2474
Langmuir 2006, 22, 2474-2481
Zero Spontaneous Curvature and Its Effects on Lamellar Phase Morphology and Vesicle Size Distributions Bret A. Coldren, Heidi Warriner, Ryan van Zanten, and Joseph A. Zasadzinski* Department of Chemical Engineering, UniVersity of California, Santa Barbara, California 93106-5080
Eric B. Sirota Exxon Research and Engineering Company, Corporate Strategic Research, Route 22 East, Annandale, New Jersey 08801 ReceiVed September 7, 2005. In Final Form: January 2, 2006 Equimolar mixtures of dodecyltrimethylammonium chloride (DTAC) and sodium octyl sulfonate (SOSo) show a vesicle phase at >99 wt % water and a single, fluid lamellar phase for water fractions below 80 wt %. This combination is consistent with the bilayer bending elasticity κ ≈ kBT and zero bilayer spontaneous curvature. Caille´ line shape analysis of the small-angle X-ray scattering from the lamellar phase shows that the effective κ depends on the lamellar d spacing consistent with a logarithmic renormalization of κ, with κo ) (0.8 ( 0.1)kBT. The vesicle size distribution determined by cryogenic transmission electron microscopy is well fit by models with zero spontaneous curvature to give (κ + (κj/2)) ) (1.7 ( 0.1)kBT, resulting in κj ) (1.8 ( 0.2)kBT. The positive value of κj and the lack of spontaneous curvature act to eliminate the spherulite defects found in the lamellar gel phases found in other catanionic mixtures. Current theories of spontaneous bilayer curvature require an excess of one or more components on opposite sides of the bilayer; the absence of such an excess at equimolar surfactant ratios explains the zero spontaneous curvature.
Introduction It is no surprise that oppositely charged surfactants mix in a highly nonideal way and in fact are able to form structures such as unilamellar vesicles that are not found in other surfactant mixtures.1 The range of self-assembled microstructures in mixtures of cationic and anionic surfactants also includes small spherical micelles, cylindrical or wormlike micelles, and other lamellar and L3 phases.2 The vesicle phases discussed here form spontaneously with no external energy input, and some vesicle phases have been observed for well over a decade, suggesting at least metastable equilibrium. The fundamental questions remain as to why vesicles form in mixtures of oppositely charged surfactants and, once formed, whether they are at thermodynamic equilibrium. The formation and stability of any surfactant aggregate depends on whether that aggregate represents the global minimum in free energy for a given composition, and there are different approaches to describing the energetics of these mixtures. Translational entropy favors many unilamellar vesicles over a smaller number of multilamellar liposomes. To examine the enthalpic part of the free energy, it is often useful to start with a mechanical description of the properties of the bilayer.3-5 In this case, the elastic energy of a bilayer is described by the two principle curvatures c1 and c2. For spherical vesicles, c1 ) c2 ) 1/R, in which R is the vesicle radius. To terms second order in curvature, the free energy of a bilayer, per unit area, is3,4
E 1 ) κ(c + c2 - 2c0)2 + κjc1c2 A 2 1
(1)
in which κ is the bending modulus, κj is the saddle splay or Gaussian modulus, and c0 is the spontaneous curvature of the * To whom correspondence should be addressed. E-mail:gorilla@ engineering.ucsb.edu. Phone: 805-893-4768. Fax: 805-893-4731. (1) Kaler, E. W.; Murthy, A. K.; Rodriguez, B. E.; Zasadzinski, J. A. N.Science 1989, 245, 1371-1374.
bilayer. To stabilize a bilayer, κ > 0, but κj > 0 for surfaces that prefer hyperbolic shapes (saddle-shaped surfaces in which the centers of curvature are on opposite sides of the surface, c1c2 < 0) and κj < 0 for surfaces that prefer elliptical shapes (spheres, ellipsoids, etc. in which the centers of curvature are on the same side of the surface, c1c2 > 0). For a chemically and physically symmetric bilayer, the spontaneous curvature c0 equals 0.3-5 Hence, a single-component bilayer cannot have a nonzero spontaneous curvature. Theory suggests that it is necessary for the bilayer or its local environment to be chemically asymmetric for spontaneous curvature to exist.5 Purely entropically stabilized vesicles have a low bending constant (κ ≈ kBT, where kB is the Boltzmann constant), so the enthalpic bending contribution to the free energy is small compared to the mixing entropy. Unilamellar vesicles are stabilized against aggregation and formation of multilamellar liposomes by both the entropy of mixing and the steric repulsion between bilayers caused by Helfrich undulations. The Helfrich undulation repulsion is a consequence of bilayer thermal fluctuations, which are damped when bilayers come into contact; this causes the bilayer entropy to be reduced and leads to a repulsive interaction.6 For bilayers in a lamellar phase of repeat spacing d and membrane thickness δ, the Helfrich undulation repulsion is
Eund )
2 3π2 (kBT) 128 κ(d - δ)2
(2)
(For free bilayer or vesicles, (d - δ) is replaced by the interbilayer (2) Kaler, E. W.; Herrington, K. L.; Iampietro, D. J.; Coldren, B.; Jung, H. T.; Zasadzinski, J. A. In Mixed Surfactant Systems, 2nd ed.; Abe, M., Scamehorn, J., Eds.; Marcel Dekker: New York, 2005; pp 298-338. (3) Frank, F. C. Discuss. Faraday Soc. 1958, 25, 19-28. (4) Helfrich, W. Z. Naturforsch. 1973, 28C, 693-703. (5) Safran, S. A.; Pincus, P. A.; Andelman, D. Science 1990, 248, 354-356. (6) Helfrich, W. Z. Naturforsch. 1978, 33A, 305-315.
