Partitioning of a polymer chain between two confining cavities: the role of electrostatic interactions

TL;DR

This paper extends a lattice field theory approach to analyze how electrostatic interactions influence the partitioning of a charged polymer chain between two confining cavities, revealing limitations of ground-state dominance assumptions.

Contribution

It generalizes a previous theory to cases without ground-state dominance, deriving full mean-field equations and applying them to a confined charged polymer system.

Findings

The mean-field equations have a unique solution.

Ground-state dominance fails under certain conditions.

Electrostatic interactions significantly affect polymer confinement.

Abstract

A recently developed lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E {\bf{60}}, 4257, (1999)] is generalized to the case where ground-state dominance in the polymer's Green's function does not apply. The full mean-field equations for the system are derived and are shown to possess a unique solution. The approach is applied to the problem of a charged Gaussian polymer chain confined to move within the region defined by two fused spheres. The failure of the notion of ground-state dominance under certain conditions even in the limit of large number of monomers is demonstrated.