Mixed Vesicle Formation on a Ternary Surfactant System

Mixed critical microaggregate concentration and mixed critical vesicle concentration have been determined from conductivity data. Furthermore, zeta po...
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Mixed Vesicle Formation on a Ternary Surfactant System: Didodecyldimethylammonium Bromide/ Dodecylethyldimethylammonium Bromide/Water Elena Junquera,† Rocı´o Arranz,‡ and Emilio Aicart*,† Departamento de Quı´mica Fı´sica I, Facultad de Ciencias Quı´micas, Universidad Complutense de Madrid, 28040-Madrid, Spain, and Centro Nacional de Biotecnologı´a, CSIC, Cantoblanco, Madrid, Spain Received April 7, 2004. In Final Form: May 21, 2004 The formation of mixed aggregates has been investigated on a ternary system consisting of two cationic surfactants with similar polar heads and two and/or one 12 carbon atom hydrophobic tail, respectively, didodecyldimethylammonium bromide and dodecylethyldimethylammonium bromide and water. The study has been carried out by means of conductivity, zeta potential, and cryogenic transmission electronic microscopy (cryo-TEM) experiments on the very diluted region. A variety of mixed aggregates, microaggregates, vesicles, and micelles has been found, depending on system composition and total surfactant concentration. Mixed critical microaggregate concentration and mixed critical vesicle concentration have been determined from conductivity data. Furthermore, zeta potential and cryo-TEM experiments allow for the characterization of the aggregates/solution interface and of the shape and size of the aggregates. This experimental evidence has also been analyzed in terms of the theoretical packing parameter, P.

I. Introduction Vesicles are double-chain surfactant aggregates that can be used as simplified models of biological membranes, drug delivery systems, and so on.1-7 The addition of a single-chain surfactant to a double-chain surfactant/water system drives to the formation of a mixed system with the appearance of mixed vesicle aggregates.3,4,8 The stability of spontaneous vesicles in amphiphilic mixed systems was analyzed by Safran et al.9,10 from a thermodynamic point of view, by considering the curvature of the inner and outer monolayers of the vesicle membrane. The presence of a single-chain surfactant on a vesicle system may induce the rupture of vesicle structures, depending on the concentration of the former, with the corresponding solubilization of the double-chain surfactants as mixed micelles. In those cases, a wide variety of aggregates and several vesicle-to-micelle transitions occur.3,11-21 These * To whom correspondence should be addressed. Fax: 34913944135. E-mail: [email protected]. http://www.ucm.es/info/ coloidal/index.html. † Universidad Complutense de Madrid. ‡ Centro Nacional de Biotecnologı´a, CSIC. (1) Fendler, J. H. Membrane Mimetic Chemistry; John Wiley & Sons: New York, 1982. (2) Fennell-Evans, D.; Ninham, B. W. J. Phys. Chem. 1986, 90, 226. (3) Rosoff, M. Vesicles; Marcel Dekker: New York, 1996. (4) Christian, S. D.; Scamehorn, J. F. Solubilization in Surfactant Aggregates; Marcel Dekker: New York, 1995; Vol. 55. (5) Barenholz, Y. Curr. Opin. Colloid Interface Sci. 2001, 6, 66. (6) Lian, T.; Ho, R. J. Y. J. Pharm. Sci. 2001, 90, 667. (7) Somasundaran, P.; Hubbard, A. Encyclopedia of Surface and Colloid Science; Marcel Dekker: Santa Barbara, CA, 2002. (8) Ollivon, M.; Lesieur, S.; Grabielle-Madelmont, C.; Paternostre, M. Biochim. Biophys. Acta 2000, 1508, 34. (9) Safran, A.; Pincus, P.; Andelman, D. Science 1990, 248, 354. (10) Safran, A.; Pincus, P. A.; Andelman, D.; MacKintosh, F. C. Phys. Rev. A: At., Mol., Opt. Phys. 1991, 43, 1071. (11) Dennis, E. A. Adv. Colloid Interface Sci. 1986, 26, 155. (12) Treiner, C.; Makayssi, A. Langmuir 1992, 8, 794. (13) De la Maza, A.; Parra, J. L. Langmuir 1995, 11, 2435. (14) Edwards, K.; Almgren, M. Langmuir 1992, 8, 824. (15) Edwards, K.; Gustafsson, J.; Almgren, M.; Karlsson, G. J. Colloid Interface Sci. 1993, 161, 299. (16) Engberts, J. B. F. N.; Kevelam, J. Curr. Opin. Colloid Interface Sci. 1996, 1, 779.

