A systematic approach to bicontinuous cubic phases in ternary amphiphilic systems

TL;DR

This paper systematically generates and compares bicontinuous cubic structures in ternary amphiphilic systems using Fourier methods, space group theories, and Ginzburg-Landau models, revealing stability and geometric properties.

Contribution

It introduces a systematic approach combining Fourier analysis and symmetry theories to generate and analyze bicontinuous cubic phases, including improved minimal surface approximations.

Findings

The gyroid G is the most stable bicontinuous cubic phase.

Single structures can closely approximate triply periodic minimal surfaces.

Stability can be derived from geometrical interface properties.

Abstract

The Fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures in the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both single and double structures are investigated; they correspond to systems with one or two monolayers in a unit cell, respectively. We show how and why single structures can be made to approach triply periodic minimal surfaces very closely, and give improved nodal approximations for G, D, I-WP and P surfaces. We demonstrate that the relative stability of the single structures can be calculated from the geometrical properties of their interfaces only. The single gyroid G turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity. The representations are used to calculate distributions of the Gaussian curvature and 2H-NMR bandshapes for C(P), C(D), S, C(Y) and F-RD surfaces.