Thermodynamics of Micellization of Aerosol OT in ... - ACS Publications

J. Phys. Chem. 1994,98, 4713-4118

4713

Thermodynamics of Micellization of Aerosol OT in Binary Mixtures of Water, Formamide, Ethylene Glycol, and Dioxane Kallol Mukherjee, Dulal C. Mukherjee,t and Satya P. Moulik' Centre for Surface Science, Department of Chemistry, Jadavpur University, Calcutta 700 032, India, and Department of Pure Chemistry, University of Calcutta, Calcutta 700 009, India Received: January 14, 1994"

The results of critical micelle concentration of aerosol O T in pure and binary mixtures of water, formamide, ethylene glycol, and dioxane determined by the methods of conductance, surface tension, spectrophotometry, and calorimetry are presented. The cmc values by the different methods are in agreement with one another and have shown positive deviations with maxima in all the binary solvent mixtures a t characteristic compositions. In this behavior, mixtures containing water are distinctly different than those without water. The watercontaining mixtures have shown both negative and positive enthalpies of micellization whereas those without water are all associated with positive enthalpy. The entropies of micellization are all positive, and they nicely compensate the enthalpies of the process. The heat capacities of the resulting mixtures have evidenced weak interaction among the molecules of the mixed solvents.

Introduction Aerosol OT (AOT) is a versatile surfactant which can easily form both and reverse" micelles including microemul~ions*-~3 in polar and nonpolar solvents, respectively. In ternary mixtures with water and oil, it may exhibit formation of lamellar as well as liquid crystalline phases under specific environmental conditions.12J3 The surfactant is nontoxic and, therefore, can be used in pharmaceutical and medicinal preparations.1617 The characteristics and formation potential of biological microemulsions using AOT and edible oils were recently reported." In micellar enzymology, employment of reverse micelles of AOT has been found to be of great significance and a good number of studies in this area have appeared in the literature.'*-20 Although the basic understanding of the surface chemical properties of AOT in aqueous medium is fairly advanced, the knowledge of the thermodynamics of its micellization in nonaqueous media (both polar and nonpolar) and in mixed solvents (both aqueous-nonaqueous and nonaqueous-nonaqueous) is meagere4 Such information on other commonly used ionic and nonionic surfactants is, on the other hand, considerable.21-26 Very recently, a detailed study on the critical micelle concentration (cmc) and thermodynamicsof micellization of AOT in a number of pure nonaqueous solventswas made.27 The present study is, therefore, a complimentaryendeavor on themicellization characteristics of AOT in mixed-solvent media. Herein we report the thermodynamics of micellization of AOT in binary combinations of water, formamide, ethylene glycol, and dioxane through the measurements of critical micelle concentrations and enthalpy of micellization employing the methods of conductance, spectrophotometry, surface tension, and calorimetry. The determination of the enthalpy of micellization from the temperature effect on the critical micelle concentration is obviously associated with appreciable error and, therefore, has been avoided. The solvents chosen have ranged between high and low polarities. Some of the combinations have the characteristics of widely varying polarities and are expected to have a significant effect on the process of micellization and its energetics. One of the solvents, i.e. glycol, has biological importance with regard to the understanding of the hydrophobic effect in relation to protein denaturation2* It is expected that the present findings would + University of Calcutta. *Abstract published in Advance ACS Abstracts, March 15, 1994.

0022-3654f 94 f 2098-4113%04.5Q f0

help in the general understanding of the process of micellization of AOT in dual polar-nonpolar surroundings. Experimental Section Materials. AOT (99%pure) was obtained from Sigma. The water content determined by Karl-Fischer titration was 3% (wf w). The solvents formamide (Fa), ethylene glycol (Eg), and dioxane (Dx) were of G. R. E. Merck quality. Their purity was checked by the determination of density, refractive index, and specific heat, as reported earlier.27 Doubly distilled conductivity water of specific conductance 3-6 pS cm-' was used as the other solvent. The conductancemeasurementswere taken on a Jenway (&sex, England) conductometer with a temperature-compensated cell of cell constant 1.39 cm-I. A Shimadzu 160 A UV-visible spectrophotometer and a matched pair of 1-cm silica cuvettes were used for the measurement of absorbance of the surfactant solutions. The surface tension measurements were taken with a Kruss (Hamburg, Germany) tensiometer which can record surface tension with an accuracy of fO. 1 dyn/cm. A TRONAC 458 isoperibol calorimeter was used for the determination of the enthalpy of micellization and the heat capacity of the resulting solution. For the details of thermometric measurements we refer to our earlier publications,27~29.~O All measurements were duplicated, and the mean values are reported and used for calculation. The measurements were taken at constant temperature with fluctuations of fO.OlO. The temperature fluctuation of the calorimetric bath was f0.0002°.

