On mixed binary surfactant systems comprising MEGA 10 and alkyltrimethylammonium bromides: A detailed physicochemical study with a critical analysis

Journal of Colloid and Interface Science 307 (2007) 543–553 www.elsevier.com/locate/jcis

On mixed binary surfactant systems comprising MEGA 10 and alkyltrimethylammonium bromides: A detailed physicochemical study with a critical analysis Gargi Basu Ray, Indranil Chakraborty, Soumen Ghosh, Satya P. Moulik ∗ Centre for Surface Science, Department of Chemistry, Jadavpur University, Kolkata 700 032, India Received 13 July 2006; accepted 30 November 2006 Available online 15 December 2006

Abstract Self-aggregation of mixed binary nonionic and ionic surfactants comprising N -methyl-N -decanoyl glucamide (MEGA 10) and alkyltrimethylammonium bromides (C12 -, C14 -, and C16 TAB) has been investigated in detail by different physical methods. The counter-ion binding, aggregation number, and polarity of the mixed micelles have been determined. The results have been analyzed in the light of the theories of Rubingh and Maeda. The thermodynamic parameters of the micellization process have been evaluated and discussed. The interfacial adsorptions of the mixed amphiphiles including their surface excesses and head-group areas have also been evaluated. Based on the head-group areas, the overall shapes of the mixed micelles have been predicted from the estimation of the amphiphile packing parameters. © 2006 Elsevier Inc. All rights reserved. Keywords: MEGA 10; Alkyltrimethylammonium bromides; Mixed micelles; Aggregation; Counter-ion binding; Energetics; Adsorption; Monomer packing

1. Introduction Surfactants are unique chemical compounds [1] to have important physicochemical properties at interfaces and in bulk of their solutions which make them useful in many chemical, physical, biophysical, pharmaceutical, and technological processes. Because of availability of numerous representatives of surfactants by way of synthesis, the studies in this field are ever increasing making them competitive and challenging [2–6]. The ionic and nonionic species have distinctions in solution properties being influenced by the nature of their head groups and tails as well as the environmental conditions. The mixtures of surfactants most often perform better than individuals. Of the different surfactant combinations, the ionic and nonionic mixtures often offer improved properties, viz. better solubilization capacity, enhanced surface activity, increased micellar catalytic property, better foaming and detergency, etc. Investigations in this field mostly use conventional surfactants, * Corresponding author. Fax: +91 33 2414 6266.

E-mail address: [email protected] (S.P. Moulik). 0021-9797/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2006.11.055

the employment of nonconventional amphiphiles remains to be much less. In this context, nonionic surfactants with sugarbased hydrophilic parts have shown differences in properties than those with poly(oxyethylene) group. Recently, alkylpolyglucoside (APG) surfactants [7–13] are gaining importance by virtue of their interesting solution properties. These nonionics have a hydrophilic sugar moiety and a hydrophobic alkanoyl chain. They possess better hydrophobicity and hydrophilicity, salinity or increase in temperature cannot bring about clouding phenomenon in their aqueous solution. They are biodegradable, dermatologically safe, and conveniently applicable in bio-membrane field [14]. They are promising in the formulations of cosmetics, food, and cleaning products, etc. But their solution and surface chemical properties have not been amply explored. This has prompted us to study the interfacial and bulk properties of one of their scantly studied representatives, MEGA 10, in combination with alkyltrimethylammonium bromides (ATABs). Only three reports on the binary mixtures of MEGA 10 with nonionic (poly(oxyethylene) alkyl ethers), anionic (sodium dodecylsulfate, SDS), and cationic surfactants (ATABs) have appeared in recent literature [15–17]. MEGA 10 (CH3 (CH2 )10 –CO–

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CH2 –CH2 (CHOH)4 CH2 OH) is an effective membrane solubilizing amphiphile [18,19]. In aqueous solution, its critical micellar concentration (CMC) is lower than that of SDS [6b, 16] and much lower than C12 TAB [5,17]. Its micellization process is endothermic [11,20] in contrast to SDS [6a,21] and C12 TAB [5], whose self-association processes are exothermic at 303 K. MEGA 10 forms fairly large micelles [11,17] in aqueous medium. The mixed micelles of MEGA 10 with SDS and Cn TABs are formed with fairly low micellar polarity [16,17]. The self-association of MEGA 10 and physicochemical characterization of the process have been elaborately explored [11,21], whereas studies on solution behaviors of their mixtures with other surfactants are only limited [15–17]. We have herein attempted a thorough physicochemical study on different aspects of binary mixtures of MEGA 10 with C12 -, C14 -, and C16 TAB in aqueous medium. The compositiondependent adsorption behavior of the mixed components at the air/solution interface in the light of thermodynamics has been explored, together with the understanding of energetics of mixed micelle formation and mutual interaction of the monomers in the micelle, the micellar aggregation number and polarity, and the monomer packing in the micelles in relation to their shapes. The short range interaction between the dissimilar alkyl chains of the binaries has been assessed, and energetic differences found in the past between the calorimetric and the van’t Hoff procedures for the self-aggregation of pure surfactants has been further demonstrated for the herein studied mixed representatives. 2. Materials The Cn TABs, C16 TAB and C12 TAB were AR grade products of Aldrich (USA); while the C14 TAB was AR grade product of Fluka (Switzerland). The nonionic surfactant MEGA 10 was a product of Dojindo Laboratories, Kumamoto, Japan and was received from Prof. G. Sugihara of Department of Chemistry, Fukuoka University, Fukuoka (Japan). It was purified by repeated recrystallization from 1:9 (v/v) mixed ethanol and ethyl ether. The cetylpyridinium chloride (CPC) used as fluorescence quencher was an AR grade product of Sigma (USA). Pyrene (Aldrich) was obtained from Dr. A.R. Das, Polymer Science Laboratory of IACS, Kolkata (India). It was purified by sublimation, followed by recrystallization from ethanol. All the surfactants were desiccated for a week before use. Doubly distilled conductivity water of conductance 2–4 µS cm−1 at 303 K was used in all solution preparation. The temperature of measurements was maintained at 303 ± 0.01 K, unless stated otherwise. 3. Methods 3.1. Tensiometry The surface tension (γ ) at the air/solution interface of the surfactant solutions was measured with a calibrated Krüss (Germany) tensiometer based on the du Noüy ring detachment method. Concentrated solution of surfactant was progressively added in steps in water, maintained at a constant temperature,

