Mean spherical approximation for charged hard spheres near a charged hard wall in a neutralizing background

1982 ◽  
Vol 76 (6) ◽  
pp. 3264-3270 ◽  
Author(s):  
J. ‐P. Badiali ◽  
M. ‐L. Rosinberg
Keyword(s):  
Hard Spheres ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Hard Wall ◽  
Charged Hard Spheres

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.

Structural relaxations in a Simple Model Molten SaltM

1995 ◽  
Vol 407 ◽  
Author(s):  
Matthias Fuchs
Keyword(s):  
Mode Coupling ◽  
Molten Salts ◽  
Hard Spheres ◽  
Equilibrium Structure ◽  
Charge Ordering ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Coupling Theory ◽  
Ionic Systems ◽  
Charged Hard Spheres

ABSTRACTThe structural relaxations of a dense, binary mixture of charged hard spheres are studied using the Mode Coupling Theory (MCT). Qualitative differences to non-ionic systems are shown to result from the long-range Coulomb interaction and charge ordering in dense molten salts. The presented non-equilibrium results are determined by the equilibrium structure, which is input using the well studied Mean Spherical Approximation.

EQUATION OF STATE AND FREEZING OF GMSA HARD SPHERES

2003 ◽  
Vol 17 (31n32) ◽  
pp. 6057-6065 ◽  
Author(s):  
M. MORADI ◽  
H. SHAHRI
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Direct Correlation Function ◽  
Generalized Mean ◽  
Simulation Results ◽  
Good Agreement

The modified-weighted-density-functional approximation (MWDA) proposed by Denton and Ashcroft, is applied to study the equation of sate and freezing of the hard spheres using the generalized mean spherical approximation (GMSA) direct correlation function (DCF). Because of the attractive tail in the DCF, the perturbation method similar to that introduced by Yoon and Kim is applied. The free energy, freezing parameters and the equation of state of the hard sphere FCC crystal are obtained. The results are compared with some other previous theories and Monte Carlo simulation. Our results are in good agreement with the simulation results.

DENSITY FUNCTIONAL THEORY AND FREEZING OF HARD SPHERES, BEYOND THE PERCUS–YEVICK APPROXIMATION

2007 ◽  
Vol 21 (07) ◽  
pp. 1089-1098 ◽  
Author(s):  
M. MORADI ◽  
A. RAZEGHIZADEH
Keyword(s):  
Density Functional Theory ◽  
Monte Carlo ◽  
Structure Factor ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Functional Theory ◽  
Weighted Density Approximation

The density functional theory for the freezing hard spheres is studied. We use a variety of the hard sphere direct correlation functions (DCFs) such as the one introduced by Roth et al. [J. Phys. Condens. Matter14, 12063 (2002)]; we call it RELK DCF, a new hard sphere DCF developed here by a combination of the RELK and the Percus–Yevick DCFs, and finally the generalized mean spherical approximation (GMSA). The structure factor, the freezing, and order parameters are calculated using these DCFs. The structure factor obtained by the new DCF is in good agreement with the Monte Carlo simulation. The best result for the freezing parameters in comparison with the Monte Carlo simulations is obtained by using our new expression for the DCF. Finally we obtain the Helmholtz free energy of the hard sphere FCC crystals using modified weighted density approximation (MWDA), and again the best results are obtained by using the new expression for the hard sphere DCF.

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