The Dipole Moment and End-to-End Length of the Isotactic Vinyl Polymer, III. Convergence of Neumann Series

Abstract

The theory of dipole moment and end-to-end length of isotactic polymer is described. The problem of convergence of the infinite series in the matrix, which expresses a transformation of the bond vector, is studied in detail, a skeletal chain of linear polymer being regarded as a vector sum of many C–C bond vectors. The method of classifying the chain configurations is given on the basis of the convergence property of the series, which is an extension of the Neumann series. The polymer chain must be Gaussian, if the segments of polymer can rotate independently of each other. The hindrance potential for the internal rotation is assumed to be of the square-well type.