Results and Discussion Dielectric Constant of the Mixed Media. The dielectric constants of the mixed-solvent media Wa-Dx, Wa-Eg, Fa-Wa, and Eg-Dx are taken from the Such values for Fa-Eg and Fa-Dx are not readily available. They are, therefore, calculated from the proportional contribution relation e = miti where Xi and et are the mole fraction and the dielectric constant of the ith component, respectively. The values may therefore grossly represent the polarities of the mixed media. CMC of AOT. The critical micelle concentrations (cmcs) of AOT determined by the methods of conductance, spectrophotometry, surface tension, and calorimetry are presented in Table 1. Several representative graphs are presented in Figures 1-3. 0 1994 American Chemical Society

4714 The Journal of Physical Chemistry, Vol. 98, No. 17, 1994

Mukherjee et al.

TABLE 1: Critical Micelle Concentration (cmc) of AOT in Mixed Solvents at 303 K cmc/m mol dm-3 mol fract XF €32 calorimetry spectrophotometry conductometry mol fract YGa 0.000 0.017 0.035 0.075 0.120 0.178 0.245 0.327 0.430 0.745

1.000 mol fract X g O.OO0 0.0 10 0.022 0.049 0.082 0.172 0.238 0.455 0.652 1.000

mol fract 92 0.00 0.22 0.30 0.39 0.49 0.72 1.oo

76.8 75.0 73.5 70.5 67.0 63.5 60.0 55.0 52.0 41.0 33.3

2.2 2.5 2.9 3.3 3.6 4.5 5.5 8.7 6.5 3.0

2.2 2.5

2.3 3.2 2.6 5.0

cmc/m mol dm-’ spectrophotometry

calorimetry

76.8 69.0 64.5 57.0 49.3 34.4 18.5 11.0 5.5 2.2

2.2 3.7 3.5 4.5 2.9 2.7 2.5 2.2 1.7

4.0 2.8 2.6

1.8

1.6

€34

3.6 7.0 6.4

3.0 0.9

1.5

€31

33.2 26.5 21.0 16.0 11.5 5.7 2.2

6.0

109 112 108 100 91

1.6 1.6 1.9 1.9 2.3

0.872 0.900 0.952 0.977 1.000

89 87 83 80 77

2.1 4.3 ‘3.0 2.8 2.2

mol fract 9 ;

6.0 3.6 2.8 3.6

0.00 0.05 0.17 0.32 0.52 0.65

2.5 2.6 2.5

cmc/m mol dm-3 calorimetry spectrophotometry 1.5 0.9 2.2 2.5 2.0 2.5 1.3 1.8

0.000 0.200 0.490 0.690 0.840

conductometry

2.0

3.3

mol fract 0.00

€33

cmc/m mol dm-’ calorimetrv surface tension

6

1.6 1.1

4.0 3.1 2.2

(D,a,) cmc/m mol dm-3 calorimetry

0.81

109.0 103.7 90.8 74.8 52.9 39.5 22.6

1.6 2.5 3.3 3.4 3.2 2.5 1.6

1.oo

2.0

1.8

e

(=it,)

