J . Phys. Chem. 1985,89, 5308-5312
5308
Effect of Temperature on the Electrical Conductlvity and the Thermodynamics of Micelle Formation of Sodium Perfiuorooctanoate Pasupati Mukerjee,* School of Pharmacy, University of Wisconsin, Madison. Wisconsin 53706
Koichi Korematsu, Makoto Okawauchi, and Gohsuke Sugihara Chemistry Department, Fukuoka University, Fukuoka City 814-01, Japan (Received: January 2, 1985;
In Final Form: July 30, 1985)
Electrical conductivities of sodium perfluorooctanoate (NaPFO) in aqueous solutions have been measured at different temperatures, and critical micellization concentrations (cmc) have been determined from such data. An examination of the slopes of the specific conductivity-concentration curves above and below the cmc indicates a major role of the solvent fluidity. A semiempirical approach has been developed for micellar solutions which indicates the importance of an additional effect above the cmc, namely, an increase at higher temperatures of the fraction of counterions free to conduct current, a. It is suggested that the small changes in a with temperature can be used to calculate the changes in j3 with temperature where 6 is the absolute value of the slope of a plot of In cmc vs. In [Na+](cmc) when cmc values are determined in the presence of added sodium salts. p values of NaPFO thus determined show a close parallel to some directly determined values for the potassium salt, KPFO, at different temperatures obtained from the literature. Free energies and enthalpies of micelle formation have been estimated from the cmc and p values by using the mass-action model. It is shown that phase separation models give significantly different estimates of enthalpy values. The estimated changes in the partial molal heat capacities on micelle formation are much higher for NaPFO when compared to hydrocarbon surfactants. This has been ascribed to the more pronounced role of chain-water interactions and water structure effects for the fluorocarbon surfactant. Solubility data of fluorocarbon gases and volume changes on micelle formation have been found to be compatible with the observed effects. NaPFO and KPFO are shown to have very similar enthalpies of micelle formation although the cmc values are significantly different. This finding is shown to be compatible with small temperature effects on short-range interactions in concentrated electrolyte solutions of sodium and potassium salts as reflected in their activity coefficients.
Introduction This paper is concerned with the effect of temperature on the critical micellization concentration (cmc) of sodium perfluorooctanoate (NaPFO), its conductance below and above the cmc, and a comparative assessment of the enthalpy of micelle formation from cmc data using a mass-action and phase separation Slopes of specific conductance-concentration curves below and above the cmc have been determined and interpreted in relation to the increase in solvent fluidity with temperature and an additional effect above the cmc arising from a temperature dependence of the fraction of counterions, a,free to contribute to the specific conductance.3 On the basis of previous a semiempirical approach has been developed for estimating the effect of temperature on a which is found to be significant. Extending this semiempirical approach, the assumption has been made that the temperature dependence of a reflects the temperature dependence of p, p being the absolute value of the slope ,, vs. XN,t curves, where X,, is the mole fraction of the of In X surfactant ion at the cmc, and XN,+is the mole fraction of counterions at the cmc including contributions from any sodium chloride added as an electrolyte. From a known value of p at 30 OC,p values a t other temperatures have been estimated. The 0 values and the cmc data have then been used for thermodynamic analysis of micelle formation. Finally, some literature data6 on cmc and p values for a closely related system, potassium perfluorooctanoate (KPFO), have been reinterpreted and comparisons have been made with the thermodynamic data and derived values of fi for NaPFO.
Many approaches have been used in estimating free energies for the formation of ionic micelles from critical micellization concentration data.3s5vs-'o Of these, approaches based on detailed models of the electrical double layerss-10 are extremely sensitive to assumptions inherent in the models and do not lead to easy estimates of the enthalpy of micelle formation. The mass-action model'-* and the charged-phase separation can be used in relatively simple manners. The superiority of the mass-action model in describing many physical properties of nonionic and ionic micellar systems has been d e m o n ~ t r a t e d . * J ] - ~In~ the present paper, it is shown that the two models lead to significantly different estimates of enthalpy changes in micelle formation of ionic surfactants even though both use identical p and cmc values. Experimental Section The materials used have been described b e f ~ r e . ~ .Electrical '~ conductance measurements were made with a Beckman A.C. conductivity bridge, Model RC-18A.7 The temperature of the thermostat was controlled within fO.OO1 OC.
