J . Chem. SOC., Faraday Trans. 1, 1988, 84(2), 551-560 Thermodynamics of Micelle Formation of Alkali-metal Perfluorononanates in Water Comparison with Hydrocarbon Analogues Inger Johnson and Gerd Olofsson" Division of Thermochemistry, Chemical Center, University of Lund, P.O. Box 124, S-221 00 Lund, Sweden The enthalpy and heat capacity changes for micelle formation of lithium perfluorononanate in water have been determined from calorimetric measurements of differential enthalpies of dilution of concentrated surfactant solution. The final concentrations varied between 0.001 and 0.025 mol dm-3 and measurements were made at four temperatures between 15 and 43.5 "C. The enthalpy of micelle formation of sodium per- fluorononanate was determined at 30 "C from measurements of differential enthalpies of solution of the crystalline surfactant.The volume change accompanying micelle formation of sodium perfluorononanate at 30 "C was determined from density measurements. In evaluating the experimental results the concentrations of surfactant in monomer and micellar forms in solutions above the c.m.c. were computed using the thermodynamic model for the association of ionic amphiphiles proposed by Jonsson and Wennerstrom. At ambient temperatures the perfluorononanate salts give closely the same enthalpy and volume changes of micelle formation as the hydrocarbon analogues. However, the heat capacity change is larger, probably stemming from a larger partial molar heat capacity contribution of the perfluoroalkyl group in the aqueous, monomeric amphiphile. The larger size of the perfluoroalkyl group means that there will be a larger number of water molecules in the first hydration layer around a perfluoroalkyl group than around the analogous alkyl group.Thus the stronger hydrophobic character of perfluorocarbon surfactants compared to the hydrocarbon analogues may be ascribed to the difference in size between the two types of hydrophobic groups. There is considerable interest in the physicochemical properties of fluorinated surfactants, but so far little thermodynamic information is available. Perfluorocarbon surfactants behave in a way similar to hydrocarbon surfactants in the formation of micelles above the critical micelle concentration (c.m.c.). However, they are more surface-active than their hydrocarbon analogues and their c.m.c.is close to that of the analogous hydrocarbon surfactant having a 1.5 times longer carbon chain.l The Krafft point, c.m.c. and surface tension of a number of aqueous perfluorinated surfactants have been studied by Shinoda and coworkers.1.2 Phase equilibria in binary systems of water and heptadecafluorononanoic acid and a number of its salts have been investigated by Fontell and Lindman.3 From these studies we concluded that the micelle formation of lithium perfluorononanate could be studied conveniently by calorimetry over an extended temperature range and that the results would be representative for other alkali- metal salts. In this paper we report calorimetric measurements of lithium per- fluorononanate leading to values of the enthalpy of micelle formation at four temperatures between 15 and 43.5 "C.The enthalpy and volume changes for micelle formation of sodium perfluorononanate at 30 "C have also been determined. The 551552 Thermodynamics of Micelle Format ion thermodynamic quantities of micelle formation are defined as the difference between the partial molar quantity of the amphiphile in the micellar state just above the c.m.c. and the partial molar quantity of the monomer at the c.m.c. It is now well established that for ionic amphiphile systems the monomer concentration decreases with increasing amphiphile concentration above the c . ~ . c . ~ - ' It is therefore necessary to evaluate the composition of the reaction solutions in order to derive a correct value of the partial molar quantity for the micellized amphiphile.' In a previous paper,' we have shown that this can be achieved by applying the thermodynamic model for the association of ionic amphiphiles proposed by Jonsson and Wennerstrom.'O-12 Materials Experimental Lithium heptadecafluorononanate, LiPFN, and sodium heptadecafluorononanate, NaPFN, used in the calorimetric measurements were the same preparations as described in ref.