The rotation-libration transition in molecular ortho-D2 under pressure

The pressure-induced transition at low temperature in crystalline ortho-D₂ from free rotation of molecules to libration about a prefered direction is evaluated by a Monte Carlo procedure and the equation of state given by Silvera and Goldman. The result is 270 ± 5 kbar, in very good agreement with the value of 278 kbar, at 5 K measured by Silvera and Wijngaarden.     

Phase coexistence and critical point determination in polydisperse fluids

Phase equilibria of fluids with variable size polydispersity have been investigated by means of Monte Carlo simulations. In the models, spherical particles of different additive diameters interact through Lennard-Jones and hard sphere Yukawa intermolecular potentials and the underlying distribution of particle sizes is a Gaussian. The Gibbs ensemble Monte Carlo technique has been applied to determine the phase coexistence far below the critical temperature. Critical points have been estimated by finite-size scaling analysis using histogram reweighting for NpT simulation data. In order to achieve efficient sampling in the vicinity of the critical points, the hyper-parallel tempering scheme has been utilized.     

Structural and thermodynamic properties of the restricted primitive model electrolyte in a mixture with uncharged hard spheres: a grand canonical Monte Carlo simulation and integral equation study

A restricted primitive model electrolyte in a mixture with uncharged hard spheres was studied at room temperature using grand canonical Monte Carlo computer simulation and Ornstein–Zernike integral equation theory in the hypernetted chain approximation (HNC). The mean spherical approximation results are also presented for a few cases. We obtained the pair distribution functions of species of the system, the dependencies of the total fluid density and the ionic fraction on the chemical potentials, the excess internal energy and the heat capacity at constant volume for a wide range of chemical potentials of the species from the simulations and HNC theory. In the majority of cases, good agreement between the theoretical predictions and simulation data is obtained. The composition of the mixture is determined by the chemical potentials of both species. The pair distribution functions have a Debye-like shape at low densities for various values of the ion fraction. By increasing the chemical potential of the uncharged component, weak trends for structuring of the solution are observed with the formation of ion-hard sphere-ion complexes. At high densities, a tendency for in-phase oscillations of ion–ion functions is observed similar to the pure electrolyte in the restricted primitive model. We analysed the chemical potential–density and the chemical potential–ion fraction projections of the equation of state in detail. Also, the heat capacity at constant volume has been calculated for the first time. The model and the results are useful for the development of the theory of inhomogeneous fluid mixtures.     

Hydrogen bonding in water

Computer simulations using density functional theory based ab initio path integral molecular dynamics have been carried out to investigate hydrogen bonding in water under ambient conditions. Structural predictions for both H2O and D2O, which include the effects of zero-point energy, thermal motion, and many body polarization effects, are contrasted with classical simulations that ignore nuclear quantum effects. The calculated effect of H/D isotope substitution on the water structure is much smaller than the difference between the classical and quantum path integral results, and is in excellent agreement with the measured H/D difference data from both neutron and x-ray scattering.     

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.     

Generalized surface thermodynamics with application to nucleation

Gibbs formulated a complete and general thermodynamics for surfaces in multicomponent fluid systems. When considering solid–fluid surfaces, he restricted attention to single-component solids in contact with fluids that could contain multiple components. Attempts that have been offered to generalize Gibbs’ results for surfaces between multicomponent solids and fluid are problematic owing to the difficulty that the surface chemical potentials for components that also reside on substitutional lattice sites in the solids are not well defined. Therefore any expressions involving these surface chemical potentials, such as the conventional definition of the surface energy, will also not be well defined. In order to formulate a general thermodynamics of equilibrium that takes into account capillary effects in systems containing surfaces between a multicomponent solids and fluids, it is shown that the concept of thermodynamic availability (exergy) can be employed that, when applied to surfaces, depends on the extensive but not the intensive variables (such as the chemical potentials) of the surfaces. Using this approach, Gibbs–Thomson–Freundlich effects for finite-size solids, an adsorption equation for solid–fluid surfaces and the thermodynamics of nucleation during solidification can be treated in a straightforward manner without referring to the ill-defined surface chemical potentials. A derivation is given that appears to be the first one that properly generalizes Gibbs’ analysis for the reversible work to form a critical nucleus to the case of solidification.     

