6596
J. Phys. Chem. B 1998, 102, 6596-6600
Comparison of the Calorimetric and van’t Hoff Enthalpy of Micelle Formation for a Nonionic Surfactant in H2O and D2O Solutions from 15 to 40 °C Gordon C. Kresheck† Department of Chemistry, UniVersity of Colorado at Colorado Springs, Colorado Springs, Colorado 80933-7150 ReceiVed: April 28, 1998; In Final Form: June 10, 1998
Relative partial molar heat content curves were obtained for a nonionic surfactant, dodecyldimethylphosphine oxide, in H2O and D2O solutions from 15 to 40 °C by titration calorimetry. The critical micelle concentration (cmc) was always lower in D2O than in H2O. The enthalpy change for micelle formation was determined at 25 °C from integration of an abbreviated form of the van’t Hoff equation assuming a temperature-independent aggregation number and heat capacity change to be 1.13 ( 0.14 and 1.75 ( 0.14 kcal/mol in H2O and D2O, respectively. The corresponding calorimetric values were 1.66 ( 0.03 and 2.07 ( 0.02 kcal/mol. The change in heat capacity obtained from the van’t Hoff equation was -113 ( 17 cal/mol-K in H2O and -140 ( 11 cal/mol-K in D2O. The corresponding values determined from the temperature dependence of the molar enthalpy were -161 ( 2 cal/mol-K in H2O and -171 ( 2 cal/mol-K in D2O. The temperature dependence of the cmc was fairly well described in both solvents using the partial molar enthalpy and heat capacity changes that accompany micelle formation.
Introduction A description of the thermodynamic parameters that accompany micelle formation may be used to explore various mechanisms of the process itself and also to provide a model system for understanding more complex ones such as colloidal stability,1 protein unfolding,2 and complex formation.3 A relatively simple pseudo-phase-separation model has been used to relate the critical micelle concentration (cmc) of nonionic surfactants to the standard free energy change for micelle formation, and it’s temperature dependence has been used to obtain the corresponding standard enthalpy (H), entropy (S), and heat capacity changes (Cp).2 However, few comparisons of the results from such treatments with direct calorimetric determinations havebeen made.4 In view of recent developments in the sensitivity and precision of calorimeters that allow a determination of the cmc and enthalpy changes for long-chain surfactants, we investigated the thermodynamics of micelle formation for a nonionic surfactant, dodecyldimethylphosphine oxide (C12DPO), using an ultrasensitive titration microcalorimeter.5 The temperature dependence of the cmc was used to estimate the van’t Hoff enthalpy changes for comparison with the calorimetric values. Differences between using H2O and D2O as a solvent were also explored for comparison with a recent theory of hydrophobic hydration.6,7 There were no calorimetric data in the literature at that time that were appropriate for this purpose in the opinion of the author7 nor at this time to our knowledge. The temperature dependence of the cmc itself was adequately described by enthalpy and heat capacity changes that accompany micelle formation of the surfactant at the cmc. Experimental Section The sample of C12DPO used in this study was obtained from BioAffinity Systems (Rockford, IL). A 1% solution of the †
Work performed at Northern Illinois University.
surfactant in D2O was prepared and found to exhibit a single sharp 31P NMR peak located at 52.5 ppm relative to 85% H3PO4 and a distinguishing P-CH3 doublet8 centered at 1.5 ppm in the 31PMR spectrum, which were similar to the data previously given for the decyl homolog.9 Elemental analysis of duplicate samples yielded values of 68.3 ( 0.05% for carbon (68.2% theoretical) and 12.85 ( 0.1% for hydrogen (12.7% theoretical). Solutions of surfactant were prepared by mass in deionized water or D2O (99.8 ( 0.1%, MSD Isotopes). Heat of dilution experiments using a MicroCal ITC titration calorimeter (MicroCal, Inc., Northampton, MA) were conducted as previously described.10,11 Stock solutions of 5.89 mM C12DPO in H2O and D2O were diluted into H2O or D2O, respectively, at temperatures ranging from 15 to 40 °C. Injection volumes were normally 5-10 µL at the early stages of the titrations and 20 µL beyond the cmc. Final concentrations were converted to molality using the density of 0.9009 g/mL for C12DPO12 and 1.1045 g/mL for D2O.13 All integrations of the raw data and curve fitting were carried out using the MicroCal Origin software. Because each injection produced an incremental change in solute concentration, the observed heat changes could be considered as differential partial molar enthalpy changes.14 The observed values were extrapolated to infinite dilution to obtain a normalized titration curve that approximately corresponds to the relative partial molar enthalpy, L h 2 as a function of solute concentration. The data above an essentially linear region, m′, were then concisely represented with the equation
L h2 )
(A1 - A2) [1 + exp (m - mo)]/∆m
+ A2
(1)
The value of A1, corresponding to the left asymptote, is approximately equal to the value of L h 2 at m′, and A2, the right asymptote, corresponds to L h 2 at the end of the titration. The definitions of ∆m and mo are given later. A relative apparent
S1089-5647(98)02046-X CCC: $15.00 © 1998 American Chemical Society Published on Web 07/31/1998
Calorimetric and van’t Hoff Enthalpy of Micelle Formation
Figure 1. Raw data obtained from 40 successive 5-µL injections of an aqueous solution of 5.89 mM C12DPO into a 1.34-mL cell initially containing water following a 2-µL injection at 15 °C. The power values were integrated using the Origin software and converted to kcal/mol of injectant (surfactant). The final concentrations were converted from the molarity to molality scale after the enthalpy changes were determined. The data from the preliminary 2-µL injection were always discarded.
