Exp-6 Fluid Research Articles

Development of an analytical exponential-6 equation of state through Monte Carlo simulations.

The exponential-6 (exp-6) potential is commonly used to model fluids at high densities. In this paper, I propose a new equation of state (EOS) in the form of an analytical expression for the excess Helmholtz free energy of an exp-6 fluid. The EOS is based on extensive Monte Carlo simulations and therefore combines the excellent accuracy of the simulations with the numerical efficiency of a polynomial expression. The mean relative error in compressibility factor and internal energy is 0.14% and 0.25% respectively, which is a significant improvement over statistical mechanical theories. The EOS was implemented into a thermochemical code in order to optimize gas parameters and evaluate its performance on pure gas data, shock compression and detonation properties. Predicted gas densities, heat capacities and speed of sound for pure gases were generally within experimental uncertainties at pressures up to 1GPa and temperatures above 300K. For polar molecules, a simple free energy correction was introduced which greatly improved accuracy at low temperature. Calculated shock Hugoniots showed excellent agreement with experimental values up to 150GPa and 10 000K, and the detonation performance was accurately predicted for a number of different types of explosives.

A new concept for augmented van der Waals equations of state

A novel approach to perturbed equations of state for simple fluids is presented and its advantages over the traditional perturbed hard sphere equations are demonstrated by its application to several model fluids. The approach is based on a short range Yukawa reference which incorporates, in addition to repulsive interactions, also attractive interactions at short separations. The considered models of common interest are the Sutherland, Lennard-Jones, and EXP6 fluids. It is shown that using the proposed approach the reference system captures a good deal of properties of the studied fluids and that an accurate equation of state can be obtained using only the crude mean field (augmented van der Waals) approach.

EXP6 fluids at extreme conditions modeled by two-Yukawa potentials

A two-Yukawa representation of the EXP6 fluids at supercritical temperatures and high pressures has been developed and examined using molecular simulations. A uniquely defined mapping of the repulsive part of the EXP6 potential curve onto the two-Yukawa potential is used. Two ranges of temperatures, one encountered in geochemical applications (T(geo) range) and the other at conditions of detonations (T(det) range), are considered and it is shown that the local structures of both fluids are practically identical. Deviations between the EXP6 and two-Yukawa potential functions at intermediate separations lead to differences in the thermodynamic properties of the two fluids at lower temperatures of the T(geo) range; at higher temperatures and in the high T(det) temperature range both the structural and thermodynamic properties of the EXP6 and two-Yukawa fluids are practically identical.

Re-entrant melting of the exp-6 fluid: the role of the repulsion softness

We investigate the phase behaviour of a system of particles interacting through the exp-6 pair potential, an interaction model that is appropriate to describe effective interatomic forces under high compression. The soft-repulsive component of the potential is being varied so as to study the effect on re-entrant melting and density anomaly. Upon increasing the repulsion softness, we find that the anomalous melting features persist and occur at lower pressures. Moreover, if we reduce the range of downward concavity in the potential by extending the hard core at the expenses of the soft-repulsive shoulder, the re-entrant part of the melting line reduces in extent so as it does the region of density anomaly.

Molecular dynamics study of the repulsive form influence of the interaction potential on structural, thermodynamic, interfacial, and transport properties

In this work, using extensive molecular dynamics simulations of several thermophysical properties, it is proposed to analyze possible relationships (in the corresponding state sense) between monoatomic fluids for which the repulsive interactions are modeled by an inverse n-power form, the Lennard-Jones 12-6 (LJ), or by an exponential one, the exponential-6 (Exp-6). To compare results between them, two possible definitions of Exp-6 potentials "equivalent" to the LJ one are proposed. In pure fluids, for a large range of thermodynamic conditions, the properties computed are the surface tension, liquid/vapor equilibrium densities, one-phase potential energy, pressure, isometric heat capacity, thermal pressure coefficient, self-diffusion, shear viscosity, and thermal conductivity. Additionally, thermodiffusion (Soret effect) has been considered in "isotopic" equimolar mixtures. It is shown that despite similarities exhibited by alike radial distribution functions, differences exist between the thermodynamic properties values provided by the LJ fluid and the two equivalent Exp-6 fluids. Nevertheless, quite surprisingly, when temperature and density are used as inputs, all three direct transport properties are shown to be nearly independent of the choice of the potential tested. Unexpectedly, these similarities hold even for thermodiffusion which is a priori very sensitive to the nature of the interactions. These results indicate that the use of an Exp-6 potential form to describe nonbonded/nonpolar interaction in molecular simulation is an alternative (more physically acceptable) to the LJ potential when dealing simultaneously with thermodynamic and transport properties. However, when only transport properties are considered (including thermodiffusion), the Exp-6 potential form should not lead to any differences compared to the LJ one.