with the help of a Hamilton microsyringe. The surface tensions were measured allowing ∼20 min time for equilibration after each addition. The experiments were duplicated to check their reproducibility. The mean values of the measurements were considered for the data analysis. The γ values were accurate within ±0.1 mN m−1 . 3.2. Conductometry The specific conductance of a surfactant solution was measured using a Jenway conductance bridge (UK) combined with a cell of unit cell constant. The concentration of the surfactant solution was increased progressively following the same protocol as in tensiometry. Measurements were taken after thorough mixing and allowing time for thermal equilibration. The experiments were duplicated and mean values of the results were reported and used. The uncertainties in the measurements were within ±2%. 3.3. Microcalorimetry An Omega ITC microcalorimeter of Microcal, Northampton (USA) was used for thermometric measurements. The calorimetric cell was calibrated following the instructions given in the instrument manual. The error in the heat of dilution was checked by using the experimental surfactant solutions both as the titre and the titrant. The observed error was within ±1.5% which was neglected in the enthalpy calculation. In the actual experiments, concentrated degassed surfactant solution (∼20 times its CMC) was taken in the microsyringe and added in steps injecting 5 µl at each step after equal time intervals (210 s) to 1.325 ml degassed water taken in the calorimeter cell under constant stirring (300 rpm) condition. The calorimeter was set to 298 K with a Neslab RTE 100 bath and scanned to the studied temperature of 303 K which fluctuated within the limit of ±0.01 K. The heat released or absorbed at each step of dilution of the surfactant solution was recorded in the instrument, and the enthalpy change per mole of injectant was calculated by the ITC software. Each run was duplicated to check reproducibility. Further details of the experimental protocol can be found in our earlier reports [20,22,23]. 3.4. Spectrophotometry (absorbance and fluorescence) 3.4.1. Absorbance Absorbance measurements were taken in a UV 1601 Shimadzu (Japan) spectrophotometer using 10 mm path length quartz cuvettes. The spectra of 2 µM pyrene in the surfactant solutions of varied strength were recorded in the 200–400 nm wavelength range. The concentration of the surfactant solution was varied from below to above the CMC by progressive addition of a concentrated surfactant solution into water with a Hamilton microsyringe. The sum of absorbances of the main peaks (AT ) in the spectra was plotted against the surfactant concentration, and the CMCs were obtained from the point of intersection of the straight lines depicted in the figure.

G. Basu Ray et al. / Journal of Colloid and Interface Science 307 (2007) 543–553

3.4.2. Fluorimetry Fluorescence measurements using pyrene as the fluorescence probe were taken in a FluoroMax-3, JOBIN YVON, Horiba (Japan), using a 10 mm path length quartz cuvette. The samples were excited at 331.5 nm and emission was recorded in the 340–450 nm range. The slit widths for both excitation and emission were fixed at 0.4 nm. Surfactant solutions were taken ten times their CMCs, and pyrene concentration in solution was kept at 2 µM (below its solubility limit of 3 µM). At this concentration, probe dimerization was absent and the distribution of the probe molecules was assumed to be guided by the Poisson equation. No components in the system other than pyrene absorbed at the wavelength of excitation so that the inner filter effect was absent. To determine the aggregation number, the quencher (CPC) was progressively added (in the range of 10–50 µM) with a Hamilton microsyringe into the surfactant solution of constant concentration containing pyrene and the fluorescence spectra were recorded. The scan time was fixed at 0.8 s for scanning each wavelength. 4. Results and discussion 4.1. CMCs of the pure and mixed systems Fig. 1 shows representative ITC enthalpograms of MEGA 10 and C14 TAB at five different mole ratios. The thermograms of pure MEGA 10 and C16 TAB are shown in the inset. The Cn TABs showed exothermicity while MEGA 10 showed endothermicity of micellization at 303 K. The enthalpograms showed transition from endothermicity to exothermicity in enthalpy of micellization (Hm ) with increase in the content of Cn TAB in the mixture. The Sigmoidal Boltzmann equation (SBE) was used for the evaluation of CMC and enthalpy of

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micellization (Hm ) following the procedure described earlier [22,23]. In the illustration, the equimolar mixture representation had low Hm and the SBE fitting was poor. The concerned Hm were, therefore, determined by the method of interpolation based on the results obtained for the other compositions. The tensiometric plots for the 1:1 molar mixtures of binaries are presented in Fig. 2, wherein the results on MEGA 10 and C12 TAB are shown in the inset. Apart from determining the CMCs from the break points, the tensiometric data also offered information on the interfacial properties of the studied pure and mixed surfactant systems. The specific conductance (κ) vs concentration plots produced breaks that corresponded to the CMCs of both ionic and ionic–nonionic mixed surfactant systems. MEGA 10–C12 TAB mixtures yielded two breaks in the plots justifying formation of two CMCs, which was also observed in calorimetric and absorption measurements. The conductivity and spectrophotometric results are depicted in Fig. 3. The calorimetric results are not presented. The formation of the second micelles might arise from the morphological change in the primary micelle at higher [surfactant]. Occurrence of two CMCs in pure and mixed micellar systems of Cn TPBs (alkyltriphenylphosphonium bromides) and Cn TABs has been reported in literature [2–5]. An explanation for the occurrence of such a phenomenon is not in hand at present. Small angle X-ray and neutron scattering (SAXS and SANS) measurements might have enlightened on this matter. We are lacking such facilities, but shall explore the matter in a future study. The CMCs of pure MEGA 10, C12 TAB, C14 TAB, and C16 TAB and their binary mixtures determined by tensiometry, conductometry, and microcalorimetry are presented in Table 1, wherein the second CMCs are shown in parentheses. It was observed that microcalorimetry produced higher CMCs for the

Fig. 1. Differential enthalpy of dilution vs [surfactant] profiles for mixed MEGA 10–C14 TAB system at 303 K. Compositions in XC14 TAB are shown against the 0 was symbols in the graph. The points are experimental; the curves are SBE fitted. For XC14 TAB = 0.5, the SBE fitting was poor and hence not shown. The Hm obtained by the method of interpolation (see text Section 4.1). Inset: pure C16 TAB and MEGA 10 at 303 K. The points are experimental; the curves are SBE fitted.

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Fig. 2. Surface tension (γ ) vs log [surfactant] profiles for the 1:1 mixtures of all the binary combinations, MEGA 10–C16 TAB, MEGA 10–C14 TAB, and MEGA 10–C12 TAB at 303 K. Inset: tensiometric profiles for pure MEGA 10 and C16 TAB at 303 K.

