Multivalent Ions in the Electrical Double Layer: The Extended Mean Spherical Approximation

1984 ◽  
Vol 131 (3) ◽  
pp. 534-539 ◽  
Author(s):  
C. J. McClanahan ◽  
D. A. McQuarrie
Keyword(s):  
Double Layer ◽  
Electrical Double Layer ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Multivalent Ions

Perturbation theory, the mean spherical approximation, and the electrical double layer

1981 ◽  
Vol 59 (13) ◽  
pp. 1903-1905 ◽  
Author(s):  
Douglas Henderson ◽  
Lesser Blum
Keyword(s):  
Perturbation Theory ◽  
Double Layer ◽  
Electrical Double Layer ◽  
Electric Double Layer ◽  
Potential Difference ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
The Mean

Simple arguments, based on perturbation theory, are used to derive expressions for the energy of a bulk ionic fluid and the potential difference in an electric double layer. These expressions are identical to those obtained from the much more elaborate mean spherical approximation.

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 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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