Self-Aggregation of Alkyltrimethylammonium Bromides (C10-, C12

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Langmuir 2005, 21, 10958-10967

Self-Aggregation of Alkyltrimethylammonium Bromides (C10-, C12-, C14-, and C16TAB) and Their Binary Mixtures in Aqueous Medium: A Critical and Comprehensive Assessment of Interfacial Behavior and Bulk Properties with Reference to Two Types of Micelle Formation G. Basu Ray,† I. Chakraborty,† S. Ghosh,† S. P. Moulik,*,† and R. Palepu*,‡ Center for Surface Science, Department of Chemistry, Jadavpur University, Kolkata-700 032, India, and Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, B2G 2W5. Received June 8, 2005. In Final Form: September 1, 2005 The detailed interfacial adsorption and micellization behavior of pure and mixed alkyltrimethylammonium bromides (ATABs: C10-, C12-, C14-, and C16TAB) were studied using tensiometric, conductometric, fluorimetric, viscometric, and calorimetric methods. The critical micellar concentration (CMC), thermodynamics of adsorption and micellization, counterion binding, aggregation number, and micellar polarity were determined. It was observed that the studied 1:1 molar mixtures of C10-C12TAB, C10-C14TAB, and C10-C16TAB, and the mixtures C12-C14TAB and C12-C16TAB at different mole ratios produced two CMCs that were supported by the conductometric, calorimetric and viscometric methods. Compared to the first micelle, the second micelle condensed more counterions and produced a higher aggregation number, but their interior polarity states were the same. The surface excess, area minimum of the ATABs at the CMC and Gibbs free energy of adsorption were evaluated and compared. The ideality/nonideality states of the mixed micelles formed in solution were tested in the light of Clint and Rubingh’s formalisms; the mixed systems were found to undergo moderate to weak synergistic interaction. The contributions of the terminal methyl group, the intermediate methylene groups, and the hydrophilic tetramethylammonium group toward the standard Gibbs free energy, enthalpy, and entropy of the micellization processes were deciphered and discussed.

Introduction In the past, the possibility of the formation of more than one kind of micelle in surfactant solutions was seldom reported. The main reasons for that were (1) the insensitivity of methods to detect the formation of a second micelle in the system and (2) the experimental concentrations of the surfactants used were normally varied only in a limited range above the critical micellar concentration (CMC). It has since been shown that a second CMC may occur at concentrations nearly 3 to 10 times that of the first CMC,1-4 and cationic surfactants having large alkyl chains in the molecule along with their mixtures with a reasonable extent of variation of the length of the alkyl chain are prone to form two CMCs.5 In such a situation, the type one micelles (with CMC1) undergo structural transition to form the second type (with CMC2). A physical property that hardly depends on the structural change of micelles would, therefore, fail to monitor the formation of a second CMC in solution. Thus, tensiometry, fluorimetry, and so forth are normally incapable of providing evidence of the double CMC formation of surfactants in solution. * Corresponding authors. E-mail: [email protected] (S.P.M); [email protected] (R.P.). † Jadavpur University. ‡ St. Francis Xavier University. (1) Kodoma, M.; Kubota, Y.; Miura, M. Bull. Chem. Soc. Jpn. 1972, 45, 2953. (2) Kubota, Y.; Kodoma, M.; Miura, M. Bull. Chem. Soc. Jpn.1973, 46, 100. (3) Kale, K.; Cusslar, E. L.; Evans, D. F. J. Phys. Chem. 1980, 84, 593. (4) Georges, J.; Chen, J. W. J. Colloid Interface Sci. 1986, 113, 143. (5) Treiner, C.; Makayssi, A. Langmuir 1992, 8, 794 and references therein.

On the other hand, conductometry and isothermal titration calorimetry (ITC) can efficiently detect the formation of two kinds of micelles of surfactants.6,7 In the former, the counterion binding phenomenon by the micelles at CMC produces a break in the conductance versus concentration plot. A structural change in the primary micelles may alter the counterion binding to affect the trend in the conductance course to register the occurrence of a second CMC. In the latter (ITC), the detection of the CMC is based on changes in the differential enthalpy of dilution (of a concentrated surfactant solution) in the enthalpogram during the process of micellization. If the changes are perceptible for the two micellization processes, both will be detected; a small change in enthalpy for the second process would fail to indicate its formation. According to reports, the methods, viz., viscometry,8 NMR,9 and solubilization,10 may also identify the formation of a second CMC in some surfactant systems. In recent years, pure and mixed cationic surfactant systems have been reported to produce two CMCs.5-7 The surfactants used have been alkyltrimethylammonium bromides (ATABs) or chlorides, alkylpyridiniumbromides, or chlorides of variable chain lengths and allied other representatives. We performed systematic and elaborate (6) Prasad, M.; Moulik, S. P.; MacDonald, A.; Palepu, R. J. Phys. Chem. B 2004, 108, 355. (7) Prasad, M.; Moulik, S. P.; Palepu, R. J. Colloid Interface Sci. 2005, 284, 658. (8) Ekwall, P.; Mandell, L.; Solyom, P. J. Colloid Interface Sci. 1971, 35, 519. (9) Fabre, H.; Kamenka, N.; Khan, A.; Lindblom, G.; Lindman, B.; Tiddy, G. J. T. J. Phys. Chem. 1980, 84, 3428. (10) Bury, R.; Treiner, C.; Chevalet, C.; Makayssi, A. Anal. Chim. Acta 1991, 251, 69.

10.1021/la051509g CCC: $30.25 © 2005 American Chemical Society Published on Web 10/14/2005

