Interaction, Stability, and Microenvironmental Properties of Mixed

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Langmuir 2000, 16, 7946-7953

Interaction, Stability, and Microenvironmental Properties of Mixed Micelles of Triton X100 and n-Alkyltrimethylammonium Bromides: Influence of Alkyl Chain Length C. Carnero Ruiz* and J. Aguiar Departamento de Fı´sica Aplicada II, Escuela Universitaria Polite´ cnica, Universidad de Ma´ laga, Campus de El Ejido, E-29013 Ma´ laga, Spain Received February 3, 2000. In Final Form: July 11, 2000 Micellar properties of binary surfactant systems of Triton X100 (TX100) with three different n-alkyltrimethylammonium bromides (n ) 12 (DTAB), 14 (TTAB), and 16 (CTAB)) were investigated by the fluorescence probe technique. The critical micelle concentration (cmc) values of the corresponding mixtures in the whole range of composition were obtained by the pyrene 1:3 ratio method. In order to estimate the interaction between the surfactants in the mixed micelles, the cmc data were treated by using the conventional regular solution approach for mixed micelles. It was found that whereas the interaction parameter values (β12) remained fairly constant for the TX100-TTAB and TX100-CTAB systems, the TX100-DTAB system was not well modeled by using that theory. However, in all cases the results showed deviation from ideal behavior. The stability of the mixed micelles was also discussed in the light of Maeda’s treatment (J. Colloid Interface Sci. 1995, 172, 98), and the observed differences between the three systems were justified on the basis of a certain steric factor due mainly to the presence of the phenyl group of TX100 in connection with the length of the monomer of the cationic component. The micropolarity of the mixed aggregates was examined by the pyrene 1:3 ratio index in micellar solutions of concentration well above the cmc. It was observed that the increasing participation of the ionic component induces the formation of more closed micelles with a more dehydrated structure. The polarized fluorescence measurements, by using diphenylbutadiene as a probe, were interpreted by using the wobbling in cone model. It was found that the order parameter decreases as the participation of the cationic surfactant in the micelle increases, indicating the formation of a less ordered structure than that of pure TX100 micelles. Data obtained in this investigation allowed to establish a clear correlation between micellar stability and microenvironmental properties of the mixed aggregates.

Introduction Surfactant solutions are used widely in numerous technical applications such as detergents, cosmetics, pharmaceuticals, enhanced oil recovery or surfactantbased separation processes, to name only a few. However, the systems employed in these applications almost always consist of a mixture of surfactants. This is so because (i) technical-grade surfactants are themselves mixtures, and the purification process may be difficult or excessively expensive, and (ii) the mixed system often behaves better than a single surfactant.1-5 The widespread use of surfactant mixtures for industrial purposes has stimulated the interest of the researchers, and in recent years many papers have been published on the solution properties of mixed surfactant systems. Most of these investigations deal with the study of certain physical properties of the solution. In particular, the variation of the critical micelle concentration (cmc) and of the size or micellar aggregation number with the composition of the system have been the most studied aspects.6-22 Moreover, because the structural * Corresponding author. E-mail: [email protected]. (1) Abe, M.; Ogino, K. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 1. (2) Hill, R. M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 317. (3) Kronberg, B. Curr. Opin. Colloid Interface Sci. 1997, 2, 456. (4) Desai, T. R.; Dixit, S. G. J. Colloid Interface Sci. 1996, 177, 471. (5) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 1618. (6) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984. (7) Graciaa, A.; Ben Ghoulam, M.; Marion, G.; Lachaise, J. J. Phys. Chem. 1989, 93, 4167. (8) Yu, Z.-J.; Zhao, G.-X. J. Colloid Interface Sci. 1993, 156, 325.

properties of the mixed aggregates can become sustantially different from those formed only by the single surfactant,1 many recent investigations were concerned with different structural aspects of micelles composed from a twocomponent surfactant mixture. These studies have commonly been performed by using some spectroscopic techniques, which provide information at a molecular level.23-32 On the other hand, it is widely recognized that (9) Rosen, M. J.; Zhu, Z. H.; Gao, T. J. Colloid Interface Sci. 1993 157, 254. (10) Hassan, P. A.; Bhagwat, S. S.; Manohar, C. Langmuir 1995, 11, 470. (11) Ivanova, N. I.; Volchkova, I. L.; Shchukin, E. D. Colloid J. 1996, 58, 178. (12) Haque, M. E.; Das, A. R.; Rakshit, A. K.; Moulik, S. P. Langmuir 1996, 12, 4084. (13) Attwood, D.; Mosquera, V.; Novas, L.; Sarmiento, F. J. Colloid Interface Sci. 1996, 179, 478. (14) Sarmiento, F.; Lo´pez-Fonta´n, J. L.; Prieto, G.; Attwood, D.; Mosquera, V. Colloid Polym. Sci. 1997, 275, 1144. (15) Filipovic-Vincekovic, N.; Juranovic, I.; Grahek, Z. Colloids Surf. A 1997, 125, 115. (16) Kameyama, K.; Muroya, A.; Takagi, T. J. Colloid Interface Sci. 1997, 196, 48. (17) Arai, T.; Takasugi, K.; Esumi, K. J. Colloid Interface Sci. 1998, 197, 94. (18) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357. (19) Feitosa, E.; Brown, W. Langmuir 1998, 14, 4460. (20) Haque, Md. E.; Das, A. R.; Moulik, S. P. J. Colloid Interface Sci. 1999, 217, 1. (21) Lo´pez-Fonta´n, J. L.; Suarez, M. J.; Mosquera, V.; Sarmiento, F. Phys. Chem. Chem. Phys. 1999, 1, 3583. (22) Iglesias, E.; Montenegro, L. Phys. Chem. Chem. Phys. 1999, 1, 4865. (23) Garamus, V.; Kameyama, K.; Kakehashi, R.; Maeda, H. Colloid Polym. Sci. 1999, 277, 868.