Fig. 3. Specific conductance (κ) vs [surfactant] profile for [MEGA 10]:[C12 TAB] = 3:7; and 1:9 at 303 K. Inset: total absorption (AT ) vs [surfactant] plot for the same systems at 303 K, AT was obtained from the summation of absorptions at four different peaks, 260, 272, 320, and 336 nm of pyrene (see Ref. [27] for details). The break points in the plots indicate two CMCs, CMC1 and CMC2 .

mixtures and the tensiometric results were the lowest. As per reports, Wilhelmy method [20] on the average underestimates CMC compared to other methods. However, the CMCs by the different methods were reasonably close (except for calorimetry at two mole fractions of XC14 TAB = 0.7 and 0.9 in its binary mixtures) and we have used the average CMC values for all calculations. The values fairly agreed with those reported by Hierrezuelo et al. [17] by fluorimetry. 4.2. Counter-ion condensation The fraction of counter-ions bound to the micelle (β) gives a fair idea of the micellar surface charge density. It was estimated from conductometry using the slope ratio method. The

method is simple and has good evaluation potential [5,24,25]. The results have been found to fairly agree with that of the EMF method [26]. The pre- and post-CMC slopes (of the linear plots of κ vs [surfactant]) S1 and S2 , respectively, were used in the relation, β = [1 − (S2 /S1 )], to get β (given in Table 1). β increased with increasing proportion of the ionic component in the mixture; the proportion of ionic component thus increased in the mixed micelles. The overall counter-ion condensation for the mixed systems followed the order MEGA 10–C16 TAB > MEGA 10– C14 TAB > MEGA 10–C12 TAB. This was the order of participation of the ionic components in the mixed micelles at a given composition corroborated by the regular solution theory to be discussed in a subsequent section. Rathman and

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Table 1 CMCs of pure MEGA 10, C16 TAB, C14 TAB, C12 TAB, and the studied binary mixtures by different methodsa at 303 K MEGA 10–C16 TAB system XCn TAB CMC (mM)

Tens. Cond. Cal. Ave.b

β

0.0

0.1

0.3

0.5

0.7

0.9

1.0

5.95 – 5.65 5.80

3.55 3.75 – 3.65

1.53 1.78 – 1.66

1.33 1.43 1.67 1.48

1.11 1.24 1.32 1.22

0.97 1.08 1.26 1.10

0.85 1.01 1.09 0.98

0

0.093

0.365

0.506

0.626

0.677

0.710

0.0

0.1

0.3

0.5

0.7

0.9

1.0

5.95 – 5.65 5.80

5.02 5.46 5.60 5.36

4.76 4.66 4.33 4.58

3.93 4.07 4.00 4.00

3.85 4.00 4.90 3.93

3.72 3.89 4.69 3.81

3.82 3.78 4.20 3.93

0

0.204

0.296

0.432

0.577

0.670

0.730

MEGA 10–C14 TAB system XCn TAB CMC (mM)

Tens. Cond. Cal. Ave.

β MEGA 10–C12 TAB system XCn TAB CMC (mM)

β

Tens. Cond. Cal. Ave.

0.0

0.1

0.3

0.5

0.7

0.9

1.0

5.95 – 5.65 5.80 0

6.41 6.46 (15.7) 6.74 6.54 0.150

6.70 6.83 (16.0) 5.80 6.44 0.156

7.57 7.01 (15.6) 7.94 7.51 0.196

9.30 9.54 (14.0) 9.90 (14.0) 9.58 0.330

11.8 12.7 (15.4) 11.7 (16.3) 12.0 0.585

16.2 15.1 16.7 16.0 0.736

a X C12 TAB = 0.7: CMC1 = 9.72, CMC2 = 14.78 mM. XC12 TAB = 0.9: CMC1 = 13.28, CMC2 = 16.91 mM by UV spectroscopy with pyrene as the probe. The errors in CMC by tensiometry, conductometry, and calorimetry were within ±4.0, ±3.0, and ±1.0%, respectively. The errors in β were within ±6.0%. b In the averaging of CMC, CMC Cal at XC14 TAB = 0.7 and 0.9 were not considered for large deviations.

Scamehorn [27] showed earlier that for CPC/nonylphenol poly(ethoxylate) (NP(EO)10 ) mixed micelles, β decreased rapidly with decreasing CPC content at its low stoichiometric composition, while in the regions of higher stoichiometric composition β decreased only feebly. 4.3. Micellar aggregation number and micellar polarity The micellar aggregation number (n) given in Table 2, Section A, was obtained by the static fluorescence quenching method using pyrene as the fluorescence probe and CPC as the quencher on the basis of the following equation,   I0 n[Q] ln (1) = , I [surfactant] − CMC where I0 and I are the fluorescence intensities without and with quencher, respectively; and [Q] is the concentration of the quencher. The plots are presented as Fig. S1 in Supplementary material. The n values fairly agreed with those of Hierrezuelo et al. [17] determined also by the static fluorescence quenching method. The nonionic surfactants are known to form larger micelles, participation of ionic component reduced the aggregation number. Rakshit et al. [15] have reported much higher aggregation number (∼140) for pure MEGA 10 by the static fluorescence quenching method. The n values obtained by Sugihara et al. [11] by the light scattering method are also in agreement with our findings. The MEGA 10–C12 TAB mixed system has evidenced formation of two CMCs (discussed in Section 4.1). The two kinds

of micelles were expected to differ in their n values similar to that witnessed for binary mixtures of Cn TABs in our previous work [5]. There, the two CMCs differed at least by five folds in magnitudes while in the present system, the differences were within two folds. Attempts to determine the aggregation numbers of the assumed two types of micelles produced nonconvincing results. The differences found were only marginal. The physical evidence in favor of two types of micelles in terms of n thus remained unexplored. The SANS could be a decisive method in this matter which is beyond the scope of our existing experimental facilities. The ratio of the fluorescence intensities of the first (373 nm) and third (383 nm) vibronic peaks (I1 /I3 ) in the pyrene spectra gave a measure of the polarity of the pyrene environment in the micelles [28]. The polarity index I1 /I3 should have an inverse dependence on environmental hydrophobicity. The values (given in Table 2, Section A) followed the order C16 TAB < C14 TAB  C12 TAB, which was the order of decreased polarity of the micelles. The highly nonpolar pyrene penetrated deeper in the interior of micelles with higher alkyl chains further away from the water penetration level (3 to 4 carbon atoms in the peripheral region) of the micelles [29]. With decreasing tail length of the Cn TABs, pyrene experienced closer proximity to the penetrated water in the lower Cn TAB micelles and consequently, the polarity index increased. Interestingly, the polarity of pure MEGA 10 micelles is comparable with that of C16 TAB and is less than that of C14 TAB and C12 TAB. This has accounted for the structural difference between the MEGA 10 micelles and the Cn TABs. Accessibility of palisade layer of MEGA 10 micelles to water was less than the Cn TAB micelles, which made

1.0 1.20/1.15/1.49 1.60/1.50/1.10 −78.9/−74.0/−55.2 0.131/0.140/0.190

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the entrapped pyrene to experience an increased nonpolar environment in MEGA 10 micelle than that in C12 TAB with comparable hydrophobic alkyl chains. In the mixed micelles, the polarity eventually increased mildly with decreasing Cn values in the Cn TABs. But lowering of polarity than the parent MEGA 10 micelle was observed at lower mole fraction of the cationics in the mixture. A structural change leading to compactness in the mixed species was envisaged.

