Time-dependent birefringence, linear dichroism, and optical rotation resulting from rigid-body rotational diffusion

Abstract

Expressions are derived for the time-dependent relaxation behavior of a monodisperse suspension of arbitrarily shaped rigid bodies, after initial alignment by an externally applied field. We show that five exponential terms are necessary for a complete description of birefringence, linear dichroism, and optical rotation decay phenomena in a force-free rotational diffusion process. The explicit form for the multiplicative coefficients of the exponential relaxation terms are presented; they are expressed in terms of the optical anisotropy tensor and a tensor characteristic of the initial alignment conditions. Symmetry constraints that involve special relationships between the optical anisotropy tensor, the alignment tensor, and the diffusion tensor or that involve the initial orientational distribution conditions, are shown to lead to a reduction in the number of required exponential relaxation terms. We concern ourselves mainly with alignment by means of an electric field in a Kerr cell, but other alignment techniques are treated in a general formalism with application to hydrodynamic flow fields. We also present an alternate formulation of the birefringence decay which provides physical insight as regards the sign and the monotonic or nonmonotonic behavior of the time-dependent relaxation process.