Thermodynamics of the soft and extended soft mean spherical model

Abstract

A new analytical theory is discussed that extends the range of the mean spherical approximation (MSA) to extreme situations where the asypmtotic limits are known. The MSA [J. K. Percus and G. Yevick, Phys. Rev. 110, 250 (1964); J. L. Lebowitz and J. K. Percus, Phys. Rev. 144, 251 (1966)] yields explicit thermodynamics and structure in terms of a single screening parameter [L. Blum, Mol. Phys. 30, 1559 (1975)]

and gives the correct high density limiting behavior of the contact pair distribution function and thermodynamics [Y. Rosenfeld and L. Blum, J. Chem. Phys. 85, 1556 (1986), Y. Rosenfeld, J. Stat. Phys. 37, 215, (1984)] and has been very useful for practical applications. However, it misses the low density limiting behavior which is implicit in the second virial coefficient. The soft mean spherical approximation (SMSA), which was proposed over 30 years ago by Blum and Narten [L. Blum and A. H. Narten, J. Chem. Phys. 56, 5197 (1972), A. H. Narten, L. Blum, and R. H. Fowler, J. Chem. Phys. 60, 3378 (1974)], corrects this problem interpolating between the MSA and the PY. It is an amazingly accurate approximation. For a given switch distance σ _sw the SMSA closure is

The present communication gives a fully analytical solution of SMSA using the Yukawa closure of the Ornstein Zernike equations [L. Blum and J. A. Hernando, in: Condensed Matter Theories, edited by S. Hernandez, J. W. Clark (Nova, New York, 2001), Vol. 16, p. 411, L. Blum and M. Arias, J. Phys.: Cond. Matter 18, S(2437), ArXiv cond-mat 0602477 (2006)]. This then leads to useful extensions that are discussed in this article.

Acknowledgements

We wish to thank Professor J.L. Lebowitz for his hospitality and for insightful discussions. The NSF has provided support through the PREM program.