Order parameter dependence of the nematic liquid crystal anchoring energy: A numerical approach

Abstract

We study the influence of the surface director disorientation and of the sub-surface director distortion on the surface order parameter and on the anchoring torque of a nematic liquid crystal (NLC). The problem is treated in the framework of the Landau-de Gennes theory with an anchoring energy of the form Tr [(Q_ij–Q_{o ij})²], where Q_ij is the NLC quadrupolar order parameter and Q_{o ij} a quadrupolar surface field. In this way both fusion mechanisms are considered: the bulk one consisting of the decrease of the order parameter induced by distortion and the surface one consisting of the decrease of the order induced by the surface disorientation. For a weak anchoring we find, analytically, that the surface mechanism is more important than the bulk mechanism. For a strong anchoring we find, numerically, that the maximum surface order decrease saturates at a value of S_B/2, where S_B is the bulk order parameter. New higher order harmonics in a_2n sin (2nδ) (n > 1) appear in the anchoring torque (δ is the angle between the actual surface director and the easy axis).