(3) and were kindly provided by Dr Fontell. The solutions of NaPFN for the density measurements were prepared by neutralizing heptadecafluorononanoic acid, HPFN (Riedel-de-Haen, West Germany) with aqueous sodium hydroxide. The purity of HPFN was checked by titration with sodium hydroxide and found to be better than 99.9 wt %. Reagent-grade water produced by a Milli-Q filtration system was used to prepare solutions.The density of 20.04 wt % LiPFN solution used in the calorimetric measurements was determined using a pycnometer and was found to be 1.098 0.001 g at 25.00 "C. The density of dilute solutions of NaPFN was measured using a Paar density meter DMA60 1. Calorimetry An LKB Batch microcalorimeter modified for titration (LKB model 2 107-357) was used for titration calorimetric measurements at 25, 35 and 43.5 "C. The reaction and reference cells, made of 18-carat gold, were filled with 5.00 cm3 pure water. While the sample of 20 wt % LiPFN solution was injected into the reaction cell, the same amount of water was introduced into the reference cell. The injection volume for each titration step was 10.59 mm3.For the titration measurements at 15 "C, an LKB-8721 reaction- solution calorimeter with a 6 cm3 glass vessel was used. The sample solution was titrated into the glass vessel by means of a stainless-steel capillary tube (length 1 m, i.d. 0.27 mm), fastened by epoxy resin to a Hamilton gas-tight syringe (1710 LT). The capillary tube passes through a tube (i.d. 1 mm) mounted in a slit at the inside of the stirrer holder and ends ca. 15 mm below the surface of the calorimeter liquid. The syringe is motor-driven and samples were injected at a rate of 0.17 mm3 s-l. The calorimeter was initially filled with 5.50 cm3 pure water and 10-25 mm3 of sample solution were injected in each titration step. The performance of this small vessel was checked and found satisfactory by measuring the enthalpy of solution of propan-1-01 in water at 25 "C.13 The measurements of the differential enthalpy of solution of crystalline NaPFN were made using an LKB-8721 reaction-solution calorimeter with a 25 cm3 glass vessel.Samples of amphiphile crystals were placed in cylindrical glass ampoules (1 cm3 volume) which had thin end walls and narrow necks which were sealed under low flame and detached. The measured enthalpy changes were corrected for a small endothermal background effect that was observed when breaking empty ampoules in the filled calorimeter vessel. The effect, which was found to be 0.05 0.01 J at 30 "C, is due mainly to the introduction of the small air bubble into the calorimeter liquid, which results in some evaporation.I .Johnson and G. Oiofsson 553 *t I 20 [ LiPFN]/mmol dm-3 T -14 t Fig. 1. Comparison between calculated (full line) and experimental (bars) titration curves at 15.1 "C. Results Differential enthalpies of dilution of 20 wt % solution of LiPFN have been measured as a function of total amphiphile concentration at 15.1, 25.0, 35.0 and 43.5 "C. The experiments consisted of successive injections of small amounts of the concentrated LiPFN solution into the calorimeter vessel initially containing pure water. The concentration change in each step was ca. 1 mmol dmP3 and the titration was ended at a total concentration of ca. 25 mmol dm-3. The measured enthalpy changes varied between 1 and 70 mJ. Results of a titration series at 15.1 "C are shown in fig. 1. The measured enthalpy changes An(obs) expressed per mole of added LiPFN