10.1021/la052448p CCC: $33.50 © 2006 American Chemical Society Published on Web 02/09/2006
Lamellar Phase Morphology and Vesicle Size
distance.) The repulsive undulation interaction can overwhelm the van der Waals attraction between bilayers (which is also proportional to (d - δ)-2) when κ is small, leading to a net repulsive interaction between bilayers and hence stable unilamellar vesicles, especially when combined with electrostatic repulsion in charged systems.7-9 Enthalpically stabilized vesicles, however, require nonzero spontaneous curvature and a larger value of the bending constant (κ > kBT). The curvature energy of forming a multilamellar liposome with many layers far from the optimal curvature is prohibitively high. In this case, the vesicles are narrowly distributed around a preferred size set by the spontaneous curvature.8,9 Spontaneous, apparently equilibrium vesicles with both narrow8-10 and broad size distributions1,2,11-15 in aqueous mixtures of a wide range of mixtures of cationic and anionic (catanionic) surfactants have been characterized by a variety of experimental techniques including small-angle neutron, X-ray, and light scattering and cryo and freeze-fracture transmission electron microscopy. The most common cationic surfactant used has been an alkytrimethylammonium bromide or tosylate, (e.g., cetyltrimethylammonium bromide (CTAB) or tosylate (CTAT)), whereas the common anionic surfactants are the sodium alkyl sulfates (e.g., sodium octyl (SOS), decyl sulfate (SDS), or dodecylbenzene sulfonate (SDBS)), which may have either a branched or comb structure. The phase diagrams of mixtures of these surfactants typically show two vesicle lobes, which are roughly symmetric on either side of the equimolar line at high water fractions (Figure 1A). One vesicle phase has a net excess of anionic surfactant, whereas the other has a net excess of cationic surfactant. For most catanionic mixtures, an insoluble precipitate forms at equimolar anion-to-cation ratios. At lower water fractions, two lamellar gel phases (MLV in Figure 1A) are found that are turbid and viscoelastic because of a highly defected, spherulite texture; the lamellar gel phases are also located roughly symmetrically about the equimolar line.16 These gels are similar to lamellar gels of dimyristoylphosphatidylcholine, pentanol, and poly(ethylene glycol) lipids17-19 and show a transition at lower water fractions to a fluid, flat bilayer phase.16,20 A simple defectbased theory of this structural progression requires that κ ≈ kBT and that c0 * 0.17-19 Cryo-TEM analysis of the vesicle size distributions and Caille´ line shape analysis of the small-angle (7) Herve´, P.; Roux, D.; Bellocq, A.-M.; Nallet, F.; Gulik-Krzywicki, T. J. Phys. II 1993, 8, 1255-1270. (8) Jung, H. T.; Coldren, B.; Zasadzinski, J. A.; Iampietro, D. J.; Kaler, E. W. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 1353-1357. (9) Jung, H. T.; Lee, Y. S.; Kaler, E. W.; Coldren, B.; Zasadzinski, J. A. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 15318-15322. (10) Iampietro, D.; Kaler, E. W. Langmuir 1999, 15, 8590-8601. (11) Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A.; Chiruvolu, S. J. Phys. Chem. 1993, 97, 13792-13802. (12) Brasher, L. L.; Herrington, K. L.; Kaler, E. W. Langmuir 1995, 11, 42674277. (13) Brasher, L. L. Phase Behavior and Microstructure of Surfactant Mixtures. Ph.D. Dissertation, University of Delaware, Newark, DE, 1996. (14) Coldren, B. A.; van Zanten, R.; Mackel, M. J.; Zasadzinski, J. A.; Jung, H. T. Langmuir 2003, 19, 5632-5639. (15) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J. Phys. Chem. 1992, 96, 6698-6707. (16) Coldren, B. Phase Behavior, Microstructure and Measured Elasticity of Catanionic Surfactant Bilayers. Ph.D. Dissertation, University of California, Santa Barbara, CA, 2002. (17) Warriner, H.; Idziak, S.; Slack, N.; Davidson, P.; Safinya, C. Science 1996, 271, 969-73. (18) Keller, S. L., Warriner, H., Safinya, C., Zasadzinski, J. A. Phys. ReV. Lett. 1997, 78, 4781-4784. (19) Warriner, H. E.; Keller, S. L.; Idziak, S. H. J.; Slack, N. L.; Davidson, P.; Zasadzinski, J. A.; Safinya, C. R. Biophys. J. 1998, 75, 272-293. (20) Coldren, B. A.; Warriner, H. E.; van Zanten, R.; Zasadzinski, J. A.; Sirota, E. B. Proc. Natl. Acad. Sci. U.S.A. 2005, in press.