molar enthalpy curve was also obtained from the raw data (∑qi/ ∑ni) and the relative partial molar enthalpy was then calculated from eq 2
L h 2 ) ΦL + m(dΦL/dm)T,P
(2)
Kinetic results are consistent with the view that micelle formation occurs in a sequential manner with one monomer added at a time to produce large micelles with an average aggregation number equal to n, including the presence of rare intermediate-sized species.15,16 The overall process may be described as consisting of n individual steps of the form
M1 + Mn-1 h Mn
Kn-1 ) Mn/(M1Mn-1)
(3)
Holtzer and Emerson17,18 have shown that the standard free energy change for the reaction represented by eq 3 may be estimated by the equation
∆Gn ) RT ln(cmc)
(4)
The temperature derivative of eq 4 yields the familiar van’t Hoff equation with an additional term that describes the temperature dependence of the most probable aggregation number.18 Holtzer and Emerson go on to show that the electrical contribution to the additional term is quite large and limits the use of the van’t Hoff equation for interpretation of the enthalpy of micelle formation for ionic surfactants. However, it is possible that this limitation may not be as severe for nonionic surfactants as for ionic surfactants. A comparison of the enthalpy changes for micellization as determined by calorimetry with ones from a van’t Hoff analysis could provide such information. Results The heat of dilution was exothermic at lower temperatures and became endothermic at 40 °C. Typical results are given in Figure 1 for the dilution of C12DPO in water at 15 °C and the
J. Phys. Chem. B, Vol. 102, No. 34, 1998 6597
Figure 2. Plot of titration data (open squares) and empirical fit of titration data above 0.163 mm according to eq 1 (solid line), relative apparent molar enthalpy data (filled circles), and relative partial molar enthalpy curve (broken line) for C12DPO in H2O at 15 °C.
resulting titration curve is given in Figure 2. The shape of this curve resembles the titration curve of C10DPO at 25 °C previously reported,11 although the it was improperly identified as an apparent instead of partial molar enthalpy curve. The data were fit to a simple first-degree equation up to m′ (0.18 mm in H2O and 0.13 mm in D2O). The variation of the coefficients with temperature was described by a linear relationship with slopes of 201 ( 27 and 251 ( 37 cal/mol-C and intercepts of -6 ( 1 and -7 ( 1 cal/mol, in H2O and D2O, respectively. Correlation coefficients of 0.85 and 0.93 described the data. The relative apparent and partial molar enthalpy curves obtained from the data contained in Figure 1 are also included in Figure 2. It may be seen that the titration curve is a good approximation of the relative partial molar enthalpy curve, which was calculated from the apparent molar enthalpy data. The only difference in general appearance of the data obtained at 15 °C and the data obtained at other temperatures in either H2O or D2O was the magnitude and/or sign of the enthalpy changes. The cmc was identified as the inflection point in the relative partial molar enthalpy curve (mo in eq 1). The value of ∆x from eq 1 reflects the steepness of the transition and averaged 0.031 + 0.007 for all of the H2O titrations, but was greater at 15 °C (0.033 ( 0.002) than at the other four temperatures investigated (0.026 ( 0.003) in D2O. The enthalpy of micelle formation corresponds to the difference between the partial molar enthalpy of the surfactant in