are plotted against total LiPFN concentration in the calorimeter vessel.The lengths of the bars indicate the change in concentration in each step. Two titration series were made at each temperature. Three different situations occur during a titration series. When the final concentration is below the c.m.c., all micelles added will break up to give monomers and the measured enthalpy changes Az(obs) will include the enthalpy of dilution of the concentrated micellar solution, AH(dil), the enthalpy of demicellization and a contribution from monomer-monomer interactions. In the c.m.c. region only a fraction a of the injected micelles will dissociate and AH(obs) will consist of AH(di1) and a fraction of the demicellization enthalpy.As the concentration increases, the degree of dissociation will decrease and at a certain concentration c(a = 0) there is no demicellization and as a consequence no change in the monomer concentration. The observed enthalpy change at this concentration equals the enthalpy of dilution AH(di1) of the concentrated LiPFN solution to the final concentration c(a = 0). In experiments with final concentration above c(a = 0), AH(obs) will contain in addition to AH(di1) a contribution from micelle formation as the monomer concentration decreases with increasing total concentration. The difference between Az(obs) measured just above and below the c.m.c. is approximately equal to the enthalpy of micelle formation AH(mic), but in order to derive a more correct value the effect of the decreasing monomer concentration above the c.m.c.must be taken into account.' The concentrations of amphiphile in the monomer and micellar states have been evaluated as a function of total concentration applying the model for the association of ionic amphiphiles proposed by Jonsson and554 Thermodynamics of Micelle Formation Table 1. Calculated concentration of LiPFN monomers as function of concentration of LiPFN in micelles at 35.0 "C c(mic) c(mon) c(mic) c(mon) /mmol dm-3 /mmol dm-3 /mmol dm-3 / m o l dm-3 0.010 0.040 0.094" 0.150 0.500 0.800 1 .ooo 1 SO0 2.000 2.500 3.000 8.774 9.109 9.399 9.498 9.800 9.877 9.900 9.9 13 9.891 9.844 9.796 4.000 5.000 6.000 8.000 10.000 12.000 16.000 20.000 24.000 30.000 9.671 9.531 9.386 9.092 8.803 8.528 8.020 7.571 7.175 6.663 a C.m.c.Wennerstrom. The processes taking place in each titration step could then be quantitatively described. The computer program used for the calculations has been described previo~sly.~ The input parameters are temperature, micelle radius, number of monomers in micelle, counterion valency and c.m.c. To be able to estimate values of the radius of the micelle and the monomer number, it is necessary to know the volume of the amphiphile molecule. Comparison bFtween densities of perfluorinated and ordinary fatty acids gives a volume of ca. 400 A3 per LiPFN molecuje. From this volume a monomer number of 20 is estimated assuming a radius of 12.4 A, which is 8 of the radius of a small, spherical micelle of sodium dodecylsulphate.The radius is thus assumed to be proportional to the number of carbon atoms in the hydrophobic chain. The same values of micelle radius and monomer number have been used at the various temperatures. Starting values of c.m.c. were read off at the breaks in the titration curves, see fig. 1. The values were adjusted slightly to get the best fit between calculated and experimental titration curves. Concentrations of LiPFN in the micellar state and the corresponding monomer concentrations calculated at 35 "C are given in table 1. There are only small changes in the relative amounts of monomers and micellized LiPFN at the other temperatures. The 20 wt YO LiPFN titrand solution was estimated to contain 99.7% in the micellar state. The linear slope of the titration curves at concentrations below the c.m.c.indicates non-ideal behaviour of the monomer solutions. The increase in AH(obs) with concentration is the same within experimental uncertainties at the various temperatures, giving a value for the monomer interaction coefficient kmon of 102 dm3 kJ mol-2. This value is very close to the slope found for SDS soluti~ns.