Results The cmc values were determined from plots of the specific conductance, K, against the molar concentration, c. Using additional density data, we recalculated the cmc values on a molal scale. These values are shown in Figure 1. the cmc values obtained from K vs. c plots are significantly higher than those (8) Stigter, D.; Overbeek, J. T. G . Proc. Int. Congr. Sur. Act., Znd, 1957 1957, I , 311.
(1) Mukerjee, P. J . Phys. Chem. 1962, 66, 1375. (2) Mukerjee, P. Ado. Colloid Interface Sci. 1967, I , 241. (3) Mukerjee, P.; Mysels, K.J.; Kapauan, P. J. Phys. Chem. 1967, 71, 4166. (4) Stainsby, G.; Alexander, A. E. Trans. Faraday SOC.1950, 46, 587. ( 5 ) Shinoda, K.;Hutchinson, E. J. Phys. Chem. 1962, 66, 577. (6) Shinoda, K.;Katsura, K.J . Phys. Chem. 1964, 68, 1568. ( 7 ) Sugihara, G . ;Mukerjee, P. J . Phys. Chem. 1981, 85, 1612.
0022-3654/85/2089-5308$01.50/0
(9) Stigter, D. J. Phys. Chem. 1975, 79, 1015. (10) Gunnarsson, G.; Joensson, B.; Wennerstroem, H. J . Phys. Chem. 1980, 84, 3114. ( 1 1) Elworthy, P. H.; Mysels, K. J. J. Colloid Sci. 1966, 21, 331. (12) Myscls, K. J.; Mukerjee, P.; Abu-Hamdiyyah, M. J . Phys. Chem. 1963, 67, 1943. (1 3) Mukerjee, P. In 'Micellization, Solubilization, and Microemulsions", Vol. 1 , Mittal, K. L., Ed.; Plenum Press: New York, 1977; pp 171-194. (14) Mukerjee, P.; Yang, Alex Y. S. J . Phys. Chem. 1976, 80, 1388.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5309
Sodium Perfluorooctanoate Micelles
TABLE I: Conductance Data and Derived Functions I 40
t
temp, OC
7''
20 25 30 40 45 50 60
1.002 0.8903 0.7975 0.6531 0.5963 0.5467 0.4666
X+Oqa
44.93 44.60 44.40 44.10 43.97 43.88 43.78
below cmc above cmc
58.0 56.5 56.7 56.4 56.6 56.7 57.1
35.3 34.2 34.1 35.3 35.9 36.0 36.5
a
Bb
0.459 0.455 0.454 0.464 0.470 0.471 0.475
0.533 0.536 0.538 0.528 0.522 0.521 0.517
and q values were estimated from data in ref 17. 7 is in CP units. b @ value at 30 'C independently determined from the variation of the cmc with added NaCI. Other i3 values calculated as 1 - a 0.008. I
20
0
40
60 TEMP (TI
Bo
Figure 1. Effect of temperature on critical micellization concentrations: sodium decyl sulfate (a), sodium perfluorooctanoate ( 0 ) ,potassium perfluorooctanoate ( 0 ) .
f 5 E
c
2 80V
'1
a .
-0 V
60 -
20
30
40 TEMP
50
60
PC)
Figure 2. Effect of temperature on the slopes of specific conductance concentration curves, d(103w)/dc, of sodium perfluorooctanoate: below cmc (0),above cmc (A).
