Configurational Averages for Chain Molecules: Higher Moments and Related Quantitites

Abstract

The higher even moments 〈r2p〉0 of the end-to-end vector r of a chain molecule are formulated according to a straightforward procedure which is free of complications for large values of p. It is generally applicable also to averages of other configuration-dependent quantities, and simplifies their treatment. The condensation of self-direct matrix products derived by Nagai for reducing the complexity of computation of higher moments is achieved directly through an appropriate transformation, which is defined for such a product of any degree. Major reductions of the orders of the statistical weight matrix and associated expressions permissible for symmetric chains are achieved succinctly by similar matrix transformations. It is pointed out that further condensations can be realized through deletion of superfluous rows and columns from the generator matrices (G, G⊗G, etc.) for the moments.