Exact analytical formulas for the distribution functions of charged hard spheres in the mean spherical approximation

1978 ◽  
Vol 19 (2) ◽  
pp. 191-200 ◽  
Author(s):  
Douglas Henderson ◽  
William R. Smith
Keyword(s):  
Hard Spheres ◽  
Distribution Functions ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Analytical Formulas ◽  
The Mean ◽  
Charged Hard Spheres

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

2021 ◽  
Vol 24 (2) ◽  
pp. 23801
Author(s):  
L. B. Bhuiyan
Keyword(s):  
Activity Coefficient ◽  
Distribution Functions ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Primitive Model ◽  
Restricted Primitive Model ◽  
Mean Activity Coefficient ◽  
Poisson Boltzmann ◽  
Electrical Part ◽  
The Mean

Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form of the modified Poisson-Boltzmann equation. Analytical expressions for the osmotic coefficient and the electrical part of the mean activity coefficient are obtained and the results for the osmotic and the mean activity coefficients are compared with that from the more established mean spherical approximation, symmetric Poisson-Boltzmann, modified Poisson-Boltzmann theories, and available Monte Carlo simulation results. The linear theories predict the thermodynamics to a remarkable degree of accuracy relative to the simulations and are consistent with the mean spherical approximation and modified Poisson-Boltzmann results. The predicted structure in the form of the radial distribution functions and the mean electrostatic potential also compare well with the corresponding results from the formal theories. The excess internal energy and the electrical part of the mean activity coefficient are shown to be identical analytically for the mean spherical approximation and the linear modified Poisson-Boltzmann theories.

Structural Properties of the Ion-Dipole Model of Electrolyte Solutions in the Bulk and Near a Charged Hard Wall.Application of the Truncated Optimized Cluster Series

1991 ◽  
Vol 46 (1-2) ◽  
pp. 8-18
Author(s):  
O. A. Pizio ◽  
Z. B. Halytch
Keyword(s):  
Electrolyte Solutions ◽  
Distribution Functions ◽  
Dipole Model ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Cluster Expansions ◽  
The Third ◽  
The Mean ◽  
Cluster Series ◽  
Bulk Case

AbstractAn ion-dipole model of electrolyte solutions in the bulk case and near a charged or uncharged hard wall is considered. A method to derive the terms of optimized cluster expansions for the distribution functions of ions and dipoles which provides a set of approximations beyond the mean spherical approximation is given. The third cluster coefficient approximation is investigated

Mean spherical approximation for charged hard spheres near a charged hard wall in a neutralizing background

1982 ◽  
Vol 76 (6) ◽  
pp. 3264-3270 ◽  
Author(s):  
J. ‐P. Badiali ◽  
M. ‐L. Rosinberg
Keyword(s):  
Hard Spheres ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Hard Wall ◽  
Charged Hard Spheres
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