A modified Poisson-Boltzmann approach to homogeneous ionic solutions

Abstract

The mean electrostatic potential approach to ionic solutions was initiated by the mean field work of Gouy and Chapman for inhomogeneous systems, and Debye and Hückel for bulk solutions. Any successful extension of the mean field theories requires an adequate treatment of both the exclusion volume and fluctuation terms. One such development has been the modified Poisson-Boltzmann approach. Although the bulk modified PoissonBoltzmann theory was introduced 35 years ago, only a limited amount of work has been put into its development due to the successful application of liquid state theories to ionic systems. We outline here the bulk modified Poisson-Boltzmann equation, comment on some of its successes, and mention some outstanding problems.

A modified Poisson–Boltzmann analysis of the capacitance behavior of the electric double layer at low temperatures

“…12 and 17͒. This numerical technique is very efficient and robust and has been used successfully to solve the bulk MPB system of equations 18 in the critical region. 19,20 The associated boundary conditions for the potential problem are ͑x͒ and d / dx continuous in x Ͼ 0, with ͑x͒ and d / dx → 0 as x → ϱ.…”

Mesoscopic theory for size- and charge-asymmetric ionic systems: I. The case of extreme asymmetry

“…For many years, theoretical studies of phase behavior in ionic solutions have been focused mainly on the special case of the restricted primitive model (RPM), in which half of equalsized charged hard spheres carry positive charge and half carry negative charge of equal magnitude, with the ions assumed to be dissolved in a structureless solvent [1,2,3,4].…”

Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory

“…One technique to express the pair distribution function in terms of mean electrostatic potentials is to use Kirkwood's charging process [14]. Taking the ion j to have a charge λ 2 e j (0 λ 2 1), then the charging process gives [15,16]…”

“…Given an appropriate fluctuation potential, an improved pair distribution function can now be found. Previous analysis [15][16][17] has derived, for a RPM,…”

“…with the first term corresponding to the DH value for small y. Both the MPB and MSA predict, above their respective y c , that the solution is damped oscillatory [15,16]. So, taking the complex conjugate pair z 1 , z 2 to be α ± iβ, equation (16) can then be written as follows:…”