Smectic Pores and Defect Cores

TL;DR

This paper analyzes Riemann's minimal surfaces, showing they are composed of two oppositely-handed helicoids, and discusses their relevance to smectic liquid crystals with screw dislocations.

Contribution

It provides an explicit description of Riemann's minimal surfaces as a sum of helicoids, linking geometric structures to smectic liquid crystal defects.

Findings

Riemann's minimal surfaces are composed of two oppositely-handed helicoids.

These surfaces model the morphology of bicontinuous lamellar systems.

The description aids in understanding smectic liquid crystals with screw dislocations.

Abstract

Riemann's minimal surfaces are a complete, embeddable, one-parameter family of minimal surfaces with translational symmetry along one direction. It's infinite number of planar ends are joined together by an array of necks, closely matching the morphology of a bicontinuous, lamellar system with pores connecting alternating layers. We demonstrate explicitly that Riemann's minimal surfaces are composed of a nonlinear sum of two oppositely-handed helicoids. This description is particularly appropriate for describing smectic liquid crystals containing two screw dislocations.