Hexagonally perforated lamellae with uniform mean curvature

Abstract

An increasing variety of self-assembling amphiphilic systems are found to exhibit a striking type of intermediate phase which comprises a one-dimensional stacking of two-dimensional networks, or perforated lamellae, often termed a mesh phase. This study focuses on idealized mesh models with the highest attainable symmetry and interfacial smoothness, namely hexagonal arrays of perforations with uniform mean-curvature throughout. The exact surfaces are constructed numerically and their geometries are analyzed in detail as a basis for assessing the deviations of observed mesh structures. The simplest network, of connectivity 3, is also compared to its 6-connected dual.