Langmuir 1996, 12, 3819-3827
3819
Effect of Surfactant Tail-Length Asymmetry on the Formation of Mixed Surfactant Vesicles Pak K. Yuet and Daniel Blankschtein* Department of Chemical Engineering and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received April 4, 1996. In Final Form: May 16, 1996X A fundamental understanding of vesicle formation and stability in mixed surfactant systems is important for the description of their phase behavior, for the application of vesicles as encapsulating devices, and for the elucidation of cholesterol gallstone formation in bile. With this in mind, we have utilized our recently developed molecular-thermodynamic theory to study the formation of vesicles in mixtures containing cetyltrimethylammonium bromide (CTAB) and sodium alkyl sulfates of various tail lengths. The theory accounts for the essential free-energy contributions to the free energy of vesiculation, gves, with particular emphasis on their relative importance and interplay in the process of vesicle formation. We found that mixed surfactant vesicles can be stabilized energetically in highly asymmetric surfactant mixtures, such as those consisting of CTAB and sodium pentyl sulfate (SPS). These vesicles are characterized by small sizes and a narrow size distribution. In contrast, in mixtures consisting of CTAB and sodium pentadecyl sulfate (SPDS), where the tail-length asymmetry is small, vesicles are stabilized entropically and are characterized by large sizes and a wide size distribution. Small vesicles are formed by placing more molecules in the outer vesicle leaflet to relieve the outer interfacial free-energy penalty. The SPS molecules, having a short hydrophobic tail, can cover the outer hydrocarbon/water interface without incurring a high packing free-energy penalty, thus making gves of small CTAB/SPS vesicles lower than that corresponding to a planar bilayer. In contrast, a high packing free-energy penalty is incurred in small CTAB/SPDS vesicles, due to the existence of a more crowded hydrophobic region. In this case, therefore, gves of finitesized vesicles is always higher than that corresponding to a planar bilayer, and the formation of vesicles in such systems is driven by the more favorable entropy of mixing. Surfactant tail-length asymmetry also affects the optimum composition of the vesicles by altering the tail transfer free-energy contribution, gtr. Decreasing surfactant tail-length asymmetry reduces gtr, which, in turn, decreases the influence of the energetics of vesicle formation, as compared to that of the entropy associated with localizing the surfactant molecules. In a mixture containing CTAB and SPDS (weight ratio ) 3/7), therefore, the entropic penalty dominates and drives the vesicle composition toward that of the bulk solution. In contrast, in highly asymmetric mixtures such as those consisting of CTAB and SPS (weight ratio ) 3/7), the optimum vesicle composition reflects a compromise between the entropic and energetic factors. The effect of decreasing surfactant tail-length asymmetry on the optimum vesicle composition is therefore similar to that of adding salt to the vesicle solution. Specifically, decreasing tail-length asymmetry reduces the energetic influence by decreasing gtr, while adding salt produces the same effect through a reduction in the electrostatic free-energy contribution, gelec.
I. Introduction The formation of phospholipid vesicles, which have been widely used as model cells in biology and medicine and are also useful as drug carriers and other industrial encapsulating devices,1-3 usually requires input of some form of energy, for example, sonication.4 These vesicles often aggregate and fuse to form large multilamellar structures within days and are believed to be thermodynamically unstable. On the other hand, certain surfactants5-10 and surfactant mixtures11-18 form vesicles spontaneously in aqueous solution. These spontaneously* To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, July 1, 1996. (1) Lasic, D. D. Am. Sci. 1992, 80, 20. (2) Lasic, D. D. Liposomes: From Physics to Applications. Elsevier Publishing Co.: Amsterdam, 1993. (3) Gregoriadis, G., Ed. Liposome Technology. Volume II: Entrapment of Drugs and Other Materials, 2nd ed.; CRC Press: Boca Raton, FL, 1988. (4) Lichtenberg, D.; Barenholz, Y. Liposomes: Preparation, Characterization, and Preservation. In Methods of Biochemical Analysis; 1992; Vol.33, p 337. Wiley: New York (5) Lin, Z.; He, M.; Scriven, L. E.; Davis, H. T. J. Phys. Chem. 1993, 97, 3571. (6) Ninham, B. W.; Evans, D. F. Faraday Discuss. Chem. Soc. 1986, 81, 1. (7) Brady, J. E.; Evans, D. F.; Kachar, B.; Ninham, B. W. J. Am. Chem. Soc. 1984, 106, 4279. (8) Ninham, B. W.; Evans, D. F.; Wei, G. J. J. Phys. Chem. 1983, 87, 5020. (9) Hashimoto, S.; Thomas, J. K.; Evans, D. F.; Mukherjee, S.; Ninham, B. W. J. Colloid Interface Sci. 1983, 95, 594.
