The spherical double layer: a hypernetted chain mean spherical approximation calculation for a model spherical colloid particle

1989 ◽  
Vol 93 (9) ◽  
pp. 3761-3768 ◽  
Author(s):  
Enrique Gonzalez-Tovar ◽  
Marcelo Lozada-Cassou
Keyword(s):  
Double Layer ◽  
Colloid Particle ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
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.

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

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.

The application of the generalized mean spherical approximation to the theory of the diffuse double layer

1981 ◽  
Vol 59 (13) ◽  
pp. 1906-1917 ◽  
Author(s):  
Douglas Henderson ◽  
Lesser Blum
Keyword(s):  
Hard Spheres ◽  
Diffuse Layer ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Diffuse Double Layer ◽  
Layer Potential ◽  
Poisson Boltzmann ◽  
Hypernetted Chain ◽  
Two Parameters ◽  
Charged Hard Spheres

A system of charged hard spheres near a uniformly charged hard wall is considered. An approximation is established by postulating a closure for the Ornstein–Zernike (OZ) equations for this system. In this paper these OZ equations are solved for a closure in which the direct correlation functions are equal to the wall-ion potentials plus a sum of exponential functions. As a specific application of this solution we use one exponential and adjust two parameters to satisfy an approximate contact value theorem and give the same diffuse layer potential as is obtained using the hypernetted chain (HNC) approximation. Once this fit is made, the density, charge, and potential profiles can be easily calculated. The agreement with the corresponding HNC results is good. Comparison with the simpler Poisson–Boltzmann theory of Gouy and Chapman (GC) shows the GC theory to be better than one would expect. However, appreciable differences between the present results and the GC results for the diffuse layer potential are found.

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