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

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