the micellar and monomer state. It was obtained by extrapolation to the cmc from the initial and final linear regions of the partial molar enthalpy data, which were obtained from the apparent molar enthalpy. This procedure yielded a value of 2995 cal/ mol from the data found in Figure 2. The heat of micelle formation was also taken as the limiting value of the titration curve because the initial and final slopes were essentially flat. This result gave rise to an enthalpy change of 2979 cal/mol from the titration curve reported in Figure 2. This value was equal in magnitude but opposite in sign to the heat of dilution extrapolated to infinite dilution (which was very accurately known). The latter procedure was used to obtain all of the enthalpy of micellization data reported in this study. A summary of the results obtained for the cmc and ∆H° at temperatures ranging from 15 to 40 °C in H2O and D2O is given in Table 1. The cmc varied by only 10% over this temperature range, but ∆H° exhibited a large negative dependence on temperature,
6598 J. Phys. Chem. B, Vol. 102, No. 34, 1998
Kresheck
TABLE 1: Summary of the Results Obtained for the cmc and Heat of Micelle Formation of C12DPO in H2O and D2O from 15 to 40 °Ca H2O T (°C) n 15 20 25 30 35 40 a
cmc (mm)
D2O ∆H° (kcal/mol)
5 0.369 ( 0.029 3.34 ( 0.19 3 0.344 ( 0.019 2.42 ( 0.04 2 0.334 ( 0.004 1.66 ( 0.03 2 0.319 ( 0.012 0.84 ( 0.01 1 (0.325)b 0.06 3 0.331 ( 0.036 -0.72 ( 0.10
n 3 3 2 2 2 2
cmc (mm)
∆H° (kcal/mol)
0.323 ( 0.006 3.87 ( 0.16 0.290 ( 0.008 2.93 ( 0.24 0.276 ( 0.009 2.07 ( 0.02 0.261 ( 0.002 1.21 ( 0.03 0.263 ( 0.008 0.38 ( 0.03 0.264 ( 0.014 -0.42 ( 0.02
n ) number of trials. b Interpolated.
TABLE 2: Summary of the Results Obtained for ∆Cp° of Micelle Formation of C12DPO in H2O and D2O ∆Cp° (cal/mol-K) method 1 2 3 4 ref 19 ref 24
H2O
D2O
-157 ( 25 -113 ( 17a -155 ( 5 to -167 ( 7 -161 ( 2 -169 ( 17 -131c
-157 ( 32 -140 ( 11b -158 ( 2 to -185 ( 3 -171 ( 2 s s
a Reference temperature was 35 °C. b Reference temperature was 37.5 °C. c This value resulted from an extrapolation of the high concentration data.
reflecting the decrease in heat capacity that is known to accompany micelle formation of alkyldimethylphosphine oxide and other surfactants in water.19,20 Attempts were made to determine ∆Cp° by the following four methods. The cmc was fit to an empirical equation,21 and the first and second derivatives were used to obtain ∆H° and ∆Cp° according to eqs 5-7, although other fitting equations have been used recently4
ln(cmc) ) a + b/T + c ln T
(5)
∆H° ) R(-b + cT)
(6)
∆Cp° ) cR
(7)
The values for the coefficients obtained from fitting to this equation using the Origin software for the D2O solutions were 542 + 106, -24484 + 4764, and -79 ( 16 for a, b, and c respectively, and 539 + 85, -24120 ( 3807, and -79 ( 13 for a, b, and c, respectively, the H2O solutions. Similar values for these coefficients were reported21 to describe the temperature dependence of a different nonionic surfactant containing the same alkyl group by Olofsson. The second method involved a fit of the cmc data to an integrated form of the van’t Hoff equation assuming a temperature-independent heat capacity (eq 8), with the reference temperature, Tr, set as the temperature for which ∆H° ) 022
ln(cmc) ) ln(cmcr) - ∆Cp°/R {Tr/T - (1 + ln(Tr) ln(1/T)} (8) The third method used the temperature dependence of the partial molar enthalpy change and eqs 9 and 10, with the reference temperature equal to 298 K.
