Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

Abstract

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker-Henderson framework. This equation of state is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1≤ d ≤3) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semiquantitative agreement.

Global isomorphism approach: Attractive Yukawa fluid, 2D case

“…4). Such reasoning is also supported by the results of [37] which show the proximity of coexistence curves for λ = 1, 1.8.…”

“…Note that correct binodal for liquid-gas equilibrium in 2D case is very hard to obtain within some perturbative approach because the non-classical 2D Ising model critical exponent β = 1/8 makes the binodal dome rather flat (see e.g. [36,37]). That is why some non perturbative approach is needed and global isomorphism provides such a path via (6).…”

Carnahan-Starling type equations of state for stable hard disk and hard sphere fluids

“…Radial distribution function (RDF) plays a key role in describing structural and equilibrium properties of fluids. Analytical expression of a radial distribution function is of critical importance for various applications, such as in the perturbation theories, where the perturbation terms are expressed in terms of the RDF [1,2,3]. For the hard sphere (3D) fluid, analytical expressions can be obtained by solving the Orstein-Zernike equation with the Percus-Yevick (PY) approximation (the PY integral equation).…”

“…For instance, in perturbation theories, integrations of an RDF w.r.t. the distance variable (radial coordinate) are required [1,2,3]; and in determining the effective hard sphere diameter for the Lennard-Jones fluid, derivative of the RDF w.r.t. diameter is demanded with Lado's perturbation theory [9].…”

Modelling adsorption using an augmented two-dimensional statistical associating fluid theory: 2D-SAFT-VR Mie

“…After describing the adsorption model and theory in Sec. II, we start our theoretical treatment calculating analytical expressions for the first-and second-order perturbation terms using an analytical approximation to the pair correlation function of hard bodies in 2D space, a strategy recently adopted by Trejos et al [31] and also discussed in [32]. The perturbation terms are validated by direct comparison with exact numerical results from Monte Carlo (MC) simulations.…”