Perturbation theory of liquids for short-ranged hard-core potentials: structure and thermodynamics of short-ranged square-well fluids

Semiclassical thermodynamic geometry

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

We study a system of few colloids confined in a small spherical cavity with event driven molecular dynamics simulations in the canonical ensemble. The colloidal particles interact through a short range square-well potential that takes into account the basic elements of attraction and excluded-volume repulsion of the interaction among colloids. We analyze the structural and thermodynamic properties of this few-body confined system in the framework of inhomogeneous fluids theory. Pair correlation function and density profile are used to determine the structure and the spatial characteristics of the system. Pressure on the walls, internal energy, and surface quantities such as surface tension and adsorption are also analyzed for a wide range of densities and temperatures. We have characterized systems from 2 to 6 confined particles, identifying distinctive qualitative behavior over the thermodynamic plane T - ρ, in a few-particle equivalent to phase diagrams of macroscopic systems. Applying the extended law of corresponding states, the square well interaction is mapped to the Asakura-Oosawa model for colloid-polymer mixtures. We link explicitly the temperature of the confined square-well fluid to the equivalent packing fraction of polymers in the Asakura-Oosawa model. Using this approach, we study the confined system of few colloids in a colloid-polymer mixture.

Convergence and low temperature adaptability analysis of the high temperature series expansion of the free energy

By appealing to the coupling parameter series expansion to calculate the first seven perturbation coefficients of the high temperature series expansion (HTSE) of the free energy, analysis of convergence and low temperature adaptability of the HTSE in calculating fluid thermodynamic properties is performed for the first time; the fluid thermodynamic properties considered include critical parameters, vapor-liquid coexistence curve, thermodynamic characteristic functions, chemical potential, pressure, and constant volume excess heat capacity. To proceed with the analysis, a well known square well model is used as sample; the well widths considered range over a wide interval, and the relevant temperatures amenable to simulation calculations (used as "exact" results to analyze the HTSE) can be both very high and very low. The main discoveries reached are summarized as follows: (1) The HTSE usually converges at the 4th-order truncation, but with decrease of the temperature considered, the lowest truncation order, which makes the HTSE to converge, tends to rise. As a conservative estimate, it is considered that the HTSE always converges for reduced temperature T* higher than 0.25, whereas for T* < 0.25 there appear signs indicating that the HTSE may diverge from the 7th-order truncation. (2) Within the temperature interval with T* ≥ 0.5, the HTSE converges approximately to the correct solution, and the HTSE can be reliably used to calculate the fluid thermodynamic properties, and within this temperature interval, the 4th-order truncation is enough; whereas for T* < 0.5, such as within the temperature interval with 0.275 ≤ T* ≤ 0.355, although the HTSE does converge, it does not converge to the correct solution, and the deviations between the HTSE calculations and MC simulations become an ever-prominent issue with the rising of the density, and the slopes of the thermodynamic properties over density are not satisfactorily represented. As a result, the HTSE is not suited for calculations for temperature interval T* < 0.5.

Structure and thermodynamics of hard-core Yukawa fluids: thermodynamic perturbation approaches

The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.