Equilibrium configurations in a nematic pi-cell under an electric field

Abstract

In this work, we study the equilibrium configurations in a nematic pi-cell under an electric field using the one-dimensional Oseen-Frank director model. The equilibrium orientational configurations that can be attained in a pi-cell are known as splay, bend, and twist. Among those, bend and twist are topologically equivalent and can be transitioned into one another as voltage varies. The transition can be continuous or abrupt depending on the material parameters. On the other hand, the splay configuration becomes asymmetric for sufficiently high voltages if the liquid crystal has a positive dielectric anisotropy. We determine those threshold voltages and characterize the order of transitions in terms of the elastic constants and the pretilt angle at the boundary.