Fluctuations-inclusive approach to phase transitions in binary mixtures (Q5955503)

A model mixture of spherical particles belonging to two different types and interacting via hard-core repulsion plus attractive tail potential is studied by means of a method called hierarchical reference theory (HRT), which was developed in [\textit{A. Parola} and \textit{L. Reatto}, Phys. Rev. A 44, 6600 (1991); and Adv. Phys. 44, 221 (1995)]. The interaction potential \(v_{ij}\) (the indices \(i,j = 1,2\) number the types of particles) is written as a sum of a singular repulsion \(v_{ij}^R\) and a long-range attraction \(w_{ij}\), both ones are spherically symmetric. It is supposed that the properties of the particles interacting via \(v_{ij}^R\) only (reference system) are known. The key idea of the method is to consider a family \(\{w_{ij}^Q \mid Q\in [0, +\infty) \}\), where \(w_{ij}^Q\) is defined by the Fourier transformation in which the Fourier components \(\tilde{w}_{ij}(k)\) of the potential \(w_{ij}\) with the wave vectors \(k<Q\) are suppressed. Such a family defines a family of models (the model with \(Q=0\) coincides with the initial one), each of which is characterized by a function of \(Q\) connected with the Helmholtz free energy density and the potentials \(w_{ij}\), \(w_{ij}^Q\). For this function, a nonlinear differential equation (DE), where differentiation is taken with respect to \(Q\), is written in terms of correlation functions. The latter obey an infinite hierarchy of equations, which in the article is approximately truncated (closed) by means of the so called Ornstein-Zernike ansatz. Basing in the properties of HRT, the authors describe the universal characteristics of the model in the vicinity of its critical point by solving a simplified version of DE. Non-universal properties of specific mixtures are obtained by means of the numerical integration of the full DE. As a result, the phase diagrams for the argon-krypton and neon-krypton mixtures are described and compared with experimental data. The phase diagrams of symmetric mixtures with different inter-type interactions are also described.