aggregates are strongly dependent on temperature, composition, and concentration of the mixed system. The vesicle or liposome (double-chain phospholipid surfactant) solubilization process has been described by Lichtenberg et al.22,23 using a three-stage model, but details of the mechanism are not clear yet. In fact, the study of these kinds of mixed ternary systems is still receiving much attention since they shed light on the mechanism of the transition between mixed vesicles and mixed micelles, providing, in addition, interesting information to understand purification, solubilization, and reconstitution processes of biological membranes.8,18,21,24-30 However, when the interaction between single-chain surfactants and vesicles takes place at much lower concentration, the single-chain surfactant is incorporated into the vesicle membrane, depending on the partition equilibrium between the vesicle bilayer and the aqueous phase, without the occurrence of vesicle breakdown. This feature affects the vesicle behavior (permeability, fluidity, etc.), offering a variety of practical applications. In fact, most of the drugs are also amphiphilic molecules that have to cross the biological membranes by appropriate channels before interacting in the organism. Thus, vesicle/ (17) Viseu, M. I.; Edwards, K.; Campos, C. S.; Costa, S. M. B. Langmuir 2000, 16, 2105. (18) Deo, N.; Somasundaran, P. Colloids Surf., A 2001, 186, 33. (19) Lopez, O.; Cocera, M.; Parra, J. L.; de la Maza, A. Colloids Surf., A 2001, 193, 221. (20) Tsao, H. K.; Tseng, W. L. J. Chem. Phys. 2001, 115, 8125. (21) Fontana, A.; De Maria, P.; Siani, G.; Robinson, B. H. Colloids Surf., B 2003, 32, 365. (22) Lichtenberg, D.; Robson; Dennis, E. A. Biochim. Biophys. Acta 1983, 737, 285. (23) Lichtenberg, D. Biochim. Biophys. Acta 1985, 821, 470. (24) Deo, N.; Somasundaran, P. Langmuir 2003, 19 (6), 2007. (25) Deo, N.; Somasundaran, P. Langmuir 2003, 19, 7271. (26) Majhi, P. R.; Blume, A. J. Phys. Chem. B 2002, 106, 10753. (27) Kawasaki, H.; Imahayashi, R.; Tanaka, S.; Almgren, M.; Karlsson, G.; Maeda, H. J. Phys. Chem. B 2003, 107, 8661. (28) Hildebrand, A.; Neubert, R.; Garidel, P.; Blume, A. Langmuir 2002, 18, 2836. (29) Hildebrand, A.; Beyer, K.; Neubert, R.; Garidel, P.; Blume, A. Colloids Surf., B 2003, 32, 335. (30) Egermayer, M.; Piculell, L. J. Phys. Chem. B 2003, 107, 14147.

