General description of orientation factors in terms of expansion of orientation distribution function in a series of spherical harmonics

Abstract

A mathematical representation of orientation distribution of structural units within the bulk polymer is given in terms of an expansion of the distribution function in a series of spherical harmonics. Each coefficient of the expanded series is discussed in general relation to the orientation factors, average degrees of orientation distribution, defined by several different authors independently. Several optical techniques to evaluate the orientation factors, the second and fourth moments of orientation distribution of crystalline and noncrystalline structural units from optical dichroic quantities, are discussed. Some graphical representations of the state of orientation are proposed, and the estimation of orientation distribution from the orientation factors of different orders is discussed quantitatively.