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

TL;DR

This paper investigates the stability of various bicontinuous cubic phases in ternary amphiphilic systems using a curvature model, revealing conditions under which these complex structures are energetically favorable.

Contribution

It introduces a detailed curvature-based framework to analyze the stability of bicontinuous cubic phases, including double structures, in ternary amphiphilic systems.

Findings

Bicontinuous cubic phases are stable over certain concentration ranges.

Negative saddle-splay modulus suppresses bicontinuous phases, but they can still exist at lower values than previously thought.

Gyroid structures are most stable among bicontinuous phases for decreasing saddle-splay modulus.

Abstract

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.