cmc/m mol dm-3 calorimetry

0.24 0.43 0.58

109.0 90.8 76.5 65.0

1.6 2.6 2.6 3.0

0.75 1.oo

52.2 33.2

2.2 1.5

4.0 1.6

The elegence of the methods to determine accurate cmcs is evidenced in them. The calorimetric method was used for all six solvent compositions; the conductance, spectrophotometry, and surface tension methods were limitedly used. In all the procedures, the concentration corresponding to an abrupt change in a property has been taken to be the cmc point. It has been found that the results of different methods fairly agree except for pure water and two compositions (X, = 0.245 and 0.327) of Wa-Eg medium where the agreements with the conductance data are poor. For the binary mixtures of Eg, Fa, and Dx with water, the cmc values have evidenced maxima which are nearly a t the mole fractions of 0.33, 0.90, and 0.048 of the second component for the combinations Wa-Eg, Fa-Wa, and Wa-Dx, respectively. Recognizing that the cmcs of AOT in the pure solvents are close (Table 1) reveals that an appreciable increase in cmc in the mixtures supports the prevalence of an effect that counteracts hydrophobic association. The maximum cmcs in the mixed compositions of the other binary combinations of Fa-Eg, Eg-Dx, and Fa-Dx are also evident. The respective mole fractions of the second component are 0.58,0.30, and 0.32. The general pattern is therefore a positive deviation of cmc in all the binary solvent compositions studied. The polarity of the medium cannot be a primary guide for this effect. For example, the dielectric constant of the Fa-Wa mixture increases with increased Fa content and in Wa-Dx it decreases with Dx content but the cmc values show a maximum in both cases. This is also true for other binary solvent combinations. When the cmc (calorimetric) and the mole fraction (3 of the lower polar solvent in the mixture are plotted in a three-coordinate graphical format, the profiles fall into two groups (Figure 4). The Wa-Dx, Wa-Eg, and Fa-Wa constitute one group of solvent, and Eg-Dx, Fa-Dx, and Fa-Eg constitute the other. Two representations from each group are presented in Figure 4. The pattern of the first group is curly and erect while that of the second is humpy 2nd short. The rise and decline of

cmcaresharpin theformer andgradualin thelatter. The presence and absence of water decide the basic nature of the overall pattern. In the overall perspective, the maximum rise in the cmc in the studied mixed media corresponds to neither nearly equal mole ratios (of the binary solvent components) nor equal dielectric constants: therefore, the features of the variation of cmc on the solvent compositions cannot be accounted for mainly due to polarity effects. Interfacial Behavior. The surface tension measurements have helped to determine the area per molecule of AOT at the air/ solvent interfaces according to the relationZ9

-

rmax = ((1/4.61)RT) e lim ( d s / d log c) cmc where rmax, A, and c represent the maximum adsorption density, the surface pressure, and the mol dm-3 concentration of AOT in bulk, respectively. The T vs log c plots are shown in Figure 3. The minimum area per AOT molecule (Amin)at the interface has been obtained from the relation Ami,, = 1018/NT,,x where N is Avogadro’s number. It is observed from Table 2 that the Ami,, values range between 1.43 and 2.57 nm2. It is more in Fa than in Wa, and the Ami,, gradually increases and maximizes at 2.57 1 nmz with increased addition of Fa in Wa. The Ami,,in Fa is approximately twice that in Wa. Repulsion between AOT molecules is more in the amide surface than on water. The free energy of adsorption (AG:,) has been estimated from the It is less spontaneous at relation29 AG:,, = A G -~ (Tcmc/rmax). the air/Fa interface than at the air/Wa interface, and it is 1.64 times greater for the latter than the former. Free Energy of Micellization. The evaluation of the free energy of micellization (AGK) from the relation AGK = RT In cmc is

The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4715

Micellization of Aerosol O T v IV

Ill

I1

1

I1 40-

20

35

1 5 10

YI

< LD

9

Wa > Eg > Dx. In the Fa-Wa medium, the free energy maximum occurs a t XW, = 0.95, which in Fa-Eg and Fa-Dx are at XQ = 0.58 and XD, = 0.30. With decrease in polarity of the second component, the maximum is shifted toward

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Mukherjee et al.

The Journal of Physical Chemistry, Vol. 98, No. 17, 1994

0.2

0.4

0.6

0.8

1.0

Figure 4. Three coordinate representations for AOT micellization in different binary mixtures at 303 K. The directions of the axes representing X,

(mole fraction of second component), c (dielectric constant), and cmc are shown in the inset.

0 XS

XS

Figure 5. Plots of thermodynamic parameters of AOT micellization in different binary solvent mixtures at 303 K. The abscissa (X,) stands for the mole fraction of the second component. e = AG:, 0 = AS:, 0 = AH:.

higher mole fraction of the first. The same trend is also maintained in the Wa-Eg, Wa-Dx, and Eg-Dx media where the maxima in the free energy change are at X E =~ 0.38, XD,= 0.05, and X D , = 0.38, respectively. For Dx as a solvent component at XD,> O S , reverse micelle formation is probable and the data and their analysis are related to the behaviors of such microassemblies.