obtained from A vs. c1/2 plots where A is the equivalent conductance. This trend has been noted before.I5 Some cmc data from the l i t e r a t ~ r eon ' ~ a hydrocarbon surfactant, sodium decyl sulfate, are also shown for comparison. The two systems have rather similar cmc values around 25 O C , but the effects of temperature on the cmc values of the two systems are quite different. The cmc values of NaPFO show a rather pronounced minimum at 45 OC. Figure 1 also shows cmc values of KPFO from the 1iteraturee6 Plots of specific conductance, K,vs. c for ionic surfactants are known to be approximately linear below the cmc and above the cmc, the slopes being different?J6 For a comparative examination of the effect of temperature on these slopes, values of d( lO'~/dc a t different temperatures were determined over the same concentration range, excluding data within 20--30% of the cmc where curvature effects are most pronounced. In these chosen regions, linearity was observed to hold within a variation of about 1% or less. Linear regressions of K vs. c data showed correlation coefficients significantly higher than 0.999. Any residual error of averaging can be expected to be reduced very significantly in the relative comparison of the data at different temperatures. Figure ~~
2 shows plots of d( 1 0 3 ~ ) / d values c below and above the cmc at different temperatures over the range of 20-60 "C. Both slopes increase with temperature, but the slopes above the cmc increase relatively more, particularly above 30 "C. Discussion Conductance Results. Aside from the intrinsic interest in the temperature dependence of conductance data above and below the cmc, the conductance data lead to an assessment of the temperature dependence of j3 which is required for thermodynamic analysis. For this reason, the conductance data are discussed first. The most important variable affecting conductance data at different temperatures is the fluidity of water. When the conductance of Na+ at infinite dilution, X+O, estimated from standard datal7 is multiplied by the viscosity of water, r), the product, X+Or) (Table I) shows only a slight decrease with temperature, the total change being about 2.6%. Thus, although the conductance of Na+ increases by a factor of 2.09 over this range, most of the variation is accounted for by the change in fluidity of water. Table I shows that the product of d(103r)/dc below the cmc of NaPFO and 9 decreases somewhat between 20 and 25 O C but then remains approximately constant over the remaining temperature range of 25 to 60 OC. It thus appears that the change in conductance of the surfactant salt in the monomeric state with temperature is primarily controlled by the fluidity of water. It has been pointed out before' that similar conclusions can be drawn when similar calculations are made using published data for sodium alkyl sulfates.I6 Over the temperature range of 20 to 50 O C where comparisons are possible, the slopes of K-c data for NaPFO below the cmc and similar reported data on a similar system, sodium decyl sulfate,16 are proportional to within a mean variation of less than 1%. In contrast to the behavior below the cmc, the product of d(1O3~)/dcand r ) above the cmc (Table I) shows a fairly systematic increase with temperature above 30 "C, the total change over the temperature range of 30 to 60 OC being about 7%. Since the slope above the cmc is primarily due to the conductance of micelles and the accompanying counterions and since the X+Op product for the counterion, Na', decreases slightly with temperature, the results indicate strongly that, with increasing temperature, a larger fraction of counterions can be considered to be free to conduct c ~ r r e n t .That ~ conductance data for sodium alkyl sulfates at different temperatures show the same pattern of behavior has also been pointed out some years ago.' To assess the effect of temperature on the average fraction of counterions which conduct current, a,we have extended the use of a semiempirical approach developed some years ago',' for estimating relative changes in cy in similar systems. It uses the equation d ( 1 0 3 ~ ) / d c= a(X+ + F p )
(1)
in which the left-hand side is the slope of the specific conductance curve above the cmc, X+ is the conductance of Na+ at the cmc,
~~
(15) Mukeriee, P.; Mysels, K. J. Norl. Stond. Ref. Dora Ser., Norl. Bur. Stand..1971, No. 36. (16)Goddard, E.D.; Benson, G. C. Can. J . Chem. 1957.35,986.
(17) Robinson, R. A.; Stokes, R. H. "Electrolyte Solutions";Butterworths: London, 1968;2nd ed.revised.
