Solid-Fluid Equilibria of Atoms with Soft Repulsive and Short-Range Cohesive Interactions.

We report molecular simulations using a relatively soft interatomic potential to determine the nature of melting under extreme conditions. At temperatures and pressures above the triple point of normal materials, the density range of two-phase solid and fluid equilibria is bounded by freezing and melting curves. We address the unresolved issue of the termination of these boundaries, i.e., whether the melting curve of a solid terminates in a critical point, exhibits a maximum, goes to an asymptotic limit, or continues indefinitely. Significantly, we observe a negative change in volume upon melting at high pressures, which is normally observed only for water. We provide unequivocal evidence that the densities of the meeting and freezing lines can merge at a melting temperature maximum point. This could be a general feature of "soft" atomic fluids at extreme pressures.

An intermolecular potential for hydrogen: Classical molecular simulation of pressure-density-temperature behavior, vapor-liquid equilibria, and critical and triple point properties.

An intermolecular potential is reported for molecular hydrogen that combines two-body interactions from ab initio data with three-body interactions. The accuracy of the two-body potential is validated by comparison with experimental second virial coefficient data. Experimental pressure-density-temperature data are used to validate the addition of three-body interactions, often yielding very accurate predictions. Classical Monte Carlo simulations that neglect quantum effects are reported for the vapor-liquid equilibria (VLE), critical properties, and the triple point. A comparison with experimental data indicates that the effect of quantum interactions is to narrow the VLE phase envelope and to lower the critical temperature. The three-body interactions have a considerable influence on the phase behavior, resulting in good agreement with the experimental density. The critical properties of the two-body + three-body potential for hydrogen provide an alternative set of input parameters to improve the accuracy of theoretical predictions at temperatures above 100 K. In the vicinity of the critical point, the coexistence densities do not obey the law of rectilinear diameters, which is a feature that has largely been overlooked in both experimental data and reference equations of state.

Accurate determination of solid-liquid equilibria by molecular simulation: Behavior of Ne, Ar, Kr, and Xe from low to high pressures.

We report the accurate determination of solid-liquid equilibria using a novel molecular simulation method that can be used for solid-liquid equilibria from low to high pressures. A re-evaluation is reported of the solid-liquid equilibria of the noble gases interacting via ab initio two-body potentials combined with three-body interactions and quantum corrections and the results are compared with both existing simulation data and experimental values. The new simulation method yields results that are generally in closer agreement with the experiment than exiting methods, highlighting the important role of the method in fully understanding the interatomic interactions responsible for solid-liquid equilibria. The quality of the comparison of simulation results with the experiment indicates that the solid-liquid equilibria of the noble gases can be now predicted with exceptional accuracy over a large range of pressures.

First-principles determination of the solid-liquid-vapor triple point: The noble gases.

We report first-principles calculations of the triple point that allow us to predict the triple point temperature of atomic fluids to an accuracy that has not been previously possible. This is achieved by proposing a molecular simulation technique that can be used for solid-liquid equilibria at arbitrarily low pressures. It is demonstrated that the triple point is significantly influenced by the choice of two-body, three-body and quantum interactions. An improved theoretical understanding of triple points is important for both science in general, and metrology in particular, as it links the Boltzmann constant and the Kelvin temperature scale to fundamental constants.

Interatomic Interactions Responsible for the Solid-Liquid and Vapor-Liquid Phase Equilibria of Neon.

The role of interatomic interactions on the solid-liquid and vapor-liquid equilibria of neon is investigated via molecular simulation using a combination of two-body ab initio, three-body, and quantum potentials. A new molecular simulation approach for determining phase equilibria is also reported and a comparison is made with the available experimental data. The combination of two-body plus quantum influences has the greatest overall impact on the accuracy of the prediction of solid-liquid equilibria. However, the combination of two-body + three-body + quantum interactions is required to approach an experimental accuracy for solid-liquid equilibria, which extends to pressures of tens of GPa. These interactions also combine to predict vapor-liquid equilibria to a very high degree of accuracy, including a very good estimate of the critical properties.