Analytic equation of state for exponential-six fluid based on the Ross variational perturbation theory and the Percus–Yevick radial distribution function of hard spheres

The analytic expressions for equation of state and thermodynamic properties have been derived for the exp-6 fluids, by using the Ross variational perturbation theory and the analytic Percus–Yevick (PY) expression of radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are fast. The comparison of the numerical results with the computer simulations shows that the precision of the analytic Ross theory is equivalent to the non-analytic modified Weeks–Chandler–Anderson (mWCA) theory, and is slightly better than the complicated optimized reference hypernetted chain (RHNC) theory.

Analytic equation of state and thermodynamic properties for He–H 2 fluid mixtures over a wide range of pressures and temperatures

The analytical expressions for the equation of state and thermo-physical quantities of Exp-6 fluid are derived based on the Ross variational perturbation theory and with the quantum effect taken into account. The formalism developed is applied to the He–H 2 mixtures. The agreement of numerical results of pressure and internal energy with MC simulations is shown far better than the analytic equation of state developed by [I. Ali, S.M. Osman, N. Sulaiman, R.N. Singh, Phys. Rev. E 69 (2004) 0561045]. The isotherms for pressure, internal energy and packing factor for five concentrations and four temperatures versus volume are calculated and analyzed. The numerical results for excess Gibbs free energy and entropy of mixing are presented. The variation of the excess Gibbs free energy of mixing, and the variation of the excess entropy of mixing versus temperature and pressure are different from and similar to that of Ali et al., respectively.

High-pressure phase diagram of the exp-6 model: The case of Xe

We investigated numerically the high-temperature--high-pressure phase diagram of xenon as modeled through the exp-6 interaction potential, which is thought to provide a reliable description of the thermal behavior of rare gases under extreme conditions. We performed a series of extensive NVT Monte Carlo simulations which, in conjunction with exact computation of the solid free energy by the Frenkel-Ladd method, allowed us to precisely locate the freezing and melting thresholds at each temperature. We find that, under isothermal compression, the exp-6 fluid freezes directly into a fcc solid; however, above 4500 K, an intermediate bcc phase becomes stable in a narrow range of pressures. The chemical potential of the hcp phase never significantly differs from that of the fcc solid of equal $T$ and $P$, though the former is found to be slightly greater than the latter. We discuss our results in the light of previous numerical studies of the same model system and of the experimental data available for xenon.

Fluid–solid boundary of the compressed EXP-6 fluids

Using recent computer simulation data and the principle of corresponding states, the boundary of stability of the compressed supercritical EXP-6 potential fluids is localized for an arbitrary potential parameter α. All existing supercritical simulation data of the EXP-6 fluids are then analyzed and assessed with respect to their potential use for derivation of an equation of state of the compressed EXP-6 fluids.

Practical equation of state and activity coefficient models based on the exp-6 fluid

Dodd L.R. and Sandler S.I., 1991. Practical equation of state and activity coefficient models based on the exp-6 fluid. Fluid Phase Equilibria, 69: 99-139. In this paper we test a partition function model recently developed for the exp-6 fluid mixture against experimental data for real fluids. This model leads to a unique size and density-dependent mixing rule providing non-quadratic density-dependence which satisfies the low-density and pure fluid boundary conditions. The equation of state calculations with this model gave good results, especially for highly asymmetric systems. Applications of a similar mixing rule to cubic engineering equations of state for real fluids yielded better predictions than the van der Waals one-fluid mixing rule. However, except in the near critical region, any clear advantage of the new density-dependent mixing rule for real fluids is lost when adjustable parameters are added. We also show that an activity coefficient model based on this exp-6 model leads to good correlations for low pressure vapor-liquid equilibria of both simple and very complex mixtures, indeed mixtures that could not easily be described by other models with the same number of parameters.

A study of the Buckingham exponential-six fluid mixtures

Extensive Monte Carlo computer simulation results for the configurational energy, compressibility and the radial distribution functions of mixtures of exponential-six molecules at 352 state points and presented. These data are used to test mixture models that have been proposed, and to develop a model which describes the exp-6 fluid quite well. Using this model, explicit expressions are obtained for the partition function for pure fluids and mixtures of exp-6 molecules.It is also shown how, by redefinition of the free volume and mean potential terms, simple models can be used to describe the behavior of exp-6 fluids and that with this definition the behavior of the exp-6 and square-well fluids are very similar.