Self-Aggregation of ATABs & Their Binary Mixtures

studies on pure and mixed surfactants of alkyltriphenylphosphonium bromides and observed a good tendency of this class of surfactants to form two kinds of micelles in both pure and mixed states. The methods of conductance and ITC were used, and associated physicochemical parameters and characteristics were evaluated. Compared to the ATABs or chlorides, the alkyltriphenylphosphonium bromides are efficient double-CMC-forming systems. Literature reports on scrutiny show that, although ATABs in pure and mixed conditions have been researched by different workers, a detailed comprehensive study taking all of the available representatives at varied molar compositions remains unexplored. We have, herein, undertaken such a detailed study on C10-, C12-, C14-, and C16TAB and their binary mixtures using the methods of tensiometry, conductometry, and microcalorimetry. Viscometry and fluorimetry were also employed for understanding the internal structural conditions of the selfaggregated species in solution. The interfacial adsorption parameters of pure and mixed ATABs, their CMC, counterion binding, aggregation number, internal polarity level of micelles, thermodynamics of micellization, and amphiphile mutual interaction in the micelles in the two states of existence in solution were evaluated and estimated, and a comprehensive physicochemical rationale for the self-aggregation of the ATABs is presented. Experimental Section Materials. The ATABs C16TAB and C12TAB were analytical reagent (AR) grade products from Aldrich (USA). The C10TAB and C14TAB were AR grade products obtained from Fluka in Germany and Fluka in Switzerland, respectively. The cetylpyridinium chloride (C16PC) used as a fluorescence quencher was an AR grade product from Sigma (USA). The surfactants were used as received. Pyrene (Aldrich) was a gift sample from Polymer Science Laboratory, IACS, Kolkata (India). It was purified by sublimation, followed by recrystallization from ethanol. All of the surfactants were desiccated for a week before use. Doubly distilled deionized water was used for all sample preparation and dilution. All measurements were taken in a temperature-controlled thermostated water bath at 303 (0.1 K. Methods. Microcalorimetry. An OMEGA, ITC microcalorimeter from Microcal, Northampton, (USA) was used for thermometric measurements. A concentrated solution of a surfactant (∼20 times the CMC) was taken in the microsyringe and added after equal time intervals of 210 s in multiple steps (32/40 additions) to 1.325 mL of water in the calorimeter cell under constant stirring (300 rpm) conditions. The heat released at each step of the dilution of the surfactant solution was recorded, and the enthalpy per mole of injectant was calculated using the ITC software. Each run was duplicated to check reproducibility. All measurements were taken at 303 ( 0.1 K, which was maintained by a Neslab (RTE 100) circulating water bath. Tensiometry. The tensions (γ) at the air/solution interface of the surfactant solutions were measured with a calibrated Kru¨ss (Germany) tensiometer by the du Nou¨y ring detachment method. The accuracy of the measurements was (0.1 mN m-1. A concentrated solution of surfactant (∼15-20 times the CMC) was progressively added with a Hamilton microsyringe to water in a container, and the surface tensions were measured, allowing adequate time for equilibration. The temperature of the system was maintained at 303 ( 0.1 K by circulating water through a jacket surrounding the container. Conductometry. Conductance measurements were taken using a Jenway conductometer (UK) using cell constant of unity. A concentrated surfactant solution (∼15-20 times the CMC) was added progressively into water in a container using a Hamilton microsyringe. Measurements were taken after thorough mixing, and the temperature equilibration was at 303 ( 0.1 K, as in the tensiometry measurements. Viscometry. Viscosity measurements were taken in a calibrated two-limbed Ostwald viscometer with a flow time of 3 min and 10 s. A concentrated surfactant solution was progressively added

Langmuir, Vol. 21, No. 24, 2005 10959 to water in the viscometer with a microsyringe and mixed thoroughly at all stages of addition prior to flow measurements. Each measurement was repeated thrice, and the average time of flow was used in the calculation. The temperature of the measurements was kept constant at 303 ( 0.1 K, which was maintained in the water bath. Fluorimetry. Fluorescence measurements using pyrene as the fluorescent probe were taken in a SPEX fluorolog spectrometer with a slit width of 1.25 mm using a 10 mm path length quartz cuvette. Excitation was done at 332 nm, and emission was recorded in the 340-450 nm range. The widths for both excitation and emission slits were fixed at 1.25 mm. Surfactant solutions were taken at 2 times their CMCs, and pyrene concentration in solution was kept around 2 µM. To determine the aggregation number, the quencher (C16PC) was added progressively (concentration varied between 0.01 and 0.3 mM dm-3) into the surfactant solution containing pyrene with a Hamilton microsyringe, and the fluorescence spectra were recorded.

Results and Discussion CMC of the ATABs. In Figures 1-3, several representative enthalpograms, conductance profiles, and tensiometric profiles of pure and mixed ATABs are illustrated. In Figure 1a, the ITC results of pure C10TAB, C12TAB, and C14TAB with both sigmoidal-Boltzman fitting (SBF) and van Oss cumulative plotting procedures for the evaluation of CMC are presented. The ITC enthalpograms of C12-C16TAB mixtures at 0.025 and 0.5 mole fractions of C16TAB, and those of C10-C12TAB, C10-C14TAB, and C10-C16TAB, each at 0.5 mole fraction, are depicted in Figure 1 panels b and c, respectively. Both procedures (SBF and van Oss) result in closely agreed CMC values. The SBF results were herein used for data treatment and analysis. It is evidenced from Figure 1b that the identification of a single or double CMC in a system can be achieved by microcalorimetry. The method of conductometry (Figure 2) can also demonstrate the formation of two CMCs. But tensiometry (Figure 3) can only detect a single CMC (the first CMC in the case of two). This point will be further discussed in a subsequent section. In Table 1, the CMC values of pure ATABs and their 1:1 molar mixtures are presented along with recent literature reports. Close agreements among our results using different methods and the reports from different laboratories were observed. However, there was one exception. For C10TAB, microcalorimetry overestimated the CMC compared to both conductometry and tensiometry. Repeating the experiments did not improve the situation. We cannot explain this discrepancy at this stage. The pure ATABs only produced a single CMC, whereas the 1:1 combinations of C10-C12TAB, C10-C14TAB, C10C16TAB, C12-C14TAB, and C12-C16TAB produced two CMCs; the 1:1 molar mixture of C14-C16TAB produced only one CMC at the studied temperature of 303 K. Among the above combinations, only C12-C16TAB produced two CMCs that were detected by calorimetry; the rest of the two-CMC-forming combinations were identified by conductometry. The phenomenon of two CMCs of alkyltriphenylphosphonium bromides and their binary mixtures was recently reported by us.6,7 The CMC values for the mixed systems of C12-C14TAB, C12-C16TAB, and C14-C16TAB at different molar ratios determined by different methods are presented in Tables 2-4. The results show good agreement. The formation of the second type of micelles in the binary combinations in ionic surfactants at higher concentration beyond the first CMC is considered to be the manifestation of a structural change.5-7 Such a transformation in the bulk is expected to alter the counterion condensation but not the interfacial tension. Hence, although conductance