Enthalpy of Micellization. The enthalpies of micellization, AHo,, at lower mole fractions of the second components for Fa-Wa, Wa-Eg, and Wa-Dx are negative except for the first pair. In the other pairs, viz. Fa-Eg, Fa-Dx, and Eg-Dx, the micellization process is endothermic at all combinations. For pure solvents, however, the AH: values are also positive. For the

Micellization of Aerosol OT

The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4717 TABLE 3 Energetic Parameters of Micellization of AOT in Different Solvent Media at 303 K - AGL/kJ

AHL/kJ

X,

mol-’

mol-’

0.000 0.017 0.035 0.075 0.120 0.180 0.250 0.330 0.430 0.750 1.ooo

15.57 15.19 14.82 14.49 14.27 13.70 13.19 12.03 12.77 14.73 16.49

2.97 -0.27 -2.57 -6.83 -10.20 -14.40 -6.14 -5.47 -0.50 +0.24 +0.19

ASl/J

mol-’ K-l Wa-Eg 4.30 4.14 3.98 3.76 3.58 3.32 3.18 2.97 2.93

(lit 4.18) (4.10) (3.98) (3.76) (3.60) (3.42) (3.24) (3.07) (2.90)

2.38

(lit 2.41)

4.30 4.18 4.00 3.56 3.32 2.97 2.70 2.17 1.97 1.67

(lit 4.18) (4.06) (3.93) (3.68) (3.43) (2.92) (2.73) (2.17) (1.93) (lit 1.69)

54.5 56.0 53.5 52.0 50.0 47.1 37.6 39.2 44.5 61.0

2.38 2.68 2.93 3.14 3.47 3.68 3.90 3.98 4.14 4.30

(lit 2.38) (2.55) (2.90) (3.22) (3.60) (3.72) (3.90) (3.98) (4.06) (lit 4.18)

55.0 55.0 56.8 60.5 56.3 57.4 54.9

2.39 2.30 2.13 2.05 2.10 1.84 1.67

(lit 2.41) (2.22) (2.13) (2.06) (1.97) (1.88) (lit 1.69)

54.50 51.06 51.20 49.30 51.20 55.05

2.38 2.26 2.36 2.46 2.37 2.38

(lit 2.385) (2.393) (2.400) (2.404) (2.408) (lit 2.414)

54.50 50.60 48.25 48.12 49.50 54.45 60.90 54.90

2.38 2.28 2.19 2.09 1.92 1.80 1.75 1.67

(lit 2.385)

61.0 49.6 40.7 25.2 13.4 -2.3 23.2 21.6 40.5 49.4 55.0

Wa-Dx

Figure 6. Enthalpy and entropy compensation plot for micellization of AOT in different binary solvent mixtures. Line A: The present data with symbols 0, 0,0 , 0 ,$, and A representing Fa-Wa, Wa-Dx, Eg-

Dx, Fa-Eg, Fa-Dx, and Wa-Eg, respectively. Line B: Calorimetric results on TX-100 micellization in Wa-Eg taken from ref 24. nonionic surfactant Triton X-100 in Wa-Eg AH: (determined calorimetrically) is negative and passes through a maximum, whereas AH: in pure Wa and Eg are positive. The head group of TX-100 (9.5 ethylene oxide (EO) groups) can enter into dipolar interaction with both Wa and Eg, and the Wa-Eg interaction is also of the same nature. During micellization of AOT, Wa-Wa and Wa-Eg bonds are initially broken (endothermic process) and they are partially reformed in the end (exothermic process). The resultant enthalpy is positive if the endothermicity of the initial process exceeds the exothermicity of the final process. TX-100 micellization in Wa-Eg has been found to follow this trend. The magnitudes of AH: are also of the same order. The enthalpies of micellization of AOT are all positive in the pure solvents herein studied.27 The reports of other workers also support this. Jha and AhluwaliaZ4have found negative enthalpy from 10% (v/v) of Eg, i.e. XQ 2 0.035, for the micellization of Triton X-100 in Wa-Eg medium. Similar are the results of Koshy and RakshiP on Brij-35 in aquopolyethylene glycol medium. In the present study, negative enthalpy has been found up to XQ d 0.45 in Wa-Eg, XD, d 0.08 in Wa-Dx, and X F d~ 0.30 in Fa-Wa media, and the enthalpies for the rest are all positive but low. These facts suggest that both molecular composition in the mixture and the types of binary combination are the guiding factors for the exo- and endothermic natures of the micellization process of AOT. The types of variation of AH: with the mole fraction of the relatively low polar component of four representative binary solvent compositions are presented in Figure 5 . The influence of the molecular composition on the thermodynamic parameters is readily observed. The organization of the mixed-solvent species to the hydrophobic tails of AOT in the premicellar state is less exothermic than the intermolecular association during the postmicellization state up to XQ = 0.5, X,, = 0.08, and XW, = 0.7 in Wa-Eg, Wa-Dx, and Fa-Wa, respectively. Beyond these limits this balance is reversed with a consequence of overall endothermicity of the process. For other mixtures, the overall compositions have minor enthalpic effects, and the resultant enthalpies are all positive but low. From the temperature coefficient of cmc in Wa-polyethylene glycol (PEG), Koshy and R a k s h P have reported negative enthalpy and positive entropy also nearly of the same order of magnitude as herein reported. From the temperature effect on the cmc of AOT determined conductometrically in aqueous medium, we have found the AH: to be 8.1 and 4.5 kJ mol-’, respectively, at 298 and 303 K. The respective calorimetrically determined AH: are 4.3 and

