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.

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We present a formalism to calculate diffusion coefficients for macromolecules with segmental flexibility. Macromolecules composed of several segments of different size and shape can be treated including assemblies with arbitrary types of flexible attachments and multiple branching. The frictional resistance tensor R and the diffusion tensor D are evaluated in generalized coordinates involving all degrees of freedom, and their general properties are established. A simplified approximate expression for R is obtained when hydrodynamic interactions between segments are omitted. We apply this approximate expression to evaluate the rotational behavior of a body composed of two cylindrically symmetric segments flexibly attached at their endpoints by a frictionless universal joint. The effect of size and shape differences of the two segments upon the principal rotational diffusion coefficients of each segment is established. Coefficients governing correlations between rotations of both segments are used to evaluate diffusion coefficients for bending and twisting motions. If the body is completely flexible, the rotational relaxation behavior of each segment reduces to that of some equivalent rigid-body with cylindrical symmetry. Effects of rigid to flexible transitions and enzymatic cleavage of segments are considered. The rotational diffusion coefficient for once-broken rods is up to 2.34 times greater than predicted by Yu and Stockmayer [J. Chem. Phys. 47, 1369 (1967)] and in good agreement with dielectric dispersion measurements by Matsumoto et al. [Macromolecules 7, 824 (1974)].

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