 14.P. Mukerjee, J. Phys. Chem., 1965, 69,4038.G . C. Krescheck, in Wafer, ed. F. Franks (Plenum Press, 1974), vol. 4, p. 99.Ref. (l), p. 46.M. F. Emerson and A. Holtzer, J. Phys. Chenz., 1967, 71, 3320.K. Shiramaya and R. Matuura, Bull. Chem. SOC. Japan, 1965, 38, 373.K. Shiramaya, M. Hagashi and R. Matuura, Bull. Chem. SOC. Japan, 1969, 42,1206.S . Miyagishi, Bull. Chem. SOC. Japan, 1976, 49, 34.lo C. Treiner and P. Tzias, A&. Chem. Ser., in press.C. Treiner, P. Tzias, M. Chemla and G. M. Poltoratskii, J.C.S. Faraday I, 1976,72,2007.l 2 D. Bax, C. L. de Ligny and A. G. Remijnse, Rec. Trau. chem., 1972,91, 1225.l3 S. Miyagishi, Bull. Chem. SOC. Japan, 1974, 47, 2972.ti N. Nishikido, Y . Moroi, H. Vehara and R. Matuura, Bull. Chem. SUC. 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Remijnese, Rec. Trau. chim., 1972, 91, 965.29 C. Treiner and P. Finas, J. Chim. phys., 1974, 71, 67.30 0. Popovych, Analyt. Chem., 1974,46,2009.31 A. W. Ralston and C. W. Hoerr, J. Amer. Chem. SOC., 1946, 68, 851.32 E. J. Cohn and J. T. Edsall, Proteins, Amino acids and Proteins (Reinhold, New York, 1943).33 R. A. Pierrotti, J. Phys. Chem., 1963, 67, 1840.P. Mukerjee, Complete table of critical miceile concentrations (N.B.S., Washington, 1967).(PAPER 6/917