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.

Relative density of states and the second virial coefficient of the hard-sphere gas

1977 ◽  
Vol 33 (1) ◽  
pp. 287-291 ◽  
Author(s):  
Richard Kayser ◽  
John E. Kilpatrick ◽  
Sigurd Y. Larsen
Keyword(s):  
Relative Density ◽  
Density Of States ◽  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient
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