~ At concentrations above 16 mmol dm-3 the injected micelles are diluted and in each titration step a small amount of micelles is formed from monomers in solution. The slight negative slope in this region is the sum of changes in micelle interactions as the micelle concentration increases and the decreasing monomer-monomer interactions. The slope in this region is temperature-dependent and equal to - 9 dm3 kJ mo1-2 at 15.1 "C, - 23 dm3 kJ mol-' at 25.0 "C, -47 dm3 kJ mo1-2 at 35 "C and -56 dm3 kJ mo1-2 at 43.5 "C.If it is assumed that the presence of micelles does not influence the monomer-monomer interactions, micelle interaction coefficients kmic can be calculated using the value of k,,, given above. The following values of kmic (in dm3 kJ mol-2) are calculated: -23 at 15.1 "C, -34 at 25.0 "C, -55 at 35.0 "C and -63 at 43.5 "C.I. Johnson and G. Olofsson 555 The observed enthalpy changes in each titration step can be expressed as: ninj AH(obs) = An AH(mic) + ninjA H(di1) + An[c.m.c. - c(mon)] k,,, + (ninj + An)[c(mic) - c(mic, a = O)] kmic (1) where ninj is the amount of injected LiPFN (in the micellar state), An is the change in the amount of LiPFN in the micellar state, AH(mic) is the enthalpy of micelle formation from monomers at the c.m.c.to give micelles at c(a = 0), where the micelle concentration is c(mic, tc = 0). The concentration c(a = 0) was evaluated from the results of the computations of monomer concentration as function of micelle concentration, cf. table 1, and values of AH(mic) and AH(di1) were estimated from plots of AH(obs) us. total concentration. Values of An for each titration step were calculated and titration curves were computed by eqn (1). Only small adjustments of the preliminary values of the c.m.c., AH(mic) and AH(di1) were needed to give good agreement between calculated and experimental titration curves. As can be seen in fig. 1, the agreement is within experimental uncertainties. Values of the c.m.c., AH(mic) and AH(di1) giving the best fits are shown in table 2.Note that if the c.m.c. had been chosen instead as the reference concentration for the micellar state, it would have changed AH(mic) by less than 0.05 kJ m0l-l.' Curves representing the partial molar content of LiPFN relative to infinitely dilute solution (H-H") at various temperatures are shown in fig. 2. These were calculated using values of the c.m.c. and AH(mic) evaluated from the calorimetric experiments, values of c(mon) and c(mic) computed from the theoretical model and values of the interaction coefficients k,,, and kmic as described above. The decrease of AH(mic) for LiPFN with increasing temperature is not linear, the change being larger between 15.1 and 25 "C than that between the higher temperatures.From the results in table 2, ACJmic) at 25" is estimated to - 500 30 J K-l mol-l. Measurements were made of differential enthalpies of solution of crystalline NaPFN as function of total amphiphile concentration at 30 "C. The experiments consisted of measuring the enthalpy changes when breaking a series of ampoules containing ca. 35 mg of amphiphile in the calorimeter which contained at the beginning 25 cm3 pure water. Two series of measurements were made and each series consisted of the consecutive breaking of seven ampoules. The concentration change was ca. 3 mmol dme3 in each step. The experiments are in many ways analogous to the LiPFN dilution experiments, but the amphiphile is introduced in the form of pure compound instead of concentrated micellar solution.The results were evaluated in the same way as described for LiPFN, the only difference when using eqn (1) being that ninj is replaced by the amount of NaPFN in the ampoule and AH(di1) by the enthalpy of solution of crystalline NaPFN to give micelles, A$H at c(a = 0). The values of k,,, and kmic found for LiPFN were also used for NaPFN. The following values were derived: c.m.c. = 9.0f0.3 mmol dmP3, AH(mic) = 4.0f0.3 kJ mol-1 and AZCH = 24.5 f0.5 kJ mol-'. The enthalpy of dissolution of crystalline NaPFN to give monomers in infinitely dilute solution was estimated to be 19.8f0.5 kJ mol-'. All values refer to 30.0 "C. The value of the c.m.c. is in good agreement with the value reported by Kuneida and Shinoda.2 The densities of seven solutions of NaPFN with concentrations ranging from 4.7 x mol kg-l have been measured at 30.3 "C.Apparent molar volumes of the solute were calculated using to 35.4 x L'@ = M,/d+ 1000(l/d- l/dy)/m (2) where L'@ is the apparent molar volume of the solute, d and dy are the densities of the solution and of water, M , is the molar mass of the solute and m is the molality of the solution. In the calculations the value dy = 0.995 548 g cmP3 has been used. The results of the density measurements are summarized in table 3. The three solutions with concentrations below the c.m.c. contain NaPFN in the monomer state and the556 Thermodynamics of Micelle Formation Table 2. Values of the c.m.c., the enthalpy of micelle formation, AH(mic), and the enthalpy of dilution, AH(dil), determined for LiPFN from calorimetric measurements of differential enthalpies of dilution of 20 wt YO LiPFN solution c.m.c.A H(mic) AH(di1)" t/"C /mmol dmP3 /kJ mol-' /kJ mo1-I 15.1 10.9 & 0.3b 12.6 k 0.3b 0.3 f 0.2b 25.0 9.3 f 0.3 6.8 k 0.3 0.8 f 0.2 43.5 10.3 & 0.5 - 1.4k0.3 1.8k0.2 35.0 9.4 & 0.3 2.4 _+ 0.3 1.2k0.2 Dilution to c(a = 0) which was found to be c.m.c. +2.6 mmol dm-3. Error limits indicate estimates of the overall uncertainty of the values. values. t (c) 2 - 1 0- 20 [ LiPFN]/mmol dm-3 (d) -2 - Fig. 2. Partial molar enthalpy content of LiPFN in solution relative to infinite dilution (Z-H") as function of total concentration. (a) 15.1 "C, (b) 25 "C, ( c ) 35 "C, (6) 43.5 "C. Table 3. Results of measurements of densities of sodium perfluorononanate solutions at 30.3 "C m d v* m(mic) VJmic) /mmol kg-' /g /cm3 mol-' /mmol kg-' /an3 mol-' 4.689 0.996 773 224.4 6.650 0.997 285 224.3 8.683 0.997 790 227.2 20.61 1.000 761 231.8 12.48 236.0 23.64 1.001 524 231.8 15.85 235.0 31.19 1.003 403 232.3 24.22 234.3 35.35 1.004 368 234.4 29.35 236.3 V,(mon) = 225 & 2 cm3 mol-', V,(mic) = 235 1 cm3 mol-l.I.Johnson and G. Olofsson 557 calculated V, is the apparent molar volume of monomeric NaPFN, V,(mon). Above the c.m.c. the solutions contain both monomers and micelles and the calculated V, is the sum of contributions from Vo(mon) and the apparent molar volume of NaPFN in micelles V,(mic). The composition of the post-micellar solutions was computed as described previously and the concentrations of NaPFN in micellar form (in mmol kg-') are given in table 3, as are the derived values of V,(mic).As the solutions are dilute, V,(mon) and V,(mic) are close approximations of the respective partial molar volumes at the c.m.c. and the volume change for micelle formation AV(mic) can be calculated as AV(mic) = V,(mic) - V,(mon). This gives A V(mic) = 10 f 2 cm3 mol-' (at 30.3 "C). Discussion The substitution of fluorine atoms for hydrogen atoms in alkyl carboxylic acids leads to a larger hydrophobic group and an increased acidity. Both these changes may influence the aggregation behaviour of perfluorinated carboxylates. Our aim has been to determine thermodynamic properties for micelle formation of a typical perfluorinated carboxylate so that the effect of the fluorine substitution on micelle formation could be analysed by comparison with hydrocarbon analogues.We found that sodium decanoate is the only alkyl carboxylate that has been studied calorimetrically and for which reliable values of AH(mic) and AC,(mic) have been determined.'