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The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
p is the electrophoretic mobility of micelles, and F is the Faraday constant. The equation involves several assumptions and approximations. For example, recent researchI8J9has given evidence for a prediction from the mass-action mode120.2'that the monomer concentration decreases somewhat above the cmc. Similarly, small changes in the equivalent conductances with concentration are expected. Many of these uncertainities are expected to cancel in the estimate of the small effect of temperature on a. A+ values at the cmc at different temperatures have been calculated from the equivalent conductance experimentally determined at the cmc, A, and a transference number, t+, of 0.7122 for Na+ estimated at 25 "C and assumed to be the same at all temperatures. This procedure is equivalent to assuming that the temperature effect on A+ and A- are the same. Since A-. is much less than A+, any uncertainty in t- has a relatively small effect on t + . If the previously estimated value of 3.9 X IO4 cm2 V 1s& for the mobility of NaPFO micelles is used,7 the value of a at 25 OC is calculated to be 0.455. This value is significantly higher than the value of 0.275 estimated for micelles of sodium dodecyl sulfate by the same proced~re.~ On the basis of this estimate of a at 25 "C, a at other temperatures can now be obtained from the equation
Following the arguments presented b e f ~ r e ,we ~ . ~have estimated the variation in 1.1 with temperature by assuming that 1.1 is inversely proportional to v, which is to be expected, and is also proportional to a. This last factor is expected to provide some correction for changes in micelle size. Table I shows the calculated values of a at different temperatures. The value of a decreases slightly between 20 and 30 OC and then increases by about 5% between 30 and 60 "C. If p is considered to be proportional to q-' alone, the estimated a values are slightly higher, by 0.001 at 20 OC, 0.004 at 40 OC, and 0.009 at 60 OC. This range of variation shows roughly the maximum uncertainties involved. A number of as yet incompletely understood factors related to properties of electrical double layers are likely to be responsible for the change in a with temperature. In order to estimate the effect of temperature on @ from the effect of temperature on a , we note that a crude interpretation of a as the "degree of dissociation" of the micelle would suggest that @ = 1 - a. A number of uncertainities pertain to the exact meaning of these q u a n t i t i e ~ . ~Empirically, .~~ however, it was found in the case of sodium dodecyl sulfate3 that the value of @, 0.69, obtained from the variation of cmc with counterion concentration, was comparable to the value of 1 - a , 0.725, where a was determined from an experimental estimate of 1.1. In the case of NaPFO, a value of 0.538 is obtained for the value of j3 from cmc variation with added NaCl at 30 0C.23 The a value in Table I would indicate a value of 0.546 for @ calculated as 1 - a. The agreement is again fairly good. This has been noted before7 although, unfortunately, a somewhat erroneous estimate of 0.56 for j3 at 30 O C was used. In view of the closeness of the absolute value of j3 a t 30 OC, obtained by the two methods, we have assumed that the relative changes in @ with temperature can be obtained from the effect of temperature on a (Table I). We, thus, calculate j3 for NaPFO as 1 - a - 0.008 at all temperatures. The discussion above and the method suggested are expected to be of some value in the interpretation and use of relatively easily determined precise conductance data in other systems in assessing temperature effects on a and j3. An error of 1% in d(103~)/dc above the cmc corresponds to a relative error of 0.003 in a or j3. The deduced values are subject to experimental verification when cmc data at different counterion concentrations and micellar mobilities at different temperatures become available for NaPFO. (18) Sasaki, T.; Hattori, M.: Sasaki, J.; Nukina, K. Bull. Chem. SOC.Jpn. 1975, 48, 1397.
(19) Kale, K. M.; Cussler, E. L.; Evans, D. F. J . Phys. Chem. 1980, 84, 593. (20) Murray, R. C.: Hartley, G . S. Trans. Faraday SOC.1935, 31, 183. (21) Mysels, K. J. J . Colloid Sci. 1955, 10, 507. (22) Mukerjee, P. unpublished work. (23) Mukerjee, P.: Yang, Alex Y. S.,unpublished work. Yang, Alex Y. S. Dissertation, University of Wisconsin, 1980.
