Chapter 11 - Electrolyte Solutions – Basic Theory

Abstract

Electrolyte solutions are mixtures of great practical importance and unique properties related to interactions of great strength and long range which lead to electroneutrality conditions and a local screening mechanism. Here we shall show how traditional Poisson–Boltzmann (PB) and Debye–Hückel (DH) theories can be derived and readily extended within the GvdW density functional theory. The PB and DH theories are obtained by neglecting the short range excluded volume mechanism of GvdW theory and applying the “mean-field approximation” to all ion–ion interactions. The character of correlation effects due to “same charge” Coulomb repulsion is illustrated for the case of the One Component Plasma (OCP) in the strong and weak coupling limits. A realistic combination (Debye–Hückel hole theory) of these two limiting correlation approximations is shown to give good agreement with MC simulation results. Salt solutions are often studied by use of the “restricted primitive model” which takes the ions to be charged hard spheres in a solvent (generally water) represented only by a relative dielectric constant (78.54 for water at 298 K). The properties of monovalent salt solutions at modest concentrations (well below 1 M) can be predicted by application of the Debye–Hückel theory to the screening of a centrally located ion by the electrolyte solution. For higher concentrations the excluded volume mechanism must be included. This leads to the corrected Debye–Hückel (CDH) theory. Interestingly, the direct entropic excluded volume effect vanishes in the CDH theory of RPM salt solutions. This follows since the adsorption of counterions and desorption of coions leaves the total ion density unchanged. Thus the change from DH to CDH theory for RPM salt solutions arises only due to the “hole correction” to the ion–ion interactions in the screening charge density. The effect is to increase the inverse Debye length κ and thereby the screening efficiency.