Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

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.

Convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is 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, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential 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. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.