Geometric Thermodynamics of Strain-Induced Crystallization in Polymers

TL;DR

This paper applies Riemannian geometric thermodynamics to analyze strain-induced crystallization in polymers, revealing how curvature relates to non-physical energy components and aiding in accurate stress prediction.

Contribution

It extends geometric thermodynamics to non-equilibrium polymer systems, identifying and correcting spurious energy contributions from Euclidean assumptions.

Findings

Curvature provides insight into conformational stretching energy.

A method to determine and remove spurious energy components.

Improved stress calculations in strain-induced crystallization.

Abstract

Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity - the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases and other open systems. In this article, we examine the implications of this curvature in a non-equilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The non-equilibrium system comprises of a rubbery polymer undergoing strain induced crystallization. The curvature is found to impart information on a spurious isochoric energy arising from the conformational stretching of already crystallized segments. This unphysical component perhaps arises as the crystallized manifold is considered Euclidean with the stretch measures defined via the Euclidean metric. The thermodynamic state associated with curvature is the key to determine the isochoric stretch and hence the spurious energy. We determine this stretch and propose a form for the spurious free energy that must be removed from the total energy in order that the correct stresses are recovered.