* At 25 "C AH(mic) = 8.75 kJ mol-'. It is derived as the difference between linear regions of the partial molar enthalpy below and above the c.m.c. extrapolated to the c.m.c. Exchanging lithium for sodium as counterion is not expected to influence AH(mic) significantly. Likewise, decreasing the alkyl chain by one CH, group will probably have a minor effect on AH(mic), as for instance nonyl- and decyl-trimethylammonium bromide were found to give closely similar AH(mic) at 25 "C, 0.20 and 0.25 kJ mol-l, re~pective1y.l~ Therefore lithium nonanate can be expected to give about the same AH(mic) as sodium decanoate.The value found for lithium perfluorononanate at 25 "C is 6.8 kJ mol-l, which is of the same order of magnitude as for sodium decanoate. The c.m.c. for LiPFN is 0.0093 mol dm-3, while it is 0.21 mol kg-l for sodium nonanate at 25 OC.16 This difference in the c.m.c. corresponds to a difference of ca. - 11 kJ mol-1 in the standard Gibbs energies of micelle formation AG: if it is calculated according to the multiple equilibrium model [AG; = (1 +p) RT In X(c.m.c.)],l' assuming the extent of counterion binding p to be the same and equal to 0.5.'' The stronger hydrophobic character of the perfluorinated surfactant leading to the lower c.m.c. is not seen in the enthalpy values and therefore can be ascribed to a more positive entropy of micelle formation. We find a value of - 500 J mol-' K-' for AC,(mic) of LiPFN at 25 "C, while ACJmic) for lithium nonanate is expected to be ca.-360 J K-' mol-'. The latter value is based on ACJmic) for sodium decanoate16 equal to -430 J K-' mol-' from which - 70 J K-' mol-', the increment to ACJmic) of a CH, group, has been s~btracted.'~ The lower AC,(mic) for LiPFN can be correlated with the larger molar volume of the perfluorinated amphiphile. The molar volume V(mic) of micellized LiPFN is ca. 235 cm3 mol-', while it will be close to 148 cm3 mol-' for lithium nonanate.20p21 The cause of the volume difference is the greater van der Waals radius of fluorine relative to hydrogen.The ratio of the volumes is in accordance with the observation by Shinoda et al. that the c.m.c. of fluorinated surfactants is close to that of an ordinary surfactant whose hydrocarbon chain length is ca. 1.5 times longer than the fluorocarbon chain.' If we assume that the milieu of the alkyl group in the micelles resembles that in liquid hydrocarbon, ACJmic) can be seen as the sum of the heat capacity contribution from changes in hydrophobic hydration of the alkyl chain and head-group contributions, ACJmic) = ACJhydr) + ACJHG). Thus for the hydrophobic group, micelle formation has the reverse characteristics of dissolution in water. Generally the surface area of non-polar solutes correlates with thermodynamic properties in water such as solubility,22 entropy changes 19 FAR I558 Thermodynamics of Micelle Formation for d i s s o l ~ t i o n ~ ~ - ~ ~ and partial molar heat capacity.26* 27 From the molar volumes the surface area of the C,F1, group can be estimated to be ca.1.25 times the surface area of the CgH17 group. The larger size of the perfluorocarbon chain will primarily affect AC,(hydr) but only secondarily the heat capacity contribution of the head group. We can therefore expect the heat capacity contribution from hydration ACJhydr) to be ca. 1.25 times larger for the C8F17 group than for the hydrocarbon group. The partial molar heat capacity in water, c;,2, of the octyl group can be estimated to be 784 J K-l mol-1 at 25 "C using the group contribution scheme.,' The heat capacity of liquid octane C,(l) is 254 J K-l mol-', which gives -530 J K-' mol-' for the heat capacity of dehydration of the octyl group, AC,(hydr) = C,( 1) - C;,2.The head-group contribution ACJHG) to AC,(mic) of lithium nonanate can then be estimated