A one-dimensional variational problem for cholesteric liquid crystals with disparate elastic constants

We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher energy penalty than other modes of deformation. The appropriate ratio of the elastic constants then gives a small parameter epsilon entering an Allen-Cahn-type energy functional augmented by a twist term. We consider the behavior of the energy as epsilon tends to zero. We demonstrate existence of the local energy minimizers classified by their overall twist, find the Gamma-limit of the relaxed energies and show that it consists of the twist and jump terms. Further, we extend our results to include the situation when the cholesteric pitch vanishes along with epsilon. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

In this study, a one-dimensional variational problem related to a model for cholesteric liquid crystals is considered, with a focus on the higher energy penalty incurred by the twist deformation of the nematic director compared to other modes of deformation. By introducing a small parameter epsilon and an Allen-Cahn-type energy functional augmented by a twist term, the behavior of the energy as epsilon approaches zero is investigated. The existence of local energy minimizers classified by their overall twist, the Gamma-limit of the relaxed energies, and the inclusion of twist and jump terms are demonstrated.