0.000 0.010 0.022 0.049 0.082 0.172 0.238 0.455 0.652 1.000

15.57 14.20 14.34 13.70 14.82 15.00 15.20 15.50 16.17 16.00

2.97 -2.11 -3.56 -2.73 -1.29 +0.56 +1.04 +1.50 +0.66 +0.63

61.0 40.0 35.8 36.5 44.9 51.4 53.6 56.4 55.6 54.9

0.000 0.200 0.490 0.690 0.840 0.872 0.900 0.952 0.977 1.ooo

16.32 16.32 15.82 15.89 15.40 15.63 13.82 14.73 14.90 15.57

+0.21 +0.63 +0.36 -0.12 -0.25 -1.35 -2.44 -2.86 -1.41 2.97

0.00 0.22 0.30 0.39 0.49 0.72 1.oo

16.49 15.50 15.20 15.75 15.20 16.50 16.00

0.19 1.18 2.01 2.58 1.85 0.55 0.63

0.000 0.242 0.426 0.580 0.750 1.ooo

16.40 15.10 15.10 14.73 15.52 16.49

0.21 0.37 0.42 0.21 0.12 0.19

0.000 0.050 0.170 0.320 0.520 0.660 0.807 1.ooo

16.32 15.20 14.50 14.40 14.57 15.20 16.32 16.00

0.21 0.13 0.12 0.18 0.42 1.30 2.16 0.65

Fa-Wa

Eg-Dx

Fa-Eg

Fa-Dx (2.300) (2.175) (2.050) (1.910) (1.8 12) 1.756) (lit 1.690)

2.97 kJ mol-’. The difference between the two modes of assessment is apparent. Entropy of Micellization. The entropies of micellization of AOT in all the studied media are positive. The trends of the variation of AS: with the mole fraction of the lower polar solvent in the mixture are similar to that of AH:. The values also range more or less within the same limit except for Wa-Eg medium where the variations of both AH: and AS: are wide. This binary mixture is special compared to the other pairs of solvent studied. From the temperature effect on the cmc of Brij-35, Koshy and Rakshit25 have also reported an exothermic heat of micellization and a positive entropy change in water-polyethyleneglycol binary mixtures. Again the magnitudes of both AH: and AS: of this

4718

The Journal of Physical Chemistry, Vol. 98, No. 17, 1994

system are fairly similar to those herein reported. Jha and A h l ~ w a l i ahave ~ ~ also reported positive hs: for TX-100 micellization in the Wa-Eg medium. The close AG: values in all the studied mixed media advocate a prospective compensation between AH: and of micellizationofAOT inall the studied solvent media. This is exemplified in Figure 6 (line A). The agreement is fairly good, the compensation temp ( Tcomp)is 290 K vis-a-vis the experimental temperature of 303 K. The line embraces all kinds of data, in which only the Wa-Eg results cover a wide range. This solvent pair is distinct in its behavior. The results of Koshyand RakshiP as well as Jha and Ahluwalia24 also follow nice AH: vs AS: linear correlations. Those of the latter authors are presented in Figure 6 (line B), with the result Tcomp = 280 K whereas 298 K is the experimental temperature. Specific Heats. The specific heats of the micellar solutions of AOT in different media recorded in Table 3 have systematically varied with thevariation in theoverall compositions of the solvents. The calculated heat capacities (Ci) from the relation Ci = xgiCi (gi and are the mass fraction and the specific heat of the ith component, respectively) are in close agreement with the experimental results except for one or two compositions: the experimental and the calculated C, values agree well within the maximum limit of the standard deviation in C,(f4.6%).Z7 These values are given in parentheses in Table 3. This agreement supports the weak resultant interaction of the binary components in the mixture which affect C,. The presence of micelles in low concentration has very minorly affected C,. Therefare, correlation of C, either with cmc or with the energetic parameters is not observed. It has been reported30 that the heat capacities of the resulting quaternary mixtures of TX- 100/heptane/butanol/water forming microemulsions exhibit values not in agreement with the calculated values. The situation in microemulsions is more complex and distinct, particularly where a large proportion of amphiphile is present, ending in a specially organized continuum.

