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.

Structure and Contact Angle in Sessile Droplets of Binary Mixtures of Lennard-Jones Chains: A Molecular Dynamics Study.

Molecular dynamics simulations were carried out to investigate cylindrical droplets consisting of binary mixtures of Lennard-Jones (LJ) fluids in contact with a solid substrate. The droplets are composed of mixtures of the monomeric LJ fluid plus linear-tangent chains of 2, 10, 20, and 30 segments per chain that interact through a harmonic potential and the spherically truncated and shifted potential Lennard-Jones. The solid surface was modeled as a semi-infinite platinum substrate with an FCC structure that interacts with the fluid by means of a LJ 9-3 potential. We place emphasis on the effect of mixing a monomeric LJ fluid with heavy components on the contact angle and on the droplet structure, especially in the liquid-solid region. The density profiles of the droplets reveal a strong discrete layering of the fluid in the vicinity of the solid-liquid interface. The layering is more pronounced at low temperatures and for mixtures of short chains (symmetric mixtures). The ordering of the fluid was much less intense for fluids of long chains (asymmetric mixtures), and some cases even show gas enrichment at the solid-liquid interface. Enrichment at the vapor-liquid interfaces and density inversion can also be observed. However, these effects are not as marked as in planar interfaces. The contact angle between the droplet and the substrate is calculated by fitting an ellipse to the vapor-liquid interface defined by the Gibbs dividing surface. In general, an increment in the concentration of the heavy component and a reduction of the temperature resulted in an increase of the contact angle, which in turn disfavored the wetting of the droplet.

Interfacial properties of binary mixtures of Lennard-Jones chains in planar interfaces by molecular dynamics simulation.

Binary mixtures of fully flexible linear tangent chains composed of bonded Lennard-Jones interaction sites (monomers) were studied using the molecular dynamics simulation in the NVT ensemble. Their interfacial properties were investigated in planar interfaces by direct simulation of an explicit liquid film in equilibrium with its vapor. A method for the calculation of long-range interactions in inhomogeneous fluids was implemented to take into account the potential truncation effects. Surface tension and the pressure tensor were calculated via the classical Irving-Kirkwood method; vapor pressure, orthobaric densities, density profiles, and Gibbs relative adsorption of the volatile component with respect to the heavy component were also obtained. The properties were studied as a function of the temperature, molar concentration of the heavy component, and the asymmetry of the mixture. According to the results of this work, the temperature loses influence on the surface tension, vapor pressure, and Gibbs relative adsorption curves as the molecular length of the heavy component increases. This suggests that the universal behavior observed in pure fluids of Lennard-Jones chains also holds for binary mixtures. The contribution of the long-range interactions turned out to account for about 60%, 20%, and 10% of the surface tension, vapor pressure, and orthobaric density final values, respectively. This contribution was even larger at high temperatures and for large molecules. Strong enrichment of the volatile component at the interface was observed in the asymmetric mixtures. One of these mixtures even showed a barotropic effect at elevated pressures and a class III phase behavior.

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.

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.

Determination of the Residual Entropy of Simple Mixtures by Monte Carlo Simulation.

Extensive Monte Carlo simulations were performed for (neon + krypton) mixtures for temperatures between 200 K and 600 K and pressures up to 1 GPa, using Lennard-Jones potentials to describe the intermolecular interactions. The residual entropies were obtained via Widom's insertion method, as well as via an integration technique. At high pressures, the residual entropy is, to a very good approximation, a linear function of λa-1, which is the reciprocal value of the average Monte Carlo displacement parameter that gives the acceptance ratio a for translational moves. The slope of this linear function varies linearly with the mole fraction and is related to the effective collision diameters of the molecules. As the displacement parameter is available during Monte Carlo simulations of fluids, its linearity with the residual entropy can be used to compute this properties with negligible computational effort at high densities, when particle insertion methods become unreliable.

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.

Characteristic Curves of the Lennard-Jones Fluid.

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

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.

Calculation of phase envelopes of fluid mixtures through parametric marching.

Two-dimensional cross-sections of the phase envelopes of fluid mixtures-in particular isotherms, isobars, and isopleths-are often computed point-by-point by incrementing a so-called marching variable and solving the equilibrium conditions at each step. The marching variable is usually pressure, temperature, or a mole fraction, depending on the application. These isolines, however, can have rather complicated shapes, so that a simple unidirectional "sweep" of the marching variable often gives merely a part of the desired isoline. It is then necessary to restart the sweep with different initial values, or to switch to another marching variable. This, however, makes it difficult to compute complete isolines automatically, without human interference. We propose here a new marching technique through which it is possible to follow isolines of arbitrary shape and thus to compute complete isolines, as long as they are contiguous.

Generalization of the friction theory for viscosity modeling.

The friction theory (FT) approach relates the viscosity of a fluid to its equation of state (EoS), and it is known to give good results for a large number of compounds over wide ranges of temperature and pressure. Previous FT versions were restricted to use EoS of the van der Waals type, i.e., EoS explicitly consisting of a repulsive and an attractive term, which limited the number of usable EoS as well as the accuracy of the viscosity predictions. In this work, the restriction is removed by means of a pragmatic generalized definition of repulsive and attractive terms based on the internal pressure concept. As a result, the FT theory can be extended to practically all types of EoS, from theoretical ones (e.g., EoS based on thermostatistical or renormalization theories) to the highly accurate empirical reference EoS. In combination with the later, the FT is shown to represent experimental viscosity data for several fluids, including water, with an accuracy as high as that required for reference models. Additionally, some relevant phenomena, such as the critical anomaly, appear to follow naturally from the physics already built into the EoS.

Unphysical Critical Curves of Binary Mixtures Predicted with GERG Models.

When applied to asymmetric binary mixtures (e.g., methane + pentane or heavier alkanes, hydrogen-containing mixtures), the GERG equation of state (GERG-2004 or GERG-2008) predicts critical curves with physically unreasonable temperature maxima above the critical temperature of the heavier component. These maxima are associated with physically impossible vapor-liquid equilibria. The phenomenon is probably caused by corrections for critical anomalies that were built into the empirical pure-fluid equations of state forming the foundation of the GERG model. These corrections ensure that the model represents thermodynamic data of pure fluids quite well even close to their critical points. For mixtures, however, the corrections can cause artifacts.

Calculating thermodynamic properties of an ionic liquid with Monte Carlo simulations with an orthorhombic and a cubic simulation box.

In contrast to the common usage of cubic simulation boxes, in this work simulations of the ionic liquid 1-n-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim][PF(6)]) were carried out in a dynamic orthorhombic simulation box over a temperature range from 313 to 373 K in a canonical harmonical simulation ensemble (NpT) with a united-atom potential based on quantum chemistry. The solubilities of the gases CO(2), CO, H(2), O(2), C(2)H(4), and H(2)O at infinite dilution were determined by means of the Widom test particle method; the results are compared with experimental data and simulation results obtained with a cubic simulation box. For gas potentials containing partial charges the results are in good agreement with the experimental data.