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Figure 1. (a) Enthalpograms of pure C10TAB, C12TAB, and C14TAB at 303 K with both SBF and van Oss cumulative plotting procedures: C10TAB at 1050 mM involving 32 injections by SBF (curve 1) and by van Oss plot (curve 1*); C12TAB at 317 mM involving 32 injections by SBF (curve 2) and by van Oss plot (curve 2*); C14TAB at 80 mM involving 25 injections by SBF (curve 3) and by van Oss plot (curve 3*). Time interval between injections: 3.5 min. (b) Enthalpograms of C12-C16TAB mixtures at 0.025 and 0.5 mole ratios of C16TAB with SBF at 303 K. The mixture at 0.025 mole fraction was 100.09 mM in the syringe, and the experiment was completed in 32 injections, whereas that at 0.5 mole fraction was 150.6 mM and required 30 injections. Time interval between injections: 3.5 min. (c) Enthalpograms of C10-C12TAB and C10-C14TAB mixtures at 0.5 mole fraction with SBF at 303 K. The C10-C12TAB mixture was 525 mM and required 37 injections, whereas the C10-C14TAB mixture was 200 mM and required 49 injections. Inset: enthalpogram of C10-C16TAB mixture at 0.5 mole fraction. The mixture was 12.5 mM, and the experiment required 32 injections. Time interval between injections: 3.5 min

Figure 2. Specific conductance (κ) vs [surfactant] plots for C12-C16TAB mixtures at 0.025 and 0.2 mole fractions of C16TAB at 303 K. Inset: specific conductance (κ) vs [surfactant] plot for C12-C14TAB at 0.1 mole fraction of C14TAB at 303 K.

measurements could detect the second CMC, tensiometric measurements could not. Transport phenomena such as viscosity were also expected to detect the two types of CMC in relation to structural change in the surfactant assemblies. In Figure 4A, the reduced viscosity of cetyltrimethylammonium bromide (CTAB) versus [surfactant] profiles (curve 1 represents that in H2O; curve 2 represents that in a 0.05 M NaBr solution) are presented. In the

Figure 3. Tensiometric results for C14TAB, C16TAB, and their mixture at 0.7 mole fraction of C16TAB at 303 K.

inset, the result of dodecyltrimethylammonium bromide (DTAB) in H2O is shown. The reduced viscosities of the CTAB-DTAB mixtures at 1:1 molar ratios (with and without salt) are presented in Figure 4B, and that of C16TAB and C12TAB at 0.05 and 0.95 mole fraction compositions, respectively (in H2O), is depicted in the inset. The plots show breaks at the CMCs of CTAB and DTAB and at both CMC1 and CMC2 for the mixtures. The initial high reduced viscosity values were the result of the adsorption of the cationic surfactants onto the negatively

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Table 1. CMCs of Pure ATABs and Their 1:1 Molar Mixtures Obtained from Different Methods along with Their β Values at 303K CMCa/mM system

surface tension

conductance CMC1(CMC2)

C10TAB C12TAB C14TAB C16TAB C10-C12 C10-C14 C10-C16 C12-C16 C12-C14 C14-C16

66.3 14.8 4.08, 3.74f 0.93, 0.815i 20.4 5.44 1.24 1.71 6.64 1.69

66.9, 65.6,b 67.6c 15.7, 15.3,b 15.19d 3.94, 3.94,b 3.78g 0.92, 0.92,j 0.81i 21.0 (55.9) 5.56 (52.8) 1.19 (51.3) 1.32 (12.3) 5.71 (12.4) 1.47, 1.50l

microcalorimetry SBF van Oss 76.9 16.7, 15.5e 4.20, 4.11h 1.09, 0.970k 26.7 7.98 1.92 1.70 (16.4) 6.44 2.03

77.7 17.2 4.56 1.07 26.9 8.22 2.02 1.69 (16.3) 6.73 (19.3) 1.94

β CMC1(CMC2) 0.685, 0.699b 0.718, 0.726b 0.727, 0.731b 0.731, 0.762b 0.604 (0.675) 0.507 (0.714) 0.443 (0.746) 0.400 (0.690) 0.610 (0.690) 0.570

a Viscosity-determined CMC values of C TAB and C TAB were 14.4 and 0.912 mM, respectively. At 0.5 mole fraction, two CMCs of 12 16 1.37 and 12.5 mM were obtained for C12-C16TAB. b Ref 34. c Ref 22. d Ref 35. e Ref 38. f Ref 37. g Ref 36. h Ref 24. i Ref 39. j Ref 40. k Ref 23. l Ref 41.

Table 2. CMCs of C12-C14TAB Mixtures Obtained from Different Methods and Their β Values at 303K CMC1 (CMC2)/mM microcalorimetry surface β XTTAB tension conductance SBF van Oss CMC1 (CMC2) 0.1 0.3 0.5 0.7 0.9

12.5 6.71 6.64 4.97 4.04

10.8 (18.0) 7.85 (13.8) 5.71 (12.4) 4.94 (13.1) 4.28 (9.72)

11.7 8.15 6.44 5.40 4.88

12.1 7.95 6.73 5.16 4.50

0.551 (0.690) 0.530 (0.671) 0.610 (0.691) 0.612 (0.710) 0.721 (0.760)

Table 3. CMCs of C12-C16TAB Mixtures Obtained from Different Methods and Their β Values at 303K CMC1a (CMC2)/mM Microcalorimetry

surface XCTAB tension conductance 0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

4.43 2.00 1.71 1.51 1.24

10.0 (15.1) 6.00 (14.5) 4.39 2.54 (12.5) 1.95 1.54 1.32 (12.3) 1.26 1.17 (11.3) 1.10 0.98

SBF

van Oss

β CMC1 (CMC2)

8.73 (15.7) 6.32 (15.1) 4.27 2.71 (15.5) 2.08 (15.8) 1.91 1.70 (16.4) 1.56 1.45 (14.8) 1.35 1.29

8.64 (15.8) 6.30 (15.1) 4.26 2.69 (15.4) 2.07 (15.7) 1.88 1.69 (16.3) 1.54 1.44 (14.8) 1.35 1.24

0.291 (0.621) 0.221 (0.590) 0.242 0.240 (0.610) 0.297 (0.651) 0.380 0.401 (0.691) 0.500 0.570 (0.700) 0.621 0.701

For XCTAB ) 0.05, viscosity-derived CMC1 and CMC2 values were 6.89 and 15.0 mM, respectively. a

Table 4. CMCs of C14-C16TAB Mixtures Obtained from Different Methods and Their β Values at 303K CMC/mM XCTAB

surface tension

conductance

0.05 0.1 0.3 0.5 0.7 0.9

3.06 2.16 1.69 1.20 1.04

2.96 1.95 1.47 1.16 0.96

Microcalorimetry SBF van Oss 3.33 2.81 2.16 2.03 1.55 1.45

3.36 2.80 2.15 1.94 1.55 1.41

β 0.625 0.565 0.570 0.632 0.703

charged glass capillary surface, offering a barrier to flow as proposed by Davies and Ridel.11 Barry and Gray12 also observed similar behavior for cationic surfactants and their mixtures with bile salts. It has been observed that the (11) Davies, J. T.; Rideal, E. K. Interfacial Phenomenon; Academic Press: New York, 1963; p 435. (12) Barry, B. W.; Gray, G. M. T. J. Colloid Interface Sci. 1975, 52, 327.