Mukerjee et al. An important point to note in this connection is that @ values determined from cmc variation with counterion concentration for a closely related system, KPFO, 0.52, 0.51, and 0.49 at 30, 40, and 5 5 OC, respectively,6 show a close parallel to the @ values estimated in Table I for NaPFO. This provides additional support for the procedure adopted. Quite independent of the use we have made of a values in calculating j3, the temperature dependence of a is of some significance in understanding micellar properties. Thermodynamic Calculations Free Energies. Free energies of micelle formation have been estimated by using the mass-action n i ~ d e l . ' - ~This % ~ model was originally formulated for investigating ion distributions and explaining the Krafft point phenomenon.20 Later, a description of an ionic micelle as possessing an ideal charge which is a small fraction of the real charge was invoked and the approach was extended to the analysis of light scattering data2' and the calculation of free energies of micelle formation.24 In subsequent examinations of the it was suggested that the slope of In cmc vs. In (counterion concentration), Le., j3, should be used for such calculations of free energies using the mole-fraction concentration scale. Some of the possible uncertainties of the model and the role of ancillary corrections such as activity coefficients were also e ~ a m i n e d . ~An , ~ ideal charge model has been revived more recently.25 In this approach also, cmc values and counterion concentrations at the cmc are used but in conjunction with activity coefficients. Here we calculate the standard free energy change associated with micelle formation per monomer, AGO,, from the cmc value in the absence of added electrolytes from the simple equation 7
AGo,/RT = -( 1 / n ) In [0.02cmc/n]
+ In (0.98cmc) + j3 In (0.98cmc)
(3)
In this equation, all concentrations are in mole-fraction units. R is the molar gas constant and T i s the absolute temperature. n is the assumed degree of aggregation. It is also assumed that 2% of the surfactant is micellized at the experimentally determined cmc value. Absolute values of AGO, are only slightly affected by any other choice. Relative values of AGO, and enthalpy values are not affected to a significant degree. The first term on the right-hand side of eq 3 corresponds to the micellar concentration at the cmc, the second term to the surfactant species, and the third term to the counterions. The small contribution of the micelles to the counterion concentration at the cmc is neglected. Activity coefficients have not been used for reasons cited beforea3 These terms are small, cancel out more or less completely in the comparison of AGO, values for NaPFO and KPFO, and are relatively inconsequential in the calculation of enthalpy values from the temperature dependence of AGO,. The meaning and significance of the mass-action model for ionic ~urfactantsl-~ will be examined later in a reinterpretation of the model.22 It may be of some interest at this point to stress a point of similarity between the mass-action approach and that based on electrical double-layer theories. As noted before,2 when electrical double-layer theories are applied to the calculation of standard free energies of micelle formation,2*8,26 aside from a relatively small activity coefficient term for the surfactant ion of the order of O.ZkT/ion for NaPFO or KPFO where k is the Boltzmann constant, the main difference is that the term containing?!, in eq 3 is replaced by -F,/kT where F,, is the electrical free energy per monomer estimated from models of electrical double layers. In further analyses of the mass-action model to be presented later,22it will be shown that -Fel/kT and the term containing j3 in eq 3 are quite similar in form. For example, the -F,,/kT estimates26from the Gouy-Chapman theory for five different sodium alkyl sulfates at different NaCI concentrations can in each case of a surfactant be represented as 6 In XN,+where XN,+is the mole fraction of Na+ at the cmc, and (24) Phillips, J. N. Trans. Faraday SOC.1955, 51, 561. (25) Cutler, S. G.; Meares, P.; Hall, D. G. J . Chem. Soc.,Faraday Trans. I 1978, 74, 1758. (26) Huisman, H. F.Proc. K . Ned. Akad. Wef.,Ser. B 1964, 67, 407.