10.1021/la049113c CCC: $27.50 © 2004 American Chemical Society Published on Web 07/02/2004

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surfactant systems are model systems that may provide information about the interaction between amphiphilic molecules and bilayer membranes. For all those reasons, some investigations concerning vesicle/surfactant studies have been focused on the subsolubilizing (sublytic) concentration region.12,21,31 Didodecyldimethylammonium bromide (di-C12DMAB) is a double-chain cationic surfactant of the quaternary alkyl ammoniun salt series that is commercially used in a wide variety of applications.32 The phase behavior of this surfactant in water has been widely characterized.33-35 Few studies have been done to analyze the formation of di-C12DMAB vesicles in the absence and presence of a single-chain surfactant. These works are mainly focused on the study of the vesicle-to-micelle transition, i.e., on the medium-to-high concentration range.17,21,31,36 However, a rigorous study in the very diluted region, just when the formation of the aggregates takes place, i.e., when microaggregates and/or mixed vesicles appear (at a concentration much lower than that corresponding to the mixed micelles formation), has not been reported yet. Recently, we have reported a study of a ternary mixed system consisting of two single-chain surfactants with hydrophobic tails of equal length and similar polar heads: dodecyltrimethylammonium bromide (C12TAB)/dodecylethyldimethylammonium bromide (C12EDMAB)/water.37 It was found that the system forms mixed micelles in the whole range of composition, at concentrations above the mixed critical micelle concentration. In the present work, the ternary system studied is di-C12DMAB/C12EDMAB/ water, i.e., the mixed system resulting from the substitution of a methyl group on the C12TAB of the previous system by another chain with 12 carbon atoms. The object is to analyze the effect of this second hydrophobic chain on the structure and properties of the monomeric and aggregate phases in aqueous solution, in the very diluted region. Several experimental techniques have been used for that purpose: (i) conductivity, mainly focused on the determination of the critical concentrations at which the different type of aggregates appear; (ii) zeta potential, aimed to the analysis of the aggregate/solution interface; and (iii) cryogenic electron transmission microscopy (cryoTEM), used to study the type, shape, and size of the vesicles. This experimental evidence has also been analyzed and discussed using a geometrical packing parameter, based on Tanford and Israelachvili models.38-41 II. Experimental Section A. Materials. di-C12DMAB and C12EDMAB were from Aldrich, with purities of 99% or greater. Both were used without further purification. Double-distilled water was deionized using a Super

Junquera et al. Q Millipore system (with a conductivity lower than 18 µS cm-1) and finally was also degassed with a vacuum pump prior to the preparation of the solutions. B. Preparation of the Samples. Solutions of an appropriate total surfactant concentration, and at the desired molar fraction, were prepared by dissolving simultaneously both di-C12DMAB and C12EDMAB in water. Once prepared, and prior to carry on the experiments, those initial solutions were sonicated for 2 h in an ultrasonic bath. These solutions were confirmed to remain in equilibrium for a long time by repeating conductivity, κ, and the zeta potential, ζ, 4 months later and obtaining, within the experimental uncertainty, the same results. C. Conductometric Measurements. Conductivity data were collected at 298.15 K ((1 mK) with a Hewlett-Packard 4263A LCR meter, using an electrode with a cell constant of 0.8129 cm-1. Mixtures were prepared from a digital buret, whose cylinder was kept at the same constant temperature of the measuring cell. The conductometer and the buret were controlled via an IEEE-488 bus and RS-232C interfaces, respectively. The experimental procedure was widely described previously.42 The accuracy on the specific conductivity κ, obtained as an average of 2400 measurements for each concentration, is believed to be better than 0.03%. The conductivity measurements were made as a function of total surfactant concentration, [S]tot ()[di-C12DMAB] + [C12EDMAB]), at several constant values of their molar fraction, R1. D. ζ-Potential Measurements. The ζ-potentials were measured with a Zetamaster 2000 (Malvern Instruments Ltd.) using a laser Doppler electrophoresis (LDE) technique, which operates with a 10 mW He-Ne laser at 633 nm. The cell used is a Zetasizer 2000 standard quartz rectangular capillary electrophoresis cell of 5 × 2 × 50 mm, which is calibrated with a zeta potential transfer standard (ζ ) -50 ( 5 mV), according to manufacturer recommendations. Temperature was controlled at 298.15 ( 0.01 K. The equipment is controlled via a RS-232C interface, with software supplied by the manufacturer. The ζ-potential measurements were made at the molar fractions studied on conductivity experiments, at two different [S]tot per molar fraction. Each ζ-potential value is taken as an average over 10 independent measurements. E. Cryogenic Transmission Electronic Microscopy Measurements. Samples for cryogenic transmission electronic microscopy (cryo-TEM) were vitrified according to the method devised by Dubochet et al.43 and also described in Llorca et al.44 Briefly, 5 µL aliquots of the different samples were applied to glow-discharged holey grids for 1 min, blotted for 5 s, and frozen rapidly in liquid ethane at -180 °C and kept at this temperature throughout the whole procedure. Images were obtained at 0°-tilt under minimum dose conditions using a field emission gun Tecnai 20 G2 microscope equipped with a Gatan cold stage operated at 200 keV. Micrographs were recorded on Kodak SO-163 film at a 29000× nominal magnification and approximately 2.5 µm under focus, and subsequently digitized in a Zeiss SCAI scanner with a sampling window corresponding to 7.24 Å/pixel. cryo-TEM experiments were done for pure di-C12DMAB solutions at 0.3 mM and for several molar fractions of the mixed system.