Figure 4. (A) Reduced viscosity vs concentration plots for C16TAB at 303 K. Solid line curve represents aqueous medium. Dotted line curve represents 0.05 M aqueous NaBr solution. Inset: Reduced viscosity vs concentration plot for C12TAB in water at 303 K. (B) Reduced viscosity vs concentration plots for C12-C16TAB mixtures at 303 K. Solid line curve denotes C16TAB results at 0.5 mole fraction in water. Dotted line curve denotes the same in 0.05 M NaBr solution. Inset: viscometric results for C12-C16TAB mixtures at 0.05 mole fraction of C16TAB at 303 K.

reduced viscosity was much larger for C16TAB than it was for C12TAB; the longer chain length in the former resisted the flow more than the latter. The effect was reduced by the presence of added salt (0.05 M NaBr) in the system (curve 2 in Figure 4A); the Na+ ions hindered the adsorption of cationic surfactants on the negatively charged glass surface of the capillary. Barry and Gray12 observed a minimum in reduced viscosity close to the CMC and an increase in ηred beyond that point. In this study, a mild rise in ηred was observed after the second break in the

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Ray et al. Table 5. Aggregation Number (n) and I1/I3 Values for the Studied ATAB Systems n at CMC1(CMC2) this work system C10TAB C12TAB C14TAB C16TAB C10-C14 (1:1) C12-C16 (1:1) C12-C14 1:1) C14-C16 (1:1) a

Figure 5. (A) Linear ln I0/I vs [quencher] plot for the determination of the aggregation number of the C12TAB system. Inset: The basic fluorescence spectra for C12TAB using Pyrene as the probe and C16PC as the quencher. (B) Linear ln I0/I vs [quencher] plot for the determination of the aggregation number of the C12-C16TAB mixture at 0.5 mole fraction of C16TAB. Inset: The basic fluorescence spectra for this system using pyrene as the probe and C16PC as the quencher.

plots for the mixed ATAB systems. The CMC, CMC1, and CMC2 obtained by viscometry are also included in the footnotes of Tables 1 and 3. Micellar Aggregation Number and Internal Polarity. The static fluorescence quenching method was used for determining the micellar aggregation number of several systems of pure and mixed ATABs. Pyrene was used as the fluorescence probe. The ratio of vibronic peaks one and three was considered to be the polarity index of the micellar interior. The equation used for obtaining the aggregation number (n) was

ln

I0 n[Q] ) I [S] - CMC

(1)

in which I and I0 are the fluorescence intensities with and without quencher, respectively; [S] and [Q] are the concentrations of the surfactant and the quencher (C16PC), respectively. From the slope of the linear plot between ln I0/I and [Q], the aggregation number, n, was determined using a constant surfactant concentration (twice the CMC). The plots for the estimation of n for pure C12TAB and for the mixed (1:1 mol/mol) system of C12-C16TAB are illustrated in Figure 5, panels A and B, respectively. In the insets of

fluorescence

simulation

lit. values

16 21 24 61 30 92, (130) 15 43, (55) 30, (35) 56, (95) 31 69 37 63

Ref 22. b Ref 42. c Ref 32.

d

40,a 31b 55,a 48,c 35d 70,a 55,c 50,e 60f 90,a 62c

I1/I3 CMC1 (CMC2) 1.36 1.27 1.10 1.06 1.05 (0.97) 1.06 (1.07) 1.10 (1.08) 1.05

Ref 35. e Ref 37. f Ref 43.

both figures, the basic fluorescence spectra are exemplified. The spectra for the mixed micellar system show evidence of two distinct sets (curves 1-7 and 7-13) corresponding to the two states of aggregation, micelle one and micelle two, respectively. It may be mentioned that the static quenching method normally underestimates n compared to the dynamic quenching method. We used the former method because of the nonavailability of timeresolved fluorescence measuring facilities. The results obtained are compared with literature data in Table 5. It was observed that the literature reports (herein collected) do not closely agree. Even the time-resolved fluorescence quenching method yielded lower values compared to the static quenching method. The results have shown that n for the second type of micelle was greater than that for the first type; that is, the second micelle was larger than the first. For C10TAB, we did not obtain convincing results by fluorimetry, even upon repeating the experiment. We also used a simulation procedure13,14 for the determination of n using the ITC-determined differential enthalpy of dilution of the ATABs based on a “mass action model”. We used this procedure earlier for the micellization of sodium dodecylbezenesulfonate (SDBS).15 This method yields an aggregation number corresponding to the CMC state of the surfactant. In other methods (flourimetry, light scattering, etc.), measurements are essentially taken at [surfactant] > CMC. It has been well documented that, above the CMC, n increases with increasing [surfactant].16-20 Thus, the n at CMC is expected to be the lowest. The lower value of n for dodecyltrimethylphosphonium bromide has indeed been realized by the simulation method compared to fluorimetry.21 In Figure 6, the good fitting of the ITC results with the simulation procedure is depicted. The n values realized for pure ATABs and their 1:1 molar mixtures are presented in column 3 of Table 5. The n values were all lower than those determined by the fluorescence quenching method. The values followed the expected trend in that the results obtained by the fluorescence quenching method were not really consistent, with the exception of the report of Evans (13) Garidel, P.; Hildebrand, A.; Neubert, R.; Blume, A. Langmuir 2000, 16, 2567. (14) Majhi, P. R.; Blume, A. Langmuir 2001, 17, 3844. (15) Hait, S. K.; Majhi, P. R.; Blume, A.; Moulik, S. P. J. Phys. Chem. B 2003, 107, 3650. (16) Acharya, K. R.; Bhattacharya, S. C.; Moulik, S. P. Ind. J. Chem. 1997, 36A, 137. (17) Fendler, J. H.; Fendler, E. J. Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975. (18) Lianos, P.; Zana, R. J. Phys. Chem. 1983, 87, 1289. (19) Lianos, P.; Lang, J. J. Colloid Interface Sci. 1983, 96, 222. (20) Lianos, P.; Viriot, M.-L.; Zana, R. J. Phys. Chem. 1984, 88, 1098 and references therein. (21) Prasad, M.; Moulik, S. P. Jadavpur University, Kolkata, India. Unpublished results, 2004.

