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.

A mean spherical approximation study of the capacitance of an electric double layer formed by a high density electrolyte

2010 ◽  
Vol 75 (3) ◽  
pp. 303-312 ◽  
Author(s):  
Douglas Henderson ◽  
Stanisław Lamperski ◽  
Christopher W. Outhwaite ◽  
Lutful Bari Bhuiyan
Keyword(s):  
Double Layer ◽  
Linear Response Theory ◽  
Differential Capacitance ◽  
Double Layers ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Simple Extension ◽  
Restricted Primitive Model ◽  
Poisson Boltzmann ◽  
Small Electrode

In a recent grand canonical Monte Carlo simulation and modified Poisson–Boltzmann (MPB) theoretical study of the differential capacitance of a restricted primitive model double layer at high electrolyte densities, Lamperski, Outhwaite and Bhuiyan (J. Phys. Chem. B 2009, 113, 8925) have reported a maximum in the differential capacitance as a function of electrode charge, in contrast to that seen in double layers at lower ionic densities. The venerable Gouy–Chapman–Stern (GCS) theory always yields a minimum and gives values for the capacitance that tend to be too small at these higher densities. In contrast, the mean spherical approximation (MSA) leads to better agreement with the simulation results than does the GCS approximation at higher densities but the agreement is not quite as good as for the MPB approximation. Since the MSA is a linear response theory, it gives predictions only for small electrode charge. Nonetheless, the MSA is of value since it leads to analytic results. A simple extension of the MSA to higher electrode charges would be valuable.

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

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