Two comments on the mean spherical approximation solution for the restricted primitive model of an electrolyte solution

1976 ◽  
Vol 37 (2) ◽  
pp. 383-385 ◽  
Author(s):  
C.W. Outhwaite
Keyword(s):  
Electrolyte Solution ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Approximation Solution ◽  
Primitive Model ◽  
Restricted Primitive Model ◽  
The Mean

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.

scholarly journals A modified Poisson–Boltzmann study of the singlet ion distribution at contact with the electrode for a planar electric double layer

2010 ◽  
Vol 75 (4) ◽  
pp. 425-446 ◽  
Author(s):  
Whasington Silvestre-Alcantara ◽  
Lutful B. Bhuiyan ◽  
Christopher W. Outhwaite ◽  
Douglas Henderson
Keyword(s):  
Double Layer ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Ion Distribution ◽  
Simulation Data ◽  
Ion Distributions ◽  
Restricted Primitive Model ◽  
Theoretical Predictions ◽  
Poisson Boltzmann ◽  
The Mean

The properties of the singlet ion distributions at and around contact in a restricted primitive model double layer are characterized in the modified Poisson–Boltzmann theory. Comparisons are made with the corresponding exact Monte Carlo simulation data, the results from the Gouy–Chapman–Stern theory coupled to an exclusion volume term, and the mean spherical approximation. Particular emphasis is given to the behaviour of the theoretical predictions in relation to the contact value theorem involving the charge profile. The simultaneous behaviour of the coion and counterion contact values is also examined. The performance of the modified Poisson–Boltzmann theory in regard to the contact value theorems is very reasonable with the contact characteristics showing semi-quantitative or better agreement overall with the simulation results. The exclusion-volume-treated Gouy–Chapman– Stern theory reveals a fortuitous cancellation of errors, while the mean spherical approximation is poor.

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