0.9 1.65/1.50/1.53 0.995/1.08/1.09 −69.5/−66.9/59.5 0.132/0.145/0.220

4.4. Interfacial behaviors of MEGA 10 and the ATABs in pure and mixed states The maximum adsorption of a surfactant at the air/solution interface was obtained from the Gibbs adsorption equation in the following form [5,6a], Γmax = − a Errors in n values were within ±5.0%. b v = 0.296, l = 1.42 for MEGA 10; v = 0.458, l = 2.18 for C TAB; v = 0.404, l = 1.93 for C TAB; v = 0.350, l = 1.67 for C TAB. c c c c 16 14 12

0.1 1.70/2.10/1.87 0.976/0.794/0.886 −49.4/−48.7/−48.4 0.183/0.272/– 0.0 3.90/3.90/3.90 0.426/0.426/0.426 −33.7/−33.7/−33.7 0.490/0.490/0.490 XCn TAB Γmax × 106 (mol m−2 ) Amin (nm2 ) G0ad (kJ mol−1 ) R Peff

R values Section B: Γmax , Amin , G0ad , and Peff System sequence at each mole fraction: MEGA 10–C16 TAB/MEGA 10–C14 TAB/MEGA 10–C12 TAB

0.3 1.23/2.00/1.76 1.35/0.842/0.942 −67.8/−52.0/−48.8 0.157/0.204/0.328

0.5 1.45/2.00/1.74 1.16/0.849/0.953 −67.1/−55.0/−49.2 0.144/0.178/0.292

0.7 1.39/1.50/1.62 1.19/1.14/1.02 −72.3/−64.7/-50.6 0.137/0.157/0.259

1.0 61/70/63 1.06/1.10/1.27 0.7 57/72/75 1.04/1.05/1.04 0.5 72/80/83 1.02/1.03/1.02 0.3 67/78/80 1.00/1.01/1.00 0.0 88/88/88 1.05/1.05/1.05 XCn TAB n I1 /I3

Section A: n and I1 /I3 values System sequence at each mole fraction: MEGA 10–C16 TAB/MEGA 10–C14 TAB/MEGA 10–C12 TAB

Table 2 The micellar aggregation numbera (n), polarity index (I1 /I3 ), surface excess (Γmax ), area minimum (Amin ), free energy of adsorption (G0ad ), and packing parameter (P )b for the pure and mixed systems at 303 K

548

1 2.303iRT

lim

C→CMC

dγ mol m−2 , d log C

(2)

where the new terms, C = [surfactant] and i is the number of species formed in solution by way of dissociation and otherwise per monomer. The minimum area per head group (Amin ) of surfactant molecules at CMC at the saturated interface was obtained from the relation, Amin =

1018 nm2 molecule−1 , NA Γmax

(3)

where NA is the Avogadro number. The calculated values of Γmax and Amin for all the compositions are presented in Table 2, Section B. The pure Cn TABs produced much lower Γmax than pure MEGA 10; mutual repulsion between the ionic head groups of the Cn TABs led to surface saturation at a comparatively lower concentration than the neutral MEGA 10 molecules. For the binary mixtures, intermediate Γmax values were found. The Amin values were complimentary to those of Γmax . The Amin for MEGA 10 was somewhat lower than the findings of Rakshit et al. [15]. The magnitude of Amin depends on the nature and type of the hydrophilic group. The ionic head groups occupy greater areas by way of mutual electrostatic repulsion. Rubingh’s analysis (to be discussed later) has estimated the proportion of the ionic components in the mixed micelles of MEGA 10–Cn TABs to vary in the order C16 TAB > C14 TAB > C12 TAB. Thus, for a given mixture, the Amin values were fairly higher in the MEGA 10–C16 TAB system than MEGA 10– C14 TAB than MEGA 10–C12 TAB. The standard Gibbs energy of adsorption (G0ads ) at the air/solution interface was obtained from the relation, G0ads = G0mic − (πCMC /Γmax ),

(4)

where G0mic is the standard Gibbs energy of micellization (discussed later), and πCMC is the surface pressure at CMC. The standard state was considered as the hypothetical state of ideal solution of unit mole fraction. The G0ads values are included in Table 2, Section B. The ratio of G0ads /G0mic was found to be ∼2 for the pure Cn TABs as well as the binary mixtures at all compositions;

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Fig. 4. Dependence of average CMCs of mixed MEGA 10–Cn TAB systems on XCn TAB at 303 K. Points are experimental; curves are according to Clint. The systems are identified in the figure by symbols.

this indicated two-fold higher thermodynamic spontaneity of the process of transfer of the surfactant monomers at the interface than their transfer from the bulk into the micelles. But for pure MEGA 10, G0ads /G0mic was found to be ∼1.46 indicating less spontaneity in the transfer of the monomers to the interface in the absence of the Cn TABs in the system. 4.5. Mutual interaction between the two types of surfactant monomers in the mixed micelles The nature of interaction between Cn TAB and MEGA 10 molecules in their mixed micelles can be understood in terms of the Clint equation [30] for ideal (noninteracting) mixed systems, 1 1 − x1 x1 + , = CMC CMC1 CMC2

(5)

where CMC denotes that of the mixed micelle, x1 is the stoichiometric mole fraction of the component 1, and CMC1 and CMC2 are the CMCs of the components 1 and 2, respectively. The CMC has been profiled against x1 in Fig. 4, which for all the three binary combinations fell below the Clint’s courses (full line curves) suggesting nonideality with synergism. Rubingh’s regular solution theory (RST) [31] was used for quantification of the effect. The RST for its simplified approach is mostly used and was considered for analysis over other complex models [32–35]. For nonideality the interaction parameter g is given by the relation,

g=

ln(x1 CMC/x1R CMC1 ) (1 − x1R )2

,

(6)

where x1R is the micellar mole fraction of component 1. x1R can be obtained from the following equation,  CMCx1  (x1R )2 ln CMC R 1 x1 (7)  = 1.  CMC(1−x (1 − x1R )2 ln CMC (1−x1R)) 2