III. Results and Discussion (31) Viseu, M. I.; Velazquez, M. M.; Campos, C. S.; Garcia-Mateos, I.; Costa, S. M. B. Langmuir 2000, 16, 4882. (32) Jungermann, E. Cationic Surfactants; Marcel Dekker: New York, 1970. (33) Warr, G. G.; Sen, R.; Fennell-Evans, D.; Trend, J. E. J. Phys. Chem. 1988, 92, 774. (34) Matsumoto, H.; Hieuchi, T.; Horie, K. Colloid Polym. Sci. 1989, 267, 71. (35) Soltero, J. F. A.; Bautista, F.; Pecina, E., Puig, J. E.; Manero, O.; Proverbio, Z.; Schulz, P. C. Colloid Polym. Sci. 2000, 278, 37. (36) Bai, G. Y.; Wang, Y.; Wang, Y.; Han, B.; Yan, H. Langmuir 2001, 17, 3522. (37) Junquera, E.; Aicart, E. Langmuir 2002, 18, 9250. (38) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (39) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley & Sons: New York, 1980. (40) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (41) Israelachvili, J. Intermolecular and Surfaces Forces with Application to Colloidal and Biological Systems; Academic Press: London, 1985.

Aqueous solutions of the di-C12DMAB (1) + C12EDMAB (2) ternary system have been characterized through conductivity, ζ-potential, and cryo-TEM measurements. Experimental values of specific conductivity, κ, are plotted as a function of total surfactant concentration, [S]tot, at several constant values of molar fraction, R1, in Figure 1. This figure deserves several remarks: (i) κ values are extremely low, compared with those reported for similar vesicle systems31 or micelle systems.37 It must be due both to the fact that the experiments reported herein have been (42) Junquera, E.; Aicart, E. Rev. Sci. Instrum. 1994, 65, 2672. (43) Dubochet, J.; Adrian, M.; Chang, J. J.; Homo, J. C.; Lepault, J.; McDowall, A. W.; Schultz, P. Q. Rev. Biophys. 1988, 21, 129. (44) Llorca, O.; McCormack, E.; Hynes, G.; Grantham, J.; Cordell, J.; Carrascosa, J. L.; Willison, K. R.; Ferna´ndez, J. J.; Valpuesta, J. M. Nature 1999, 402, 693.

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Figure 1. Plot of specific conductivity, κ, as a function of total surfactant concentration, [S]tot at 298.15 K, at various fixed values of the molar fraction, R1, for the mixed system di-C12DMAB (1) + C12EDMAB (2).

