Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
1999-03-27
Phys. Rev. E 59: 5528 - 5541 (1999)
Physics
Condensed Matter
Soft Condensed Matter
Revtex, 24 pages with 13 EPS-figures included, to appear in Phys. Rev. E 59(5) (May 1999)
Scientific paper
10.1103/PhysRevE.59.5528
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.
Gompper Gerhard
Schwarz Ulrich S.
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