∆H° ) ∆Hr + ∆Cpr - BTr (T - Tr) + B/2 (T2 - Tr2) ∆Cp° ) ∆Cpr + B(T - Tr)
(9) (10)
Finally, eq 9 was used with B ) 0, which corresponds to the restriction that ∆Cp° did not vary over the temperature range investigated. In this case, this method is equivalent to Method 2, except the temperature dependence of the enthalpy rather than the cmc is used for fitting purposes. The results from each analysis are given in Table 2. The least arbitrary and most rigorous approach is to allow ∆Cp° to vary with temperature (Method 3), and the results from this analysis will be used for comparative purposes. There is a small difference in the value of ∆Cp°, considering the experimental errors, between using Method 3 or 4. Therefore, it may be concluded that ∆Cp° for C12DPO is slightly dependent on temperature as noted for other nonionic surfactants.23 However, there is a large difference
Figure 3. Plot of the cmc against temperature for C12DPO in H2O (filled squares) and D2O (open squares) solutions and values calculated from eq 8 using the data given in Table 3 (solid lines).
between the values of ∆Cp° determined from the van’t Hoff analysis (Method 2) and the direct calorimetric method (Method 3 or 4). The second-derivative approach (Method 1) gave a value that was equal to that obtained by Method 3 at 15 °C. It may also be pointed out that our earlier value obtained from continuous enthalpy titrations in H2O at four temperatures19 is within experimental error of the result from Method 4 (with no allowance for a possible temperature variation of ∆Cp° in either case). The value obtained from direct heat capacity measurements24 was slightly lower than our current calorimetric values. The van’t Hoff enthalpy change was determined from eq 10 with B ) 0 and the ∆Cp° value reported in Table 2 for Method 2 for comparison with the calorimetric values given in Table 1. The van’t Hoff enthalpy change ranged from 2.26 to -0.57 kcal/ mol in D2O and from 3.15 to -0.35 kcal/mol in H2O at 15 and 40 °C, respectively, whereas the calorimetric enthalpy change ranged from 3.87 to -0.42 kcal/mol in D2O and from 3.34 to -0.72 kcal/mol in H2O. The temperature dependence of the cmc was calculated from the calorimetric enthalpy of micelle formation and corresponding heat capacity changes assuming that the cmc corresponds to an equilibrium property of the system,25 where
R ln(cmc) ) R ln(cmcr) + [∆Hr - Tr∆Cp° + Tr2(B/2) (1/T - 1/Tr)] - (∆Cpr - Tr B) ln(T/Tr) (B/2) (T - Tr) (11) The results from this calculation are given in Figure 3 using calorimetric values of ∆H° and ∆Cp°. A summary of the
Calorimetric and van’t Hoff Enthalpy of Micelle Formation
J. Phys. Chem. B, Vol. 102, No. 34, 1998 6599
TABLE 3: Summary of the Values Used to Determine the Temperature Dependence of the cmc from 15 to 40 °C by the Calorimetric Methoda
of the values obtained by Method 1, although only calorimetry yielded data of sufficient precision to detect the isotope effect. The heat capacity changes determined from the use of the integrated van’t Hoff equation (Method 2) are ∼25% less than the calorimetric values with B ) 0 (Method 4). The value determined by extrapolation of the direct measurement of the heat capacity25 falls between these latter two values. The value of the cmc for C12APO in H2O, identified as mo, is in good agreement with the literature (0.327 ( 0.004 mm for our current value at 25 °C and 0.34 mm at 23.6 °C from surface tension measurements29). Our value at 30 °C (0.32 ( 0.01 mm) is a little lower than our previous value19 obtained from continuous enthalpy titrations (0.5 mM) or a value obtained from light scattering (0.57 mM30). It is not unusual to find slightly different values for the cmc for the same compound when determined by different methods.20 The surface tension method may probably be regarded as giving the more reliable determination. It is interesting that the standard enthalpy of micellization in H2O reported by Clint and Walker,29 which was derived from the tangent of a plot of ln(cmc) against 1/T, was 2.0 kcal/mol at 23.6 °C versus our partial molar enthalpy change of 1.66 ( 0.03 kcal/mol at 25 °C (Table 1). They also reported that the apparent molar value of ∆H° for C9DPO that they obtained from calorimetry (2.9 kcal/mol) was greater than their result from the temperature dependence of the cmc (2.75 kcal/ mol). Our plots of ln(cmc) versus 1/T (not shown) for C12DPO exhibited less curvature than the one cited by Clint and Walker for