Temperature dependence of the primitive-model double-layer differential capacitance: a hypernetted chain/mean spherical approximation calculation

1988 ◽  
Vol 92 (22) ◽  
pp. 6408-6413 ◽  
Author(s):  
Luis Mier y Teran ◽  
Enrique Diaz-Herrera ◽  
Marcelo Lozada-Cassou ◽  
Douglas Henderson
Keyword(s):  
Temperature Dependence ◽  
Double Layer ◽  
Differential Capacitance ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Primitive Model ◽  
Hypernetted Chain ◽  
Approximation Calculation

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.

scholarly journals Some Analytic Expressions for the Capacitance and Profiles of the Electric Double Layer Formed by Ions Near an Electrode

2015 ◽  
Vol 43 (2) ◽  
pp. 55-66
Author(s):  
Douglas Henderson
Keyword(s):  
Double Layer ◽  
Electric Double Layer ◽  
Practical Importance ◽  
Differential Capacitance ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Low Concentrations ◽  
Analytic Expressions ◽  
Poisson Boltzmann ◽  
High Concentrations

Abstract The electric double layer, which is of practical importance, is described. Two theories that yield analytic results, the venerable Poisson-Boltzmann or Gouy-Chapman-Stern theory and the more recent mean spherical approximation, are discussed. The Gouy-Chapman-Stern theory fails to account for the size of the ions nor for correlations amoung the ions. The mean spherical approximation overcomes, to some extent, these deficiencies but is applicable only for small electrode charge. A hybrid description that overcomes some of these problems is presented. While not perfect, it gives results for the differential capacitance that are typical of those of an ionic liquid. In particular, the differential capacitance can pass from having a double hump at low concentrations to a single hump at high concentrations.

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.

Primitive model for highly asymmetric electrolytes. Associative mean spherical approximation

1997 ◽  
Vol 236 (1-2) ◽  
pp. 85-96 ◽  
Author(s):  
Yu.V. Kalyuzhnyi ◽  
L. Blum ◽  
M.F. Holovko ◽  
I.A. Protsykevytch
Keyword(s):  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Primitive Model

Hypernetted-chain theories of the primitive model double layer

1985 ◽  
Vol 54 (3) ◽  
pp. 509-524 ◽  
Author(s):  
Steven L. Carnie
Keyword(s):  
Double Layer ◽  
Primitive Model ◽  
Hypernetted Chain

An extended mean spherical approximation calculation of the potential of an electrified interface

1980 ◽  
Vol 71 (3) ◽  
pp. 569-571 ◽  
Author(s):  
Douglas Henderson ◽  
Lesser Blum ◽  
Donald A. Mcquarrie ◽  
Wilmer Olivares
Keyword(s):  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Electrified Interface ◽  
Approximation Calculation
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