Jiří Kolafa

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.

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.

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.

Effect of short- and long-range forces on the structure of water: temperature and density dependence

The individual effects of short-range and long-range forces on the structure of water, a prerequisite for developing a perturbation theory, are assessed using a decomposition of realistic water—water potential models into trial potentials. Computer simulations for one typical liquid density and a number of temperatures ranging from the freezing temperature up to supercritical ones, and for several densities on a supercritical isotherm were performed. The trial potentials were constructed from the ST2 and TIP4P potentials and it is shown that for both potentials the results are practically identical. It is shown that (i) regardless of the thermo-dynamic conditions and potential models used, the structure of water and the mutual orientational arrangement of water molecules, given by a set of site—site correlation functions, are determined nearly exclusively only by the short range forces, and (ii) for high density states the effect of the short range electrostatic part of the intermolecular potential on the...

Effect of short and long range forces on the structure of water. II. Orientational ordering and the dielectric constant

The effects of short and long range interactions on the structure of water, both spatial and orientational, has been studied in detail by computing the full pair correlation function, site-site correlation functions, 2-dimensional site-site correlation functions in the (r OO, r OH) and (r OO, r HH) planes, dipole-dipole correlation function, radial Kirkwood g factor, and the dielectric constant. Two model potentials, the T1P4P and ST2, and their short range versions have been considered at ambient and elevated temperatures and under supercritical conditions. The Ewald summation under different conditions has been used to investigate also their effect on results. An analysis of the results shows that although all site-site correlation functions for the short and long range systems are similar, the orientational ordering in systems of different range may be considerably different, this evidence being provided mainly by the dipole-dipole correlation function and the radial Kirkwood factor. The orientational ordering is only short range in long range systems, whereas in short range systems the hydrogen bonding gives rise to a damped long range regular pattern of alignment. Nonetheless, the resulting dielectric constants for the short and long range systems coincide within the combined error bars. All findings are more pronounced at low temperatures but otherwise they are only marginally temperature and density dependent.

Autocorrelations and subseries averages in Monte Carlo Simulations

The process of averages over consecutive sufficiently long subseries of data obtained from Monte Carlo or, with some restrictions, from molecular dynamics simulations of statistical systems is analysed with respect to decay of autocorrelations with increasing lag. A simple expression for the error of the total average is derived the tested on a model system. Comparison is made with other approaches.

Effect of short- and long-range forces on the properties of fluids. III. Dipolar and quadrupolar fluids

Using realistic pair potential models for acetone and carbon dioxide, both the spatial and orientational structure of these two typical multipolar (i.e. dipolar and quadrupolar, respectively) fluids is investigated in detail by computing the complete set of the site-site correlation functions, multipole-multipole correlation functions, and selected 2D correlation functions. The effect of the range of interactions on both the structural and thermodynamic properties of these fluids is studied by decomposing the potential into short- and long-range parts in the same manner as for water [Kolafa, J. and Nezbeda, I., 2000, Molec. Phys., 98, 1505; Nezbeda, I. and Lísal, M., 2001, Molec. Phys., 99, 291]. It is found that the spatial arrangement of the molecules is only marginally affected by the long-range forces. The effect of the electrostatic interactions is significant at short separations and cannot be neglected but nevertheless the overall structure of the short-range and full systems is similar as well as their dielectric constants. These findings are also reflected in the dependence of the thermodynamic properties on the potential range with the short-range models providing a very good approximation to those of the full system.

Accurate equation of state of the hard sphere fluid in stable and metastable regions

New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly optimized molecular dynamics calculations in the range of reduced densities 0.20–1.03. The relative inaccuracy at the 95% confidence level is better than 0.00004 for all densities but the last deeply metastable point. This accuracy requires careful examination of finite size effects and other possible sources of errors and applying corrections. The data are fitted to a power series in y/(1 − y), where y is the packing fraction; the coefficients are determined so that virial coefficients B2 to B6 are reproduced. To do this, values of B5 and B6 are accurately recalculated. Virial coefficients up to B11 are then estimated from the equation of state.

Primitive models of associated liquids. Equation of state, liquid-gas phase transition, and percolation threshold

An analytic equation of state of an arbitrary primitive model of associated liquids, based on Wertheims thermodynamic perturbation theory, is given. The equations for the models of ammonia (spherical core) and methanol (non-spherical core) are then examined in detail, and it is shown that they give only one fluid phase. An attempt is made to link this result to the H-bond network: using the Cayley tree approximation no percolation threshold has been found for these two models, i.e. their molecules may form clusters of finite size only. This finding contrasts with the result for the model of water which may form infinite clusters and exhibits the liquid-gas phase transition.