Exponential-six Potential Research Articles

Exponential-six potential scaling for the calculation of free energies in molecular simulations

An adjustable, scaled form of the exponential-six (exp-6) potential is presented. The potential form allows stable scaling from a fully interacting exp-6 system to a non-interacting reference system for the direct computation of free energy differences or efficient particle growth simulations, particularly for high-density systems. Additional scaling parameters were introduced to overcome known endpoint effects, whereby reducing the potential to an ideal gas state can produce singularities in simulation averages or prohibit the sampling of close particle distances. The scaled potential is validated in several ways, using Hamiltonian thermodynamic integration, by comparison to vapour–liquid and solid–liquid coexistence free energies reported in the literature, and by the application of the Gibbs–Helmholtz equation. Forms of the scaled exp-6 potential for its implementation into molecular simulations and the thermodynamic integration methods are also developed.

Molecular dynamics study on the effect of interaction potentials on the pressures of high density helium

The thermodynamic properties of pure high density helium and helium bubbles in metals are investigated using molecular dynamics method. The Lennard-Jones potential and the exponential-six potential are used to describe the interaction between helium atoms respectively. The results show that the short-range repulsive part of He–He potential has a great effect upon the pressure of pure high density helium. Because the exponential-six potential is softer than the Lennard-Jones potential in short-range part, the pressures of pure high density helium obtained by the exponential-six potential are lower and have a better agreement with available experimental data. For helium bubbles in metals, the He-Metal interactions can influence the uniformity of helium atoms within helium bubbles so that the pressures inside helium bubbles are higher than that of pure helium with the same average density. However, the differences between them decrease with increasing temperature.

Vapor-liquid nucleation of argon: Exploration of various intermolecular potentials

The homogeneous vapor-liquid nucleation of argon has been explored at T=70 and 90 K using classical nucleation theory, semiempirical density functional theory, and Monte Carlo simulations using the aggregation-volume-bias algorithm with umbrella sampling and histogram-reweighting. In contrast with previous simulation studies, which employed only the Lennard-Jones intermolecular potential, the current studies were carried out using various pair potentials including the Lennard-Jones potential, a modified Buckingham exponential-six potential, the Barker-Fisher-Watts pair potential, and a recent ab initio potential developed using the method of effective diameters. It was found that the differences in the free energy of formation of the critical nuclei between the potentials cannot be explained solely in terms of the difference in macroscopic properties of the potentials, which gives a possible reason for the failure of classical nucleation theory.

Molecular dynamics simulation of the pressure–volume–temperature data of xenon for a nuclear fuel

The exact equation of state for the fission gas is necessary for the accurate prediction of the fission gas behavior in a nuclear fuel. However, certain kinds of extrapolating data are used to construct and verify the equations of state for the fission gas because experimental data are very limited at high temperatures and pressures that are encountered in the nuclear fuel. To fill the lack of experimental data for the fission gas, the behavior of Xe gas atoms was investigated by molecular dynamics simulation assuming an exponential-six potential. The molecular dynamics simulation produced reasonable pressure–volume–temperature data for Xe and the simulation results were compared with existing equations of state for Xe.

Analytic equation of state for the exponential-six fluids based on the Ross variational perturbation theory

An analytic expression of radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan–Starling equation of state (EOS). The comparison with the Monte-Carlo data and the Percus-Yevick expression shows that the expression developed gives out better results. The expression is very simple that can make most perturbation theories become analytic ones, and a simple analytic EOS for the fluids with continuous exponential-six potential is established based on the Ross variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original non-analytic theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one.

Estimate of the barrier to and rate of dissociation of dense nitrogen under shock conditions.

A simple method is introduced to estimate the barrier to dissociation of nitrogen under shock conditions. A free-energy curve is constructed from quantum-mechanical calculations of the ground-state potential well for ${\mathrm{N}}_{2}$, the model exponential-six potential for the dissociated state, and the additional chemical potential (due to the surrounding dense media) in the hard-sphere approximation. The curves are adjusted to yield behavior in agreement with equilibrium thermodynamic calculations. The barriers are several electron volts, decreasing with pressure. Estimates for the prefactor in an Arrhenius rate expression are based on the recent computer simulations of nitrogen vibrational relaxation [B. Holian, J. Chem. Phys. 84, 3138 (1986)]. Time scales for reaction vary from microseconds to tenths of nanoseconds with increasing shock pressure.

Helium at high density

We show that all available high pressure equation of state and melting data for helium can be fitted with an exponential-six potential. This potential is slightly softer than the best theoretical pair potentials and thus implies the existence of attractive many- body forces. The theory also predicts a zero Kelvin fcc to bcc phase transition at 10.6 Mbar, and a maximum temperature of 690 K for the fcc phase.

Calculated specific surface energy of molybdenite (MoS2)

The interlayer binding energy of hexagonal molybdenum disulfide at 0 K was calculated employing an exponential-six potential function summed over all sulfur neighbors across the interlayer gap. A rigid-layer, two-dimensional lattice model was assumed. Experimental values of the equilibrium lattice constants, the lattice constants under pressure, and the bulk modulus in the $c$ direction were used to determine the parameters of the potential. The interlayer binding energy was calculated to be -520 \ifmmode\pm\else\textpm\fi{} 40 erg/${\mathrm{cm}}^{2}$---giving a specific surface energy of ---260 \ifmmode\pm\else\textpm\fi{} 20 erg/${\mathrm{cm}}^{2}$. The depth of the exponential-six potential (in temperature units) is 764 K, which is close to the temperature of an experimentally observed sintering process. The calculation was repeated using a Lennard-Jones potential, resulting in -490 \ifmmode\pm\else\textpm\fi{} 40 erg/${\mathrm{cm}}^{2}$ for the interlayer binding energy and a well depth of 703 K.

Thermal conductivity of binary and ternary mixtures of helium, neon and xenon

A conductivity cell of the thick-wire variety of the hot-wire type has been employed to measure the thermal conductivity of the binary and ternary systems: He-Ne, He-Xe, Ne-Xe and He-Ne-Xe. The values are reported in each case as a function of composition at 30, 50, 70 and 90°c. These results are interpreted on the basis of the rigorous Chapman-Enskog kinetic theory using the well-known modified Buckingham exponential-six potential. Some commonly employed approximate, empirical semi-empirical procedures of computing the thermal conductivity of gas mixtures are also discussed and critically examined on the basis of these data.

Transport properties of some simple non-polar gases on the Morse potential

The experimental viscosity, thermal conductivity and diffusion data of Ne, Ar, Kr, Xe, CH4 and N2 have been interpreted in terms of the Morse potential, with the aid of the kinetic-theory collision integrals for this potential tabulated by Lovell and Hirschfelder. The potential parameters determined from the crystal properties and the second virial coefficient are found to describe the transport properties only approximately. More detailed investigations are desirable to throw light on the relative merit of this new potential as compared to the well-known modified Buckingham exponential-six potential.