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5311
Sodium Perfluorooctanoate Micelles TABLE 11 Free Energies of Micelle Formation AGO,, kcal/mol AGO,, kcal/mol
temp,OC
NaPFO
20 2s 30 40 45
-6.1 1 -6.25 -6.39 -6.59 -6.61
KPFO' -6.42 -6.61
temp,OC
NaPFO
50 55 60
-6.16
KPFO" -6.19
-6.89
IO 85
-6.19 -6.85
"Calculated from cmc and @ values published by Shinoda and Katsura6 using eq 3. 6 is a constant. The value of 6 varies from 0.516 for sodium dodecyl sulfate to 0.410 for sodium octyl sulfate. The mean variations from this proportionality of Fel/kT to In XN,+are less than O.lkT for any alkyl sulfate system. In this interpretation, therefore, the main difference between the two approaches is that the mass-action model uses the experimentally determined fl In XNA+for assessing the electrical interactions whereas -FeI/kT is somewhat larger than 6. In the corresponds to 6 In X,,+. case of sodium dodecyl sulfate, for example, an estimate of 0.69 for p3 should be compared to the above estimate of 0.52 for 6. This difference is likely to be a measure of many well-known physical and mathematical deficiencies of the Gouy-Chapman type theories based on the Poisson-Boltzmann equations2 and will be examined later.22 It is interesting to note that the form of the mass-action eq 3 has recently received some support in a theory based on the Poisson-Boltzmann equation, although the calculated magnitudes of p differ significantly from experimental values.*' The AGO, values of NaPFO have been calculated by using eq 3 with an assumed n value of 15. Previously, a value of 20 was used for n.' Interpretation of I9F N M R data for NaPF023-28 suggests that 15 is a better number. Only small differences in AGO, are involved here. AGO, values obtained by using the mass-action model (eq 3) have also been calculated from cmc and p values for KPFO reported by Shinoda and Kat" assuming n to be 15 also. These AGO, data in Table I1 show that AGO, changes significantly with temperature for both systems and that NaPFO and KPFO have nearly identical AGO, values considering that an error of 0.01 in the estimated p value corresponds to an error of 0.07 in AGo,/RT. The deficiencies of phase separation models for micelle formation have been n ~ t e d . ~ $ " -If' ~the charged phase separation mode15s6is used on a formal basis to calculate the standard free energy change from the equation AGo,/RT = (1 + p) In cmc (4)
as is often done, the differences from calculations based on the mass-action model, eq 3, are primarily due to the term involving the micelle concentration in eq 3. This term tends to be very small when n is large and thus the charged phase separation model provides a fair approximation in such cases, particularly for relative comparisons. Enthalpy of Micelle Formation. The enthalpy of micelle formation, AHo,, has often been calculated by using a phase separation model, originally used by Stainsby and A l e ~ a n d e r , ~ according to the equation AHo, = - 2 R P ( d In cmc/dT)
(5)
In a modification of this phase separation model, the charged phase separation m ~ d e l ,the ~ , ~equation used is
AW, = -(1
+ p ) R P ( d In cmc/dT)
(6)
It was pointed out some years ago that it is necessary to take into consideration not only the temperature variation of the cmc but that of p as well in applying the mass-action model for calculating enthalpy changes.'.2 This point of view has also been adopted later by Hall and others.25 (27) Evans, D. F.; Mitchell, D. J.; Ninham, B . W. J . Phys. Chem. 1984, 88, 6344. (28) Funasaki, N.; Yang, Alex Y . S.;Mukerjee, P., unpublished work.
-9 5 2e
29
31
30
33
32
34
T - ' x IO'
Figure 3. AGO,/RTvalues for sodium perfluorooctanoate (0) and potassium perfluorooctanoate (A)plotted against 1/T. The error bar indicates the uncertainty due to fO.O1 in the @ value. TABLE III: Enthalpy of Micelle Formation, A H o , (kcal/mol)
est
temp, "C
mass-action model"
eq 6'
25 60 35 41.5 55 62.5 11.5
+2.2 +0.8 -0.3 -2.3 -3.3 -4.4
(1.6)
eq 5c
1.o -0.8
1.3 -1.1
-2.3 -3.3
-3.1 -4.6
