Mesophases with chiral structure under constant electric field constrained by parallel plates with soft anchoring boundary conditions

Abstract

In this work, we present a new approach based on Euler-Lagrange equilibrium equations analysed from the phase space (PS) perspective to investigate states of elastic deformation of Cholesteric Liquid Crystals (N*) confined, which present an intrinsic chiral structure; between parallel plates by imposing soft anchoring boundary conditions (SAC) under a constant electric field-induced perpendicular to the plates. By minimizing the Frank-Oseen (FO) energy density, we obtain a set of equilibrium state integral equations and corresponding boundary conditions. We establish planar conditions on the plates that force the optical axis to align with a specific direction at the plates. We verify the convergence between SAC to strong anchoring conditions (SSC) whether the ratio between surface and bulk energy tends to infinity, under this condition we examine the different configurations of N* by variating the parameters of control, including a variation of potential difference. We also give a detailed derivation of the threshold electric field value, we show that above this value, there is a transition from N to N*, and below this value transition, N* to focal conic texture is observed. We discuss our results and address our conclusions.