Thermodynamic consistency by a modified Perkus–Yevick theory using the Mittag-Leffler function

Abstract

Closure relations that satisfies thermodynamical consistencies are very important, for it implies physical consistent Ornstein–Zernike equation solutions. The method proposed by Percus (1962), which uses the functional Taylor expansion to obtain closure relations, is presented along with the particular generating functional considered to retrieve the Percus–Yevick (PY) approximation. The main assumption for this particular case, which takes into account the low density limit, is discussed. Based on this argument, it was proposed a modified generating functional with no prior considerations about the system density. As an example, the two-parameters Mittag-Leffler function was used. Since it generalizes the exponential function, the parameters determined at low densities retrieves the PY approximation. For higher densities it was possible to obtain parameters which lead to pressure consistent results, in good agreement with those found in literature.