S0743-7463(96)00321-6 CCC: $12.00
forming vesicles are believed to be thermodynamically stable in the sense that they are more resistant to aggregation and fusion and that no energy input, besides gentle mixing, is required for their formation. This contrasting behavior between the traditional and the spontaneously-forming vesicles has posed challenging problems in understanding how vesicles are formed in various surfactant systems and has also sparked significant interest in both experimental and theoretical studies of mixed surfactant vesicles.19-21 A fundamental understanding of vesicle formation in mixed surfactant systems (10) Talmon, Y.; Evans, D. F.; Ninham, B. W. Science 1983, 221, 1047. (11) Murthy, A. K.; Kaler, E. W.; Zasadzinski, J. A. J. Colloid Interface Sci. 1991, 145, 598. (12) Hauser, H. Chem. Phys. Lipids 1987, 43, 283. (13) Gabriel, N. E.; Roberts, M. F. Biochemistry 1984, 23, 4011. (14) Brasher, L. L.; Herrington, K. L.; Kaler, E. Langmuir 1995, 11, 4267. (15) Kaler, E. W.; Murthy, A. K.; Rodriguez, B. E.; Zasadzinski, J. A. N. Science 1989, 245, 1371. (16) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J. Phys. Chem. 1992, 96, 6698. (17) Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A.; Chiruvolu, S. J. Phys. Chem. 1993, 97, 13792. (18) Kondo, Y.; Uchiyama, H.; Yoshino, N.; Nishiyama, K.; Abe, M. Langmuir 1995, 11, 2380. (19) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (20) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. Biochim. Biophys. Acta 1977, 470, 185. (21) Carnie, S.; Israelachvili, J. N.; Pailthorpe, B. A. Biochim. Biophys. Acta 1979, 554, 340.
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is essential in the study of the phase behavior of these systems. In addition, understanding vesicle formation is also important from an applied viewpoint. In industry, for example, the mechanism of vesicle formation plays an important role in determining the stability and size distribution of vesicles, which are critical issues in the application of vesicles as encapsulating devices. In medicine, the mechanism of vesicle formation may prove to be an important aspect in understanding the formation of cholesterol gallstones in bile.22-25 Various aspects of unilamellar vesicles have been studied theoretically by borrowing concepts from membrane elasticity theory,26,27 including vesicle shape deformation,28-31 phase behavior,32-34 and membrane rigidity.35-38 In an attempt to provide a theoretical basis for the spontaneous formation of vesicles in surfactant mixtures, Safran and co-workers32,39,40 suggested that mixed vesicles can form as a result of the energetic advantage of finite-sized vesicles over a planar bilayer, a mechanism referred to as “energetic stabilization”. In particular, specific interactions between the hydrophilic moieties of the surfactant molecules (hereafter referred to as “heads”) in a mixture of cationic and anionic surfactants may lead to a difference in composition between the outer and inner vesicle leaflets. This composition difference can, in turn, alter the spontaneous curvature of the vesicle bilayer, causing a finite-sized vesicle to have a lower free energy than that corresponding to a planar bilayer. Dan and Safran also found41 that vesicles composed of mixtures of diblock copolymers can be stabilized energetically by similar mechanisms32,39,40 through the asymmetry in the polymer chains residing in the aqueous environments. In a recent paper, we have developed a detailed molecular-thermodynamic theory to describe the formation of mixed vesicles.42 This theory permits one to study, from a fundamental viewpoint, the effect of surfactant molecular structure on vesicle properties, including vesicle size, composition, and surface potentials. Applying our theory to a cationic/anionic surfactant mixture containing cetyltrimethylammonium bromide (CTAB) and sodium octyl sulfate (SOS), we found that CTAB/SOS vesicles are stabilized entropically. In other words, CTAB/SOS vesicles are not energetically preferred, but rather, their formation is due to the entropic advantage associated with a multiplicity of finite-sized (22) Lee, S. P.; Park, H. Z.; Madani, H.; Kaler, E. W. Am. J. Physiol. 1987, 252, G374. (23) So¨mjen, G. J.; Gilat, T. J. Lipid Res. 1985, 26, 699. (24) So¨mjen, G. J.; Gilat, T. FEBS Lett. 1983, 156, 265. (25) Mazer, N. A.; Carey, M. C. Biochemistry 1983, 22, 426. (26) Helfrich, W. Z. Naturforsch. 1973, 28c, 693. (27) Kle´man, M. Proc. R. Soc. London Ser. A 1976, 347, 387. (28) Andelman, D.; Kawakatsu, T.; Kawasaki, K. Europhys. Lett. 1992, 19, 57. (29) Taniguchi, T.; Kawasaki, K.; Andelman, D.; Kawakatsu, T. Condens. Matter Mater. Commun. 