Equilibrium unilamellar vesicles are stabilized by one of two distinct mechanisms depending on the value of the bending constant. Helfrich undulations ensure that the interbilayer potential is always repulsive when the bending constant, K, is of order k BT. When K Ͼ Ͼ k BT, unilamellar vesicles are stabilized by the spontaneous curvature that picks out a particular vesicle radius; other radii are disfavored energetically. We present measurements of the bilayer elastic constant and the spontaneous curvature, R o, for three different systems of equilibrium vesicles by an analysis of the vesicle size distribution determined by cryo-transmission electron microscopy and smallangle neutron scattering. For cetyltrimethylammonium bromide (CTAB)͞sodium octyl sulfonate catanionic vesicles, K ‫؍‬ .7 k BT, suggesting that the unilamellar vesicles are stabilized by Helfrich-undulation repulsions. However, for CTAB and sodium perfluorooctanoate (FC7) vesicles, K ‫؍‬ 6 kBT, suggesting stabilization by the energetic costs of deviations from the spontaneous curvature. Adding electrolyte to the sodium perfluorooctanoate͞CTAB vesicles leads to vesicles with two bilayers; the attractive interactions between the bilayers can overcome the cost of small deviations from the spontaneous curvature to form two-layer vesicles, but larger deviations to form three and more layer vesicles are prohibited. Vesicles with a discrete numbers of bilayers at equilibrium are possible only for bilayers with a large bending modulus coupled with a spontaneous curvature.

In mixtures of cetyltrimethylammonium bromide (CTAB) and sodium perfluorooctanoate (FC 7) in aqueous solution, novel bilayer cylinders with hemispherical end caps and open, flat discs coexist with spherical unilamellar vesicles, apparently at equilibrium. Such equilibrium among bilayer cylinders, spheres, and discs is only possible for systems with a spontaneous curvature, R o, and a positive Gaussian curvature modulus, . We have measured the size distributions of the spherical vesicles, cylinders, and discs by using cryo-electron microscopy; a simple analysis of this length distribution allows us to independently determine that the mean curvature modulus, Ϸ 5 ؎ 1 kBT and Ϸ 2 ؎ 1 kBT. This is one of the few situations in which R o, , and can be determined from the same experiment. From a similar analysis of the disk size distribution, we find that the edges of the discs are likely stabilized by excess CTAB. The fraction of discs, spherical vesicles, and cylinders depends on the CTAB͞FC 7 mole ratio: increasing CTAB favors discs, while decreasing CTAB favors cylinders. This control over aggregate shape with surfactant concentration may be useful for the design of templates for polymerization, mesoporous silicates, etc.cryogenic transmission electron microscopy ͉ surfactants ͉ vesicles T he starting point for the description of bilayer organization in solution is the harmonic approximation to the bending free energy (1):R 1 and R 2 are the principle radii of curvature of the structures, R o is the spontaneous radius of curvature, and are the mean and Gaussian curvature elastic constants, respectively, and A is the area of the bilayer membrane. The harmonic approximation is appropriate when the membrane thickness (1-3) [here Ϸ3 nm (4)] and the Debye length for ionic surfactants (2, 5, 6) [also Ϸ1-3 nm (4)] are small compared with R 1 and R 2 (Ϸ20-30 nm, see Fig. 1). The differences of the bending free energy, F B , of different aggregate geometries can often be of the order of k B T, leading to the possibility of multiple structures in equilibrium.The two elastic constants, and , play very different roles in determining bilayer organization. The magnitude of reflects the energy needed to bend the bilayer away from its spontaneous radius of curvature, R o . For ϳ k B T, thermal fluctuations give rise to significant curvature fluctuations, which lead to a net repulsive interaction between bilayers at short distances. This steric repulsion can stabilize unilamellar vesicles over multilamellar liposomes (3,4,7,8). Larger values of (ӷk B T), combined with a spontaneous curvature that picks out a particular vesicle radius, lead to unilamellar vesicles as the curvature variations inherent to multilamellar structures are energetically prohibited (3,4,9). A spontaneous bilayer curvature (1͞R o 0) is only possible when nonideal surfactant mixing causes the interior and exterior monolayers of the vesicle bilayer to have different compositions or environments (3, 10, 11).influences only the topology (and hence the number) of t...

Hollow polymer spheres of styrene and divinyl benzene can be templated from catanionic equilibrium vesicles formed by cetyltrimethylammonium tosylate (CTAT) and sodium dodecylbenzenesulfonate (SDBS) or cetyltrimethylammonium bromide (CTAB) and sodium octyl sulfate (SOS). Characterization by many methods suggests the microstructure of the equilibrium vesicle template is left largely intact in the final polymer product. The particles have an average radius of ca. 60 nm and a membrane shell less than 10 nm thick. The cross-linked hollow polymer vesicles are robust and withstand complete drying and resuspension in water with no apparent change in microstructure. The polymer membrane surfaces can be functionalized by sulfonation or surfactant adsorption, and this functionalization prevents aggregation of the polymer particles when they are resuspended in water.

