From the Plateau problem to periodic minimal surfaces in lipids, surfactants and diblock copolymers

TL;DR

This paper introduces a new method for generating periodic minimal surfaces using a Landau-Ginzburg model, demonstrating its effectiveness on known surfaces and discovering new complex structures relevant to lipid, surfactant, and copolymer systems.

Contribution

A novel approach based on the Landau-Ginzburg model for creating and analyzing complex periodic minimal surfaces, including new structures and high-genus phases.

Findings

Successfully generated four known minimal surfaces

Discovered two new cubic symmetry surfaces

Showed how to obtain high-genus and n-tuply-continuous phases

Abstract

We present the novel method for generation of periodic surfaces based on the simple Landau-Ginzburg model of microemulsion. We test the method on four minimal surfaces (P,D,G, and I-WP), find two new surfaces of cubic symmetry, show how to obtain periodic surfaces of high genus and n-tuply-continuous phases. We point that the Landau model used here should be generic for all systems characterized by internal interfaces, including the diblock copolymer systems.