Figure 2. Plot of specific conductivity, κ, as a function of total surfactant concentration, [S]tot at 298.15 K, at the molar fraction, R1 ) 0.798, in the medium concentration range, for the mixed system di-C12DMAB (1) + C12EDMAB (2).

carried out in a very diluted region and to the lower mobility of vesicle aggregates with respect to micelles. (ii) Due to the lower solubility of di-C12DMAB with respect to C12EDMAB, the higher the total surfactant concentration at constant R1, the higher the molar fraction of the double-chain surfactant in the aggregate, X1agg, becomes. In other words, di-C12DMAB is almost totally forming the aggregate as it is incorporated to the mixed system. (iii) A variety of different behaviors can be observed as a function of [S]tot, at constant molar fraction (following a curve along the x-axis), and as a function of molar fraction, at constant [S]tot (following a vertical line along the y-axis). This feature contrasts again with the trends found for a C12EDMAB (1) + C12TAB (2) ternary system,37 which forms only mixed micelles above the critical micelle concentration (cmc*). Given that the polar heads are almost identical in di-C12DMAB, C12EDMAB, and C12TAB surfactants, the unusual κ trends reported herein must be only due to the hydrophobic double-chain of di-C12DMAB. (iv) All curves show a double break on κ, this feature being more evident as R1 increases, with the exception of the pure di-C12DMAB (R1 ) 1), where only one break on the property has been detected. With the aim of confirming this double change, the curves for which this feature was not clearly observed in the very diluted range were measured again, covering a wider concentration range. Figure 2 shows, as an example, the results obtained for R1 ) 0.798, in both the very and medium diluted concentration ranges. Similar plots were drawn for the other molar fractions. This figure shows, with total clarity, the above-mentioned double change in the diluted region, well below the micelle region, not reported previously in the literature. This fact, together with the very good agreement on the results from both experiments, reveals the extremely good reproducibility of our κ technique. Several cryo-TEM experiments were carried out to assign this double change to the possible formation of different types of colloidal aggregates. Figure 3 shows the images taken of the vitrified samples for pure di-C12DMAB solution at 0.31 mM, well above the break observed for κ

in Figure 1. A low concentration of spherical unilamellar vesicles with a homogeneous size ranging from 20 to 50 nm can be observed. Accordingly, the change observed on κ (Figure 1), calculated from the concentration at which the third derivative of the experimental property is equal to zero ((∂3κ/∂c3) ) 0), is assigned to the critical vesicle concentration, CVC, for pure di-C12DMAB vesicles. The value of CVC ) 0.165 mM is in agreement with some literature data,12,31,34 although other reported values are lower.35,45 This value is about 100 times lower than that determined as well in our laboratory for the cmc of C12EDMAB (cmc ) 13.97 mM)37 from conductivity data. Given that the polar heads of both surfactants are similar, the presence of two chains in di-C12DMAB is clearly responsible for the decrease not only of its solubility in water but also of the concentration at which the surfactant aggregates. In the case of the mixed system, cryo-TEM experiments were run on two samples for each molar fraction: (i) at [S]tot between the two breaks on κ; and (ii) at [S]tot well above the second change on κ. Vesicles were not observed for the former samples (i) at any molar fraction, pointing to the presence of mixed microaggregates in this concentration range, not detectable by cryo-TEM. In this case, the microaggregates should be smaller than 4-5 nm in diameter, which is the approximate size of the micelles. This behavior, which was also found in the very diluted region of mixed ternary surfactant/alcohol/water systems from ultrasonic absorption results,46-48 is normally shown by mixed systems where the two components are quite different. However, Figure 4 shows, as an example, the images taken of the vitrified samples for the mixed diC12DMAB (1) + C12EDMAB (2) system at R1 ) 0.447 ([S]tot ) 1.518 mM) and R1 ) 0.769 ([S]tot ) 2.532 mM), both well (45) Caria, A.; Regev, O.; Khan, A. J. Colloid Interface Sci. 1998, 200, 19. (46) Jobe, D. J.; Verrall, R. E.; Skalski, B.; Aicart, E. J. Phys. Chem. 1992, 96, 6811. (47) Aicart, E.; Jobe, D. J.; Skalski, B. D.; Verrall, R. E. J. Phys. Chem. 1992, 96, 2348. (48) Verrall, R. E.; Jobe, D. J.; Aicart, E. J. Mol. Liq. 1995, 65/66, 195.

