Liquid-Vapor Transition from a Microscopic Theory: Beyond the Maxwell Construction

Abstract

A smooth cutoff formulation of the hierarchical reference theory (HRT) is developed and applied to a Yukawa fluid. The HRT equations are derived and numerically solved leading to the expected renormalization group structure in the critical region, nonclassical critical exponents and scaling laws, a convex free energy in the whole phase diagram (including the two-phase region), finite compressibility at coexistence, together with a fully satisfactory comparison with available numerical simulations. This theory, which also guarantees the correct short range behavior of two body correlations, represents a major improvement over the existing liquid-state theories.

Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system

“…The concept of RG has also been applied to the analysis of classical liquids, see, e.g., Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein, which include the hierarchical reference theory (HRT) [5][6][7][8][9][10] known as a combination of RG and thermodynamic perturbation theory, the application of Wilson's phase-space cell method [11][12][13], and RG with respect to the scale transformation of density [14].…”

Application of the functional renormalization group method to classical free energy models

“…A rigorous, molecularly based approach to applying the renormalization group method to classical fluids is the hierarchical reference theory (HRT) . This method accounts for the influence of long‐range density fluctuations by examining the changes in the free energy of a fluid with changes in the underlying interaction potential.…”

“…HRT is able to accurately describe the crossover from the universal behavior of the free energy near the critical point to its more specific, molecularly dependent properties outside the critical region. This method has been successful in describing the properties of simple fluids and mixtures . The main shortcomings of this approach are its complexity and computational requirements.…”

Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: Molecular dynamics simulations

“…[4][5][6][7][8][9][10][11] Recently, renewed attention has been paid to hard-core attractive Yukawa fluids with short attraction range. [12][13][14][15][16][17][18][19] This interest stems mainly because they capture the most important features of real systems, such as interfacial and coexistence properties which rule many industrial processes and biological phenomena.…”