Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals

Abstract

We apply the minimum energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures; and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle point structures. When the applied voltage exceeds its critical value below the threshold of the Fréedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths. * tenischev.

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

“…As opposed to the case of unwinding transition with negligibly small free twisting number previously studied in Ref. [41], it turned out that the half-turn numbers of metastable helix state branches and the elastic anisotropy are the governing factors for q 0 -dependence of the critical field of the Fréedericksz transition. As a consequence the Fréedericksz thresholds for the helical structures involved in the transitions are generally different and we shall study how the free energy barriers of such transitions depend on the electric field and the anchoring conditions.…”

“…In this section, dependence of the energy barriers on the applied voltage will be the subject of our primary concern. For this purpose, we, following our previous work [41], shall use the minimum-energy path (MEP) approach. Leaving aside technical details about the numerical procedure described in Refs.…”

“…Leaving aside technical details about the numerical procedure described in Refs. [40,41], we just briefly comment on the geodesic nudged elastic band (GNEB) method to find MEPs between local minima on the curved manifolds [34]. This approach involves taking an initial guess of a path between the two minima of the free energy surface and systematically bringing that to the nearest MEP.…”

“…As in Ref. [41], the anchoring energy W ν (n) that enters the surface contribution to the CLC free energy functional:…”

“…In Ref. [40,41] the approach based on MEPs was applied to explore field-induced distortions of the free energy landscape in CLC cells subjected to external (magnetic or electric) fields. These distortions are known to lead to a variety of field-induced orientational effects such as the Fréedericksz and unwinding transitions.…”