1993, 1, 75. (30) Kawakatsu, T.; Andelman, D.; Kawasaki, K.; Taniguchi, T. J. Phys. II 1993, 3, 971. (31) Taniguchi, T.; Kawasaki, K.; Andelman, D.; Kawakatsu, T. J. Phys. II 1994, 4, 1333. (32) Safran, S. A.; Pincus, P. A.; Andelman, D.; MacKintosh, F. C. Phys. Rev. A 1991, 43, 1071. (33) Andelman, D.; Kozlov, M.; Helfrich, W. Europhys. Lett. 1994, 25, 231. (34) Morse, D. C.; Milner, S. T. Europhys. Lett. 1994, 26, 565. (35) Mitchell, D. J.; Ninham, B. W. Langmuir 1989, 5, 1121. (36) Fogden, A.; Mitchell, D. J.; Ninham, B. W. Langmuir 1990, 6, 159. (37) Fogden, A.; Ninham, B. W. Langmuir 1991, 7, 590. (38) Winterhalter, M.; Helfrich, W. J. Phys. Chem. 1992, 96, 327. (39) Safran, S. A.; Pincus, P. A.; Andelman, D. Science 1990, 248, 354. (40) Safran, S. A.; MacKintosh, F. C.; Pincus, P. A.; Andelman, D. Prog. Colloid Polym. Sci. 1991, 84, 3. (41) Dan, N.; Safran, S. A. Macromolecules 1994, 27, 5766. (42) Yuet, P. K.; Blankschtein, D. Langmuir 1996, 12, 3802.
Yuet and Blankschtein
vesicles over that corresponding to one large planar bilayer. More importantly, we found that chain packing in the vesicle bilayer plays an important role in determining the behavior of the free energy of vesiculation.43 This indicates that, in addition to specific interactions between the surfactant heads, other mechanisms, such as chain packing, may also be responsible for the spontaneous formation of vesicles in surfactant mixtures. In the present paper, we apply our theory to describe the formation of vesicles in systems containing CTAB and various sodium alkyl sulfate surfactants. In particular, we are interested in understanding how the asymmetry between the hydrophobic moieties (hereafter referred to as “tails”) of the cationic and anionic surfactants affects the formation and stability of mixed vesicles in these complex fluids.44 The remainder of the paper is organized as follows. In section II, we briefly discuss the molecular-thermodynamic theory utilized to describe a vesicle solution. In section III, we first describe the mixed surfactant systems of interest and then present several results, including vesicle size and composition distributions, as predicted by the theory, as well as a thorough discussion of the theoretical findings. Finally, in section IV, we present concluding remarks. II. Molecular-Thermodynamic Theory of Vesicle Solution The molecular-thermodynamic theory described below has been presented in the preceding paper in this issue,42 and the interested reader should refer to ref 42 for complete details. Consider a three-component system containing surfactant A, surfactant B, and water in which mixed vesicles consisting of surfactants A and B are formed. The total Gibbs free energy of the vesicle solution, G, can be expressed as42
G ) Go + Gmix + Gint
(1)
where Go is the standard-state free energy, Gmix is the free energy associated with mixing the various species, including surfactant monomers, vesicles, and water molecules, in the solution, and Gint is the free energy associated with the interactions among the various species.45 The chosen standard state corresponds to one in which all the surfactant monomers and vesicles exist in isolation at infinite dilution without mixing. Since a typical cationic/anionic vesicular system contains only a small amount (1 to 2 wt %) of surfactant,46 we assume that the mixing is ideal and that the interactions among the various species are negligible. In the context of this free-energy model, the following expression for the vesicle size and composition distribution is obtained42 nF n(1-F) X(n,F) ) X1A X1B exp(-ngves/kT)
(2)
where X(n,F) is the mole fraction of vesicles having aggregation number n and composition F, which is defined as the mole fraction of surfactant A in the vesicle, X1A and X1B are the mole fractions of surfactant A and B monomers, respectively, k is the Boltzmann constant, T is the absolute temperature, and gves is the free energy of vesiculation, which is the total free-energy change per molecule associated with the process by which a vesicle of aggregation number n and composition F is formed by assembling nF (43) Here, “vesiculation” refers to the process by which the surfactant monomers are taken from the aqueous environment to form a vesicle. (44) Recently, May and Ben-Shaul (May, S.; Ben-Shaul, A. J. Chem. Phys. 1995, 103, 3839) have also studied the effect of surfactant taillength asymmetry on vesicle stabilization using the curvature-expansion approach. (45) Blankschtein, D.; Thurston, G. M.; Benedek, G. B. J. Chem. Phys. 1986, 85, 7268. (46) Herrington, K. L. Phase Behavior and Microstructure in Aqueous Mixtures of Oppositely Charged Surfactants. Ph.D. Thesis, University of Delaware, 1994.