Molecular dynamics simulations of PVP kinetic inhibitor in liquid water and hydrate/liquid water systems

The possible effects of PVP (poly(N-vinylpyrrolidone)) on the properties of liquid and water in clathrate hydrate has been investigated using NVT molecular dynamics simulations. A model for a monomer of the PVP polymer is immersed in three systems, liquid water, a unit cell of a hydrate in liquid water with a hydrate former and a third system where some of the liquid water molecules of this last system are replaced by a PVP monomer. Both molecular dynamics simulation and integral equation theory predict hydrogen bonding between the double bonded oxygen in the PVP ring and hydrogens in water. For the composite system, the PVP monomer has a preference for hydrogen bonding to hydrogens from the water molecules at the surface of the hydrate lattice. The simulations indicate that the PVP monomer tends to orient perpendicular to the hydrate surface. For the model systems in this study PVP may form hydrogen bonds with liquid water through the double bonded oxygen in the ring. When a hydrate crystal is immersed in the liquid water phase this hydrogen bonding is shifted towards the hydrate due to a more favourable Coulomb interaction involving hydrogens from more than one water molecule at the hydrate surface. The PVP monomer has a preference for perpendicular orientation with respect to the hydrate surface. A scheme is suggested for the characterization of kinetic hydrate inhibitors based on molecular dynamics simulations and on three basic properties. In addition to the energy between the active groups of the inhibitor and hydrate water another point of focus is the free energy changes in the interactions between the inhibitor and water as the charges are changed from zero to the original model charges. In particular the difference between this integral for the (hydrate water)–(PVP monomer) interaction and the (liquid water)–(PVP inhibitor) interaction should reflect the driving forces in freezing the inhibitor out from the liquid water phase and onto the hydrate surface. The third property in the characterization scheme is the diffusivities of groups connecting to the hydrate crystal, relative to the diffusivities of the hydrate crystal. Results are presented from simulations where a small cavity with a methane model as a guest is immersed in liquid water with free methane molecules at a temperature of 150K. Changes in structure, diffusivities and energy indicate a tendency towards a more solid–like structurde around the cavity.     

Quantum fluids in the Kähler parametrization

In this Letter we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the Kähler parametrization. This fluid model describes a large set of interesting systems such as the power law energy density fluids, Chaplygin gas, etc. In order to maintain the generality of the model, we apply the BRST method in the reduced phase space in which the fluid degrees of freedom are just the fluid potentials and the fluid current is classically resolved in terms of them. We determine the physical states in this setting, the time evolution and the path integral formulation.     

Simulation of fluid-solid coexistence via thermodynamic integration using a modified cell model

Despite recent advances, precise simulation of fluid-solid transitions still remains a challenging task. Thermodynamic integration techniques are the simplest methods to study fluid-solid coexistence. These methods are based on the calculation of the free energies of the fluid and the solid phases, starting from a state of known free energy which is usually an ideal-gas state. Despite their simplicity, the main drawback of thermodynamic integration techniques is the large number of states that must be simulated. In the present work, a thermodynamic integration technique, which reduces the number of simulated states, is proposed and tested on a system of particles interacting via an inverse twelfth-power potential energy function. The simulations are implemented at constant pressure and the solid phase is modeled according to the constrained cell model of Hoover and Ree. The fluid and the solid phases are linked together by performing constant-pressure simulations of a modified cell model. The modified cell model, which was originally proposed by Hoover and Ree, facilitates transitions between the fluid and the solid phase by tuning a homogeneous external field. This model is simulated on a constant-pressure path for a series of progressively increasing values of the field, thus allowing for direct determination of the free energy difference between the fluid and the solid phase via histogram reweighting. The size-dependent results are analyzed using histogram reweighting and finite-size scaling techniques. The scaling analysis is based on studying the size-dependent behavior of the second- and higher-order derivatives of the free energy as well as the dimensionless moment ratios of the order parameter. The results clearly demonstrate the importance of accounting for size effects in simulation studies of fluid-solid transitions.     

