A calculation of orientational relaxation in nematic liquid crystals

This paper discusses the transition in a nematic liquid crystal from a strongly distorted orientation of the anisotropic axis to uniform alignment in a situation of some practical interest. If a nematic with positive dielectric or diamagnetic anisotropy is initially at rest between parallel plates with the anisotropic axis uniformly aligned parallel to the solid surfaces, application of a sufficiently strong electric or magnetic field perpendicular to the plates rotates this axis through almost a right angle, except in the immediate vicinity of the solid boundaries. Relaxation following the removal of the field is not straightforward, since the changing orientation induces fluid motion which in turn influences the orientation. Existing theoretical investigations of this phenomenon either restrict attention to small distortions, or employ rather complex numerical methods to obtain predictions from continuum theory. This paper, however, describes an approximate analysis of the relevant continuum equations leading to a solution in the form of infinite series, which considerably reduces the computational effort required to obtain detailed predictions. The series can either be used directly to describe the initial transient motion, or by a simple inverse interpolation technique they can be used to calculate a self-consistently linearized solution valid throughout the motion. Besides confirming the important rôle of the induced fluid motion, these solutions are also used to examine the extent to which the motion varies with the physical properties of the nematic and with the initial distortion.