Thermodynamics of deformation of an isolated polymer chain

Summary

Deformation-dependent change in internal energy of a polymer chain affects also conformational entropy as a result of dependence of statistical characteristics upon the distribution of rotational isomers in the chain. Formulas describing deformation-dependent internal energy (distribution of rotational isomers), free energy and length of statistical segment have been derived using a model of rotational isomers, and assuming non-Gaussian conformational statistics. Example computations have been performed for polyethylene. The computations show decrease in the fraction of gauche isomers with increasing deformation, and the decrease is stronger for shorter chains, especially for the chains composed of less than 10³ C-C bonds. Corrections related to the non-Gaussian statistics and finite molecular weight lead to lower fraction of the gauche component in the chain. Fraction of gauche isomers in a deformed polyethylene chain has been calculated numerically byAllegra andAvitabile (10) using a method of matrices proposed byFlory (11). Although the authors (10) received qualitatively comparable results with our results, they discussed the subject for Gaussian chains in terms of different measure of chain deformation, 1, which does not show clearly the effect of the chain length. Calculations presented in this paper provide analytical formulas for the deformation-dependent thermodynamic and statistical characteristics of a deformed chain macromolecule with non-Gaussian statistics and finite molecular weight. As a result of the decrease of gauche isomers the length of statistical segment increases with increasing chain deformation, and it increases stronger for shorter chains. Temperature effect on the behaviour of a deformed chain macromolecule is also discussed. General formula for the elastic force and “local” stress tensor have been derived.