Ivo Nezbeda

THE LENNARD-JONES FLUID : AN ACCURATE ANALYTIC AND THEORETICALLY-BASED EQUATION OF STATE

Abstract A new analytic equation of state for the Lennard-Jones fluid is proposed. The equation is based on a perturbed virial expansion with a theoretically defined temperature-dependent reference hard sphere term. The expansion is written for the Helmholtz free energy which guarantees the thermodynamic consistency of the pressure and internal energy. The equation covers much wider range of temperatures (up to seven times the critical temperature) than existing equations and is significantly more accurate and has less parameters than the best equation available to date, the modified Benedict-Webb-Rubin equation due to Johnson, Zollweg, and Gubbins (1993, Mol. Phys. 78: 591-618). As a side-product, highly accurate explicit analytic correlations of the hard sphere diameters, as given by both the hybrid Barker-Henderson and Weeks-Chandler-Andersen theories, have been obtained. Computer simulation data to be regressed by the equation have been compiled from several sources and critically assessed. It has been shown that many literature data for state points with a large compressibility are subject to large systematic finite-size errors. Additional simulations on a series of systems of different sizes have been therefore performed to facilitate the extrapolation to the thermodynamic limit in the region close to the critical point.

Monte Carlo simulations on primitive models of water and methanol

The recently introduced primitive model of associated liquids which accounts for both short-ranged repulsions due to excluded volume effects and strongly directional hydrogen bonding has been extended to water and methanol. Hard spheres and homonuclear dumbbells have been considered to mimic the cores of water and methanol molecules, respectively, while the H-bonding has been mimicked by localized square-well attractions. For a number of temperatures and densities thermodynamic and structural properties as well as parameters characterizing association in the system have been evaluated by Monte Carlo simulations; low density properties have been determined analytically. Special attention has also been paid to the effectiveness of the simulation and error analysis.

Equation of state for hard dumbbells

Abstract An equation of state, proposed recently for hard convex bodies, is employed for the description of the P—V—T behaviour of hard dumbbells. Theoretical values of the second and the third virial coefficients and the compressibility factor agree well the Monte Carlo data.

Vapor-liquid equilibria from the triple point up to the critical point for the new generation of TIP4P-like models: TIP4P/Ew, TIP4P/2005, and TIP4P/ice

The vapor-liquid equilibria of three recently proposed water models have been computed using Gibbs-Duhem simulations. These models are TIP4P/Ew, TIP4P/2005, and TIP4P/ice and can be considered as modified versions of the TIP4P model. By design TIP4P reproduces the vaporization enthalpy of water at room temperature, whereas TIP4P/Ew and TIP4P/2005 match the temperature of maximum density and TIP4P/ice the melting temperature of water. Recently, the melting point for each of these models has been computed, making it possible for the first time to compute the complete vapor-liquid equilibria curve from the triple point to the critical point. From the coexistence results at high temperature, it is possible to estimate the critical properties of these models. None of them is capable of reproducing accurately the critical pressure or the vapor pressures and densities. Additionally, in the cases of TIP4P and TIP4P/ice the critical temperatures are too low and too high, respectively, compared to the experimental value. However, models accounting for the density maximum of water, such as TIP4P/Ew and TIP4P/2005 provide a better estimate of the critical temperature. In particular, TIP4P/2005 provides a critical temperature just 7 K below the experimental result as well as an extraordinarily good description of the liquid densities from the triple point to the critical point. All TIP4P-like models present a ratio of the triple point temperature to the critical point temperature of about 0.39, compared with the experimental value of 0.42. As is the case for any effective potential neglecting many body forces, TIP4P/2005 fails in describing simultaneously the vapor and the liquid phases of water. However, it can be considered as one of the best effective potentials of water for describing condensed phases, both liquid and solid. In fact, it provides a completely coherent view of the phase diagram of water including fluid-solid, solid-solid, and vapor-liquid equilibria.

A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation

Abstract A new version of the test particle method for determining the chemical potential by Monte Carlo simulations is proposed. The method, applicable to any fluid at any density, combines the Widoms test particle insertion method with the ideas of the scaled particle theory, gradual insertion method and multistage sampling. Its applicability is exemplified by evaluating the chemical potential of the hard sphere fluid at a very high density in semi-grand-canonical and grand-canonical ensembles. A theory estimating the efficiency (i.e. statistical errors) of the method is proposed and the results are compared with the Widoms and gradual insertion methods, and the analytic results.

A simple model for associated fluids

A simple site–site interaction type of model fluid is proposed to describe, on a primitive level, fluids which exhibit association (H bonding). Computer simulations have been performed on the model to obtain the site–site correlation functions, equation of state, average internal energy, specific heat, g1 and g2 factors, and concentration of polymeric species. The results show that the model is able to capture the basic qualitative properties of real associated liquids.

Virial expansion and an improved equation of state for the hard convex molecule system

Abstract The fourth virial coefficient of hard spherocylinders is calculated using the Monte-Carlo technique and the fifth one by means of a recurrence formula. From an analysis of the reduced virial series a new equation of state is then developed which provides excellent agreement with pseudoexperimental data.

Statistical thermodynamics of interaction-site molecules

A theoretical study of the statistical mechanical description of a system composed of interaction-site molecules is made using the site-site correlation function approach. The system of hard dumb-bells is then studied in detail. The problem of excluded volume of a pair of spheres embedded in the dumb-bells is solved, which enables one to evaluate the second virial coefficient and to derive an approximate equation of state in a closed analytical form. The equation of state obtained shows good agreement with Monte Carlo data.

An examination of the five-site potential (TIP5P) for water

Parameterization of the five-site model (TIP5P) for water [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000)] has been examined by several computer simulation methods accounting properly for long-range forces. The structural and thermodynamic properties at a pressure of 1 atm over the temperature range (−25 °C,+75 °C) and the vapor–liquid coexistence have been determined. It is shown that the simple spherical cutoff method used in the original simulations to find optimized parameters of this five-site model yields results that differ from those obtained by both the Ewald summation and reaction field methods. Consequently, the pivot property to which the parameters were adjusted, the location of the density maximum at 1 atm, does not agree with experimental values. The equilibrium properties then show only a fair agreement with experimental data and are uniformly inferior to those of the four-site TIP4P water over the entire coexistence range.

Primitive model of water: III. Analytic theoretical results with anomalies for the thermodynamic properties

Using the extended thermodynamic perturbation theory of Wertheim, closed simple analytic expressions for the internal energy and pressure of the primitive model of water are derived and examined in detail. The equation of state, which has a form of a perturbed hard sphere equation, exhibits the same anomaly in temperature dependence of the isothermal compressibility as real water. The low value of the critical compressibility factor is in close agreement with the experimental value for real water.