Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Structural and thermodynamic properties of hard-sphere fluids

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixtures are also discussed.

Fifth-order thermodynamic perturbation theory of uniform and nonuniform fluids

A recently proposed numerical third-order thermodynamic perturbation theory (TPT) is extended to its fifth-order counterpart. Extensive performance evaluation based on several model potentials indicates that the fifth-order version is generally superior to both the third-order version and a well-known second-order macroscopic compressibility approximation TPT, and is at least comparable to an accurate self-consistent Ornstein-Zernike integral equation approximation (SCOZA) with regard to predictions of varying bulk thermodynamic properties. A bulk second-order direct correlation function (DCF) free of numerical solution of a bulk OZ integral equation, is proposed, which, in combination with the framework of classical density functional theory (DFT) and a thermodynamic consistency condition, extends the uniform fifth-order TPT to nonuniform case. Grand canonical ensemble Monte Carlo simulation is carried out to produce density profile of a core-softened fluid confined in a hard spherical cavity, the resultant density profile is employed to evaluate the performance of the present nonuniform fifth-order TPT and a recently proposed third +second-order perturbation DFT. It is found that the present nonuniform fifth-order TPT is generally more accurate than the third+second-order perturbation DFT. Additional advantages of the present nonuniform fifth-order TPT over the third +second-order perturbation DFT is discussed.

Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.

Performance Evaluation of Third-Order Thermodynamic Perturbation Theory and Comparison with Existing Liquid State Theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.