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.

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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