Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5):5528-41. doi: 10.1103/physreve.59.5528.

Systematic approach to bicontinuous cubic phases in ternary amphiphilic systems.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

U S Schwarz, G Gompper

PMID: 11969532 DOI: 10.1103/physreve.59.5528

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-nuclear-magnetic-resonance band shapes for C(P), C(D), S, C(Y), and F-RD surfaces.

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• Journal Article