Combining intermolecular potentials for the prediction of fluid properties: Two-body and three-body interactions.

The ability to combine intermolecular potentials without loss of information is investigated. Molecular simulation results for both vapor-liquid equilibria and supercritical isochoric heat capacities are reported for different combinations of n-m potentials. The role of both additional cohesion and repulsive terms is determined. The 12-8-6 potential obtained by adding an m = 6 contribution to the 12-8 potential significantly broadens the phase envelope, which remains inside of the 12-6 envelope. In contrast, the 12+9-6 potential that involves an additional n = 9 repulsive contribution lifts the phase envelope above the 12-6 values. The 12-8-6 potential significantly reduces the maximum and minimum observed for the isochoric heat capacity at supercritical conditions. In contrast, the additional repulsion of the 12+9-6 potential has a relatively small influence on the supercritical behavior of the isochoric heat capacity. Significantly, a comparison of vapor-liquid equilibria data for two-body only simulations for Ar, Kr, and Xe indicates that there is very good agreement with the 12-8-6 data. This means that the 12-8-6 potential may provide a useful description of two-body only interactions for the noble gases. The 12+9-8 potential at least partially reproduces vapor-liquid properties of noble gases interacting via two-body plus three-body interactions. In general, the combination of potentials provides a mechanism of simplifying the calculation of two-body and two-body plus three-body interactions.

Effect of the range of particle cohesion on the phase behavior and thermodynamic properties of fluids.

Molecular simulations are performed for the (m + 1, m) potential to systematically investigate the effect of changing the range of particle cohesion on both vapor-liquid equilibria and thermodynamic properties of fluids. The results are reported for m = 4-11, which represent a progressive narrowing of the potential energy well. The conventional Lennard-Jones potential is used as a reference point for normal fluid behavior. Small values of m result in a broadening of the phase envelope compared with the Lennard-Jones potential, whereas a contraction is observed in other cases. The critical properties are reported, and a relationship between the critical temperature and the Boyle temperature is determined. The low values of the critical compressibility factor when m < 6 reflect the behavior observed for real fluids such as n-alkanes. The results for supercritical thermodynamic properties are much more varied. Properties such as pressure, potential energy, isochoric thermal pressure coefficient, and thermal expansion coefficient vary consistently with m, whereas other properties such as the Joule-Thomson coefficient exhibit much more nuanced behavior. Maximum and minimum values are reported for both the isochoric heat capacity and isothermal compressibility. A minimum in the speed of sound is also observed.

Vapor-liquid equilibria and cohesive r-4 interactions.

The role of cohesive r-4 interactions on the existence of a vapor phase and the formation of vapor-liquid equilibria is investigated by performing molecular simulations for the n-4 potential. The cohesive r-4 interactions delay the emergence of a vapor phase until very high temperatures. The critical temperature is up to 5 times higher than normal fluids, as represented by the Lennard-Jones potential. The greatest overall influence on vapor-liquid equilibria is observed for the 5-4 potential, which is the lowest repulsive limit of the potential. Increasing n initially mitigates the influence of r-4 interactions, but the moderating influence declines for n > 12. A relationship is reported between the critical temperature and the Boyle temperature, which allows the critical temperature to be determined for a given n value. The n-4 potential could provide valuable insight into the behavior of non-conventional materials with both very low vapor pressures at elevated temperatures and highly dipolar interactions.

Ab Initio Interatomic Potentials and the Classical Molecular Simulation Prediction of the Thermophysical Properties of Helium.