1

The equation was iteratively solved for x1R using a computer programme. The activity co-efficients of both ionic and nonionic components in the mixed micelles f1R and f2R , respectively, were obtained from the relations, 2    f1R = exp g 1 − x1R ,   2  f2R = exp g x1R . (8) The values of the parameters x1R , g, f1R , and f2R for the studied systems are given in Table 3, Section A. The negative g values supported synergistic interaction between MEGA 10 and Cn TABs in the mixed micelles. In the ionic/nonionic mixed micelles, synergism arises owing to the reduction of the electrostatic repulsion between the ionic components by the presence of the nonionic components. The Cn TABs took fair shares in the formation of the mixed aggregates than MEGA 10, and at comparable solution compositions, because of grater hydrophobicity, C16 TAB’s contribution was greater than the other two representatives. The presence of Cn TABs of varied alkyl chain lengths resulted in dissimilar interactions with MEGA 10 producing different g for them. According to RST, for a particular system g should remain independent of composition which is often not realized in practice. In this study, the parameter was found to be composition dependent like earlier reports on anionic– nonionic mixtures of sodium oleate with the alcohol ethoxylates and that of sodium decylsulfate with poly(oxyethylene) glycol n-nonylphenyl ethers [36–38]. We have herein reported the average values (gave ) as very often done [2,17,39] to assess the

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Table 3 R , g, f1R , f2R and Maeda’s parameters B0 , B1 , B2 , Gmic , and (1 + β)Gmic at 303 K for the mixed micellar systems The Rubingh’s parameters XC n TAB R Section A: XC , g, f1R , and f2R values n TAB System sequence at each mole fraction: MEGA 10–C16 TAB/MEGA 10–C14 TAB/MEGA 10–C12 TAB

XCn TAB R XC n TAB g f1R

0.1 0.41/0.16/– −0.29/−0.22/– 0.91/0.86/–

0.3 0.63/0.41/0.20 −1.6/−0.44/−0.79 0.81/0.86/0.60

0.5 0.79/0.58/0.32 −1.1/−0.75/−0.67 0.96/0.88/0.73

0.7 0.89/0.73/0.47 −1.8/−0.59/−0.41 0.98/0.96/0.89

0.9 0.99/0.89/0.72 –/−1.75/−0.75 1.02/0.98/0.94

f2R

9.16/0.14/–

0.19/0.14/0.40

4.42/0.12/0.27

2.09/4.23/0.11

−2.04/2.09/6.25

Section B: B0 , B1 , B2 , Gmic and (1 + β)Gmic values System sequence at each mole fraction: MEGA 10–C16 TAB/MEGA 10–C14 TAB/MEGA 10–C12 TAB B0 a B1 a B2 a Gmic /kJ mol−1 (1 + β)Gmic /kJ mol−1

−9.17 (−9.20)/−9.17 (−9.20)/−9.17 (−9.20) −3.29 (−3.089)/−0.797 (−1.00)/0.362 (0.799) 1.52 (1.36)/0.408 (0.630)/0.652 (0.210) −23.9/−23.3/−23.0 −25.2/−23.6/−22.7 −26.1/−28.0/−26.5 −34.5/−30.6/−26.2

−26.3/−23.9/−22.2 −39.6/−34.2/−26.6

−27.0/−24.0/−21.7 −44.0/−37.8/−28.8

−27.5/−24.1/−21.0 −46.1/−40.2/−33.2

a Parenthetic values were of Hierrezuelo et al. [18].

extent of interaction. The gave were found to be −1.52, −0.88, and −0.65 for MEGA 10–C16 TAB, MEGA 10–C14 TAB, and MEGA 10–C12 TAB combinations, respectively. In this averaging, the g values at XCn TAB = 0.1 were not considered for their wide variations from the rest. A point of anomaly in the determination of g may be mentioned here. It has been reported in the past [2,4,37,40,41] that the iterative procedure to evaluate g from Eq. (6) may become susceptible to small variations in the magnitude of CMC for certain compositions. For some specific values, g may become also indeterminable. Similar situation arose for MEGA 10– C16 TAB for XC16 TAB = 0.1 and 0.9. Besides, the f2R values for XC16 TAB = 0.1, 0.5, 0.7, and 0.9, and for XC12 TAB = 0.9 in the combinations were fairly greater than unity. These arose due to the limitations of the Rubingh’s formalism. The nonconsideration of the effects like counter-ion binding, chain length mismatch, ionic strength variation, etc. could be the reasons for affecting the evaluation procedure and the results. We have made a comparison of our RST results with that of Hierrezuelo et al. [17] wherein the XCRn TAB values at our studied compositions were not reported. Those were obtained using their mixed micelle CMC values in Eq. (8). The two reports fairly agreed save some anomalies beyond XCn TAB > 0.6 for C14 - and C16 TAB mixed system. Maeda [42] in his phenomenological treatment on ionic– nonionic mixed micelle formation (based on phase separation model) has suggested a quantitative understanding of the micellar stability in terms of the free energy of micellization (Gmic ) using a three parameter equation,   Gmic = RT B0 + B1 x1 + B2 x12 , (9) where B0 is an independent term related to the CMC of the nonionic component (component 2), and is given by the relation, B0 = ln CMC2 .

(10)

B1 accounts for the standard free energy change when a nonionic surfactant monomer in the pure nonionic micelle is replaced by an ionic one: it arises from short-range interaction of

the components. B2 is taken to be the electrostatic interaction parameter g considered in Rubingh’s formalism with changed sign (B2 = −g). B1 and B2 are inter related with each other through their CMCs by the relation, ln

CMC1 = B1 + B2 . CMC2

(11)

The parameters B0 , B1 , and B2 evaluated for the MEGA 10– ATAB combinations are presented in Table 3, Section B, wherein the results of Hierrezuelo et al. [17] are compared. The B0 values of the two reports nicely agreed. The B1 and B2 values for the system containing C16 TAB were also comparable. Such values for MEGA 10–C14 TAB and MEGA 10– C12 TAB differed since our CMC values for these combinations were not in good agreement with Hierrezuelo et al. But the results suggested manifestation of short-range interaction between the nonionic and the ionic components with dissimilar chain lengths. The values of the three parameters B0 , B1 , and B2 for a number of ionic/nonionic surfactant pairs have been reported by Maeda [42] for the understanding of the nature of interaction among the pairs. We have calculated the Gmic for all the three studied binary surfactant mixtures; the values are given in Table 3, Section B. For the MEGA 10–C12 TAB system, the thermodynamic spontaneity was less compared with that in MEGA 10–C14 TAB and MEGA 10–C16 TAB. In the latter two, spontaneity increased with increasing stoichiometric content of the ionic component in the mixture, which was fairly constant for the former. We infer that with increasing alkyl chain length short-range interaction displayed better compatibility between MEGA 10 and the Cn TABs to register better synergism. Like Rubingh, Maeda’s treatment [42] of free energy of mixed micelle formation ignores the contribution of the bound counter-ions. The calculated Gmic by the relation, therefore, did not corroborate with the G0mic calculated from the free energy relation considering the counter-ion binding (by Eq. (12) to be discussed below). For total agreement, Eq. (9) requires to be multiplied by the term (1 + β). For low values of g, the multiplication term (1 + β) ≈ 1 and both the methods should

