Stress tensor of inhomogeneous flexible polymer chain solutions beyond the ground-state dominance approximation.

Abstract

We derive the stress tensor of a flexible polymer solution within the Gaussian-chain self-consistent field theory (SCFT) without invoking the ground-state dominance (GSD) approximation. Starting from a covariant formulation of the single-chain partition function in a background metric, we obtain the symmetric stress tensor expressed through the full Edwards propagators. The result contains the local interaction pressure, the ideal translational pressure of chains, and a conformational contribution originating from the metric dependence of the Edwards operator. It provides the local counterpart of earlier global stress formulas in polymer SCFT and gives a thermomechanical generalization of the GSD conformational stress. We demonstrate that the GSD conformational stress tensor-previously used in studies of capillary-induced self-coacervation and confined polyelectrolytes-is recovered exactly as the lowest-mode limit. The derived stress tensor is applied to a slit geometry to obtain the disjoining pressure, providing a framework for mechanical calculations in confined polymer systems beyond the GSD regime. For ideal chains between hard repulsive walls, we show that the local stress reproduces the exact depletion pressure and that higher Edwards modes become essential in wide pores, where the GSD approximation fails to recover the correct bulk limit.