n-nonylmethyl sulfoxide (C9MSO), but the same trend clearly existed for C12DPO and C9MSO. Fairly close agreement exists between the data reported by Clint and Walker29 for C10DPO in water and our previous values for the cmc and partial molar enthalpy change. For example, the values for the cmc and ∆H° were 3.88 mM and 2.65 kcal/mol, respectively, at 23.6 °C from surface tension measurements and 4.185 ( 0.014 mm and 2.321 ( 0.005 kcal/mol, respectively, in H2O at 25 °C from calorimetry. Thus, the enthalpy change derived from the temperature dependence of the cmc using an equation of the same form as the van’t Hoff equation without a heat capacity term yields enthalpy data that agree with the calorimetric enthalpy data. The cmc of several ionic surfactants has been shown to be lower in D2O than in H2O.27,31-34 Data for nonionic surfactants are sparse,9,11 but consistent with the findings for ionic surfactants. Because nonionic surfactants do not dissociate to produce charged micelles and counterions, the dominant factor that leads to the formation of nonionic micelles must be favorable interactions between nonpolar side chains.35 This result reaffirms the conclusion that hydrophobic bonds are stronger in D2O than in H2O over the temperature range investigated and they become stronger as the temperature is raised.31 However, although electrostatic factors are not involved with nonionic surfactants, the possible effect of the variation of n with temperature could be responsible for differences between calorimetric and van’t Hoff enthalpy values.18 It is our opinion, and that of others, that differences between the molar enthalpy of a surfactant in micelles of different average sizes at a given temperature is not known, but it may be35 or is likely to be23 small. The fact that our titration curves level off just above the cmc is evidence that the molar enthalpy of the surfactant in the micellar state and the monomer concentration are not changing, even if n is changing, unless there is some unusual compensating effect taking place. Muller6,7 has recently adopted a hydrogen bond model of hydrophobic hydration to account for the thermodynamic
parameter
H 2O
D2O
∆Hr B ∆Cpr mo
1664 ( 30 cal/mol 0.5 ( 0.3 cal/mol-K2 -162 ( 2 cal/mol-K 0.334 ( 0.004 mm
2068 ( 20 cal/mol 1.1 ( 0.1 cal/mol-K2 -174 ( 1 cal/mol-K 0.276 ( 0.009 mm
a
Method described in text.
TABLE 4: Summary of the Deuterium Isotope Effect on the Thermodynamics of Micelle Formation for C12DPO at Various Temperatures T (°C)
-∆∆G° (cal/mol)a
∆∆H° (cal/mol)b
∆∆S° (cal/mol-K)
∆∆Cp° (cal/mol-K)c
15 20 25 30 35 40
5 38 51 58 66 75
530 510 410 370 320 300
1.86 1.87 1.55 1.41 1.25 1.19
-18 -15 -12 -9 -6 -3
a Concentration units of mole fraction were used for this calculation. Data from Table 1 were used for this calculation. c ∆∆Cp° was determined from eq 10 using the values of ∆Cp° and B given in Table 3.
b
quantities required for this calculation is given in Table 3. However, the calculated values are not as temperature dependent as the experimental ones. The need to use partial molar values for this purpose was recently emphasized by Desnoyers and Perron.25 Finally, the deuterium isotope effect on the thermodynamic parameters, ∆∆Y°, for micelle formation was determined, where
∆∆Y° ) ∆Y°(D2O) - ∆Y°(H2O)
(12)
The values of ∆Y° corresponding to the standard free energy and entropy changes were evaluated at each temperature investigated using eqs 13 and 14, respectively
∆G° ) RT ln {cmc(D2O)/cmc(H2O)}
(13)
∆S° ) ∆H° - ∆G°/T
(14)
This procedure is the same as that used previously to determine other solvent effects on micelle formation, making use of a phase-separation model and a Clausis-Clapeyron type of equation.2 A summary of these values is given in Table 4. The standard free energy change (∆G°) for micelle formation is more favorable in D2O than in H2O at all temperatures. The difference in free energy change is less favorable at 15 °C (-5 cal/mol) than at 40 °C ( -75 cal/mol). Both the standard enthalpy and entropy change decrease with an increase in temperature. The difference between the standard partial molar heat capacity for micelle formation in D2O and H2O becomes less negative as the temperature increased. Discussion The sigmoidal shape of the titration curves observed at all temperatures in H2O and D2O for C12DPO resembled the sigmoidal shape reported for D10DPO.11 The partial molar enthalpy data for these long-chain alkyldimethylphosphine oxides resemble those of other long-chain nonionic surfactants26 rather than ionic surfactants.27,28 Heat capacity changes determined for micelle formation from the calorimetric enthalpy change are within experimental error
