## An analysis of the fluctuation potential in the modified Poisson-Boltzmann Theory for primitive model electrolytes

##### Resumen

The fluctuation potential problem in the modified Poisson-Boltzmann approach to charged fluids is analyzed to obtain an approximate analytic solution for a symmetric valency restricted primitive model electrolyte. The solution is valid for all ranges of interionic distances, including contact values. The structure of the electrolyte is described using radial distribution functions determined through the implementation of the fluctuation potential solution in the theory. Aspects of thermodynamics of the solution, viz., configurational reduced energies and osmotic coefficients are also calculated. Results have been obtained for symmetric valency 1:1 electrolyte system with the following physical parameters: ionic diameter d = 4.25×10[superscript -10] m, relative permittivity ε[subscript r] =78.5, absolute temperature T = 298 K, and molar concentrations c = 0.1038 M, 0.425 M, 1.00 M, and 1.968 M. The ion-ion radial distribution functions are compared with the corresponding results from the symmetric Poisson-Boltzmann and the conventional modified Poisson- Boltzmann theories. Contact values of the radial distributions, reduced configurational energies, and osmotic coefficients have also been compared, as functions of electrolyte concentration, with these theories, and additionally with the Debye-Hückel theory and Monte Carlo simulation data from the literature. The results show very good agreement with the Monte Carlo data, and some improvement for radial distribution contact values and osmotic coefficients relative to these theories. The reduced energy curve shows excellent agreement with Monte Carlo data for molarities up to 1 mol/dm[superscript 3]. Radial distribution contact values for the charge asymmetric RPM 2:1 valency system at the same physical parameters of the 1:1 ,except for valence, case were also calculated and compared with the corresponding hypernetted chain theory from the literature. Good agreement was found for all concentrations considered. An ion size asymmetric primitive model extension to the theory is also presented. Osmotic coefficients are calculated and compared to simulation data from the literature for a primitive model electrolyte at the physical parameters: diameter of the large negative ion is 4.25×10[superscript -10]m, the temperature T=298 K, the dielectric constant of the electrolyte ε[subscript r] = 78.5, electrolyte concentration 0.425mol/dm[superscript 3], and the size asymmetry parameter α = 0.4, 0.6, and 0.8. Good agreement between the results and the MC simulation was found.