The First Three Coefficients in the High Temperature Series Expansion of Free Energy for Simple Potential Models with Hard-Sphere Cores and Continuous Tails

Abstract

The first three coefficients of the high temperature series expansion (HTSE) of the Helmholtz free energy for a number of simple potential models with hard-sphere cores plus continuous tails are obtained for the first time from Monte Carlo simulations. The potential models considered include Square-well, Sutherland, attractive Yukawa, and triangle-well with different potential ranges, as well as a model potential qualitatively resembling the depletion potential in colloidal dispersions. The simulation data are used to evaluate performance of a recent coupling parameter series expansion (CPSE) in calculating for these coefficients, and a traditional macroscopic compressibility approximation (MCA) for the second-order coefficient only. A comprehensive comparison based on these coefficients from the two theoretical approaches and simulations enables one to conclude that (i) unlike one common experience that the widely used MCA usually underestimates the second-order coefficient, the MCA can both overestimate and underestimate the second-order coefficient, and worsens as the range of the potential decreases; and (ii) in contrast, the CPSE not only reproduce the trends in the density dependence of the perturbation coefficients, even the third one, observed in the simulations, but also the agreement is quantitative in most cases, and this clearly highlights the potential of the CPSE in providing accurate estimations for the higher-order coefficients, thus giving rise to an accurate higher-order HTSE.

Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models

“…However, the calculations of the perturbation terms from simulations for n > 2 for potentials with continuous tails is computationally very demanding and so, in general, only the firstand second-order perturbation coefficients have been reported for a number of these potential models. An exception is a recent paper from us, 21 in which also the term for n = 3 was reported for several potential models with continuous tails. In this work, we have carried out simulations in the NVT ensemble of the reference HS fluid to obtain the values of a 1 to a 4 from expressions (5)- (8) for the potential models described above with different potential parameters.…”