6600 J. Phys. Chem. B, Vol. 102, No. 34, 1998 changes that accompany the transfer of nonpolar solutes from H2O to D2O. He indicated that according to his model, the excess molar heat capacities of nonpolar solutes should be 10 to 15% larger in D2O than in H2O, but data available at that time were not accurate enough to allow a test of that conclusion.7 Our results for the difference between the values for micelle formation (Table 4) correspond to the transfer of a surfactant monomer at infinite dilution from D2O to H2O to the extent that the thermodynamic properties of the surfactant in the micellar form at a given temperature are the same in H2O and D2O. The transfer of the surfactant would include a polar and nonpolar contribution, but it would be expected that the entropy and heat capacity changes would be dominated by the hydrophobic effect. Our data would seem to allow a conditional test of his model, the conditions being the uncertainty about the relative importance of the polar and nonpolar portions of the surfactant molecule and the lack of scaling to take into account the differences in size of methane and our surfactant. The calculated heat capacity change by Muller for the transfer of methane from H2O to D2O at 25 °C (8 cal/mol-K) is less than the experimental value for the transfer of C12DPO (12 cal/mol-K). The sign of the calculated enthalpy and entropy changes for the second of the two parametersets reported by Muller is the same as our experimental values, and the same trend with temperature is noted with the data from both parameter sets and for our data. Subject to more pertinent tests, our results would seem to support some of the conclusions from the use of this theory. References and Notes (1) Desnoyers, J. E. J. Surface Sci. Technol. 1989, 5, 289. (2) Ray, A.; Ne´methy, G. J. Phys. Chem. 1971, 209, 801. (3) Ha, J. H., Spolar, R. S.; Record, M. T., Jr. J. Mol. Biol. 1989, 209, 801. (4) Onori, G.; Santucci, A. J. Phys. Chem. 1997, 101, 4662. (5) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L.-N. Anal. Biochem. 1989, 179, 131.
Kresheck (6) Muller, N. Acc. Chem. Res. 1990, 23, 23. (7) Muller, N. J. Solution Chem. 1991, 20, 669. (8) Laughlin, R. G. J. Org. Chem. 1965, 30, 1322. (9) Kresheck, G. C.; Jones, C. J. Colloid Interface Sci. 1980, 77, 278. (10) Kresheck, G. C.; Vitello, L. B.; Erman, J. E. Biochemistry 1995, 34, 8398. (11) Kresheck, G. C. J. Colloid Interface Sci. 1997, 187, 542. (12) Benjamin, L. J. Phys. Chem. 1966, 70, 3790. (13) Conway, B. E.; Laliberte´, L. H. J. Phys. Chem. 1968, 72, 4317. (14) Klotz, I. M.; Rosenberg, R. M. Chemical Thremodynamics, 4th ed.; Benjamin/Cummings Publishing: Menlo Park, CA, 1986; Chapter 18. (15) Aniansson, E. A. G.; Wall, S. N. J. Phys. Chem. 1974, 78, 1024. (16) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905. (17) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1965, 69, 3718. (18) Holtzer, A.; Holtzer, M. F. J. Phys. Chem. 1974, 78, 1442. (19) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (20) Kresheck, G. C. Surfactants In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum: New York, 1975; Vol. IV, pp 95-167. (21) Olofsson, G. J. Phys. Chem. 1983, 87, 4000. (22) Naghibi, H.; Tamura, A.; Sturtevant, J. Proc. Natl. Acad. U.S.A. 1995, 92, 5597. (23) Desnoyers, J. E.; Caron, G. C.; DeLisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397. (24) Perron, G.; Yamashita, F.; Martin, P.; Desnoyers, J. E. J. Colloid Interface Sci. 1991, 144, 222. (25) Desnoyers, J. E.; Perron, G. Langmuir 1996, 12, 4044. (26) . Andersson, B.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4087. (27) Maa, Y. F.; Chen, S. H. J. Colloid Interface Sci. 1987, 115, 437. (28) Desnoyers, J.; DeLisi, R.; Perron, G. Pure Appl. Chem. 1980, 52, 433. (29) Clint, J. H.; Walker, T. J. Chem. Soc., Faraday Trans 1 1975, 71, 946. (30) Herrmann, K. W.; Brushmiller, J. G.; Courchene, W. L. J. Phys. Chem. 1966, 70, 2909. (31) Kresheck, G. C.; Schneider, H. A.; Scheraga, H. A. J. Phys. Chem. 1966, 70, 2909. (32) Mukerjee, P.; Kapauan, P.; Meyer, H. G. J. Phys. Chem. 1966, 70, 783. (33) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 3320. (34) Chang, N. J.; Kaler, E. W. J. Phys. Chem. 1985, 89, 3996. (35) Olofsson, G. J. Phys. Chem. 1985, 89, 1473.