to be 170 J K-l mol-1 from ACJHG) = AC,(mic) - ACJhydr). For the perfluoro-octyl group ACJhydr) then becomes -660 J K-l mol-1 (-530 x 1.25), and ACJmic) for LiPFN can be calculated to be -490 J K-l mol-l. This estimate agrees well with the experimental value and the difference between ACJmic) for the hydrocarbon and perfluorocarbon nonanates can be fully rationalized in terms of the relative sizes of the hydrophobic groups. A much larger AC,(mic) has been derived for sodium perfluoro-octanoate from c.m.c. measurements between 20 and 60 "C and a value of - 1250 J K-' mol-' is reported at 25 0C.29 In view of the present result this value does not seem realistic.Probable reasons for the overestimate of ACJmic) are magnification in the successive differentiations of errors in derived values of c.m.c. and deficiencies in the relation expressing the temperature variation of the c.m.c. The similarity in the micellization properties of the alkyl and perfluoroalkyl- carboxylates is also seen in the volume change which is closely the same. Vikingstad et al. have determined A V(mic) for a series of sodiumalkylcarboxylates from both density measurements and conductance measurements at varying pressures.2o The agreement between the two methods was good. For R8C0,Na they found AV(mic) = 9.6k0.4 cm3 mol-1 and they observed a slow increase with increasing alkyl chain length from 8.9 cm3 mol-1 for R,CO,Na to 11.2 cm3 mol-1 for RllC02Na.20 We find AV(mic) = 10+2 cm3 mol-' for C,F17C0,Na, in good agreement with these values.A higher value of AV(mic) equal to 19.4 cm3 mol-' has been derived from a high-pressure study of C7F15C02Na.30 We believe that errors propagated in the derivation of A V(mic) at 1 atm? from the conductance measurements may be larger than that estimated by the authors and the reason for the discrepancy. Shinoda et al. have determined a value of 21.5 1 cm3 mol-l for AV(mic) of C7F17C0,H at 30 "C from dilatometric measure- m e n t ~ . ~ ~ Unlike alkanoic acids, perfluorocarbon acids form micelles and liquid crystalline phases in binary systems with water. In the study of phase equilibria in aqueous systems of perfluorononanoic acid and a number of its salts, Fontell and Lindman3 found that the aggregation behaviour of HPFN (and its dimethyl- and diethyl-ammonium salts) differed significantly from that of its alkali-metal salts.They ascribe the difference to a low degree of ionization of the aggregates. The perfluorononanoic acid would act as a weak acid in aggregates, while it is a fairly strong acid as monomers in aqueous solution. The perfluoro-octanoic acid can be expected to behave in a similar way' and the volume change observed for micelle formation would include the volume contribution from protonation. This contribution can be expected to be significant, as for instance the protonation of acetic acid at infinite dilution is accompanied by a volume change of 11.5 cm3 rnol-l.,l We suggest that the major part of the difference between our value of 10 cm3 mol-1 for LiPFN and the value of 21.5 cm3 mol-1 found for C,F,,CO,H may be due to the volume change from protonation of the acid.Thus there is no need to assume any difference between hydrocarbon and fluorocarbon groups in the strength of t 1 atm = 101 325 Pa.I . Johnson and G. Olofsson 5 59 interaction with water or perturbation of solvation water. The stronger hydrophobicity of perfluorocarbon surfactants as manifested by their high surface activity compared to the hydrocarbon analogues may well arise from the size difference leading to an increased surface area of the hydrophobic group. Note added in proof. Recently results of volumetric measurements on LiPFN solutions were Their values for V&mon), V#(mic) and A V(mic) are significantly higher than the values we find for NaPFN.Therefore we have made additional measurements on LiPFN solutions at 25 "C. The sample