G. Basu Ray et al. / Journal of Colloid and Interface Science 307 (2007) 543–553

551

0 of the mixed MEGA 10–C TAB systems: (A) (2, 1) X Fig. 5. (G0m /T ) vs (1/T ) plots to derive Hm n C16 TAB = 1.0, 0.5; (Q, P) XC14 TAB = 1.0, 0.5; (a, e) XC12 TAB = 1.0, 0.5. (B) (2, 1) XC16 TAB = 0.7, 0.3; (Q, P) XC14 TAB = 0.7, 0.3; (a, e) XC12 TAB = 0.7, 0.3. Average correlation coefficient = 0.986.

produce comparable results. Such was the observation of Rakshit et al. [38] on mixed Brij 35–C14 TAB system. In their work, Hierrezuelo et al. [17] did not evaluate the thermodynamic parameters. We have observed appreciable β values so that correction of Gmic of Maeda needed to be done. Both Gmic and corrected values (Gcorr mic ) are presented in Table 3, Section B. The latter nicely tallied with the G0mic obtained from Eq. (12), and recorded in Table 4, column 3. Maeda’s treatment thus gives only a partial understanding of the energetics of the process. 4.6. Thermodynamics of micellization In this study, the standard Gibbs free energy change was calculated employing both the mass action model and the pseudophase model [43]. Thus,     RT 0 ln 2n2 (1 + β) Gmic = (1 + β)RT ln XCMC + n (mass action model, MM), (12) G0mic = (1 + β)RT ln XCMC (pseudo phase model, PM).

(13)

The enthalpy change for the process of micellization was directly determined from isothermal titration calorimetry [22,23], so that, 0 (Cal). Hmic = Hmic

(14)

Since the micellization of the Cn TABs was exothermic and that of MEGA 10 was endothermic at the studied temperature, 303 K, several binary compositions resulted in much narrow and condensed enthalpograms from which determination 0 needed careful analysis and verification by of CMC and Hmic repetitive measurements. A discussion on this point has been made in Section 4.1 with reference to Fig. 1. This has prompted

0 by the van’t Hoff method. The us also to estimate the Hmic CMCs of the mixed systems at five to six different temperatures were determined by the conductance method from the break points of the plots between κ and [surfactant]. A representative plot for 1:1 molar mixture of MEGA 10–C16 TAB is shown as Fig. S2 and the derived CMCs for the experimented systems at different temperatures are presented as Table S1 in Supplementary material. The plot of (G0mic /T ) against T −1 0 from the slope by the least squares was used to get the Hmic 0 values are included procedure (Fig. 5). The evaluated Hmic in Table 4 along with the calorimetric results. The van’t Hoff method of analysis was also considered for another reason. In recent years, we have shown fair disagreements between calorimetric and van’t Hoff enthalpies of micellization particularly for ionic surfactants [44–46]. Even CMCs determined by the calorimetric method at different temperatures when processed by the van’t Hoff procedure have shown large differences. These discrepancies have been accounted for the differences between the principles of the two kinds of assessments; the calorimetric method is an integral method whereas the van’t Hoff procedure is a differential method. The entropy changes of micellization were obtained from the Gibbs–Helmholtz re0 = (H 0 − G0 )/T . The G0 lation, Smic mic mic mic values by both MM and PM were quite close, MM values being slightly lower than the PM values. The values suggested best participation of C16 TAB among the three Cn TABs in the formation of mixed micelles. 0 by calorimetry declined with increasThe moderate Hmic ing mole fraction of the ionic component in solution with a change in sign that manifested at higher mole fraction with decreasing alkyl chain length of the Cn TAB component. It resulted from the endothermic–exothermic balance between the interacted MEGA 10 and the Cn TABs. 0 by the van’t Hoff procedure were all exotherThe Hmic mic and several fold higher. The associated process of changing

552

G. Basu Ray et al. / Journal of Colloid and Interface Science 307 (2007) 543–553

Table 4 0 , and S 0 for pure MEGA The thermodynamic parametersa G0mic , Hmic mic 10, C16 TAB, C14 TAB, and C12 TAB and the studied binary mixtures at 303 K

the formula of Tanford [48]. Thus,

MEGA 10–C16 TAB system

where lmax is the maximum length of the chain. The volume contribution of the hydrophobic chain was also suggested by Tanford:

XCn TAB 0.0 0.1 0.3 0.5 0.7 0.9 1.0

G0mic (kJ mol−1 )

0 (kJ mol−1 ) Hmic

0 (J mol−1 ) Smic

PM

MM

SBE

van’t Hoff

SBE

van’t Hoff

−23.1 −26.5 −35.8 −40.0 −43.9 −45.8 −47.2

−22.8 – −35.5 −39.6 −43.5 – −46.8

+3.11 – – −2.27 −5.84 −9.30 −7.69

– −48.6 −47.8 −47.0 −45.9 −45.5 −44.8

86.5 – – 123 126 120 130

– −69.9 −38.8 −22.7 −6.17 1.06 7.26

MEGA 10–C14 TAB system XCn TAB

G0mic (kJ mol−1 )

0 (kJ mol−1 ) Hmic

0 (J mol−1 ) Smic

PM 0.0 0.1 0.3 0.5 0.7 0.9 1.0

−23.1 −28.0 −30.7 −34.4 −38.0 −40.3 −41.7

MM

SBE

van’t Hoff

SBE

van’t Hoff

−22.8 – −30.4 −34.1 −37.6 – −41.3

+3.11 +3.00 +1.72 +0.531 −3.11 −6.36 −6.98

– −41.4 −39.7 −33.4 −30.8 −23.8 −18.6

86.5 102 107 115 115 112 114

– −44.2 −30.0 3.04 23.8 54.5 76.7

MEGA 10–C12 TAB system XCn TAB 0.0 0.1 0.3 0.5 0.7 0.9 1.0

G0mic (kJ mol−1 )