10.1021/la000154s CCC: $19.00 © 2000 American Chemical Society Published on Web 09/19/2000

Mixed Micelles of Triton X100 and D-, T-, and CTAB

a number of micellar properties depend on the structural and dynamic features of the aggregates, and these are related to the composition of the micellar phase. Since this composition cannot be measured directly, but calculated using a proper mixing model, mixed surfactant systems have also been the object of study from a theoretical point of view.33-36 In this respect are particularly remarkable the efforts recently carried out by the Blankschtein’s group5,37-41 in order to provide not only a comprehensive and understandable theory, but also to be capable of predicting the properties of mixed surfactant systems. Besides, there are other interesting aspects which have been less studied. This is the case of certain microenvironmental properties, which also depend on the composition of the mixed micelles and are of interest in several technical applications. For instance, the local polarity of micelles, the so-called micropolarity, is of great importance in investigations dealing with micellar catalysis, as polarity can alter not only the velocity but also the mechanism of the reaction.1 Although most of the mixed systems investigated are concerned with mixtures of anionic and nonionic surfactants, those formed by cationic-nonionic mixtures are also interesting from both fundamental and practical points of view. For example, pure cationic surfactants are poor detergents since they neutralize the negative charges on fibers or solutes, but it has been shown that this property can be improved by using a cationic-nonionic mixture.2 In this paper we report an experimental study on the micellar properties of aqueous solutions containing mixtures of the nonionic surfactant Triton X100 (TX100) with three different n-alkyltrimethylammonium bromides: dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), and cetyltrimethylammonium bromide (CTAB). This study is on the line of a recent investigation carried out in our laboratory,42 in which we examined the micellar properties of the systems TX100-C12E8, TX100-SDS, and TX100CTAB itself. The results of this last system have been included in the present paper for comparison. Both investigations were performed by using the fluorescence probe technique, which has proved to be a powerful tool in the study of aggregation of pure43,44 and mixed surfactant systems,26,36,45 due mainly to its capacity for obtaining microstructural information of the aggregates. (24) Lusvardi, K. M.; Full, A. P.; Kaler, E. W. Langmuir 1995, 11, 487. (25) McDonald, J. A.; Rennie, A. R. Langmuir 1995, 11, 1493. (26) Huang, J. B.; Zhao, G.-X. Colloid Polym. Sci. 1996, 274, 747. (27) Garamus, V. M. Langmuir 1997, 13, 6388. (28) Zhang, H.; Dubin, P. L. J. Colloid Interface Sci. 1997, 186, 264. (29) Zana, R.; Le´vy, H.; Danino, D.; Talmon, Y.; Kwetkat, K. Langmuir 1997, 13, 402. (30) Zana, R.; Le´vy, H.; Kwetkat, K. J. Colloid Interface Sci. 1998, 197, 370. (31) Aswal, V. K.; Goyal, P. S. Physica B 1998, 245, 73. (32) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.; Thomas, R. K.; Lu, J. R.; Warren, N. J. Phys. Chem. B 1999, 103, 5204. (33) Nishikido, N. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 23, and references herein. (34) Maeda, H. J. Colloid Interface Sci. 1995, 172, 98. (35) Georgiev, G. S. Colloid Polym. Sci. 1996, 274, 49. (36) Rodenas, E.; Valiente, M.; Villafruela, M. S. J. Phys. Chem. B 1999, 103, 4549. (37) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5567. (38) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5579. (39) Shiloach, A.; Blankschtein, D. Langmuir 1997, 13, 3968. (40) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 4105. (41) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 7166. (42) Carnero Ruiz, C.; Aguiar, J. Mol. Phys. 1999, 97, 1095; Mol. Phys. 2000, 98, 699. (43) Zana, R. In Surfactant Solutions: New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987: p 241. (44) Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: New York, 1987; Chapter 2.