The ability of modern ab initio potentials to predict the thermophysical properties of helium is investigated. A new interatomic potential for helium is reported that is based on the latest available ab initio data and that is much more computationally efficient than other ab initio potentials, without sacrificing accuracy. The role of both two-body and three-body interactions is evaluated using classical Monte Carlo and molecular dynamics simulations. Data are reported for the second virial coefficient, vapor-liquid equilibria, acentric factor, compressibility factor, enthalpy, speed of sound, and isobaric heat capacity. Three-body interactions have a minor influence on the properties of helium with the exception of the estimated critical properties. The influence of quantum particle behavior is relevant at temperatures typically below 200 K. For example, the experimental maximum in the isobaric heat capacities (along isobars) of helium is not observed in the classical simulations and can be attributed to quantum particle behavior. However, above this temperature, helium behaves like a classical fluid and its thermodynamic properties can be adequately predicted by determining only two-body interactions.

Structural behavior of fluids from the vapor and liquid region to the supercritical phase.

A metric (χ) is introduced to quantify the relative proportion of particles having a specified number of near neighbors that are characteristic of liquid-phase properties. It can be used as a simple alternative to other methods for the investigation of some aspects of percolation behavior. Values of χ are obtained from molecular-dynamics simulations spanning the heterogeneous vapor and liquid region and the supercritical phase of the Lennard-Jones fluid. The supercritical phase can be delineated into regions of different structural properties. At different isochoric subcritical conditions, the temperature versus χ behavior shows evidence of inflections, which are associated with the onset of transitions from the vapor and liquid region to the supercritical phase. The analysis suggests a phenomenological requirement for the critical point in terms of a near-equal proportion of near neighbors with gaslike and liquidlike characteristics.

The Widom Line and the Lennard-Jones Potential.

The phenomenological behavior of the Widom line above the vapor-liquid critical point for the Lennard-Jones (LJ) potential is investigated using four accurate equations of state (EoS) and a comparison with molecular dynamics (MD) simulation data. This involved calculating the supercritical maximum values of the isochoric heat capacity (CV), isobaric heat capacity (Cp), isothermal compressibility (ßT), and thermal expansion coefficient (αp). All LJ EoS predict the pressure (p)-temperature (T) Widom line behavior. In contrast, the T-density (ρ) Widom line behavior, observed in MD simulations, is not predicted by any LJ EoS. The calculations highlight the important role of ßT in determining the range of p and T for which Widom line behavior is observed. Analysis of MD data for the supercritical maximum/minimum of CV and Cp suggests the extension of a Clausius-Clapeyron-type relationship from the triple point to the supercritical region. This provides a new description of the Widom line as the near critical part of this larger curve for which other thermodynamic functions also have maximum values.

Thermodynamic properties and anomalous behavior of double-Gaussian core model potential fluids.

The structural, thermodynamic, and vapor-liquid equilibria properties of the double-Gaussian core model (DGM) potential are studied via molecular simulation. Results are presented for the pressure (p), potential energy (U), isochoric and isobaric heat capacities (C_{V,p}), isothermal compressibility (ß_{T}), isochoric thermal pressure coefficient (γ_{V}), thermal expansion coefficient (α_{p}), speed of sound (ω_{0}), and the Joule-Thomson coefficient (µ_{JT}), which are compared with simulations for the Gaussian core model (GCM) potential. A feature of the simulations is that both the GCM and DGM potentials reproduce many of the anomalous properties of water, such as a maximum density, γ_{V}<0, maximum values for both α_{p} and ß_{T}, and minimum values in both C_{p} and ω_{0}. The presence of attractive interaction enhances the anomalies and also yields some additional features such as a more structured vapor phase and Joule-Thomson inversion.

Fully a priori prediction of the vapor-liquid equilibria of Ar, Kr, and Xe from ab initio two-body plus three-body interatomic potentials.

