Relation between the initial slope of some electro-optic decays and the moments of the distribution of size

Abstract

Several well defined average values of the rotatory diffusion constant D of a polydisperse system can be obtained using the initial slope of the free decay of different electro-optical phenomena and different degrees of orientation. The type of average depends also on the orientation mechanism. The type of average and its relation to the corresponding moments of the size distribution, which have been previously misused, are derived for rod-like and disc-like particles, different mechanisms of orientation, and two types of electro-optical effect: birefringence (or dichroism) and light scattering in an electric field. Re-examination of the agreement claimed by previous authors between averages of D measured by this technique and calculated from a distribution of size derived from electron micrographs illustrate the difficulties of the measurements at saturation of orientation, and the role of an exact knowledge of the orientation mechanism. Possible experiments are discussed. Two parameters analytical distribution functions, well suited for the expression of the differen moments appearing in the theory, are indicated.