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The aim of the investigation presented here is double: on the one hand, we have focused on the influence of the alkyl chain length of n-alkyltrimethylammonium bromides in the aggregation behavior of the respective systems and, on the other, we have attempted to establish a correlation between microenvironmental properties and thermodynamic stability of mixed micelles, evaluated on the basis of theoretical mixing model derived parameters.34,46,47 Experimental Section Materials. All surfactants used in this study, TX100 (>99.6%), DTAB (≈99%), TTAB (≈99%), and CTAB (≈99%), were obtained from Sigma and due to their high purity were used as received. The samples of pyrene (Sigma) and diphenylbutadiene (Aldrich) were the same as those employed previously42 and were also used without further purification. Stock solutions of these fluorescence probes were prepared in absolute ethanol. Water was doubly distilled (Millipore) and all experiments were performed with freshly prepared solutions. Instrumentation. All fluorescence measurements were recorded on a SPEX FluoroMax-2 steady-state spectrofluorometer in the “S” mode with band-passes for excitation and emission monochromators of 1.05 nm. The apparatus uses a 150 W xenon lamp as the excitation source and is equipped with a thermostated cell housing. The sample chamber was thermostated to 25 °C using a Julabo F20 circulating water bath, which allowed temperature control to (0.1 °C. Fluorescence anisotropies were measured in the same apparatus provided with a polarization accessory which uses the L-format instrumental configuration48 and an automatic interchangeable wheel with Glan-Thompson polarizers. The steady-state fluorescence anisotropy values were determined as

r)

IV - GIH IV + 2GIH

(1)

where the subscripts of the fluorescence intensity values (I) refer to vertical (V) and horizontal (H) polarizer orientations. The instrumental correction factor G, required for the L-format configuration, was automatically determined by the software supplied by the manufacturer, and all fluorescence anisotropy values were averaged over an integration time of 20 s. Methods. Cmc values in each binary surfactant mixture were obtained by the pyrene 1:3 ratio method.43,44,49 Different binary solutions with a total surfactant concentration of 20 or 40 mM for the three systems investigated were prepared. The composition of the solutions was expressed in molar fraction (Ri) of the respective surfactants, defined as

Ri )

[Si] [Si] + [Sj]

(2)

where [Si] and [Sj] are the molar concentrations of the surfactants i and j in the solution. Working solutions of lower concentration were prepared by adding the appropriate amount of a pyrene stock solution in ethanol. The added volume of this solution was 0.1% of the volume of solution, so that this small amount of solvent had no effect on the micellar system. Fluorescence emission spectra of these solutions were recorded employing an excitation wavelength of 337 nm, and the intensities I1 and I3 were measured at the wavelengths corresponding to the first and third vibronic band located near 373 and 384 nm. The ratio I1/I3 is the so-called pyrene 1:3 ratio (Py 1:3). Some experiments, particularly at high ionic component concentrations, were repeated several times until (45) Turro, N. J.; Kuo, P.-L.; Somasundaran, P.; Wong, K. J. Phys. Chem. 1986, 90, 288. (46) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K., Ed.; Plenum: New York, 1979; Vol. I, p 337. (47) Holland, P. M. Adv. Colloid Interface Sci. 1986, 26, 111. (48) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983; Chapter 5. (49) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039.

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Figure 2. Experimental (b) and predicted (lines) critical micelle concentration of TX100-DTAB mixtures as a function of the mole fraction of DTAB. The dashed line represents the phase separation model prediction for an ideal behavior whereas the solid line is the best fit to the data according to the regular solution approach with β12 ) -2.6. (The error bars are smaller than the size of the symbols.)

Figure 1. Plots of pyrene 1:3 ratio (Py (1:3)) versus total concentration of surfactant in (A) pure DTAB, showing how the cmc is determined, and (B) different mixtures of the TX100TTAB system. a good reproducibility was achieved. The errors in cmc values are estimated to be less than 7%. Micropolarities of the mixed micelles were obtained following the pyrene probing method proposed by Turro et al.45 For this purpose, solutions with a total surfactant concentration well above the corresponding cmc were prepared. The apparent dielectric constants of mixed systems were estimated by using a calibration line obtained, under our experimental conditions, by plotting the Py 1:3 values as a function of the dielectric constant in a number of reference solvents. For the fluorescence polarization studies we have used diphenylbutadiene (DPB) as a probe. In this case, micellar solutions with a total surfactant concentration of 20, 40, and 50 mM for the TX100-CTAB, TX100-TTAB, and TX100-DTAB systems, respectively, and 12 µM in DPB, were prepared. Here the added volume of ethanolic solution containing the probe was 0.3% of the total volume of the solution. We also checked that this amount of solvent had no influence on the system. With the purpose of achieving a complete solubilization of the probe, the resultant solutions were sonicated at least for 10 min at 40 °C, as we tested that with this time the fluorescence anisotropy values obtained were analogous to those measured after 2 h of sonication at the same temperature. Fluorescence anisotropies were recorded using excitation and emission wavelengths of 334 and 380 nm, respectively. All fluorescence anisotropy values presented in this paper are the mean value of three individual determinations. In all cases the errors in the values given for r are less than 3%.