e,

Conclusions (1) The micellization of AOT in mixed binary solvent media depends on the types of molecular combinations in the solvents rather than their polarities. (2) The process where water is one of the solvent components can be both exothermic and endothermic; in the absence of water the process is marginally exothermic. (3) In all the solvent media, AOT micellizes with positive entropy, which nicely compensates the enthalpy. (4) The heat capacities of the resulting solutions support a state of weak interaction among the mixed-solvent molecules.

Acknowledgment. Financial support to K.M. from C.S.I.R., Government of India, to carry out the work is thankfully acknowledged.

Mukherjee et al.

References and Notes (1) Williams, E. F.; Woodbury, N. Y.; Dixon, J. K. J . Colloid Interface Sci 1957, 12, 452. (2) Kitahara, A.; Kobayashi, T.; Tachibana, T. J. Phys. Chem. 1962,66, 363. (3) Pal, M. K.; Pal, P. K. J . Phys. Chem. 1990, 94, 2557. (4) Kim, V.; Pak, S.E.; Kharlmove, I. M.; Frolov, Y. G. Kolloidn. Zh. 1986, 48, 830. (5) Kotlarchyk, M.; Huang, J. S.;Chem, S. H. J . Phys. Chem. 1985,89, 4382. (6) Tamura,K.;Schelly, Z.A. J.Am. Chem.Soc. 1981,103,1013; 1981, 103, 1018. (7) Rouviere, J.;Couret, J. M.; Lindheimer,M.;Dejardin, J. L.; Marrony, R. J. Chim. Phys. Chim. Eiol. 1979, 76(3), 289; 297. (8) Borkovec, M.; Eicke, H. F.; Hammerich, H.; Das Gupta, B. J. Phys. Chem. 1988,92, 206. (9) Jada, A.; Lang, J.; Zana, R. J . Phys. Chem. 1990, 94, 350. (10) Bisal, S.R.; Bhattacharya, P. K.; Moulik, S.P. J . Phys. Chem. 1990, 94, 350. (1 1) Paul, B. K.; Moulik, S. P. Indian J . Eiochem. Eiophys. 1991,28,174. Mitra, N.; Mukhopadhyay, L.; Bhattacharya, P. K.; Moulik, S. P. Indian J .

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Miyagishi, S. Bull. Chem. SOC.Jpn. 1975,48(8), 2348. Panda, L.; Behera, G. B. J . Indian Chem. SOC.1985, LXII, 44. Jha, R.; Ahluwalia, J. C. J. Phys. Chem. 1991, 95, 7782. Koshy, L.; Rakshit, A. K. Bull. Chem. SOC.Jpn. 1991, 64, 2612. Gharibi, H.; Palepu, R.; Bloor,D. M.; Wyn-Jones, E. Lungmuir 1992, Mukherjee, K.; Mukherjee, D. C.; Moulik, S.P. Lungmuir 1993, 9, Nozaki, Y.; Tanford, C. J. Biol. Chem. 1965, 240, 3568. Jana, P. K.; Moulik, S.P. J . Phys. Chem. 1991, 95, 9525. (30) Das, M. L.; Bhattacharya, P. K.; Moulik, S.P.; Das, A. R. Lungmuir

1992, 8, 2135. (31) Harned, H. S.;Owen, B. B. The Physical Chemistry of Electrolyte Solutions; American Chemical Society: New York, 1943. (32) Bag, B.; Das, M. N. Indian J. Chem. 1982, 21A, 1035. (33) Rohdewald, P.; Moldner, M. J. Phys. Chem. 1973, 77, 373. (34) Timmermans, J. The Physic0 Chemical Constants of Binary System in Concentrated Solutions; INC. New York, 1959; Vol. 2.