Replacement Factor in a Linear Chain

Abstract

A harmonic analysis of linear chains in terms of the classical phase integral was conducted in order to calculate the replacement factor, i.e., the partition function for the internal degrees of freedom that an isolated segment does not have because it is not part of an infinite chain. The replacement free energy is given by $F_n\left(\mathrm{rep}\right)=-kT\ln \left(\frac{\mathrm{kT}\sqrt{n}}{\hslash {\omega }_D}\right),$ where $n$ is the number of atoms in the segment and ${\omega }_D$ is the Debye frequency. It is concluded that the replacement factor is correctly calculated in terms of center-of-mass motions of segments only by considering just those contributions for which the internal cluster co-ordinates remain fixed.