trapolations of the rapidly varying part of the plot and of the nearly horizontal part at high surfactant concentration (see Figure 1A). The cmc values obtained in the case of pure surfactants, 0.33 mM for TX100, 15.2 mM for DTAB, 3.83 mM for TTAB, and 1.00 mM for CTAB, compare well with literature values.21,25,44 In this work we have used Rubingh’s nonideal mixing model46 to analyze the cmc data of the mixed systems investigated. Nonideality can be analyzed by using a regular solution theory,46,47 which introduces an interaction parameter (β12) to charaterize the interactions between the two surfactant species in the mixed micelle. This interaction parameter is related to the activity coefficients of the surfactants within the micelle by

f1 ) exp β12(1 - x1)2

(3a)

f2 ) exp β12x12

(3b)

where x1 is the mole fraction of the surfactant 1 in the mixed micelle, which can be calculated solving iteratively the eq 4

( )

x12 ln 2

(1 - x1) ln

(

)

(1 - R1)C* (1 - x1)C2

)1

(4)

where C* is the cmc of the binary systems and C1 and C2 are the cmc for pure surfactants 1 and 2, respectively. Subsequently, the interaction parameter β12 can be evaluated from the eq 5

( )

ln

Results and Discussion Cmc, Interaction, and Stability. Figure 1 shows the variations of Py 1:3 with the total concentration of surfactant in DTAB and a number of mixtures of the TX100-TTAB system of different compositions. The results obtained for all mixtures investigated were found to be similar to those shown in Figure 1. In all cases the Py 1:3 presents a sigmoidal decrease as the micellar concentration increases. Following Zana et al.,29,30 the cmc values were obtained from the interception of the ex-

R1C* x1C1

β12 )

R1C* x1C1

(1 - x1)2

(5)

β12 is an indication not only of the degree of interaction between the two surfactants but also accounts for the deviation from ideality. A negative value of β12 implies an attractive interaction; the more negative the β12 value the greater the attraction. Figures 2-4 show the cmc values obtained experimen-

Mixed Micelles of Triton X100 and D-, T-, and CTAB

Figure 3. Experimental (O) and predicted (lines) critical micelle concentration of TX100-TTAB mixtures as a function of the mole fraction of TTAB. The dashed line represents the phase separation model prediction for an ideal behavior whereas the solid line is the best fit to the data according to the regular solution approach with β12 ) -1.7.

Figure 4. Experimental (9) and predicted (lines) critical micelle concentration of TX100-CTAB mixtures as a function of the mole fraction of CTAB. The dashed line represents the phase separation model prediction for an ideal behavior whereas the solid line is the best fit to the data according to the regular solution approach with β12 ) -1.0. (The experimental cmc values are from ref 42.)

tally for the three systems investigated as a function of the mole fraction of cosurfactant in the solution (R2). In these figures it can be observed that mixed cmc experimental values are lower than those obtained by assuming an ideal behavior. This negative deviation from ideality indicates a certain attractive interaction between the two surfactants forming the mixed system. From eqs 4 and 5, and by using an iterative method, we have obtained the β12 and the micellar composition (xi) values corresponding to each composition of the studied systems. It was found for the TX100-CTAB system that β12 values obtained across the whole mole fraction range stay rather constant at a value of β12 ) -1.0. However, in the case of the other two mixtures variable β12 values at different compositions of the system were observed. In order to obtain a characteristic β12 value for these systems, we have performed a regression analysis of the cmc experimental data. The best fit of these data gives a value of β12 ) -1.7 for the TX100-TTAB system and of β12 ) -2.6 for the TX100-DTAB one. Figure 5 shows the variation of x2, as obtained from eq 4, with the composition of the solution (R2). In this figure it is clearly observed that whereas there is a good agreement between the experimental data and those predicted by the regular solution theory for the

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Figure 5. Plots of x2 versus R2 for the three studied systems. The lines represent the behavior according to the regular solution with: β12 ) -2.6 for the TX100-DTAB system (b), β12 ) -1.7 for the TX100-TTAB system (O), and β12 ) -1.0 for the TX100-CTAB system (9).

TX100-CTAB system, increasing differences appear as the alkyl chain length of the cosurfactant decreases. These differences can be attributed to experimental errors in the cmc determination for the TX100-TTAB system, but the magnitude of the discrepancies in the case of the TX100-DTAB system could indicate that the TX100DTAB system cannot be modeled by using Rubingh’s approach. With regard to the fact that the regular solution theory looks fine if represented in terms of the monomer composition (Figure 2) but gives worse results when plotted against the micelle composition (Figure 5), as observed in the case of the TX100-DTAB system, it must be pointed out that a similar but more pronounced behavior has recently been reported.23 In any case, from the data in Figure 5 it can be inferred that at low mole fraction of cosurfactant the mixed micelle is mostly formed by TX100 monomers and only when the cosurfactant concentration is high does its participation in the mixed micelle become significant. This behavior also depends on the length of the alkyl chain of the cosurfactant. For a fixed composition of the solution it is observed that the participation of the cosurfactant in the mixed micelle increases as its alkyl chain length is greater. As mentioned above, variations of β12 values with composition for the TX100-TTAB and TX100-DTAB systems were observed. Particularly, we found that β12 values become more negative as the mole fraction of the cosurfactant decreases, this trend being more sharp in the case of TX100-DTAB. In general, this behavior could be rationalized taking into account the role of the repulsive interactions of the headgroups of the cationic surfactant in the stability of the mixed micelles. Note that the intercalation of nonionic surfactants in the mixed micelle prevents these repulsive interactions from achieving the electrostatic stabilization of the micelle. It is interesting to point out that some authors4 have justified similar variations of β12 with the composition in systems formed by cationic and nonionic surfactants consisting of polyoxyethylene (POE) groups, on the basis of the repulsive interactions between the head cationic groups and oxonium ions formed in the hydrophilic moiety of the nonionic surfactant. Although this effect could contribute to the overall electrostatic interactions in the mixed system, as the cosurfactants employed in this work have the same headgroup, it seems clear that secondary effects of steric character may be taken into account to explain the tendency shown by our experimental data.

