Supercritical fluid of particles with a Yukawa potential: a new approximation for the direct correlation function and the Widom line
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.
scientific article; zbMATH DE number 6697838