Free energy pathways of a Multistable Liquid Crystal Device

TL;DR

This paper models a bistable liquid crystal device using Landau-de Gennes theory, computing minimum energy pathways and transition states to understand how the system transitions between stable equilibria under different surface anchoring conditions.

Contribution

It introduces a systematic computation of transition pathways and free energy barriers in a Landau-de Gennes model of a bistable liquid crystal device, revealing defect-mediated and defect-free pathways.

Findings

Transition pathways depend on surface anchoring strength.

Defect-mediated pathways occur at strong anchoring.

Weak anchoring leads to a cusp catastrophe with a transition state.

Abstract

The planar bistable device [Tsakonas \textit{et al., Appl. Phys. Lett.}, 2007, {\textbf{90}}, 111913] is known to have two distinct classes of stable equilibria: the diagonal and rotated solutions. We model this device within the two-dimensional Landau-de Gennes theory, with a surface potential and without any external fields. We systematically compute a special class of transition pathways, referred to as minimum energy pathways, between the stable equilibria that provide new information about how the equilibria are connected in the Landau-de Gennes free energy landscape. These transition pathways exhibit an intermediate transition state, which is a saddle point of the Landau-de Gennes free energy. We numerically compute the structural details of the transition states, the optimal transition pathways and the free energy barriers between the equilibria, as a function of the surface anchoring strength. For strong anchoring, the transition pathways are mediated by defects whereas we get defect-free transition pathways for moderate and weak anchoring. In the weak anchoring limit, we recover a cusp catastrophe situation for which the rotated state acts as a transition state connecting two different diagonal states.