A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble

A grand canonical Monte Carlo (GCMC) simulation method is presented for the determination of the phase equilibria of mixtures. The coexistence is derived by expanding the pressure into a Taylor series as a function of the temperature and the chemical potentials that are the independent intensive variables of the grand canonical ensemble. The coefficients of the Taylor series can be calculated from ensemble averages and fluctuation formulae that are obtained from GCMC simulations in both phases. The method is able to produce the equilibrium data in a certain domain of the (T, p) plane from two GCMC simulations. The vapour-liquid equilibrium results obtained for a Lennard-Jones mixture agree well with the corresponding Gibbs ensemble Monte Carlo data.     

Heterogeneity of activated carbons in adsorption of phenols from aqueous solutions—Comparison of experimental isotherm data and simulation predictions

Surface heterogeneity of activated carbons is usually characterized by adsorption energy distribution (AED) functions which can be estimated from the experimental adsorption isotherms by inverting integral equation. The experimental data of phenol adsorption from aqueous solution on activated carbons prepared from polyacrylonitrile (PAN) and polyethylene terephthalate (PET) have been taken from literature. AED functions for phenol adsorption, generated by application of regularization method have been verified. The Grand Canonical Monte Carlo (GCMC) simulation technique has been used as verification tool. The definitive stage of verification was comparison of experimental adsorption data and those obtained by utilization GCMC simulations. Necessary information for performing of simulations has been provided by parameters of AED functions calculated by regularization method.     

Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.     

The phase coexistence method to obtain surface free energies and nucleation barriers: a brief review

ABSTRACT

A recently developed method where one analyses the finite size effects associated with liquid–solid phase equilibria including vapour–crystal coexistence is briefly reviewed. It is shown that the estimation of the chemical potential of the vapour surrounding the crystal as function of the crystal volume yields information on the bulk coexistence conditions, when an extrapolation to the thermodynamic limit is performed. Estimating the pressure of the fluid surrounding the crystal nucleus in the finite simulation box and the volume of this nucleus that coexists with the fluid in thermal equilibrium, an estimate for the total surface excess free energy can be obtained, which to a very good approximation is independent of the size of the simulation box. The free energy barrier against homogeneous nucleation of crystals thus can be estimated as a function of the nucleus volume. Monte Carlo simulations for the soft effective Asakura–Oosawa model of colloid-polymer mixtures which form face-centered cubic colloidal crystals are used to exemplify this method, computing the surface excess free energy of these crystals over a wide range of crystal volumes, without the need to characterise the non-spherical crystal shape. A possible extension of these concepts to heterogeneous nucleation is also briefly discussed.     

Quantum nuclear effects on the location of hydrogen above and below the palladium (100) surface

We report ab initio path integral molecular dynamics simulations of hydrogen and deuterium adsorbed on and absorbed in the Pd(100) surface at 100 K. Significant quantum nuclear effects are found by comparing with conventional ab initio molecular dynamics simulations with classical nuclei. For on-surface adsorption, hydrogen resides higher above the surface when quantum nuclear effects are included, an effect which brings the computed height into better agreement with experimental measurements. For sub-surface absorption, the classical and quantum simulations differ in an even more significant manner: the classically stable subsurface tetrahedral position is unstable when quantum nuclear effects are accounted for. This study provides insight that aids in the interpretation of experimental results and, more generally, underscores that despite the computational cost ab initio path integral molecular dynamics simulations of surface and subsurface adsorption are now feasible.     

Critical evaluation and thermodynamic modeling of the Mn–Cr–O system for the oxidation of SOFC interconnect

A complete critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties of the Mn–Cr–O system at 1 bar total pressure are presented. Optimized equations for the thermodynamic properties of all phases are obtained, which reproduce all available and reliable thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions and oxygen partial pressures. As results of optimization, the Gibbs energy function of MnCr₂O₄ is for the first time properly estimated and the discrepancies of the phase diagram experiments of the Mn–Cr–O system are resolved. In particular, unexplored phase diagrams and thermodynamic properties of the Mn–Cr–O system of importance for the oxidation of SOFC interconnect are predicted on the basis of the optimized model parameters. The database of the model parameters can be used along with software for Gibbs energy minimization in order to calculate any type of phase diagram sections and thermodynamic properties.     

