Dynamics of a Liquid Crystal close to the Fr\'eedericksz transition

TL;DR

This study combines experimental and numerical methods to show that the director dynamics of a liquid crystal near the Fréedericksz transition cannot be accurately described by the traditional Landau-Ginzburg equation due to boundary and approximation issues.

Contribution

It demonstrates the limitations of the Landau-Ginzburg model for liquid crystal dynamics near the transition and highlights the importance of boundary conditions and finite anchoring energy.

Findings

Landau-Ginzburg equation fails to describe director dynamics near FT

Finite anchoring energy affects transition behavior

Boundary asymmetries influence liquid crystal dynamics

Abstract

We report experimental and numerical evidences that the dynamics of the director of a liquid crystal driven by an electric field close to the critical point of the Fr\'eedericksz Transition(FT) is not described by a Landau-Ginzburg (LG) equation as it is usually done in literature. The reasons are related to the very crude approximations done to obtain this equation, to the finite value of the anchoring energy and to small asymmetries on boundary conditions. We also discuss the difference between the use of LG equation for the statics and the dynamics. These results are useful in all cases where FT is used as an example for other orientational transitions.