Hysteresis and Freedericksz thresholds for twisted states in chiral nematic liquid crystals: Minimum-energy path approach

TL;DR

This paper investigates the energy pathways and hysteresis phenomena in twisted states of chiral nematic liquid crystals under electric fields, revealing how thresholds and energy barriers depend on material parameters and transition order.

Contribution

It introduces a minimum-energy path approach to analyze hysteresis and thresholds in chiral nematic liquid crystals, highlighting the first-order nature of certain transitions.

Findings

Threshold voltage increases with free twisting wave number.

Energy barriers exhibit hysteresis with electric field variation.

Transition from planar to tilted states is first order, unlike the second-order Freedericksz transition.

Abstract

We study minimum-energy pathways (MEPs) between the branches of metastable helical structures in chiral nematic liquid crystals (CNLCs)subjected to the electric field applied across the cell. By performing stability analysis we have found that, for the branches with non-vanishing half-turn number, the threshold (critical) voltage of the Freedericksz transition is an increasing function of the free twisting wave number. The curves for the threshold voltage depend on the elastic anisotropy and determine the zero-field critical free twisting number where the director out-of-plane fluctuations destabilize the CNLC helix. For each MEP passing through a first order saddle point we have computed the energy barrier as the energy difference between the saddle-point and the initial structures at different values of the applied field. In our calculations, where the initial approximation for a MEP at the next step was determined by the MEP obtained at the previous step, the electric field dependence of the energy barrier is found to exhibit the hysteresis. This is the hysteresis of electrically driven transition of the saddle-point configuration between the planar and the tilted structures involving out-of-plane director deformations. It turned out that, by contrast to the second-order Freedericksz transition, this transition is first order and we have studied how it depends on the zenithal anchoring energy strength.