Fully a priori predictions are reported for the vapor-liquid equilibria (VLE) properties of Ar, Kr, and Xe using molecular simulation techniques and recently developed ab initio two-body interatomic potentials. Simulation data are reported at temperatures from near the triple point to close to the critical point. The two-body ab initio potentials exaggerate the size of the experimental VLE temperature-density envelope, overestimating the critical temperature and underestimating the vapor pressure. These deficiencies can be partially rectified by the addition of a density-dependent three-body term. At many temperatures, the ab initio + three-body simulations for Kr and Xe predict the vapor pressure to an accuracy that is close to experimental uncertainty. The predicted VLE coexisting densities for Xe almost match experimental data. The improvement with experiment is also reflected in more accurate enthalpies of vaporization. The fully a priori predictions for all of the VLE properties of either Kr or Xe are noticeably superior to simulations using the Lennard-Jones potential.

Flow of water through carbon nanotubes predicted by different atomistic water models.

Nonequilibrium molecular dynamics simulations are reported to investigate the influence of different atomistic water models on the predicted flow behavior in carbon nanotubes (CNTs) with diameters between 0.81 nm and 1.9 nm. The comparison was made using rigid three-site [simplified point charge (SPC), extended SPC (SCP/E), and transferable intermolecular potential three point (TIP3P)] and four-site (TIP4P and TIP4P/2005) models. In addition, a flexible three-site model (SPC/Fw) was also investigated. The effect of different simulation conditions was determined by generating a flux across the CNT using either a pressure gradient across a membrane separating two water reservoirs or a periodic CNT with a constant force applied to each water molecule. Simulations involving the two water reservoirs indicate that the flux is strongly dependent on the choice of water model, which confirms earlier work. By contrast, this strong model dependency is not a feature of the periodic CNT simulations. Instead, the flux depends mainly on the pore diameter and the molecular density of water inside the CNT. The influence of the water model becomes very small in the periodic CNT simulations, which eliminates distorting entrance/exit effects.

Two-body interatomic potentials for He, Ne, Ar, Kr, and Xe from ab initio data.

A new method is reported for developing accurate two-body interatomic potentials from existing ab initio data. The method avoids the computational complexity of alternative methods without sacrificing accuracy. Two-body potentials are developed for He, Ne, Ar, Kr, and Xe, which accurately reproduce the potential energy at all inter-atomic separations. Monte Carlo simulations of the pressure, radial distribution function, and isochoric heat capacity using the simplified potential indicate that the results are in very close, and sometimes almost indistinguishable, agreement with more complicated current state-of-the-art two-body potentials.

Erratum: Phase diagram of the Weeks-Chandler-Andersen potential from very low to high temperatures and pressures [Phys. Rev. E 80, 061101 (2009)].

This corrects the article DOI: 10.1103/PhysRevE.80.061101.

Molecular simulation of orthobaric isochoric heat capacities near the critical point.

A molecular simulation strategy is investigated for detecting the divergence of the isochoric heat capacity (C_{V}) on the vapor and liquid coexistence branches of a fluid near the critical point. The procedure is applied to the empirical Lennard-Jones potential and accurate state-of-the-art ab initio two-body and two-body + three-body potentials for argon. Simulations with the Lennard-Jones potential predict the divergence of C_{V}, and the phenomenon is also observed for both two-body and two-body + three body potentials. The potentials also correctly predict the crossover between vapor and liquid C_{V} values and the subcritical liquid C_{V} minimum, which marks the commencement C_{V} divergence. The effect of three-body interactions is to delay the onset of divergence to higher subcritical temperatures.

Two-body intermolecular potentials from second virial coefficient properties.

A method is reported that enables second virial coefficient properties to be used to obtain relatively simple two-body intermolecular potentials. Generic n-m Lennard-Jones/Mie potentials are transformed into two-body potentials for neon, argon, krypton, and xenon. Comparison with results from highly accurate ab initio potentials indicates good agreement. A complete potential for real fluids is obtained by combining the two-body potentials with a density-dependent term for three-body interactions. Vapor-liquid equilibria molecular simulation data for the new potentials are compared with the experiment, which demonstrates the effectiveness of the two- and three-body contributions. The combination of the two-body 10-8 Lennard-Jones/Mie potential and three-body term is a good overall choice for the noble gases.