scholarly journals Fourth virial coefficient of additive hard-sphere mixtures in the Percus–Yevick and hypernetted-chain approximations

2014 ◽  
Vol 140 (13) ◽  
pp. 134507 ◽  
Author(s):  
Elena Beltrán-Heredia ◽  
Andrés Santos
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Hypernetted Chain

Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential

2018 ◽  
Vol 149 (16) ◽  
pp. 164907
Author(s):  
César Alejandro Báez ◽  
Alexis Torres-Carbajal ◽  
Ramón Castañeda-Priego ◽  
Alejandro Villada-Balbuena ◽  
José Miguel Méndez-Alcaraz ◽  
...  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Physical Criterion ◽  
Continuous Potential

The analytical evaluation of the first-order density cluster integral in the radial distribution function

1970 ◽  
Vol 320 (1542) ◽  
pp. 323-348 ◽  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Scattering Data ◽  
X Ray ◽  
Lennard Jones ◽  
X Ray Scattering ◽  
Cluster Integrals ◽  
Square Well ◽  
Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

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.

Fifth virial coefficient of hard sphere mixture

1998 ◽  
Vol 94 (5) ◽  
pp. 877-879 ◽  
Author(s):  
R.J. WHEATLEY ◽  
F. SAIJA ◽  
P.V. GIAQUINTA
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient

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
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