Hypernetted‐chain closure with bridge diagrams. Asymmetric hard sphere mixtures

1990 ◽  
Vol 92 (8) ◽  
pp. 4970-4982 ◽  
Author(s):  
Phil Attard ◽  
G. N. Patey
Keyword(s):  
Hard Sphere ◽  
Hypernetted Chain

scholarly journals Radial Distribution Function for a Hard Sphere Liquid: A Modified Percus-Yevick and Hypernetted-Chain Closure Relations

2021 ◽  
Author(s):  
Felipe Carvalho ◽  
João Pedro Braga
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Hard Sphere ◽  
Closure Relation ◽  
Hard Sphere Liquid ◽  
Hypernetted Chain ◽  
Closure Relations ◽  
Chain Approximation ◽  
New Strategies

Establishment of the radial distribution function by solving the Ornstein-Zernike equation is still an important problem, even more than a hundred years after the original paper publication. New strategies and approximations are common in the literature. A crucial step in this process consists in defining a closure relation which retrieves correlation functions in agreement with experiments or molecular simulations. In this paper, the functional Taylor expansion, as proposed by J. K. Percus, is applied to introduce two new closure relations: one that modifies the Percus‑Yevick closure relation and another one modifying the Hypernetted-Chain approximation. These new approximations will be applied to a hard sphere system. An improvement for the radial distribution function is observed in both cases. For some densities a greater accuracy, by a factor of five times compared to the original approximations, was obtained.

Molecular dynamics of a hard-sphere fluid between two walls: a comparison with the three-point extension hypernetted chain approximation

1990 ◽  
Vol 175 (1-2) ◽  
pp. 111-116 ◽  
Author(s):  
José Alejandre ◽  
Marcelo Lozada-Cassou ◽  
Enrique González-Tovar ◽  
Gustavo A. Chapela
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Hard Sphere Fluid ◽  
Point Extension ◽  
Hypernetted Chain ◽  
Chain Approximation

scholarly journals Structure and thermodynamics of the dipolar hard sphere fluid from the reference‐hypernetted chain equation with minimized free energy

1986 ◽  
Vol 85 (5) ◽  
pp. 2916-2921 ◽  
Author(s):  
F. Lado ◽  
M. Lombardero ◽  
E. Enciso ◽  
S. Lago ◽  
J. L. F. Abascal
Keyword(s):  
Free Energy ◽  
Hard Sphere ◽  
Hard Sphere Fluid ◽  
Chain Equation ◽  
Hypernetted Chain

ADSORPTION OF A SIMPLE FLUID IN A QUENCHED TWO-COMPONENT HARD SPHERE MATRIX REPLICA ORNSTEIN–ZERNIKE EQUATIONS

1999 ◽  
Vol 10 (07) ◽  
pp. 1271-1279
Author(s):  
MIGUEL MAYORGA ◽  
OREST PIZIO ◽  
STEFAN SOKOLOWSKI
Keyword(s):  
Hard Sphere ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Hard Sphere Model ◽  
Simple Fluid ◽  
Matrix Interactions ◽  
Hypernetted Chain ◽  
Repulsive Forces

Using the replica Ornstein–Zernike (ROZ) integral equations, we investigate the adsorption of a simple fluid in a hard sphere quenched matrix made of two species. Our main focus is in the dependencies of the density of fluid species on the chemical potential in matrices with different microporosity and for several compositions. The simple fluid is considered by using a hard sphere model. The fluid-matrix interactions are assumed either solely repulsive or attractive of the Yukawa type. The ROZ equations are supplemented by both the Percus–Yevick (PY) and the hypernetted chain (HNC) closures. The PY closure is used to study the model with solely repulsive forces (reference system) and then the contribution of attractive forces into adsorption is included in the mean field approximation. On the other hand, the HNC approximation is used to get insight into the structure of adsorbed fluid and the fluid-matrix correlations in the presence of attractive forces.

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