Supercritical fluid of particles with a Yukawa potential: a new approximation for the direct correlation function and the Widom line
type: Item
instance of: scholarly article
title: Supercritical fluid of particles with a Yukawa potential: a new approximation for the direct correlation function and the Widom line
zbMATH Open document ID: 1366.82017
DOI: 10.1134/S0040577916120126
author: E. E. Tareyeva
author: V. N. Ryzhov
published in: Theoretical and Mathematical Physics
publication date: 2017-03-28T00:00:00Z
review text: The paper proposes a linearized generalized mean spherical approximation for a model with a hard-core potential added by an arbitrary number of Yukawa potentials. An analytical expression is obtained for the direct correlation function \(C(r)\), allowing one to construct the complete thermodynamics of the considered system. The function as a whole satisfies the Ornstein-Zernike equation in the approximation linear in \(\beta\phi\), where \(\beta\) is the inverse temperature and \(\phi(r)\) is the potential outside the sphere. The used approach is similar to the one developed by Baxter for the exact solution of the hard-sphere model. The model allows obtaining analytical results in the case of the sum of Yukawa potentials, because a sufficient number of terms of the sum can approximate any potential with good accuracy. First, the approximation is described in detail and obtains a general result for the approximate direct correlation function. In the case of a two-term Yukawa potential initiating the Lennard-Jones potential, an analytical model is constructed similar to the van der Waals model. The authors calculate the critical point and consider the behavior of the correlation length, isothermal density fluctuations and isothermal compressibility in the supercritical region. The lines of maxima of these values form a single curve (sometimes called the Widom line) only in a neighborhood of the critical point. This allows concluding that the Widom line is not a well-defined notion and cannot be used to divide the supercritical region into fluid and vapor parts.
Mathematics Subject Classification ID: 82B27
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 82C26
zbMATH DE Number: 6697838
zbMATH Keywords: direct correlation function
zbMATH Keywords: supercritical fluid
zbMATH Keywords: Widom line
zbMATH Keywords: Yukawa potential
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
cites work: Q3999842
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description: scientific article; zbMATH DE number 6697838