Stable configurations in hybrid nematic cells in relation to thickness and surface order

Abstract

Abstract The phase diagram of equilibrium configurations in thin hybrid nematic cells has been investigated in the framework of Landau-de Gennes theory extended to include weak surface anchoring. Surface interactions linear in the tensor order parameter were assumed and biaxiality was induced by the surfaces. It was found that in addition to the usual configuration where the director bends continuously from one plate to the other, there is also a possible configuration where bend does not occur, but where there is an eigenvalue exchange; i.e. the eigenvector of the tensor order parameter associated with the eigenvalue of the largest magnitude is different in different regions of the cell. Furthermore, for very small cell thickness a third possibility occurs: the eigenvector corresponding to the eigenvalue with the largest magnitude is uniform throughout the cell; it is either parallel or perpendicular to both plates depending upon the dominant surface interaction. Continuous transitions occur between the different configurations.