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Table 1. Interaction Parameters According to Maeda’s Approach for the Different Mixed Surfactant Systems system

B0

B1

B2

TX100-DTAB TX100-TTAB TX100-CTAB

-1.1 -1.1 -1.1

1.23 0.75 0.11

2.6 1.7 1.0

Recently, Maeda34 has proposed a new approach for mixed micelles involving ionic species. In the formulation of Maeda, which is based on the phase separation model, the thermodynamic stability is described by Gmic, which is given, as a function of the mole fraction of the ionic component in the mixed micelle, by

Gmic ) B0 + B1x2 + B2x22 RT

Figure 6. Schematic representation of a TX100 micelle according to the model proposed by Robson and Dennis.50

(6)

Here B0 is an independent term related to the cmc of the nonionic component by

B0 ) ln C1

(7)

The second parameter, B1, is related to the standard free energy change upon replacement of a nonionic monomer in the nonionic pure micelle with an ionic monomer,34 and the last coefficient, B2, is equivalent to β12 in the regular solution theory, specifically

B2 ) -β12

(8)

Finally, the parameters B1 and B2 are related to the cmc values of pure systems by

()

C2 ) B1 + B2 ln C1

(9)

Consequently, when B2 is evaluated, one can obtain B1 from eq 9. In Table 1 are presented the values of these parameters that we have obtained for our systems. As can be seen, B1 is always positive and small in magnitude but decreases when the length of the alkyl chain of cosurfactant increases. According to Maeda,34 the transfer process of an ionic surfactant monomer to the nonionic micelle consists of two different contributions: the interaction between the headgroups and the interaction between the hydrocarbon chains. When the hydrocarbon chains are of the same kind, the first contribution is predominant, however, when there is dissimilarity between the hydrocarbon tails the interactions between these tails become more significant, and as a consequence the value of the parameter B1 increases. In the original paper,34 Maeda analyzes, among others, three systems consisting of a common nonionic surfactant; decaethylene glycol nonylphenyl ether (NPE10), with three different ionic surfactants: cetylpyridinium chloride (CPC), decylpyridinium chloride (DPC), and sodium dodecyl sulfate (SDS), the respective B1 values being -0.74 for CPC/NPE10, 4.31 for DPC/NPE10, and 1.01 for SDS/NPE10. For these systems Maeda indicates that as the hydrocarbon tail dissimilarity is small, the difference observed in the B1 values should be interpreted in terms of a steric factor due to the presence of the phenyl group of NPE10. In our case, since the headgroup of the ionic species is the same in the three systems, and given that the contribution from hydrocarbon tail dissimilarity is rather small, it seems clear that the trend observed in B1 (Table 1) is determined primarily by a certain steric factor due to the presence of the phenyl group of TX100, as suggested by Maeda.

Figure 7. Stability of TX100 mixed micelles versus the composition of the mixed micelle. Symbols as in Figure 5.

According to Robson and Dennis,50 we will assume that the TX100 micelle has a prolate ellipsoid shape with a semiaxis of 52 and 27 Å for the long and short dimension, respectively, its structure consisting of a hydrated POE mantle, which takes up around 83% of the total volume, and a hydrocarbon core, such as shown schematically in Figure 6. On the other hand, we have used the HyperChem molecular calculation package to determine the lengths of the whole molecules of cationic surfactants, obtaining 16.4, 19.0, and 21.5 Å for DTAB, TTAB, and CTAB, respectively. These values as compared with the dimensions of the TX100 micelle explain the trend observed in the B1 values, indicating that, from a steric point of view, the incorporation of CTAB monomers in the TX100 micelle produces a minor distortion in their micellar structure. As a consequence, the TX100-CTAB mixture is the system showing a minor deviation from the ideal behavior. Finally, we have estimated the stability of the mixed systems as a function of the micellar composition on the basis of the description proposed by Maeda. Figure 7 shows the dependence of ∆Gmic/RT on micellar composition, where ∆Gmic/RT is defined as the stability relative to that of TX100 pure micelles. As can be seen in Figure 7, the stability of the three mixed systems decreases when the participation of the cosurfactant increases. This behavior is reasonable as the incorporation of ionic monomers is associated with an increase of the charge density, causing the electrostatic destabilization of the system. In addition, it is also observed that for a fixed micellar composition, i.e., for a x2 constant value, the stability of the mixed system decreases as the alkyl chain length of the cosurfactant becomes smaller. This is consistent with the steric compatibility between the two surfactants in the mixed micelle, as discussed above. (50) Robson, R. J.; Dennis, E. A. J. Phys. Chem. 1977, 81, 1075.

