A simple approach to the dielectric relaxation behaviour of a liquid crystalline polymer and its application to the determination of the director order parameter for partially aligned materials

A theory for the dielectric relaxation behaviour of a partially aligned liquid crystalline (LC) material is described. It is shown, quite generally, that the complex dielectric permittivity may be expressed in terms of the parallel (?_‖) and perpendicular (?_?) components for the permittivity of the mesophase and S_d, the director order parameter, where ?_‖ and ?_? may themselves be expressed in terms of molecular quantities, including S the mesophase order parameter. The theory is applied to experimental data for a nematic siloxane LC side-chain polymer. The consistency of the derived values of S_d provides experimental confirmation of our approach. In addition, dielectric isosbestic points are observed in both loss factor and capacitance data as the sample alignment is varied, providing further confirmation of our approach. The variation of S_d with time for a sample being realigned from planar to homeotropic in an electric field is determined from dielectric measurements and the form of S_d(t) is briefly discussed.