A density functional study of a twisted nematic cell and its relation to the Frank–Oseen theory

Abstract

The numerical results for the twist angle profile xi(z) across a slab-shaped nematic cell obtained from a density functional theory (DFT) are compared to the predictions of the macroscopic Frank-Oseen theory. The latter theory predicts that xi"(z)=0, and this is also seen to be the case for the DFT results. These do, however, verify the Frank-Oseen relation, lambda+/-W+/-=K2, between the de Gennes extrapolation length (lambda+/-), the anchoring energy per unit area of the (+/-) cell wall (W+/-), and the elastic constant of the nematic for twist deformations (K2), only if W+/- is nonlinearly related to the amplitude of the anchoring term of the DFT.