Phase coexistence and dynamic properties of water in nanopores

The dynamical properties of a confined fluid depend strongly on the (spatially varying) density. Its knowledge is therefore an important prerequisite for molecular-dynamics (MD) simulations and the analysis of experimental data. In a mixed Gibbs ensemble Monte Carlo (GEMC)/MD simulation approach we first apply the GEMC method to find possible phase states of water in hydrophilic and hydrophobic nanopores. The obtained phase diagrams evidence that a two-phase state is the most probable state of a fluid in incompletely filled pores in a wide range of temperature and level of pore filling. Pronounced variations of the average and local densities are observed. Subsequently, we apply constant-volume MD simulations to obtain water diffusion coefficients and to study their spatial variation along the pore radius. In general, water diffusivity slightly decreases in a hydrophilic pore and noticeably increases in a hydrophobic pore (up to about 40% with respect to the bulk value). In the range of gradual density variations the local diffusivity essentially follows the inverse density and the water binding energy. The diffusivity in the quasi-two-dimensional water layers near the hydrophilic wall decreases by 10 to 20% with respect to the bulk value. The average diffusivity of water in incompletely filled pore is discussed on the basis of the water diffusivities in the coexisting phases.Received: 1 January 2003, Published online: 14 October 2003PACS: 61.20.Ja Computer simulation of liquid structure - 64.70.Fx Liquid-vapor transitions     

Parallelized sampling of the Gibbs ensemble

An expression for the probability distribution of NVT-like sub-ensembles constituting the Gibbs ensemble is derived. Knowledge of this distribution makes it possible to carry out the simulation without the explicit exchange of real particles between the simulation boxes and to evaluate directly any Gibbs ensemble average from a series of independent simultaneous simulations (Monte Carlo or molecular dynamics) performed on a set of NVT-likt sub-ensembles with the fixed distribution of particles. An implementation of the method, which is tailored mainly for complex systems, is exemplified for the square-well fluid, and its efficiency and results are compared with those obtained from the conventional Gibbs ensemble simulations.     

Thermodynamic and transport properties of nitrogen and butane mixtures

A force field has been developed to describe the phase behaviour, interfacial, and transport properties of nitrogen and hydrocarbon mixtures under conditions relevant to those found in the high pressure extraction of oil from underground reservoirs. A Gibbs ensemble Monte Carlo method is used to parametrize intermolecular potentials for the pure components by matching experimental and simulated liquid and vapour coexisting densities. Also the surface tension, diffusion coefficient and shear viscosity of nitrogen and its mixtures with butane have been determined. The latter properties were obtained by canonical molecular dynamics simulations. The diffusion coefficient and shear viscosity were calculated by a Green-Kubo method. Results for pure nitrogen are given for temperatures ranging from 70 K to 110K. For mixtures of nitrogen with butane, results are presented at 339.4 K and 380.2 K. Good agreement is found between the results of simulations and available experimental data.     

Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions

The Green’s function associated with a Klein–Gordon particle moving in a D-dimensional space under the action of vector plus scalar q-deformed Hulthén potentials is constructed by path integration for \({q \geq 1}\) and \({\frac{1}{\alpha} \ln q < r < \infty}\). An appropriate approximation of the centrifugal potential term and the technique of space-time transformation are used to reduce the path integral for the generalized Hulthén potentials into a path integral for q-deformed Rosen–Morse potential. Explicit path integration leads to the radial Green’s function for any l state in closed form. The energy spectrum and the correctly normalized wave functions, for a state of orbital quantum number \({l \geq 0}\), are obtained. Eventually, the vector q-deformed Hulthén potential and the Coulomb potentials in D dimensions are considered as special cases.