The S'S^{' '} and H'T Minimal Surfaces and their Application to Structural Modelling of Intermediate Phases
Abstract
A geometric basis is presented for the analysis of possible structures of anisotropic liquidcrystalline phases of surfactantwater mixtures between the hexagonal and lamellar phase regions. As a starting point the candidates among the triply periodic minimal surfaces partitioning symmetrically distinct labyrinths are considered. The two simplest examples of this type of bicontinuous geometry are the tetragonal S'S^{' '} and hexagonal H'T surfaces of genus 4. Using the exact parametrizations, their cell dimensions, vertex positions, areas and volumes are calculated. These details of the minimal surfaces are useful both in assessing the possibility of such bicontinuous intermediate phases and for generating the corresponding constant meancurvature families which embrace other topologies, including the interesting mesh structures.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 September 1996
 Bibcode:
 1996RSPSA.354.2159F