"NaPFO and KPFO values combined. *Estimated by Shinoda and Katsura6for KPFO using the charged phase separation model, 6. The value at 25 OC corresponds to NaPFO. 'Estimated by using the phase separation model, eq 5, for KPFO. Since changes in p in the mass-action model are incorporated in AGO, values at different temperatures, AHo, can be readily determined from the slope of AGo,/RT vs. 1 / T plots (Figure 3). The data for NaPFO and KPFO here are sufficiently close to indicate that AHO, values obtained by using the mass-action model are very similar for the two salts. The AHo, values estimated for the three different models are given in Table 111. Because of the well-known difficulties of determining enthalpy values from van't Hoff plots, the A H o , values are unlikely to be more reliable than about f 0 . 5 kcal/mol, particularly at high temperatures. It is clear, however, that the mass-action model and the charged phase separation model give significantly different AHo, values even though both approaches use identical /3 and cmc values. These differences arise from the neglect of the temperature dependence of p in the charged phase separation model. The mass-action model estimates are more positive at 25 O C and significantly more negative at temperatures 35 OC and above. According to the mass-action model, the values of AGO,, AHo,, and the standard entropy change, AS",, associated with micelle formation are -6.25 kcal/mol, +2.2 kcal/mol, and 28 eu, respectively, at 25 O C . At 55 "C, the values change to -6.76 kcal/mol, -3.3 kcal/mol, and 11 eu. The general trends in AHo, and the ASo, values with temperature found for SPFO and KPFO are qualitatively consistent with those observed for hydrocarbon There are interesting quantitative differences, however. The change in heat capacity on micelle formation, ACpo,for the fluorocarbon surfactants is about -300 cal/(mol K) at 25 "C and -140 cal/(mol K) at 55 OC. These estimates are uncertain by about 20%. Nevertheless, there seem to be a pronounced effect of temperature on ACpo which is qualitatively similar to those reported on the changes in heat capacity on micelle formation (AC,) at the cmc measured by calorimetry on nonyltrimethylammonium bromide30 (29) Musbally, G. M.; Perron, G.; Desnoyers, J. E. J . Colloid Interface Sci. 1976, 54, 80. (30) de Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J . Colloid Inierface Sci. 1979, 71, 147. (31) de Lisi, R.; Perron, G.; Desnoyers, J. E. Can. J . Chem. 1980, 58, 359.
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The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
Mukerjee et al.
and sodium d e ~ a n o a t e . ~Between ' 5 and 45 O C , the value of AC, certainties. Since a major contribution to the highACpo values becomes more positive by 36 cal/(mol K) in the former case and in micelle formation must derive from the removal of chains from 24 cal/(mol K) in the latter. However, the magnitude of the water and the associated heat capacity effects, the fluorocarbon change in AC,' with temperature for the fluorocarbon surfactants surfactants may be expected to show greater ACpo values on is significantly greater. The absolute value of ACPoat 25 O C is micelle formation from the solubility behavior of fluorocarbon also much higher than the AC, value of -102 cal/(mol K) for a gases. Also consistent with this analysis is the finding that the comparable hydrocarbon surfactant, sodium decyl sulfate volume increase on micelle formation is more than twice as high (SDeS) .29 for SPFO than for SDeS,7 even though their cmc values are Both the higher numerical magnitude of ACPo itself for the similar. This indicates a more pronounced role of water-structure fluorocarbon surfactants and its temperature dependence are effects for SPFO as in the case of the heat capacities. qualitatively compatible with some deductions made earlier about Finally, we would like to draw attention to the similarity of the relative hydrophobic character of SPFO and SDeS3* SPFO NaPFO and KPFO in the derived thermodynamic quantities. In and SDeS have similar cmc values (Figure 1). At 25 O C , the free the case of dodecyl sulfates, it was found3 that the K+ salt shows energy of micelle formation, AGO,, for SDeS is -7.06 kcal/m01.~~ a slightly more negative AGO, than the Na+ salt by about 4.1RT. AGO, for SPFO (Table 11) is more positive by about 0.8 kcal/mol. Small differences in free energies arising from ionic specificity On the other hand, some surface tension and adsorption data at effects between even relatively similar counterions such as K+ and the air/water interface showed a reversal: the free energy of Na+ are to be expected because of short-range interactions in the adsorption of SPFO is considerably more negative than that of inner part of the double layer at the micelle-water interface where This apparently anomalous result counterion concentrations are expected to be high, up to several SDeS by about 3.2 kcal/m01.