0 (kJ mol−1 ) Hmic

0 (J mol−1 ) Smic

PM

MM

SBE

van’t Hoff

SBE

−23.1 −26.2 −26.4 −26.8 −29.0 −33.7 −35.7

−22.8 – −26.1 −26.6 −28.7 – −35.3

+3.11 +3.20 +2.23 +2.40 – – −2.80

– −17.2 −15.6 −13.3 −11.9 −10.3 −9.15

86.5 97.0 94.4 96.5 – – 108

van’t Hoff – 30.4 34.7 45.2 56.8 76.4 83.3

a The errors in G0 , H 0 , and S 0 were within 3.0, 5.0, and 7.0%, mic mic mic respectively.

aggregation number, solvation–desolvation, head-group repulsion, orientation and other nonspecific processes contributed their shares to the integral enthalpy of calorimetry. The lower and higher degree of disagreements between the two methods depend on the types of the aggregated species, their compositions and environment. The ionic systems are more prone to such effects than the nonionics. 4.7. Amphiphile packing in micelles According to Israelachvili [47], the nature of amphiphile packing in micelles and their structural geometry can be predicted using a packing parameter (P ) defined by the relation, v , P= (15) Alc where lc is the maximum effective length of the hydrophobic chain of a monomer, A is the surface area of the head group, and v is the volume of the hydrophobic chain considered to be fluid and incompressible. The critical or effective length for a saturated hydrocarbon chain with Cn number of carbon atoms can be obtained from

lc  lmax ≈ (0.154 + 0.1265Cn ) nm,

v = (0.0274 + 0.0269Cn ) nm3 .

(16)

(17)

Another requirement for calculating P , is the value of A. In our earlier works [6a,49], the head-group cross-sectional areas at CMC, i.e., Amin obtained from tensiometry were used, but this Amin corresponds to an interfacial property of the surfactant monolayer and is supposed to be different from the actual A value at the micellar surface. In the absence of an exact estimation, we have used the Amin values in our calculation. For the mixed micelles, we used the equation of Peffect as in the earlier study [49],    vi ximic v Peffect = (18) =  , Alc effect ( Ai ximic )lc where ximic and Ai are the micellar mole fraction and the Amin of the ith component in the mixed micelle, respectively. The packing parameters for all the three binary mixtures at all compositions are presented in Table 2, Section B. The micellar mole fraction obtained from Rubingh’s model was used as ximic in the calculation. The shape and type of amphiphilic aggregates can be predicted from the magnitude of P or Peff . For spherical assemblies, P  0.333; for nonspherical shape, 0.333 < P < 0.5; for vesicles and bilayers, 0.5 < P < 1 and for inverted structures P > 1. According to the above rationale, the ionic Cn TABs produced spherical micelles while nonionic MEGA 10 yielded nonspherical (prolate or oblate) micelles. Usually, nonionic surfactants tend to form nonspherical micelles as reported for Brij 56 [49] and Triton X 100 [45]. For MEGA 10–C16 TAB and MEGA 10–C14 TAB mixtures, the mixed micelles were all spherical in shape, but in MEGA 10–C12 TAB system at XC12 TAB = 0 to 0.3 composition, due to predominance of MEGA 10 in the mixed micelle, the micellar shapes were nonspherical. SANS measurements [50] on the herein studied systems could lend support to the abovedescribed features. Such facility is not available to us at present. 5. Conclusions MEGA 10–Cn TAB combines represent examples of compatible surfactant pairs manifesting synergism in their mixed micelles with fairly large negative Rubingh interaction parameter, g. Although the topologies of the mixed micelles and their state of aggregation have only minor dependence on solution composition, the micellar composition has perceptible dependence on it. The ionic component takes a greater share in the micelles than the nonionic because of their self-aggregation tendency at lower concentration than MEGA 10. The negative values of the Maeda’s parameter B1 has spoken in favor of short-range attractive interaction related to hydrocarbon chain dissimilarities between the nonionic and ionic amphiphile components that increase with increasing alkyl chain in the Cn TAB.

G. Basu Ray et al. / Journal of Colloid and Interface Science 307 (2007) 543–553

But the Gibbs free energy of micellization by Maeda’s formalism is appreciably lower than that is obtained from Eq. (13). The discrepancy arises for the neglect of counter-ion condensation in Maeda’s treatment, which is considered to be a weakness of the formalism. Further, the complete thermodynamic analysis reveals a striking difference between the values of Hm0 and S 0 found from the indirect van’t Hoff method and the direct calorimetric method. The calorimetry measures the resultant heat of different involved physical chemical processes during amphiphile self-association whereas the differential method of van’t Hoff essentially measures the heat of micelle formation and hence the difference. Further work in this direction is warranted. Acknowledgments G.B.R. and I.C. thank CSIR for a JRF and a SRF, respectively. S.P.M. thanks INSA for a Senior Scientist position during the tenure of which this work was performed. Our sincere appreciation to Dr. D.N. Nath of IACS, Kolkata for assisting us in fluorescence spectral measurements. Supplementary material The online version of this article contains additional supplementary material. Please visit DOI: 10.1016/j.jcis.2006.11.055. References [1] (a) S.P. Moulik, Curr. Sci. 71 (1996) 368; (b) J.H. Clint, Surfactant Aggregation, Blackie, London, New York, 1991, published in USA by Chapman & Hall. [2] C. Treiner, A. Makayassi, Langmuir 8 (1992) 794, and references therein. [3] M. Prasad, S.P. Moulik, A. MacDonald, R. Palepu, J. Phys. Chem. B 108 (2004) 355. [4] M. Prasad, S.P. Moulik, R. Palepu, J. Colloid Interface Sci. 284 (2005) 658. [5] G. Basu Ray, I. Chakraborty, S. Ghosh, S.P. Moulik, R. Palepu, Langmuir 21 (2005) 10958. [6] (a) G. Basu Ray, I. Chakraborty, S. Ghosh, S.P. Moulik, Colloid Polym. Sci., in press; (b) P.C. Griffiths, N. Hirst, A. Paul, S.M. King, R.K. Heenan, R. Farley, Langmuir 20 (2004) 6904. [7] (a) P.C. Griffiths, P. Stilbs, K. Paulsen, A.H. Howe, A.R. Pitt, J. Phys. Chem. B 101 (1997) 915; (b) P.C. Griffiths, A.Y.F. Cheung, G.J. Finney, C. Farley, A.R. Pitt, A.M. Howe, S.M. King, R.K. Heenan, B.L. Bales, Langmuir 18 (2002) 1065; (c) K. Kameyama, A. Muroya, T. Takagi, J. Colloid Interface Sci. 196 (1998) 48. [8] J.D. Hines, R.K. Thomas, P.R. Garret, G.K. Rennie, J. Penfold, J. Phys. Chem. B 101 (1997) 9216. [9] (a) T. Arai, K. Takasugi, K. Esumi, J. Colloid Interface Sci. 197 (1998) 94; (b) P. Liljekvist, B. Kronberg, J. Colloid Interface Sci. 222 (2000) 159; (c) J.C. Drummond, G.G. Warr, F. Griesser, B.W. Ninham, D.F. Evans, J. Phys. Chem. 89 (1985) 2103; (d) Y. Yunomiya, T. Kunitake, T. Tanaka, G. Sugihara, T. Nakashima, J. Colloid Interface Sci. 208 (1998) 1. [10] M.L. Sierra, M. Svensson, Langmuir 15 (1999) 2301. [11] T. Okano, T. Tamura, Y. Abe, T. Tsuchida, S. Lee, G. Sugihara, Langmuir 16 (2000) 1508. [12] M.J. Rosen, S.B. Sulthana, J. Colloid Interface Sci. 239 (2001) 528.