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Figure 3. cryo-TEM photographies of pure di-C12DMAB vesicles at 0.3 mM.

above the break observed on κ in Figure 1 for each molar fraction. These photographs revealed a larger amount of vesicles of varying shape and size with respect to those observed in Figure 3 for the pure double-chain surfactant. The presence of open vesicles, characteristic of intermediate structures in the vesicle-to-micelle transition, has not been found in any of the micrographs analyzed. The vesicles are essentially unilamellar at R1 ) 0.447, with an average diameter of about 190 nm, although a very low concentration of rodlike or onionskin structures (MLV vesicles) appears. However, the vesicles seen at R1 ) 0.769 show a more homogeneous unilamellar spherical shape with a lower average size (average diameter of about 165 nm). It seems that as R1 increases, the average size of the vesicle decreases. The thermodynamic stability of spontaneous vesicles has been analyzed by Safran et al.9,10 This group presented a model assuming a nonideal mixing of the surfactants within both monolayers of the vesicle. The model was based in the hypothesis that the curvature of the two monolayers has to be almost equal in magnitude, but opposite in sign (positive in the outer monolayer and negative in the inner monolayer). This fact can only be possible if the two monolayers have an asymmetric composition. Accordingly, as the total molar fraction R1 decreases, the content in single-chain surfactant must increase in the inner layer and even more in the outer layer. This feature will lead a lower inner curvature and, thus, to a bigger vesicle, as has been experimentally found from cryo-TEM experiments. With all these cryo-TEM results, the first and second breaks on κ (Figure 1), calculated as well as the concentrations at which the third derivative of specific conductivity is equal to zero, were assigned to the mixed critical microaggregates concentration, CAC*, and mixed critical vesicle concentration, CVC*, respectively. These results are reported in Table 1 for all the molar fractions and represented as a function of R1 in Figure 5. As can be observed, both critical concentrations increase with R1, the CVC* being shifted toward higher values due to the presence of the microaggregates. Although the formation of mixed micelles consisting of di-C12DMAB and C12EDMAB surfactants is out of the scope of this work, the measurement of specific conductivity as a function of [S]tot at constant R1 ) 0.798 has been repeated,

as an example, in a concentration range (0 < [S]tot < 0.025 M), concentrated enough to allow the formation of the mixed micelles (plot not shown). In fact, a “third” break on κ was obtained (following the same method previously explained) at cmc* ) 12.90 mM, in total agreement with cmc* values found in the literature for a similar ternary system (di-C12DMAB/C12TAB/H2O).31 The formation of mixed vesicle aggregates has been confirmed by ζ-potential measurements. The ζ-potential was calculated from the experimental electrophoretic mobility, µE, by using the Henry equation:49,50

ζ)

3η µ 20rf(κDa) E

(1)

where the permittivity of the vacuum, 0, the relative permittivity of the medium, r, and the viscosity of water, η, were taken as 8.854 × 10-4 J-1 C2 m-1, 78.5, and 8.904 × 10-12 N‚m-2‚s, respectively. The factor f(κDa) is the Henry function, which depends on the particle shape, κD being the reciprocal Debye length and a the particle radius, taken from cryo-TEM results. For spheres with κDa > 1, f(κDa) is given by49,50

f(κDa) )

9 3 330 75 + 2 2(κDa) 2(κ a)2 (κ a)3 D

(2)

D

Figure 6 shows the ζ-potential values as a function of the molar fraction R1, at two [S]tot well above the second break on conductivity, i.e., for solutions that contain mixed vesicles. As can be seen in the figure, the ζ-potential is constant, around 60 ( 6 mV, within the experimental error. This independency of the ζ-potential with both the molar fraction of the system and the total surfactant concentration contrasts with the changes observed on conductivity and cryo-TEM experiments. It can be explained considering that the ζ-potential is a property of the aggregate surface, and in this case this surface is (49) Hunter, R. J. Zeta Potential in Collois Science. Principles and Applications; Academic Presss: London, 1981. (50) Oshima, H.; Furusawa, K. Electrical Phenomena at Interfaces. Fundamentals, Measurements, and Applications; Marcel Dekker: New York, 1998.