Assembling structures to divide space controllably and spontaneously into subunits at the nanometer scale is a significant challenge, although one that biology has solved in two distinct ways: prokaryotes and eukaryotes. Prokaryotes have a single compartment delimited by one or more lipid-protein membranes. Eukaryotes have nested-membrane structures that provide internal compartments--such as the cell nucleus and cell organelles in which specialized functions are carried out. We have developed a simple method of creating nested bilayer compartments in vitro via the "interdigitated" bilayer phase formed by adding ethanol to a variety of saturated phospholipids. At temperatures below the gel-liquid crystalline transition, T(m), the interdigitated lipid-ethanol sheets are rigid and flat; when the temperature is raised above T(m), the sheets become flexible and close on themselves and the surrounding solution to form closed compartments. During this closure, the sheets can entrap other vesicles, biological macromolecules, or colloidal particles. The result is efficient and spontaneous encapsulation without disruption of even fragile materials to form biomimetic nano-environments for possible use in drug delivery, colloidal stabilization, or as microreactors. The vesosome structure can take full advantage of the 40 years of progress in liposome development including steric stabilization, pH loading of drugs, and intrinsic biocompatibility. However, the multiple compartments of the vesosome give better protection to the interior contents in serum, leading to extended release of model compounds in comparison to unilamellar liposomes.

Constructing compartments to divide space controllably and spontaneously into subunits at the submicron scale is a significant challenge facing nanotechnology. We have developed a simple method of creating nanocompartments in vitro via the "interdigitated" bilayer phase formed by adding ethanol to a variety of saturated phospholipids. At temperatures below the gel-liquid crystalline transition, Tm, the interdigitated lipid-ethanol sheets are rigid and flat; when the temperature is raised above Tm, the sheets become flexible and close on themselves and the surrounding solution to form closed compartments. During this closure, the sheets can entrap other vesicles, biological macromolecules, or colloidal particles. The result is efficient and spontaneous encapsulation without disruption of even fragile materials to form biomimetic nanoenvironments for possible use in drug delivery, in colloidal stabilization, or as microreactors.

Three methods of evaluating vesicle mean radii and polydispersity, quasi-elastic light scattering (QLS), freeze-fracture electron microscopy (FF-TEM), and cryo-transmission electron microscopy (cryo-TEM), were used to determine the size distributions of spontaneous vesicles made from mixtures of cetyltrimethylammonium tosylate (CTAT) and sodium dodecylbenzene sulfonate (SDBS). While QLS is probably the most commonly used method to size vesicles, it is limited to measures of the mean hydrodynamic radius and an estimate of the polydispersity, both of which are heavily weighted toward the largest structures in the solution. Cryo-TEM can provide the entire size distribution of the outer diameters of spherical vesicles, from which the sum of the Helfrich bilayer elastic parameters, K ) κ + κ j/2 and the spontaneous curvature radius, R0, can be determined. FF-TEM can provide the number-average mean diameter and polydispersity once the influence of the fracture plane has been factored into the distribution, thereby confirming the cryo-TEM size distribution. For 7:3 wt CTAT/SDBS at 1% total surfactant in water, K ) κ + κ j/2 ) 0.15 ( 0.03 kBT and R0 ) 55 nm ( 10 nm. For CTAT/SDBS, w/w, at 2% total surfactant, K ) 0.54 kT ( 0.05 kBT and R0 ) 36 nm ( 1 nm. We find that surfactant mixing is likely the origin of the low bilayer elasticity in catanionic vesicles. However, the lower value of K in the CTAT-rich sample is likely due to the hydrophobic tosylate counterion increasing the area per headgroup.

Mixtures of cetyltrimethylammonium tosylate (CTAT) and sodium dodecylbenzene sulfonate (SDBS) in water form a fluid lamellar phase at ≤40 wt % water but surprisingly turn into viscous gels at higher water fractions. The gels are characterized by spherulite and other bilayer defects consistent with a low bending elasticity, κ ∼ k B T , and a nonzero spontaneous curvature. Caillé analysis of the small-angle x-ray line shape confirms that for 7:3 wt:wt CTAT:SDBS bilayers at 50% water, κ = 0.62 ± 0.09 k B T and κ̄ = −0.9 ± 0.2 k B T . For 13:7 wt:wt CTAT:SDBS bilayers, the measured bending elasticity decreases with increasing water dilution in good agreement with predictions based on renormalization theory, giving κ o = 0.28 k B T . These results show that surfactant mixing is sufficient to make κ ∼ k B T , which promotes strong, Helfrich-type repulsion between bilayers that can dominate the van der Waals attraction. These are necessary conditions for spontaneous vesicles formed at even higher water fractions to be equilibrium structures.

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 kappa approximately k(B)T and zero bilayer spontaneous curvature. Caillé line shape analysis of the small-angle X-ray scattering from the lamellar phase shows that the effective kappa depends on the lamellar d spacing consistent with a logarithmic renormalization of kappa, with kappa(o) = (0.8 +/- 0.1)k(B)T. The vesicle size distribution determined by cryogenic transmission electron microscopy is well fit by models with zero spontaneous curvature to give (kappa + (kappa/2)) = (1.7 +/- 0.1)k(B)T, resulting in kappa = (1.8 +/- 0.2)k(B)T. The positive value of kappa 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.