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Figure 6. Enthalpy per mole of surfactant vs volume of surfactant added plots at 303 K. Points are experimental, curves are simulated. (a) C12TAB; cell volume ) 1.325 mL, [C12TAB] ) 200 mM, volume added in each step ) 5 µL, time interval between two injections ) 3.5 min. (b) C14TAB; cell volume ) 1.325 mL, [C14TAB] ) 69.1 mM, volume added in each step ) 10 µL, time interval between two injections ) 3.5 min. (c) C12-C16TAB (1:1 mol/mol) for first micellization; cell volume ) 1.325 mL, [C12-C16TAB] ) 18.8 mM, volume added in each step ) 5 µL, time interval between two injections ) 3.5 min. (d) C12-C16TAB (1:1 mol/mol) for second micellization; cell volume ) 1.325 mL, [C12-C16TAB] ) 150.6 mM, volume added in each step ) 10 µL, time interval between two injections ) 3.5 min. (e) C10-C14TAB (1:1 mol/mol); cell volume ) 1.325 mL, [C10-C14TAB] ) 525 mM, volume added in each step ) 5 µL, time interval between two injections ) 3.5 min. (f) C10-C16TAB (1:1 mol/mol); cell volume ) 1.325 mL, [C10-C16TAB] ) 12.5 mM, volume added in each step ) 10 µL, time interval between two injections ) 3.5 min.

et al.22 For C12-C16TAB, two CMCs corresponded to two n values of 30 and 35, respectively. In Table 5, the I1/I3 values of pyrene solubilized in the two types of micelles are also shown. All of the values were less than two and close to one another. A mild chainlength-dependence on the polarity of the pure micelles

was observed. The interiors of the micelles all consisted of alkyl chains; structural change was not expected to affect the internal polarity. The pyrene environments were thus similar and appreciably nonpolar. (22) Evans, D. F.; Allen, M.; Ninham, B. W.; Fouda, A. J. Solution Chem. 1984, 13, 87.

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Counterion Binding of Micelles. In Tables 1-4, the counterion binding fractions (β) are also presented. In their computation, both the Evans equation and the slope ratio method were tried. Evans equation:22

1000S2 )

(n - m)2 4/3

n

(1000S1 - λC) +

(n - m) λC n

(2)

in which S1 and S2 are the first and second slopes of the specific conductance versus concentration plot, respectively, n is the aggregation number, m is the number of counterions bound to a micelle, and λc is the equivalent conductance of the counterion. In the actual calculation, the equivalent conductance of Br- at infinite dilution was used because dilute solutions of the surfactants were used in the study. From known values of n, m can be calculated from eq 1 to get β () m/n). Slope ratio method:

β ) 1 - S2/S1

(3)

in which S1 and S2 are the slopes of the κ versus [surfactant] profiles in the pre and post micellar states, respectively. The parameter β can thus be directly obtained from this equation. The n values obtained from both the fluorescence method and the simulation method (Table 5) were used to obtain m/n from eq 2; it was also obtained from eq 3. The second method has been observed to produce lower values of β to the extent of ∼10%. Because the calculation of β by eq 2 required us to determine too many n values for the systems under our plan, we used the n values obtained from eq 3 for the thermodynamic calculations. Behavior of ATABs at the Air/Solution Interface. The air/solution interface data are contained in Table 6 for pure ATABs and 1:1 molar mixtures of C10-CnTAB combinations. The surface excess quantity at the CMC (Γmax) was obtained from the Gibbs adsorption equation:

Γmax ) -

1

Lt

dγ

4.606RT CfCMC d log C

(4)

in which γ is the surface tension at the CMC, and the other terms have their usual significance. The dγ/d log C factor was obtained from the slopes of the linear γ versus log C plots (representation shown in Figure 3). The minimum area of the amphiphile molecules (amin) at the surfactant-saturated monolayer at the air/solution interface was obtained from the relation

amin )

1018 NΓmax

(5)

in which N is Avogadro’s number. The standard Gibbs free energy of adsorption was obtained from the relation

∆G0ad ) ∆G0m -

πCMC Γmax

(6)

in which ∆G0m is the standard Gibbs free energy of micellization (which will be discussed later), and πCMC is the surface pressure at CMC and is equal to γCMC - γwater. The results are presented in Table 6. From the slope of the linear plot of ∆G0ad versus carbon number (Cn), the free energy of adsorption per mole of CH2 group was found to be -5.5 kJ mol-1. The contribution of the hydrophilic

Table 6. Γmax, amin, and ∆G0ad Values of Pure ATABs and C10-CnTAB 1:1 Molar Mixtures system|

Γmax × 106/mol m-2

amin/nm2

∆G0ad/kJ mol-1

C10TAB C12TAB C14TAB C16TAB C10-C12 C10-C14 C10-C16

1.68 1.49 1.15 1.03 1.65 1.55 1.20

1.0 1.1 1.5 1.6 1.0 1.1 1.4

-52.0 -60.8 -73.9 -84.2 -80.1 -58.5 -69.1

Table 7. Γmax, amin, and ∆G0ad Values for the Studied Molar Mixtures of C12-C14TAB, C12-C16TAB, and C14-C16TAB Systems interfacial parameters

system

molar ratios Γmax × 106/mol m-2 amin/nm2 ∆G0ad/kJ mol-1 Γmax × 106/mol m-2 amin/nm2 ∆G0ad/kJ mol-1 Γmax × 106/mol m-2 amin/nm2 ∆G0ad/kJ mol-1

C12-C16TAB 0.1 0.3 0.84 0.71 1.98 2.34 -74.9 -89.5

0.5 1.26 1.32 -65.0

0.7 1.50 1.10 -67.1

0.9 0.88 1.88 -87.6

C12-C14TAB 1.79 1.61 1.67 0.93 1.03 0.99 -52.8 -55.2 -58.3

1.67 0.99 -58.7

2.47 0.67 -54.8

C14-C16TAB 0.97 1.30 0.79 1.71 1.27 2.11 -78.7 -68.0 -88.6

1.19 1.40 -72.6

0.70 2.35 -99.4

headgroup to ∆G0ad was found to be 3.58 kJ mol-1 from the intercept of the plot. The interfacial adsorption parameters for C10-CnTAB and the rest of the binary combinations (C12-C14TAB, C12-C16TAB, and C14-C16TAB) are presented in Tables 6 and 7. It is acknowledged that the interfacial properties depend on the type of amphiphiles and their combinations. For mixed systems, the interfacial composition may differ from the bulk composition. The ATABs under study had the same trimethylammonium headgroup but differed in their chain length. It will be shown in a subsequent section that the chain length difference produced nonideality in their binary mixtures in the bulk. The same would also be true at the interface. Energetics of Micellization. The standard Gibbs free energy, enthalpy, and entropy changes for micellization, ∆G0m, ∆H0m and ∆S0m, respectively, were obtained from the following relations according to the phase separation model:

∆G0m) (1 + β)RT ln XCMC

(7)

∆H0m) (∆H0m)cal

(8)

∆S0m) (∆H0m - ∆G0m)/T

(9)

in which the new term XCMC is the CMC of a surfactant expressed in mole fraction units. The results for the pure surfactants and the 1:1 molar mixtures are presented in Table 8. The micellization process of the pure ATABs became more and more exothermic and spontaneous with increasing alkyl chain length; the entropy change became more positive. The trends were similar for the mixed systems of C10TAB with an increasing chain length of the second component. But the magnitudes of the parameters ∆G0m and ∆S0m were moderately large compared to ∆H0m. The much-decreased spontaneity of the micellization of the mixed binary combinations relative to the pure components was due to

Self-Aggregation of ATABs & Their Binary Mixtures Table 8. Thermodynamic Parameters for the Micellization of Pure ATABs and 1:1 Molar Mixtures at 303K system

∆G0m (kJ mol-1)

a ∆G0(M) m (kJ mol-1)

∆H0m (kJ mol-1)

∆S0m (JK-1 mol-1)

C10TAB C12TAB C14TAB C16TAB C10-C12 C10-C14 C10-C16 C12-C16 C12-C14 C14-C16

-28.0 -35.1 -41.3 -47.3 -30.9 -33.6 -37.4 -36.7 (-34.6) -36.7 -40.4

-27.0 -34.2 -40.5 -46.6 -29.5 -32.5 -36.6 -36.0 (-34.0) -36.1 -39.8

-1.62 -2.18 -6.14 -7.26 -2.30 -3.47 -4.31 -3.90 (-1.11) -4.90 -7.40

87.0 109 116 132 94.4 99.5 109 108 (110) 105 109

a

(M) ) free energy of micellization calculated by Moroi’s method.

the increased CMC of the combinations on account of the presence of C10TAB in them. The complete energetic understanding for the second type of micelle formation was not possible for most of the combinations because of the inability of calorimetry to detect the process and hence the lack of ∆H0m data. From the conductometric findings, it can be only stated that the second process was less spontaneous than the first and was associated with increased counterion binding. The only combination that produced the second CMC by calorimetry was the C12-C16TAB pair. The energetic parameters for C12-C14TAB, C12-C16TAB, and C14-C16TAB are given in Table 9. On a comparative basis, the range of variation of the parameters for the three different systems was not wide. It was essentially guided by the alkyl chain length effect. For C12-C16TAB mixtures, both conductance and calorimetry produced two CMCs. The first process was more spontaneous than the second and the ∆H0m for the first was more exothermic than that of the second. In this context, a comparison of the calorimetric (ITC) results for CMC of the mixed systems of C12-C16TAB and C14-C16TAB obtained by Blandamer et al.23,24 with our results is relevant. For the C12-C16TAB system,23 they observed a decrease in the CMC with increasing C16TAB in the mixture and considered the incorporation of C12TAB in the C16TAB micelles to account for the decrease in CMC. They also observed the relative insensitivity of ∆H0m with a mean value of -10.9 kJ mol-1 at different RC12TAB values in the mixture. Their results contradict our findings in which the changing of both the CMCmix and ∆H0m at different mixed proportions of C12TAB and C16TAB was observed (Tables 3 and 9). Furthermore, we observed the formation of two CMCs, which Blandamer et al. did not observe. In the case of C14-C16TAB mixed systems, they reported24 the CMC and ∆H0m values at 298.2 K, whereas our results were reported at 303 K. But the magnitudes of CMC were lower, and the ∆H0m obtained by them was comparable to ours, with the exception of deviations for a few of the lower RC16TAB combinations. Note that the initial portion of their enthalpograms in the lower concentration range were parallel to [surfactant] (similar to ideal plots rarely obtained in practice), and the CMC values were considered at the first break on the lower side of the concentration and not at the inflection points. Hence their values were lower than ours. (23) Blandamer, M. J.; Cullis, P. M.; Soldi, L. G.; Chowdoji Rao, K.; Subha, M. C. S. J. Therm. Anal. 1996, 46, 1583. (24) Blandamer, M. J.; Briggs, B.; Cullis, P. M.; Engberts, J. B. F. N. Phys. Chem. Chem. Phys. 2002, 2, 5146.

Langmuir, Vol. 21, No. 24, 2005 10965

We also used the mass action equation of Moroi25 to evaluate ∆G0m using n from the simulation method (Table 5) and the counterion binding extents, β, from Table 1:

∆G0m ) (1 + β)RT ln XCMC + (RT/n) ln[2n2 (1 + β)] (10) The results are shown in column 3 of Table 8. The “pseudophase model” shows a little more spontaneity in the micellization process than does the “mass action model”. The findings were similar for the self-aggregation of SDBS in aqueous medium.15 For large values of n, the results from the two models become equivalent. The dependence of the energetic parameters on the surfactant headgroup, the methylene group (CH2), and the terminal methyl group (CH3) of the ATABs was estimated from the following consideration of additivity:

∆G0m ) ∆G0m (H) + Cn-1 ∆G0m (CH2) + ∆G0m (CH3) (11a) ∆H0m ) ∆H0m (H) + Cn-1 ∆H0m (CH2) + ∆H0m(CH3) (11b) ∆S0m ) ∆S0m (H) + Cn-1 ∆S0m (CH2) + ∆S0m (CH3) (11c) The first terms in these equations stand for the hydrophilic part, the second terms stand for the contribution from the methylene group, and the third terms denote the contribution of the methyl group. We took ∆G0m(CH3)26 ) -8.40 kJ mol-1 and plotted [∆G0m - ∆G0m (CH3)] against (Cn-1) to get ∆G0m (CH2) from the slope and ∆G0m (H) from the intercept. Likewise, taking ∆H0m (CH3) ) -6.96 kJ mol-1, and ∆S0m (CH3) ) 4.75 J mol-1K-1 from the literature,27 we evaluated the ∆H0m (CH2) and ∆H0m (H) as well as the ∆S0m (CH2) and ∆S0m (H) values. The results are presented in Table 10. The literature values28 of ∆G0m (CH2) range between -2.2 and -2.9 kJ mol-1. We observed6 a value of -2.0 kJ mol-1 for the large headgroup-containing surfactants, alkyltriphenylphosphonium bromides. For the ATABs, the observed ∆G0m (CH2) ) -3.26 kJ mol-1 value nearly agrees with the upper limit of the literature reports. For the micellization of ATAB monomers in aqueous medium, the contribution of headgroup hydrophilicity was nonspontaneous with associated endothermic enthalpy and positive entropy. Such contributions from the CH2 and CH3 groups are also listed in the table; their enthalpies were negative and their entropies were positive. The values of ∆G0ad(CH2) and ∆G0ad(H) presented in the previous section and the footnote of Table 10 appreciably differed from that of ∆G0m(CH2) and ∆G0m(H). The sign and magnitudes of the parameters suggested that the interfacial adsorption process is more favored than micellization in the bulk. Mutual Interaction of Surfactants in Micelles. The components in the binary mixtures of the ATABs are expected to mutually interact in the mixed micelles. This is anticipated to arise from the chain length difference of the studied ATABs. The interaction might lead to non(25) Moroi, Y. Micelles, Theoretical and Applied Aspects; Plenum Press: New York, 1992. (26) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley-Interscience: New York, 1980. (27) Okawanchi, M.; Hagio, M.; Ikawa, Y.; Sugihara, G.; Murata, Y.; Tanaka, M. Bull. Chem. Soc. Jpn. 1987, 60, 2718. (28) Mukherjee, P. Adv. Colloid Interface Sci. 1967, 1, 241.

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Ray et al.

Table 9. Composition-Dependent Thermodynamic Parameters for the Micellization of C12-C14TAB, C12-C16TAB, and C14-C16TAB Mixtures at 303K thermodynamic parameters

system

molar ratios ∆G0m/kJ mol-1 ∆H0m/kJ mol-1 ∆S0m/JK-1 mol-1

0.025

0.05

0.1 -33.0 -2.64 101

0.2

∆G0m/kJ mol-1 CMC1, CMC2 ∆H0m/kJ mol-1 CMC1, CMC2 ∆S0m/JK-1 mol-1 CMC1, CMC2

-28.5, -33.4 -0.4, -0.97 92.7, 107

-27.9, -32.9 -0.5, -0.72 90.6, 106

-29.6

-31.0, -33.0 -1.0, -0.87 96.4, 106

-0.7 95.6

-40.5 -3.4 123

∆G0m/kJ mol-1 ∆H0m/kJ mol-1 ∆S0m/JK-1 mol-1

C12-C14TAB 0.3 0.4 -33.1 -3.75 99.8

0.5 -36.7 -4.90 105

0.6

0.7 -37.5 -5.79 105

0.8

0.9 -40.4 -6.71 112

C12-C16TAB -33.1, -35.8 -34.0 -3.0, -3.7 -1.01 99.4, 106 109

-36.7, -34.6 -3.9, -1.11 108, 110

-39.6

-41.8, -35.3 -5.5, 1.20 120, 112

-43.4

-45.7

-6.3

-6.2

122

130

C14-C16TAB -40.0 -5.1 115

-40.4 -7.4 109

Table 10. Thermodynamic Contributionsa of the Hydrophilic Head Group (H), CH2, and CH3 Groups for the Micellization and Interfacial Adsorptionbof ATABs at 303K ∆G0m(H)

9.63

∆G0m(CH2)

-3.26

∆G0m(CH3)

-8.40

∆H0m(H)

15.2

∆H0m(CH2)

-1.04

∆H0m(CH3)

-6.96

∆S0m(H)

19.2

∆S0m(CH2)

7.23

∆S0m(CH3)

4.75

a ∆G0 and ∆H0 values are in kJ mol-1; ∆S0 values m m m mol-1. b ∆G0ad(CH2) ) -5.5 kJ mol-1; ∆G0ad(H) ) 3.58

are in JK-1 kJ mol-1.

ideality, producing synergistic/antagonistic behavior. This can be readily tested with Clint’s proposition.29 There have been several attempts made to quantify nonideality, for which the treatment of Rubingh30 has received much attention because it is relatively simple. A general comparison of different nonideal combinations can be found in the literature.31,32 We have herein analyzed our results in terms of the equations of Clint and Rubingh to assess the ideality/nonideality behaviors of the binary combinations of the ATABs. Clint equation:

Ra 1 - Ra 1 ) + CMCab CMCa CMCb

-4.9 114

-43.1 -8.1 116

-45.3 -8.9 120

the interaction parameter g can be calculated from the relation

g)

ln(Racab/xaCMCa) (1 - xa)2

(14)

The activity coefficients of the components fa and fb can be obtained from the following equations:

fa ) exp[g(1 - xa)2]

(15a)

fb ) exp[gxa2]

(15b)

In Figure 7, the deviations from Clint’s formalism of the mixed ATABs are depicted. The combinations show synergistic behavior. Among C12-C14TAB, C14-C16TAB, and C12-C16TAB, the combination C14-C16TAB shows very nominal deviation from Clint’s formalism (the combination was, on the whole, ideal). It may be mentioned here that Blandamer et al.23 reported repulsion or antagonism between C14 and C16TAB because of the hydrophobic mismatch (repulsion) of the chains, which contradicted our findings. Of course, their method of analysis was

(12)

in which Ra is the stoichiometric mole fraction of the component a in the binary mixture, and CMCa, CMCb, and CMCab are the CMCs of component a, component b, and the mixed micelle, respectively. Rubingh equation:

xa2 ln (Racab/xaCMCa) (1 - xa)2 ln{(1 - Ra)cab/(1 - xa)CMCb}

) 1 (13)

in which Ra and xa are the mole fractions of component a in the prepared solution and the mixed micelle, respectively. The equation can be iteratively solved for xa, and (29) Clint, J. H. J. Chem. Soc., Faraday Trans. 1975, 171, 1327. (30) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley: New York, 1989. (31) Haque, M. E.; Das, A. R.; Rakshit, A. K.; Moulik, S. P. Langmuir 1996, 12, 4084. (32) Junquera, E.; Aicart, E. Langmuir 2002, 18, 9250 and references therein.

Figure 7. Dependence of CMCab on the concentration of the second component for C12-C14TAB, C12-C16TAB, and C14C16TAB (inset) at 303 K. The curves are according to Clint; the points are experimental.