553

[13] P. Del Burgo, E. Junquera, E. Aicart, Langmuir 20 (2004) 1587. [14] M.T. Garcia, I. Ribosa, E. Campos, J. Leal Sanchez, Chemosphere 35 (1997) 545. [15] S.B. Sulthana, P.V.C. Rao, S.G.T. Bhat, T.Y. Nakano, G. Sugihara, A.K. Rakshit, Langmuir 16 (2000) 980. [16] J.M. Hierrezuelo, J. Aguiar, C.C. Ruiz, Langmuir 20 (2004) 10419, and references therein. [17] J.M. Hierrezuelo, J. Aguiar, C.C. Ruiz, J. Colloid Interface Sci. 294 (2006) 449, and references therein. [18] M. Kidric, J. Petrovic, V. Soskic, D. Trajkovic, Br. J. Pharmacol. 83 (1984) 687. [19] F. Yu, R.E. McCarty, Arch. Biochem. Biophys. 61 (1985) 238. [20] M. Prasad, I. Chakraborty, A.K. Rakshit, S.P. Moulik, J. Phys. Chem. B 110 (2006) 9815. [21] T. Okano, Y. Abe, M. Tanaka, Bull. Chem. Soc. Jpn. 60 (1987) 2718. [22] P.R. Majhi, S.P. Moulik, Langmuir 14 (1998) 3986. [23] S.K. Hait, P.R. Majhi, A. Blume, S.P. Moulik, J. Phys. Chem. B 107 (2003) 3650. [24] (a) M. Abu-Hamdiyyah, L. Al-Mansour, J. Phys. Chem. 83 (1979) 2236; (b) H. Hoffmann, G. Platz, H. Rehage, W. Schott, W. Ulbricht, Ber. Bunsen-Ges. Phys. Chem. 85 (1981) 255. [25] (a) M. Benrraou, B.L. Bales, R. Zana, J. Phys. Chem. B 107 (2003) 13432; (b) A.C.F. Ribiero, V.M.M. Lobo, A.J.M. Valente, E.F.G. Azevedo, M. da G. Miguel, H.D. Burrows, Colloid Polym. Sci. 283 (2004) 277; (c) R. Delisi, A. Inglese, S. Milioto, A. Pellerito, Langmuir 13 (1997) 192. [26] (a) D.F. Evans, M. Allen, B.W. Ninham, A. Fonda, J. Sol. Chem. 13 (1984) 87; (b) K.M. Kale, E.L. Cussler, D.F. Evans, J. Phys. Chem. 84 (1980) 593; (c) K.M. Kale, E.L. Cussler, D.F. Evans, J. Sol. Chem. 11 (1983) 581; (d) A. Bandyopadhyay, S.P. Moulik, Colloid Polym. Sci. 266 (1988) 455. [27] J.F. Rathman, J.F. Scamehorn, J. Phys. Chem. B 88 (1984) 5807. [28] K. Kalyansundaran, J.K. Thomas, J. Am. Chem. Soc. 99 (1977) 2039. [29] G. Basu Ray, I. Chakraborty, S.P. Moulik, J. Colloid Interface Sci. 294 (2006) 248. [30] J.H. Clint, J. Chem. Soc. Faraday Trans. 71 (1975) 1327. [31] D.N. Rubingh, in: Solution Chemistry of Surfactants, Plenum, New York, 1979. [32] K. Motomura, M. Yamanaka, M. Aratono, Colloid Polym. Sci. 262 (1984) 948. [33] G.S. Georgiev, Colloid Polym. Sci. 274 (1996) 49. [34] R. Nagarajan, Langmuir 1 (1985) 331. [35] R. Nagarajan, Adv. Colloid Interface Sci. 26 (1986) 205. [36] S.K. Suri, H.S. Randhawa, J. Surf. Sci. Technol. 5 (1989) 385. [37] P.K. Jana, S.P. Moulik, J. Phys. Chem. 95 (1991) 9525. [38] K. Shivaji Sharma, S.R. Patil, A.K. Rakshit, K. Glenn, M. Doiron, R.M. Palepu, P.A. Hassan, J. Phys. Chem. B 108 (2004) 12804. [39] M.P. Rodgers, C.C. Rodgers, A.K. Rakshit, R.M. Palepu, Colloid Polym. Sci. 281 (2003) 800. [40] Md.E. Haque, S.P. Moulik, A.K. Rakshit, A.R. Das, Langmuir 12 (1996) 4084. [41] H. Kawamura, M. Manabe, H. Saio, H. Takahashi, S. Takunaga, Niihama Kogyo Koto Senmon Gakko Kiyo Rikogaku-hen 25 (1989) 86. [42] H. Maeda, J. Colloid Interface Sci. 172 (1995) 98. [43] Y. Moroi, Micelle: Theoretical and Applied Aspects, Plenum, New York, 1992. [44] A. Chatterjee, S.P. Moulik, S.K. Sanyal, B.K. Mishra, P.M. Puri, J. Phys. Chem. 105 (2001) 12823. [45] A. Chatterjee, S. Maiti, S.K. Sanyal, S.P. Moulik, Langmuir 18 (2002) 2998. [46] I. Chakraborty, S.P. Moulik, J. Phys. Chem., submitted for publication. [47] J.N. Israelachvili, Intermolecular and Surface Forces, second ed., Academic Press, London, 1991. [48] C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Wiley, New York, 1980. [49] T. Chakraborty, S. Ghosh, S.P. Moulik, J. Phys. Chem. B 109 (2005) 14813. [50] G. Garg, P.A. Hassan, V.K. Aswal, S.K. Kulshreshtha, J. Phys. Chem. B 109 (2005) 1340.