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Figure 4. cryo-TEM photographies of mixed di-C12DMAB + C12EDMAB vesicles: (a) at molar fraction, R1) 0.447 and [S]tot ) 1.518 mM; (b) at molar fraction, R1) 0.769 and [S]tot ) 2.532 mM. Table 1. Values of Experimental Molar Fraction, r1, Mixed Critical Microaggregates Concentration, CAC*, and Mixed Critical Vesicles Concentration, CVC*, Obtained from Experimental Conductivity Data for the Mixed System di-C12DMAB (1) + C12EDMAB (2)a R1 0 0.202 0.384 0.478 0.606 0.795 0.798 0.895 1

CAC* (mM) 0.356 0.395 0.422 0.480

CVC* (mM) 0.428 0.508 0.584 0.759 1.359

Assuming a Gouy-Chapman double layer, the surface charge density enclosed by the shear plane, σζ, can be obtained by using the Loeb equation for a z:z electrolyte:51

σζ )

[ ( )

( )]

20rκDkBT zeζ zeζ 2 tanh sinh + ze 2kBT κDa 4kBT

(3)

Uncertainties on CAC* and CVC* are estimated to be less than (5 × 10-6. b Reference 34. c Reference 12. d Reference 31.

where e is the elemental charge, z is the valence of the ion, kB is the Boltzmann constant, and T is the absolute temperature. This equation, which includes a correction term that takes into account the curvature of the vesicle, is not normally used in the literature since it needs information about the size of the particle. It decreases the error on the calculation of σζ from 20 to 5%.50 In this work, σζ values were calculated using eq 3 for each ζ-potential and a values (determined from cryo-TEM results), and

practically of the same type, irrespective of the molar fraction and concentration, given that the ionic head of di-C12DMAB and C12EDMAB is quite similar.

(51) Loeb, A. L.; Overbeek, J. T. G.; Wiersema, P. H. The Electrical Double Layer Around a Spherical Colloid Particle; MIT Press: Cambridge, MA, 1961.

0.552 0.657 0.165, 0.14,b 0.16,c 0.18d

a

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Figure 5. Plot of CAC* (solid squares) and CVC* (open circles) as a function of the molar fraction, R1, for the mixed system di-C12DMAB (1) + C12EDMAB (2).

Junquera et al.

Figure 7. Plot of surface charge density, σζ, as a function of a function of the molar fraction, R1, for various [S]tot concentrations of the mixed system di-C12DMAB (1) + C12EDMAB (2).

surfactant solutions, although the analysis of the formation of mixed aggregates is more complicated. For example, in catanionic systems (cationic + anionic surfactant system) the strong electrostatic attraction between the opposite charged headgroups is the predominant force driving to the formation of vesicles.3 In other cases, as lipid + single-chain surfactant systems, vesicles can also be obtained in appropriate conditions, but its thermodynamic stability is still receiving much attention.13-15,52,53 In bicationic or bianionic surfactant systems, there is not much synergism because of the same charged headgroups. In particular, in the bicationic system studied in this work (di-C12DMAB + C12EDMAB), where both surfactants have not only a similar headgroup but also an identical hydrocarbon tail, it is expected that molecular packing characteristics are responsible for the aggregation process instead of electrostatic interactions. The packing parameter, P, proposed by Israelachvili,41 relates the molecular characteristics of a surfactant as

P) Figure 6. Plot of ζ-potential as a function of the molar fraction, R1, for the mixed system di-C12DMAB (1) + C12EDMAB (2).

