Abstract
The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.
Highlights
Published: 5 August 2021Liquid state theory deals with correlation functions, such as the pair-distribution function, to describe the structural and thermodynamics properties of fluids [1]
The Ornstein–Zernike equation (OZE), which relates the direct and total correlation functions, is known to have excellent predictive power when supplemented with appropriate closure relations
The main aim in this paper is to analyze the convergence of coupling-parameter expansion (CPE) for solving the OZE
Summary
Liquid state theory deals with correlation functions, such as the pair-distribution function, to describe the structural and thermodynamics properties of fluids [1]. Perturbation theories based purely on the fluid free energy mostly use the hard sphere model as the reference system [14] This is because of the availability of simulation data on hard sphere systems in very accurate parameter forms [13]. The main objective of the paper is to obtain results on the convergence of CPE, in particular, the two-phase region where OZE shows the occurrence of multiple and complex solutions. The overall conclusion emerging from this analysis is that CPE is a practical approach for obtaining thermodynamic properties of one-component fluids interacting via general potentials. Thermodynamic models of fluid properties, in the two-phase region, are essential in applications involving equations of state of liquid metals [19,20], which are important in high pressure physics. It is expected that CPE will find good use in generating the equations of state data [21] in the fluid domain
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