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surfactant A monomers and n(1-F) surfactant B monomers.47 If gves is known, one can then calculate the monomer concentrations by satisfying the mass balances corresponding to surfactants A and B, that is,
∑n∫ FX(n,F) dF
(3)
∑n∫ (1-F)X(n,F) dF
(4)
XAt ) X1A +
1
0
n
XBt ) X1B +
1
n
0
where XAt and XBt are the total mole fractions of surfactants A and B, respectively. We have developed a detailed molecular model to calculate gves. In this model, gves is written as a sum of five free-energy contributions, that is,42
gves ) gtr + gpack + gσ + gsteric + gelec
(5)
The following paragraphs briefly discuss these free-energy contributions and explain how they can be estimated from only knowledge of the molecular structures of the surfactant molecules and the solution conditions. Transfer Free Energy, gtr. This free-energy contribution captures the hydrophobic effect driving the surfactant selfassembly in aqueous solutions and can be expressed as
gtr ) F∆µtr,A + (1 - F)∆µtr,B + gm
Interfacial Free Energy, gσ. The interfacial free-energy change accounts for the free energy required to create the outer and inner hydrocarbon/water interfaces during the formation of vesicles. This free-energy contribution is expressed as follows42
gσ ) f σ j o(ao - a j *o ) + (1 - f )σ j i(ai - a j *i )
where ao (ai ), a j o* (a j i*), and σ j o (σ j i) are the area per molecule, the molar-average shielded area per molecule, and the curvaturecorrected molar-average interfacial tension at the outer (inner) interface, respectively. The shielded area is the area occupied by the surfactant head at the interface, which reduces the area of contact between the hydrophobic region and water. The interfacial tension is corrected for the vesicle curvature using the Tolman equation.42,53 Steric Free Energy, gsteric. Treating the surfactant heads as hard disks, and using the scaled-particle theory equation of state for hard-disk mixtures,54-56 the steric free energy per molecule, gsteric, can be calculated as the excess free energy associated with the process by which the surfactant heads are brought from infinitely apart to the outer and inner vesicle surfaces. Mathematically, gsteric can be expressed as follows42
[
( )] [
a j ho πd h o2/4 gsteric )f - ln 1 kT a′o - a j ho a′o
(1 - f )
(6)
where ∆µtr,A and ∆µtr,B are the free-energy changes associated with transferring the tails of surfactants A and B, respectively, from the aqueous environment to their corresponding pure liquid hydrocarbon phases. For linear alkyl tails, ∆µtr,k (k ) A or B ) can be estimated using an empirical formula based on experimental solubility correlations, which relates ∆µtr,k to the carbon number of the tail.42,48 The free energy per molecule due to mixing in the outer and inner leaflets, gm, is estimated using the ideal mixing model as a first approximation.42 Packing Free Energy, gpack. The surfactant tails in the vesicle hydrophobic region are in a different conformational state from those in bulk hydrocarbon, since they are anchored at one end on either the outer or inner vesicle interfaces. This, in turn, restricts the number of conformations that each surfactant tail can adopt. The free-energy penalty associated with these conformational restrictions is estimated as the free-energy difference between a tail packed in a vesicle and a tail in bulk hydrocarbon. In this study, we adapt the mean-field approach developed by Szleifer, Ben-Shaul, and Gelbart49 to the vesicle geometry in the calculation of gpack.42,49,50 Briefly, this approach involves the calculation of the lateral pressure profiles in the outer and inner vesicle leaflets. The lateral pressure can be viewed as the pressure required to compress, or “straighten”, the tail in order to maintain an uniform density, which is assumed to be equal to that of bulk hydrocarbon. Knowing the lateral pressure profiles one can calculate the single-chain probability distribution and then compute gpack as well as other average chain properties, such as the chain segment density distribution. Using the rotational isomeric state model,51 we generate gpack for various surfactant pairs (see section III) and for a fixed number (≈2000) of vesicle configurations.52 For any other configurations, then, gpack is obtained by interpolation. (47) A note of caution here is that the size and composition distribution given in eq 2 is only an approximate expression. Indeed, statisticalmechanical arguments show that, within the context of ideal mixing, a pre-exponential factor proportional to n-1/2 should be present in eq 2.64 However, the value of this factor is typically very small (
