Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature

We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various bicontinuous cubic phases. For the latter case we consider both single structures (one monolayer) and double structures (two monolayers). Their interfaces are modeled by the triply periodic surfaces of constant mean curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the different bicontinuous cubic phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. For vanishing saddle-splay modulus $\bar \kappa$, almost every phase considered has some region of stability in the Gibbs triangle. Although bicontinuous cubic phases are suppressed by sufficiently negative values of the saddle-splay modulus $\bar \kappa$, we find that they can exist for considerably lower values than obtained previously. The most stable bicontinuous cubic phases with decreasing $\bar \kappa < 0$ are the single and double gyroid structures since they combine favorable topological properties with extreme volume fractions.Comment: Revtex, 23 pages with 10 Postscript files included, to appear in J. Chem. Phys. 112 (6) (February 2000

Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Numerical simulations of complex fluid-fluid interface dynamics

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.Comment: 24 pages, 12 figure