Mixed Micelles of Triton X100 and D-, T-, and CTAB

Figure 8. Pyrene 1:3 ratio index as a function of the mole fraction of cosurfactant in the solution. Symbols as in Figure 5.

Micropolarity. Local polarity of micelles, or micropolarity, is an important property because changes in micropolarity can reveal structural changes in micellar aggregates. Py 1:3 is well-known to be a sensitive indicator of the polarity of the environment around the probe,43-45,49 and has been employed widely as a structural probe in many applications. As pyrene is preferentially solubilized close to the surface of micelles, in the so-called palisade layer,43,44 the polarity sensed by the probe reflects the grade of water penetration in this region of the micelle. In order to study the effect of the incorporation of cosurfactant in the TX100 micelle, we have monitored the Py 1:3, in micellar solutions of concentrations well above the cmc, as a function of the solution composition. Figure 8 shows the results of these experiments, where we observe, first, that the pure cationic surfactants present a lower polarity than the micelles formed by the nonionic surfactant, indicating a smaller water penetration in those micelles. In addition, for cationic single surfactant systems it is observed that when the alkyl chain length increases the micropolarity of the micelles becomes smaller, indicating that pyrene is more effectively prevented from being influenced by water molecules. Second, it also shows a gradual decrease of polarity as the cosurfactant content increases in the mixed system. Being this effect more marked as the alkyl chain length of the cosurfactant increases. A priori, as the participation of the cationic component becomes more significant and the presence of charged headgroups increases, an enhacement of micropolarity should be expected. However, the increasing charge density may lead to ion-dipole interactions between the headgroups of the cationic surfactant and the ethylene oxide groups of TX100. These interactions can produce the release of water molecules (hydrogenbonded or trapped) from the POE shell of TX100. Consequently, the minor polarity of the mixed systems as compared with the pure TX100 one indicates the formation of more closed micelles, where the penetration of water is more restricted and, therefore, with a more dehydrated structure. On the other hand, we have attempted to evaluate the micropolarity of the mixed micelles by using the method proposed by Turro et al.45 According to these authors the apparent dielectric constant of a mixed aggregate can be estimated by using the following relation

 ) x11 + x22

(10)

where 1 and 2 are the apparent dielectric constant of

Langmuir, Vol. 16, No. 21, 2000 7951

Figure 9. Calibration line (r ) 0.9988) for the determination of the apparent dielectric constant as obtained by measuring the pyrene 1:3 ratio index in a series of reference solvents: 1 f Et2O, 2 f EtOH, 3 f MeOH, 4 f MeOH-H2O (4:1), 5 f MeOH-H2O (3:2), 6 f MeOH-H2O (2:3).

pure micelles of components 1 and 2, respectively, and where x1 and x2 are the mole fractions of components 1 and 2 in the mixed aggregate. The aforementioned authors also suggest that this method can be used to determine the micellar composition, which was just the procedure followed by Tokuoka et al.51 to determine the micellar composition in a number of mixed surfactant systems. In order to apply this procedure to our systems, we have prepared a calibration line in which we have monitored the Py 1:3, measured under our experimental conditions, as a function of the dielectric constant by using a number of reference solvents. Figure 9 shows the calibration line obtained. In this manner, we have estimated the apparent dielectric constants of pure and mixed micelles, denoted by (Py). Moreover, by using the x1 and x2 values as obtained from the regular solution theory and the eq 10, we have calculated the apparent dielectric constant values for the different mixed systems, denoted as (x). All these values are listed in Table 2. For the TX100-DTAB system it is observed that (i) both (Py) and (x) are roughly insensitive to the system composition, and (ii) there are not large changes between the values obtained from both methods; however, we think that this is due to the fact that the apparent dielectric constant values of both pure systems are very similar. On the other hand, for the TX100-TTAB and TX100-CTAB systems, which are fairly well modeled by the regular solution approach, a continuous decrease is observed for both parameters as the participation of cosurfactant increases in the system. In addition, for these two systems it can be seen that at low participation of cosurfactant there is a reasonable agreeement between (Py) and (x). However, when the participation of cosurfactant increases, greater differences are observed in both systems. We have previously found42 that, for systems well modeled by the regular solution theory, as the greater the deviations of the ideal behavior, the greater the differences between (Py) and (x) values. From this point of view, the similar trend observed for TX100-TTAB and TX100-CTAB could be interpreted on the basis of an analogous deviation of the ideal behavior for both systems. From these observations and others previously reported,42 it can be inferred that the method based on eq 10 for the determination of the micellar composition only can be applied when the mixture is well described by the regular solution theory and at low (51) Tokuoka, A.; Uchiyama, H.; Abe, M. J. Phys. Chem. 1994, 98, 6167.