Self-Aggregation of ATABs & Their Binary Mixtures Table 11. Interaction Parameters (g), Micellar Mole Fractions of Component Two (Xb), and Activity Coefficients fa and fb of Binary Mixturesaat 303K C12-C14TAB XCTAB (mixture)

g(R)

Xb(R)

fa

fb

0.1 0.3 0.5 0.7

-0.45 -0.44 -0.36 -0.06

0.34 0.62 0.78 0.90

0.82 0.94 0.98 0.99

0.95 0.85 0.80 0.95

C12-C16TAB XTTAB (mixture)

g(R)

Xb(R)

fa

fb

0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-1.55 -2.21 -2.03 -2.45 -2.56 -2.21 -2.16 -1.70 -2.61

0.37 0.46 0.57 0.66 0.71 0.78 0.83 0.88 0.94

0.54 0.52 0.68 0.75 0.80 0.89 0.94 0.97 0.99

0.81 0.62 0.52 0.35 0.27 0.26 0.23 0.27 0.09

C10-CnTAB (1:1 molar mixtures) systems

g(R)

Xb(R)

fa

fb

C10-C12 C10-C14 C10-C16

-0.35 -2.82 -4.04

0.81 0.80 0.91

0.99 0.89 0.97

0.79 0.16 0.03

a The C -C TAB combination behaved ideally and followed 14 16 Clint’s equation.

different from that of Rubingh. Similar to our observations, the CMCab values obtained by Blandamer et al. were also lower than Clint’s proposition, indicating synergistic interaction between the components. It therefore remains to be understood why the results of two approaches (Rubingh and Blandamer) differ radically. The interaction parameter g, the mole fraction of the higher chain length component in the mixture (xb), and the activity coefficients (fa and fb) of the components in the mixtures are presented in Table 11. The synergism between the two components in the mixtures was evidenced from the negative g values; their magnitudes accounted for the strength of the interaction. It was noted that, for both C12-C16TAB and C12-C14TAB, large positive g values were obtained at higher mole fractions of xb > 0.7; they even resulted with the condition for inequation. From our experience, we concluded that this was partly due to an error in the CMC and the inaccuracy of the theory because we had noticed in the past that, at certain mole fractions for certain mixed systems, the iteration method to estimate g from eq 13 did not converge, that is, produce a condition for inequation.7,33 The g values for C10-C12TAB, C10-C14TAB, and (33) Jana, P. K.; Moulik, S. P. J. Phys. Chem. 1991, 95, 9525. (34) Ribeiro, A. C. F.; Lobo, V. M. M.; Valente, A. J. M.; Azevedo, E. F. G.; Miguel, M. da G.; Burrows, H. D. Colloid Polym. Sci. 2004, 283, 277. (35) Rodriguez, A.; Junquera, E.; del Burgo, P.; Aicart, E. J. Colloid Interface Sci. 2004, 269, 476. (36) Carpena, P.; Aguiar, J.; Bernaola-Galvan, P.; Carnero Ruiz, C. Langmuir 2002, 18, 6054 (37) Shivaji Sharma, K.; Patil, S. R.; Rakshit, A. K.; Glenn, K.; Doiron, M.; Palepu, R. M.; Hassan, P. A. J. Phys. Chem. B 2004, 108, 12804. (38) Stodghill, S. P.; Smith, A. E.; O’Haver, J. H. Langmuir 2004, 20, 11387. (39) Chakraborty, T.; Ghosh, S.; Moulik, S. P. J. Phys. Chem. B 2005, 109, 14813.

Langmuir, Vol. 21, No. 24, 2005 10967

C10-C16TAB at 1:1 molar ratios were all negative and increased in the order of the increasing chain length of the second component, evidencing increasing synergism. It was further observed that the g values for C12-C14TAB and C12-C16TAB were nearly constant at average values of -2.17 and -0.42, respectively. Although constant g is expected, according to Rubingh’s treatment, it is seldom obtained for mixed binary surfactant combinations. Furthermore, the mole fraction of the second component (Xb) in the mixed micelle was greater than the stoichiometric mole fraction (Ra) for all of the studied compositions. The mixed micelles were composed of greater extents of the lower CMC components, that is, component b. The activity coefficients of both of the components in C12-C14TAB combinations were close to unity for small g values, signifying only mild deviation of the mixed system from ideality. The C12-C16TAB system deviated more, and hence the activity coefficients also deviated more from unity, particularly that of the second component, with increasing stoichiometric mole fraction in the combination. Similar trends of the activity coefficients were observed for the 1:1 molar combinations of C10TAB with C12, C14, and C16 components. Conclusions 1. The mixed binaries of C10-, C12-, C14- and C16TAB mostly form two CMCs with concentration differences of ∼1.5-10 times, depending on the system type and composition. 2. The second micelle binds more counterions than does the first with higher aggregation of monomers in the micelle. 3. The aggregation number of the amphiphiles at the CMC point is lower than that at concentrations above the CMC. 4. Despite chain length difference or mismatch, the binary components undergo moderate synergistic interaction in the mixed micelles. 5. The Gibbs free energy and enthalpy of the transfer of the polar (CH3)3 N+ headgroup of the ATABs from the bulk water to the micelle were fairly positive, and the associated entropy of transfer was moderately positive. The transfer enthalpy obtained in this study (-3.26 kJ mol-1 at 303 K) for one methylene group (CH2) closely agreed with that of the literature reports (-3.00 kJ mol-1 at 298 K). Acknowledgment. The work was done in a collaborative project by utilizing a research grant from the St. Francis Xavier University, Canada to the Centre for Surface Science, Jadavpur University. G.B.R. and I.C. thank CSIR, Govt. of India for the financial support. S.P.M. thanks INSA, Govt. of India for a Senior Scientist position. R.P. acknowledges funding from NSERC of Canada in the form of an operating grant. Authors thank P.R. Majhi of the University of California (San Francisco) for the Scientist simulation program. LA051509G (40) Mukherjee, P., Mysels K. J. Critical Micellar Concentration of Aqueous Surfactant Systems; U.S. National Bureau of Standards: Washington, DC, 1971. (41) Rodgers, M. P.; Rodgers, C. C.; Rakshit, A. K.; Palepu, R. M. Colloid Polym. Sci. 2003, 281, 800. (42) Villetti, M. A.; Borsali, R.; Crespo, J. S.; Soldi, V.; Fukada, K. Macromol. Chem. Phys. 2004, 205, 907. (43) Bakshi, M. S. Colloid Polym. Sci. 2000, 278, 524.