Comparison of Hypernetted Chain Equation and Monte Carlo Results for a System of Charged Hard Spheres

1970 ◽  
Vol 52 (2) ◽  
pp. 1013-1014 ◽  
Author(s):  
P. N. Vorontsov‐Veliaminov ◽  
A. M. Eliashevich ◽  
J. C. Rasaiah ◽  
H. L. Friedman
Keyword(s):  
Monte Carlo ◽  
Hard Spheres ◽  
Chain Equation ◽  
Hypernetted Chain ◽  
Charged Hard Spheres

Sum rules for the pair-correlation functions of inhomogeneous fluids: results for the hard-sphere–hard-wall system

1987 ◽  
Vol 410 (1839) ◽  
pp. 409-420 ◽  
Keyword(s):  
Sum Rules ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Distribution Functions ◽  
Hard Wall ◽  
Chain Equation ◽  
Hypernetted Chain ◽  
Chain Approximation ◽  
Derivatives Of

Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett–Mou–Buff–Wertheim and the Born–Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus–Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus–Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.

scholarly journals Ionic solution near an uncharged surface with image forces

1981 ◽  
Vol 59 (13) ◽  
pp. 1998-2003 ◽  
Author(s):  
T. Croxton ◽  
D. A. McQuarrie ◽  
G. N. Patey ◽  
G. M. Torrie ◽  
J. P. Valleau
Keyword(s):  
Dielectric Constant ◽  
Monte Carlo ◽  
Monte Carlo Data ◽  
Ion Density ◽  
Primitive Model ◽  
Monte Carlo Computation ◽  
Restricted Primitive Model ◽  
Integral Equation Approach ◽  
Chain Equation ◽  
Hypernetted Chain

We studied the ion density in a dilute electrolyte solution which is next to an uncharged surface at which there is a discontinuity in the dielectric constant. In particular, we treated the restricted primitive model of a 1–1 aqueous solution next to a pure phase of unit dielectric constant. This served as a primitive model of the interface between an electrolytic solution and the air. Monte Carlo data are presented: the image forces are included and treated exactly. The model was also treated using the Born–Green–Yvon (BGY) integral equation approach; a modification of BGY theory which ensures electroneutrality is in very good agreement with the Monte Carlo data. The use of a "screened self-image" approximation to the potential energy has been tested using Monte Carlo computation and is found to be inadequate for the present model. Hypernetted-chain equation results using this approximation are also reported.

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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