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Ruiz and Aguiar

Table 2. Apparent Dielectric Constant for the Different Mixed Surfactant Systems As Obtained from Both the Calibration Line in Figure 9, E(Py), and Eq 10, E(x), at 25 °C systema

R2

x2

(Py)b

(x)b

TX100-DTAB

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.00 0.13 0.13 0.15 0.21 1.00 0.00 0.11 0.15 0.24 0.33 1.00 0.00 0.14 0.26 0.38 0.54 1.00

31.6 30.1 29.9 29.6 29.6 30.0 31.6 29.3 29.0 28.5 28.4 28.3 31.6 29.2 28.2 27.5 27.0 26.8

31.6 31.3 31.3 31.3 31.3 30.0 31.6 31.2 31.1 30.8 30.5 28.3 31.6 30.9 30.3 29.8 29.0 26.8

TX100-TTAB

TX100-CTAB

a The total surfactant concentrations used were 50, 40, and 20 mM for the mixtures TX100-DTAB, TX100-TTAB, and TX100CTAB, respectively. b The errors in (Py) and (x) are estimated to be within (7.0% and (8.0%, respectively.

cosurfactant content, or in the case that the mixed system behaves ideally. Fluorescence Anisotropy Studies. As stated above, the structure of TX100 micelles consists of a tightly packed deep core of hydrocarbon and a hydrated POE shell occupying the major part of the volume of the micelle.50 It is also assumed that the interactions between water molecules and the POE groups play a critical role in the packing of the hydrophilic mantle in the micelle.52 Therefore, the progressive incorporation of cationic surfactant molecules in the structure of the TX100 micelles will produce a lack of hydration, consistent with a decrease of micellar micropolarity, accompained with a reduction of order in the POE mantle. In addition, the increase of the repulsive interations between the headgroups of the cationic surfactants will also contribute to a looseness of the structure in the palisade layer of the micelle. With the purpose of studying the effect of the cosurfactant participation in the structure of TX100 micelles, we have performed polarized fluorescence measurements by using DPB as a fluorescence probe. The behavior of this probe in micellar media has been previously well characterized by Jobe and Verral,53 and was later used by us to examine structural changes in single54,55 and mixed micelles.42 The steady-state anisotropy (r) is related to the viscosity around the probe (η) by Perrin’s equation

r0 kTτ )1+ r Vη

(11)

where r0 is the limiting value of emission anisotropy obtained in the absence of rotational freedom, τ is the average lifetime of the fluorophore excited state, T is the absolute temperature, k is the Boltzmann constant, and V is the effective molecular volume of the probe. Therefore, the anisotropy is considered as an index of the microviscosity or rigidity in the microenvironment of the probe.43,44 However, some assumptions inherent to the application (52) Ribeiro, A. A.; Dennis, E. A. In Nonionic Surfactants: Physical Chemistry; Shick, M. J., Ed.; Marcel Dekker: New York, 1987; p 971. (53) Jobe, D. J.; Verrall, R. E. Langmuir 1990, 6, 1750. (54) Carnero Ruiz, C. Colloids Surf. A 1999, 147, 349. (55) Carnero Ruiz, C. J. Colloid Interface Sci. 2000, 221, 262.

of the steady-state depolarization method to obtain microviscosities in micelles have been demonstrated to be not justified.56 In addition, the concept of microviscosity has recently been critically discussed on the basis of the diffusion coefficients for the molecule probes in micelles.57 Accordingly, we have focused not on determining absolute values of microviscosities around the probe, but rather on evaluating the relative changes in the micellar structure upon the system composition. The degree of depolarization of the fluorescence emission of a molecule probe is a measure of its rotational diffusion during the excited lifetime. However, in highly structured microenvironments, the rotational diffusion of the probe is restrained and, as a consequence, the probe does not assume all posible orientations with equal probability. In addition, the dynamic conditions of the medium controlling the speed with which the probe does its motion must also be taken into account. Therefore, the steady-state fluorescence anisotropy can be resolved into two components, one static (r∞) and another dynamic (rd):58,59

r ) r∞ + rd

(12)

According to the wobbling in cone model proposed by Kinosita et al.,60 the rotation of a molecule probe is assumed to occur in a square well potential such that its rotation is unhindered until a certain angle θC is reached, the rotation beyond this angle being energetically impossible. The region where the movement of the dye molecule takes place is assumed for simplicity as a cone, θC being the semicone angle. A second important parameter for this model is the order parameter, S, which measures the equilibrium orientational distribution of the probe and which decreases with increasing mobility of the dye in the medium. That is, S is a structural parameter which gives information about the organization or order of the site of solubilization of the molecule probe. The static component (r∞) of the steady-state anisotropy can be related to the square of order parameter (S) by

r∞ ) S2; 0 e S e 1 r0

(13)

where r0 is equal to 0.346 for DPB.53 On the other hand, the critical angle θC and the order parameter S are related by the equation61

S ) 0.5 cos θC(1 + cos θC)

(14)

From semiempirical considerations, Pottel et al.62 have derived a relationship between the order parameter and the steady-state anisotropy given by

