Energy surface and minimum energy paths for Fr\'{e}edericksz transitions in bistable cholesteric liquid crystals

TL;DR

This paper analyzes the energy landscape of cholesteric liquid crystals to understand the stability, transition paths, and effects of external fields on their director configurations, especially focusing on the Fréedericksz transition.

Contribution

It introduces a method to compute minimum energy paths for Fréedericksz transitions using the geodesic nudged elastic band approach, linking energy barriers to transition dynamics.

Findings

Identifies stable and transition states on the energy surface.

Calculates energy barriers between states.

Provides insights into thermal stability and transition kinetics.

Abstract

The multidimensional energy surface of a cholesteric liquid crystal in a planar cell is investigated as a function of spherical coordinates determining the director orientation. Minima on the energy surface correspond to the stable states with particular director distribution. External electric and magnetic fields deform the energy surface and positions of minima. It can lead to the transitions between states, known as the Fr\'{e}edericksz effect. Transitions can be continuous or discontinuous depending on parameters of the liquid crystal which determine an energy surface. In a case of discontinuous transition when a barrier between stable states is comparable with the thermal energy, the activation transitions may occur and it leads to the modification of characteristics of the Fr\'{e}edericksz effect with temperature without explicit temperature dependencies of liquid crystal parameters. Minimum energy path between stable states on the energy surface for the Fr\'{e}edericksz transition is found using geodesic nudged elastic band method. Knowledge of this path, which has maximal statistical weight among all other paths, gives the information about a barrier between stable states and configuration of director orientation during the transition. It also allows one to estimate the stability of states with respect to the thermal fluctuations and their lifetime when the system is close to the Fr\'{e}edericksz transition.