Bounds on Solutions of the Poisson-Boltzmann Equation near Infinite Dilution-The Moderately Charged Case

Abstract

Upper and lower bounds on solutions of the nonlinear Poisson-Boltzmann equation are obtained for the case where the so-called surface charge parameter is less than unity (the moderately charged case). The relationship of these bounds with Manning's limiting law theory for polyelectrolytes is discussed. In particular, we are able to provide rigorous justification (different from Manning's own justification which is based on cluster theory) for Manning's use of the Debye-Hückel approximation.