Langmuir, Vol. 22, No. 6, 2006 2475
Figure 1. (a) Partial phase diagram of CTAT/SDBS/water at 25 °C. Typical of most catanionic mixtures, the phase diagram is roughly symmetric about the equimolar line. Two vesicle lobes (V) are found at high water fractions, one with an excess of CTAT and the other with an excess of SDBS. An insoluble precipitate forms along the equimolar line. The symmetric MLV phases are onionlike multilamellar spherulites with no excess water that form a lamellar gel similar to DMPC/pentanol/polymer lipid gels.17-19 Not indicated are micellar phases at either extreme of the surfactant mixing ratio. (b) Partial phase diagram of DTAC/SOSo/water at 25 °C. M represents spherical micelle phases, R represents a viscous rodlike micelle phase, and V represents unilamellar vesicles. Instead of two symmetric lobes, both the vesicle and lamellar phase occur along the equimolar line. The lamellar phase consists of flat stacks at all compositionssno MLV spherulite phase is observed.
X-ray scattering16,19,21-23 confirm that κ ≈ kBT for all of the catanionic systems studied thus far.16,20 This shows that surfactant mixing can lead to low bending constants24 and is consistent with the entropic stabilization of spontaneous vesicles and the formation of defects in the lamellar gel phases.16,20 However, mixtures of DTAC and SOSo do not follow this typical phase progression. The shorter chain lengths apparently inhibit the formation of a precipitate at equimolar concentration and instead lead to a single vesicle phase and a single, fluid lamellar phase. Caille´ line shape analysis of the small-angle X-ray scattering16,19,21-23 from the lamellar phase shows that κ ≈ kBT as in other entropically stabilized catanionic mixtures. The lack of spherulite texture in the lamellar phase suggests that the spontaneous radius of curvature is large (spontaneous curvature (21) Safinya, C.; Roux, D.; Smith, G. S.; Sinha, S. K.; Dimon, P.; Clark, N.; Bellocq, A. M.Phys. ReV. Lett. 1986, 57, 2718-2721. (22) Safinya, C. R.; Sirota, E. B.; Roux, D.; Smith, G. S. Phys. ReV. Lett. 1989, 62, 1134-1137. (23) Roux, D.; Safinya, C. R. J. Phys. (Orsay, Fr.) 1988, 49, 307-318. (24) Szleifer, I., Kramer, D., Benshaul, A., Gelbart, W. M., J. Chem. Phys. 1990, 92, 6800-6817.
2476 Langmuir, Vol. 22, No. 6, 2006
Coldren et al.
is near zero) compared to the d spacing of the lamellar phase. The DTAC/SOSo vesicle size distribution determined by cryoTEM can be fit equally well by a one-parameter model with c0 ) 0 or by a two-parameter model with a finite c0. Hence, at equimolar ratios, the necessary composition asymmetry for spontaneous curvature is small to nonexistent, but surfactant mixing can still make κ ≈ kBT, as required for the entropic stabilization of vesicles and a highly swollen lamellar phase. Materials Cetyltrimethylammonium p-toluenesulfonate (98% pure, CTAT, Sigma), dodecyltrimethylammonium chloride (98% pure, Fluka), sodium 1-octylsulfonate (SOSo, 99% pure, Lancaster Chemical), and dodecylbenzene sulfonate (SDBS, 98% pure, TCI America) were used as received. In all experiments, water was purified by the Milli-Q process, which results in a resistance of 18.2 MΩ. Brine solutions were prepared from mixtures of Milli-Q water and NaCl salt of >99.9% purity (Aldrich) to minimize the effect of electrostatics on the X-ray line shape. At these salt concentrations, the Debye screening length is
