Moments and Distribution Functions for Polymer Chains of Finite Length. I. Theory.

摘要

The persistence vector representing the configurational average of the end-to-end vector r for a chain molecule, and the configurational average of the vector g extending from the beginning of the chain to its center of mass, and discussed. These and other vectors and related tensors are expressed in a reference frame defined by the first two bonds of the chain. Algebraic relations between the various vectors and tensors characterizing the spatial distribution of the chain are derived, and matrix generators for their evaluation are presented. The spatial distribution of the remote end of chain in the reference frame embedded in its first two bonds is discussed in terms of the vector p = r - a representing the displacement from the mean position of the terminus of r. The density distribution function W (p) is developed in terms of the moments of vector p with the aid of three-dimensional tensor polynomials which are analogs of the Hermite polynomials.