Irreversible Thermodynamics of Nonequilibrium Alignment Phenomena in Molecular Liquids and in Liquid Crystals

Abstract To treat nonequilibrium alignment phenomena in molecular liquids and in liquids crystals two points of the usual irreversible thermodynamics have to be modified. Firstly, in the specific energy a term quadratic in the alignment tensor is included. Secondly, terms up to 4th order in the alignment are taken into account in the entropy for a nonequilibrium situation. Then the entropy production is calculated. Constitutive laws are set up for the friction pressure tensor and for the tensor which characterizes the decay and the production of the alignment in the balance equation for the alignment tensor. As a first application, the nonlinear relaxation equation for the alignment is considered. For a uni-axial alignment zero and nonzero stable stationary values of the order parameter are found for temperatures above and below the temperature T K at which the transition from the isotropic to the nematic phase takes place. Small deviations from the equilibrium alignment decay exponentially. For temperatures below T K the relaxation time turns out to be anisotropic. In the appendix, the entropy associated with the alignment is calculated for a special case.