~~ could be rationalized by considering the interactions responsible m ~ l e s / l i t e r . ~ 'It~ ~is~of some interest to examine if any such small for the expression of hydrophobicity in surface activity and micelle difference in interactions of Na+ and K+ in these micelles can give f ~ r m a t i o n . ~In , ' ~the case of hydrocarbon surfactants it has been rise to significant differences in the values of AHo, for NaPFO shown that major contributions to free energies of adsorption and and KPFO. To the extent short-range interactions between ions micelle formation derive from the interactions of the chains with are reflected in molal activity coefficients (y) of electrolyte solutions at high concentration^,'^ y and the effect of temperature the surface in the former case and with each other in the case of micelles. These interactions along with the interactions responsible on y provide rough measures of the possible range of ionic specificity and enthalpy effects.22 Some typical data are given below for removing the chains from water produce the total hydrophobic for illustrative purposes. At 1 m concentration, the molal activity contributions to the free energy change^.^,'^ The heat of vaporization of perfluoroheptane, 8.69 kcal/mol, is considerably less c~efficients'~ of sodium and potassium chlorides are 0.639 (NaCI) than that for decane, 12.3 kcal/mol, indicating the weaker and 0.589 (KCl) a t the freezing points of the solutions, 0.657 (NaCl) and 0.604 (KCl) at 25 OC, and 0.655 (NaCl) at 60 OC. chain-chain interactions expected for SPFO as compared to SDeS At the same concentration, the activity coefficients of sodium and in their micelles.32 Thus the roughly similar free energies of micelle potassium acetates are 0.781 and 0.819 at their freezing points formation for SDeS and SPFO indicate a significantly greater contribution to the free energy arising from the removal of the and 0.757 and 0.783 at 25 O C . The chlorides and acetates were chain from water for the fluorocarbon surfactant. This factor chosen for illustrative purposes because they show a reversal of sequence between Na+ and K+ at both freezing temperatures and makes a proportionately greater contribution to the free energy 25 OC. They also show a reversal of temperature effects on y of adsorption of the fluorocarbon ~ u r f a c t a n t .Comparison ~~ of between these two temperatures: y values of the chlorides increase solubility data of hydrocarbon and fluorocarbon gases in water somewhat between the freezing points and 25 OC, whereas those provides further justification of the conclusion regarding the more of the acetates decrease somewhat. The important point is that important role of chain-water interactions in the case of the in both cases the relatiue values of y for Na+ and K+ salts remain fluorocarbon systems. It has been pointed out qualitatively that essentially the same at both temperatures. Thus the short-range the lower solubilities of fluorocarbon gases compared to hydroin these two model systems suggest that the AH', carbon gases in water indicate their greater h y d r o p h o b i ~ i t y ~ ~ , ~interactions ~ values for NaPFO and KPFO should not show any appreciable which is also reflected in the lower cmc values of fluorocarbon difference. The AGO, values of NaPFO and KPFO in Figure surfactants of the same chain length. The available data35,36 3 have essentially the same dependence on temperature, and, indicate that at low pressures CF4 is less soluble than CH4 by a therefore, the AH", for the two systems are essentially identical factor of 6.7 at 25 "C, CzF6 is less soluble than CzH6 by a factor of 32 at 25 "C, and C3Fs is less soluble than C3H8by a factor and bear out the expectations. Since the AGO, values were derived of 68 at 15 OC. The absolute magnitudes and the chain-length from /?values from different sources, the results provide strong effects are large. The partial molal heat capacities (cal/(mol K)) arguments regarding the consistency of the procedure and the associated with the process of solution have been estimated to be treatment employed in this paper. 50 for CH4 and 72 for C2H636compared to 98 for CF4 and 173 Acknowledgment. This material is based in part on work for C2F6.35 These considerably more positive values for the supported by the National Science Foundation under Grants fluorocarbon gases and the chain-length effect are noteworthy and ENG-78-16860 and CPE 8216450. appear to be real even after considerations of experimental unRegistry No. NaPFO, 335-95-5. (32) (33) (34) (35) (36)
Mukerjee, P.; Handa, T. J . Phys. Chem. 1981, 85, 2298. Mukerjee, P. Kolloid 2.2.Polym. 1970, 236, 76. Mukerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, No. 9, 239. Wen, W.-Y.; Muccitelli, J. A. J . Solution Chem. 1979, 8, 225. Wilhelm, E.; Battino, R.; Wilcock, R. J. Chem. Reu. 1977, 77, 219.
(37) Mukerjee, P. J . Phys. Chem. 1962, 66, 1733. (38) Mukerjee, P.; Cardinal, J. R.; Desai, N. R. In "Micellization, Solubilization, and Microemulsions", Vol. 1 , Mittal, K. L., Ed.; Plenum Press: New York, 1977; pp 241-61.
