Ionic excesses and entropies in mean-field screening models

Abstract

We examine how the mean-field ionic screening excess associated with a charged macromolecule depends upon the macromolecule's geometric conformation and net charge. Our approach involves expanding about Debye–Hückel theory, which allows us to derive a series of general results that establish explicit connections between the ionic excess, non-linear screening mechanisms, and the mobile ion entropy. We conclude with an analysis of the ionic screening entropy in familiar models for polyelectrolyte force-extension behavior, and we find the changes in this entropy are often quite substantial relative to the total free energy differences characterizing a polyelectrolyte's extended and compact states.