An analysis of the fluctuation potential in the modified Poisson-Boltzmann theory for restricted primitive model electrolytes

Abstract

An approximate analytical solution to the fluctuation potential problem in the modified Poisson-Boltzmann theory of electrolyte solutions in the restricted primitive model is presented. The solution is valid for all inter-ionic distances, including contact values. The fluctuation potential solution is implemented in the theory to describe the structure of the electrolyte in terms of the radial distribution functions, and to calculate some aspects of thermodynamics, viz., configurational reduced energies, and osmotic coefficients. The calculations have been made for symmetric valence 1:1 systems at the physical parameters of ionic diameter 4.25 × 10 −10 m, relative permittivity 78.5, absolute temperature 298 K, and molar concentrations 0.1038, 0.425, 1.00, and 1.968. Radial distribution functions are compared with the corresponding results from the symmetric Poisson-Boltzmann, and the conventional and modified Poisson-Boltzmann theories. Comparisons have also been done for the contact values of the radial distributions, reduced configurational energies, and osmotic coefficients as functions of electrolyte concentration. Some Monte Carlo simulation data from the literature are also included in the assessment of the thermodynamic predictions. Results show a very good agreement with the Monte Carlo results and some improvement for osmotic coefficients and radial distribution functions contact values relative to these theories. The reduced energy curve shows excellent agreement with Monte Carlo data for molarities up to 1 mol/dm 3 .

Thermodynamics of primitive model electrolytes in the symmetric and modified Poisson-Boltzmann theories. A comparative study with Monte Carlo simulations

“…The RPM and the PM have been extensively used over the years in formal statistical mechanical theories to describe the structure and thermodynamics of charged fluids in the bulk and near charged interfaces. Mention can be made of liquid structure integral equations such as the hypernetted chain [13] and the mean spherical approximation [13][14][15], and potential based approaches, viz., the symmetric Poisson-Boltzmann (SPB) [16][17][18][19] and modified Poisson-Boltzmann (MPB) [19][20][21][22] theories. Parallel numerical simulations, for example, using Monte Carlo (MC) and Molecular Dynamics simulations [23] have been valuable in theoretical developments.…”

Structure and thermodynamics in the linear modified Poisson-Boltzmann theories in restricted primitive model electrolytes

“…These features of the LMPB theories can be useful in the routine, everyday analysis of experimental data. Similarly, in the analysis of numerically intensive theoretical problems (see for example, reference [52]) the use of LMPB analytical expressions as initial input in iterative processes can prove to be useful. Furthermore, the success of the LMPB approach in analyzing the thermodynamics of 1:1 valency systems makes this a potentially attractive method that can be used to explore more complex situations such as higher valency systems [44] and/or systems with a variable dielectric constant [53].…”