S r ) r0 1 + S - S 2

(15)

so, from steady-state fluorescence anisotropy measurements, it is possible to determine the order parameter (S) and hence the critical angle (θC). In this manner, mea(56) Grieser, F.; Drummond, C. J. J. Phys. Chem. 1988, 92, 5580. (57) Maiti, N. C.; Krishna, M, M. G.; Britto, P. J.; Periasamy, N. J. Phys, Chem. B 1997, 101, 11051. (58) Chantres, J. R.; Elorza, B.; Elorza, M. A.; Rodado, P. Int. J. Pharm. 1996, 138, 139. (59) Komaromy-Hiller, G.; von Wandruszka, R. J. Colloid Interface Sci. 1996, 177, 156. (60) Kinosita, K.; Kawato, S.; Ikegami, A. Biophys. J. 1977, 20, 289. (61) Lipari, G.; Szabo, A. 1980, Biophys. J. 1980, 30, 489. (62) Pottel, H.; van der Meer, B. W.; Herreman, W. Biochim. Biophys. Acta 1983, 730, 181.

Mixed Micelles of Triton X100 and D-, T-, and CTAB Table 3. Steady-State Fluorescence Anisotropy (r) of DPB Solubilized in the Mixed Surfactant Systems and Structural Parameters (Order Parameter S and Critical Angle θC) of the Wobbling in Cone Model in Micellar Solutions of Different Compositions, at 25 °C systema

R2

r

S

θC/deg

TX100-DTAB

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.286 0.272 0.252 0.236 0.214 0.204 0.286 0.260 0.242 0.228 0.223 0.221 0.296 0.264 0.248 0.234 0.233 0.230

0.90 0.87 0.83 0.79 0.74 0.71 0.90 0.85 0.81 0.77 0.76 0.76 0.92 0.86 0.82 0.79 0.79 0.78

21.3 24.4 28.1 31.5 35.4 37.6 21.3 26.3 29.8 33.1 33.9 33.9 19.1 25.7 28.9 31.6 31.6 32.0

TX100-TTAB

TX100-CTAB

a

Concentrations as in Table 2.

surements of steady-state anisotropy provide a simple means of monitoring the processes in which the micellar microstructure is affected in any way. The values for r, S, and θC obtained for our systems in the whole range of composition are given in Table 3. From its data it is observed that the fluorescence emission of the probe is in all cases highly polarized, indicating a strong interaction between probe and micelle. It can also be seen that the anisotropy values in single nonionic micelles are higher than in single cationic micelles, indicating that the packing is less tight in these systems. This is mainly due to the contribution of two factors: the existence of electrostatic repulsions between the surfactant headgroup and a smaller hydration of the hydrophilic mantle in the ionic systems. On the other hand, the referred data suggest that in the micellar structure experiments there is a lack of order as the presence of cosurfactant increases in the mixed micelle. It is observed that while the order parameter undergoes a progressive decrease, θC increases with the participation of cosurfactant in the mixed system, indicating that the equilibrium orientational distribution of the molecule probe is less constrained in the mixed system as compared to the pure TX100 system. These observations are consistent with a decrease of hydration of the mixed micelles, as revealed by a reduction in the micellar micropolarity, and with an increase of the repulsive interactions between the headgroups of cationic surfactants as these replace some TX100

Langmuir, Vol. 16, No. 21, 2000 7953

molecules in the aggregate. In addition, data in Table 3 indicate that the effect produced in the structure of the micelle, revealed by the order parameter, increases as the alkyl chain length of cosurfactant becomes smaller. Note that although the CTAB is the cosurfactant rising, a greater level of participation in the mixed aggregate produces a minor effect in the order parameter. This behavior probably arises from the existence of two compensating effects: (i) the formation of mixed micelles with a more dehydrated structure, as seen in micropolarity studies, and (ii) the tighter packing of the surfactant alkyl chains due to the greater steric compatibility between CTAB and TX100 monomers, as discussed previously. Conclusions In the present study we have found that binary systems formed by the nonionic surfactant TX100 and three different n-alkyltrimethylammonium bromides show deviation from the ideal behavior. We have shown that the stability of the mixed micelles depends on the alkyl chain length of the cosurfactant, increasing the stability as the length of its hydrocarbon chain becomes greater. This fact has been interpreted in terms of steric compatibility between the surfactants forming the mixed micelle. From the micropolarity assays, it can be deduced that the progressive participation of cosurfactant on the mixed micelle induces the formation of more closed micelles, in which water penetration is more restricted. This effect also depends on the alkyl chain length of the cosurfactant, the CTAB being the one which causes a major influence due to the greater participation level in the mixed aggregate. The fluorescence depolarization measurements indicate that the incorporation of cosurfactant causes a lack of order in the micellar structure of TX100, which has been attributed to the contribution of two effects: (i) the formation of a more dehydrated structure, and (ii) the increase of the repulsive interactions between the headgroups of the cationic surfactants. Despite the fact that the CTAB is the cosurfactant producing mixed micelles with a more dehydrated structure, it is also the cosurfactant causing the formation of mixed aggregate with more ordered structures. This behavior has been justified on the basis of a good steric compatibility between TX100 and CTAB to form mixed micelles. These structural considerations in connection with the stability studies suggest that the micellar stability is related to the formation of mixed aggregates with a better packing of the surfactant monomers and, consequently, with a more ordered structure. LA000154S