are represented as a function of R1 at various [S]tot in Figure 7. As seen in the figure, σζ is almost constant with the molar fraction and the [S]tot of the system, as the ζ-potential also shows in Figure 6. It is well-known that the size, shape, and nature of the aggregates formed in solution depends on the free Gibbs energy of the system, the optimum aggregate being that one with a minimum value for this magnitude.41 The total free energy results from two main factors, i.e., the repulsive energy, coming from the head polar groups, and the attractive energy, coming from the hydrocarbon chain packing. Accordingly, surfactant molecules aggregate as spherical, rodlike, or globular micelles, vesicles/liposomes, bilayers, lamellar phases, and so on, depending on their molecular characteristics. Those features are general in colloids and can be applied to not only pure but also mixed

v aolc

(4)

where ν and lc are the volume and the length of the hydrophobic tail, respectively, and ao is the area of the polar head. The aggregate will be a spherical micelle for P < 1/3, a globular micelle for 1/2 < P < 1/3, a vesicle or a flexible bilayer for 1/2 < P < 1, and a plane bilayer for P ≈ 1. The values of ν and lc can be obtained according to Tanford’s model38,39,54 using the equations

lc ≈ 0.154 + 0.1265n nm

(5)

v ≈ (27.4 + 26.9n)10-3 nm3

(6)

where n is the number of carbon atoms on the hydrocarbon (52) Edwards, K.; Almgren, M.; Bellare, J.; Brown, W. Langmuir 1989, 5, 473. (53) Edwards, K.; Almgren, M. J. Colloid Interface Sci. 1991, 147, 1. (54) Tanford, C. J. Phys. Chem. 1974, 78, 2469.

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Table 2. Theoretical Values of the Structural Parameters, ν, ao, and lc, for the Pure Surfactants, di-C12DMAB and C12EDMAB, and the Packing Parameter, P, of the Corresponding Aggregates surfactant

ν (Å3)

a0 (Å2)

lc (Å)

P

C12EDMAB di-C12DMAB

350.2 700.4

75 75

16.68 16.68

0.28 0.56

tail. The value of ao can be determined from the aggregation number of the single-chain surfactant assuming spherical micelles.37,55 Table 2 reports the values of these geometrical parameters calculated for the surfactants used in this work. Packing parameters values of P ) 0.56 for di-C12DMAB and P ) 0.28 for C12EDMAB are in total agreement with the vesicle geometry found herein from cryo-TEM experiments for the double-chain surfactant and the spherical micelle geometry for its single-chain counterpart previously reported37,55 from fluorescence results. Accordingly, an effective packing parameter can be defined for the mixed aggregates3

Peffective )

( ) v aolc

effective

)

vdi-SXdi-Sagg + vSXSagg (ao,di-SXdi-Sagg + ao,SXSagg)lc (7)

where the suffixes di-S and S refer to the double-chain surfactant and the single-chain surfactant, respectively; Xiagg is the molar fraction in the aggregate. This effective packing parameter varies in the present case from 0.28 for the pure C12DMAB micelles to 0.56 for the pure diC12DMAB vesicles, justifying the mixed aggregation behavior experimentally found in this work as the [S]tot increases at constant R1. Experimental results on Xiagg would be necessary to confirm this conclusion. However, the method proposed by us37 to calculate Ximic on mixed micelle systems from conductivity experiments cannot be applied in the present case due to the high difference among the CVC of di-C12DMAB and the cmc of C12DMAB, even with our highly precise conductometric technique. We are currently checking the method on mixed vesicle systems with less difference between these two critical concentrations, as is the case when the single-chain surfactant is long enough and the double-chain surfactant is shorter. Acknowledgment. The authors thank the DGES (MEC of Spain), Project No. BQU2002-586, for supporting this work. Authors thank J. M. Valpuesta and J. L. Carrascosa for their assistance on cryo-TEM experiments. LA049113C (55) Junquera, E.; Pen˜a, L.; Aicart, E. Langmuir 1997, 13, 219.