# Competition brings out the best: Modeling the frustration between curvature energy and chain stretching energy of lyotropic liquid crystals in bicontinuous cubic phases

## TL;DR

This paper models the competition between curvature and chain stretching energies in lyotropic liquid crystals within bicontinuous cubic phases, revealing a compromise geometry that explains observed phase sequences.

## Contribution

It introduces a model that balances curvature and chain stretching energies, providing insights into the formation of bicontinuous cubic phases in lyotropic liquid crystals.

## Key findings

- The model reproduces the G--D--P phase sequence observed experimentally.
- A compromise geometry between two extreme surface types is identified.
- The approach combines theoretical calculations with real system data.

## Abstract

It is commonly considered that the frustration between the curvature energy and the chain stretching energy plays an important role in the formation of lyotropic liquid crystals in bicontinuous cubic phases. Theoretic and numeric calculations were performed for two extreme cases: Parallel surfaces eliminate the variance of the chain length; constant mean curvature surfaces eliminate the variance of the mean curvature. We have implemented a model with Brakke's Surface Evolver which allows a competition between the two variances. The result shows a compromise of the two limiting geometries. With data from real systems, we are able to recover the G--D--P phase sequence which was observed in experiments.