Relaxation of the Alignment Tensor in the Isotropic and Nematic Phases of Liquid Crystals in the Presence of an External Field

Abstract

The relaxation of the alignment tensor specifying the molecular orientation both in the isotropic and in the nematic phases of liquid crystals is analyzed starting from a nonlinear relaxation equation. The presence of an orientating external (electric or magnetic) field is taken into account. The general solution of the equation is presented for the case of an uniaxial alignment. The dynamics of the alignment after an instantaneous switching on or off of a field is treated in some detail. Depending on the values of the temperature and the strength of the applied field, exponential or nonexponential decay processes are found. In the latter case the speed of relaxation shows an alternation fast-slow-fast.