Chapter 12 - Applications of the Corrected Debye–Hückel Theory

Abstract

The Corrected Debye–Hückel (CDH) theory plays a special role in that it is in many ways the logical generalization of the van der Waals theory to electrolyte solutions. It accounts for ion size by the same excluded volume mechanism as vdW theory but it extends the mean field treatment of electrostatic interactions to account for correlations in the linear response approximation as in the Debye–Hückel theory. The CDH theory is here applied first to restricted primitive model (RPM) electrolytes where MC simulations and HNC integral equation theory have provided accurate properties for comparison. It is found that CDH theory remains accurate up to over 1 M concentrations for monovalent ions, an order of magnitude larger than can be reliably handled by DH theory. The second step is to extend the theory to unrestricted primitive models (UPM) where the cations and anions are of different diameters. It is shown in comparison with MC and HNC results that a common diameter can be found by fitting such that the corresponding RPM electrolyte has properties in good agreement with the original UPM electrolyte again up to about 1 M for monovalent ions. If a linear average diameter or between species diameter is used as common ion diameter the concentration of good accuracy is roughly halved but still much better than DH theory. Finally, the CDH theory is applied to experimental salt solutions where hydration effects are expected to increase ion sizes. It is shown that fitting of a common ion diameter d allows both mean activity and osmotic coefficients to be reproduced up to about 1 M for monovalent salts. Higher valency decreases the range of concentrations where the theory is of useful accuracy. It is shown that the dependence of the relative dielectric constant εr on the salt concentration can be accounted for in the CDH theory to increase its range of validity to well over molar concentrations in many cases. The phenomenon of surface complexation, i.e., surface charging by association or dissociation of ions, typically protons, from surface sites in the presence of an electrolyte solution, is described, and the CDH theory extended to resolve the pH-dependence of the surface charge density. For low pH and salt concentration in the solution the screening of the surface is partially by a nonlinear ion association mechanism which is possible to addend to create the CDH-SC theory of surface complexation. This theory is in good agreement with both experiment and simulation. It is able to resolve the observed curvature dependence of the stabilization of charged nanoparticles by the screening of a surrounding salt solution.