preparation, density measurements and evaluation of V4 were made as described for NaPFN. We find V&mon) = 223 + 1 cm3 mol-l, V4(mic) = 237f 1 cm3 mol-1 and AV(mic) = 14+2 cm3 mol-l, in good agreement with our results for NaPFN. The reason for the discrepancy between our results and those reported by La Mesa and Sesta is obscure. However, we note that they report values of c.m.c. for LiPFN and NaPFN that are less than half the values we find. Our values are in good agreement with those reported in ref. (2) and (1 8).The statement by La Mesa and Sesta that according to recent n.m.r. self-diffusion experiment^^^ NaPFN is almost completely associated at concentrations close to 4 x mol dmW3 appears to be a misunderstanding. The skilful1 assistance in the calorimetric measurements of Mrs S. Bergstrom and Miss C. Wigand is gratefully acknowledged. This work has been financially supported by the Swedish Natural Science Research Council. References 1 K. Shinoda, M. Hato and T. Hayashi J. Phys. Chem., 1972, 76, 909. 2 H. Kuneida and K. Shinoda, J. Phys. Chem., 1976, 80, 2468. 3 K. Fontell and B. Lindman, J. Phys. Chem., 1983, 87, 3289. 4 T. Sasaki, M. Hattori, J. Sasaki and K. Nukina, Bull. Chem. Soc. Jpn, 1975, 48, 1397. 5 E. A. G. Ananiansson, S. N. Wall, M. Almgren, H.Hoffman, I. Kielman, W. Ulbricht, R. Zana, 6 S . G. Cutler, P. Meares and D. G. Hall, J. Chem. Soc., Faraday Trans. 1, 1978, 74, 1758. 7 E. Vikingstad, J. Colloid Interface Sci., 1979, 72, 68. 8 K. M. Kale, E. L. Cussler and D. F. Evans, J. Solution Chem., 1982, 11, 581. 9 I. Johnson, B. Jonsson and G. Olofsson, submitted. J. Lang and C. Tondre, J. Phys. Chem., 1976, 80, 905. 10 G. Gunnarsson, B. Jonsson and H. Wennerstrom, J. Phys. Chem., 1980, 84, 3114. 11 B. Jonsson and H. Wennerstrom, J. Colloid interface Sci., 1981, 80, 482. 12 B. Jonsson, G. Gunnarsson and H. Wennerstrom, in Solution Behaviour of Surfactants: Theoretical and Applied Aspects, ed. K. L. Mittal and E. J. Fendler (Plenum Press, New York, 1982), vol. 1, p. 317. 13 D. HallCn, S - 0 . Nilsson, W. Rothschild and I. Wadso, J. Chem. Thermodyn., 1986, 18, 429. 14 R. De Lisi, G. Perron and J. E. Desnoyers, Can. J. Chem., 1980, 58, 959. 15 R. De Lisi, C. Ostigny, G. Perron and J. E. Desnoyers, J. Colloid Interface Sci., 1979, 71, 147. 16 E. Vikingstad, A. Skauge and H. Hsjland, J. Colloid Interface Sci., 1978, 66, 240. 17 P. Stenius, S. Backlund and P. Ekwall, in Thermodynamics and Transport Properties of Organic Salts, ed. P. Franzosini and M. Sanensi, IUPAC Chemical Data Series No. 28 (Pergamon Press, Oxford, 1980). 18 H. Hoffmann, G. Platz, H. Rehage, K. Reizlein and W. Ulbricht, Makromol. Chem., 1981, 182, 451. 19 G. M. Musbally, G. Perron and J. E. Desnoyers, J . Colloid Interface Sci., 1974, 48, 494. 20 E. Vikingstad, A. Skauge and H. Hrajland, J. Colloid interface Sci., 1978, 66, 240. 21 F. J. Miller, Chem. Rev., 1971, 71, 147. 22 R. B. Hermann, J. Phys Chem., 1972, 76, 2754. 23 S. J. Gill and I. Wadso, Proc. Natl Acad. Sci. USA, 1976, 73, 2955. 24 S. F. Dec and S. J. Gill, J. Solution Chem., 1984, 23, 27. 25 E. Wilhelm, R. Battino and R. J. Wilcock, Chem. Rev., 1977, 77, 219. 26 N. Nichols, R. Skold, C. Spink, J. Suurkuusk and I. Wadso, J . Chem. Thermodyn., 1976, 8, 1081. 27 S. J. Gill, S . F. Dec, G. Olofsson and I. Wadso, J. Phys. Chem., 1985, 89, 3758. 19-2560 Thermodynamics of Micelle Formation 28 Landolt- Bornstein, Zahlenwerte und Funktionen, II Band, 4 Teil Kalorische Zustandgrossen (Springer 29 P. Mukerjee, K. Korematsu, M. akawauchi and G. Sugihara, J. Phys. Chem., 1985, 89, 5308. 30 G. Sugihara and P. Mukerjee, J. Phys. Chem., 1981, 85, 1612. 31 K. Shinoda and T. Soda, J. Phys. Chem., 1963, 67, 2072. 32 C. La Mesa and B. Sesta, J . Phys. Chem., 1987, 91, 1450. 33 J. Carlfors and P. Stilbs, J . Phys. Chem., 1984, 88, 4410. Verlag, Berlin, 1967). Paper 7/584; Received 1st April, 1987