Towards a unified view of fluids

Influence of repulsion on entropy scaling and density scaling of monatomic fluids

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points. Comparisons to equations of state, literature data, and transport property correlations are made. Although the absolute transport property values within a given potential model class may strongly depend on the repulsive exponent, it is found that the repulsive steepness plays a negligible role when entropy scaling is applied. Hence, the plus-scaled transport properties of n, 6 Mie, exponential-six, and Tang-Toennies fluids lie basically on one master curve, which closely corresponds with entropy scaling correlations for the Lennard-Jones fluid. This trend is confirmed by literature data of n, 6 Mie, and exponential-six fluids. Furthermore, entropy scaling holds for state points where the Pearson correlation coefficient R is well below 0.9. The condition R > 0.9 for strongly correlating liquids is thus not necessary for the successful application of entropy scaling, pointing out that isomorph theory may be a part of a more general framework that is behind the success of entropy scaling. Density scaling reveals a strong influence of the repulsive exponent on this particular approach.

Structure of Simple Dipolar Water-Like Fluids: Primitive Model and Hard Tetrahedra

Dipolar versions of two qualitatively different types of simple short range model fluids which exhibit the phenomenon of hydrogen bonding and which could thus serve as a reference in equations of state for associating fluids have been considered: the primitive model of water descending from the TIP4P model and the fluid of hard tetrahedra. The hydrogen bonding structure exhibited by the latter model results from purely repulsive interactions whereas in the first model the "hydrogen bonding interaction" is explicitly incorporated in the model. Since the water molecules bear a strong dipole moment, the effect of the added dipole-dipole interaction on the structure of the two short-range models is therefore examined considering them both in the full and screened dipole-dipole modifications. It is found that the hydrogen bonding structure in the primitive model resulting from the site-site interactions is so strong that the additional dipole-dipole interaction has only a marginal effect on its structure and contributes thus only to the internal energy. On the contrary, even only a weak dipole-dipole interaction destroys the original hydrogen bonding structure of the hard tetrahedron fluid; to preserve it, a screened dipole-dipole interaction has to be used in the equation of state development.

Nonlocal density functional theory of water taking into account many-body dipole correlations: binodal and surface tension of 'liquid-vapour' interface

In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard-Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory, dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid-vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the electrostatic interactions at the many-body level is able to describe the liquid-vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid-vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Extended excluded volume: Its origin and consequences

In contrast to the common intuitive/speculative approach based on an analysis of thermodynamic or structural data of (nonpolar) fluids, the statistical mechanical approach is used to extend the excluded volume concept to all other types of fluids. The (extended) excluded volume incorporates, in addition to common nonelectrostatic interactions defining the shape and size of the molecules, also the short-range part of the repulsive interactions between the embedded Coulombic sites. In this study we show that the extended excluded volume concept correctly predicts the behavior of the partial molar volume (PMV) at infinite dilution in different solvents and, particularly, differences between nonpolar and associating solvents. The concept is then applied to estimate the PMV of methanol in water.

Excess equimolar radius of liquid drops

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from the radius defined by the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analyzed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated and shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter σ. In these simulations, the magnitude of the excess equimolar radius is shown to be smaller than σ/2. This suggests that the surface tension of liquid drops at the nanometer length scale is much closer to that of the planar vapor-liquid interface than reported in studies based on the mechanical route.

Rigid probe solutes in a smectic-A liquid crystal: an unconventional route to the latter's positional order parameters

Biphenylene and pyrene were dissolved in the nematic and smectic-A phases of the liquid crystal 4,4'-di-n-heptyl-azoxybenzene and the orientational order parameters of both solutes and solvent measured via proton and deuteron nuclear-magnetic-resonance spectroscopy. This new data set was then merged with the one previously obtained, formed by 4,4'-di-chloro-benzene and naphthalene as solutes in the same solvent, and the resulting overall data set analyzed with a statistical thermodynamic density-functional theory to provide positional-orientational distribution functions of the various solutes along with the smectic solvent's positional order parameters.

Water and aqueous solutions: simple non-speculative model approach

Different ways of molecular modeling of water are analyzed and their similarities and differences identified. An up-to-date summary of achievements of a general approach to common rigid site-site interaction models of molecular fluids applied to water and aqueous solutions is then presented and discussed. The method is based on considering only a short-range part of a total realistic potential (such as SPC/E or TIPxP) which determines the structure of water (and fluids in general). A simplification of the interactions at short intermolecular separations leads then to simple models, called primitive models. Quite accurate results in an analytic form for the thermodynamic properties of the models are obtained using the thermodynamic perturbation theory. It is shown that the properly constructed primitive models reproduce, qualitatively, anomalies of pure water and basic characteristics of hydrophobic hydration. The concept of an extended excluded volume, based on pseudo-hard bodies, is introduced and exemplified by considering the partial molar volume of apolar solutes. Potential future development towards a theory of water based on the primitive models as a reference with the long-range contributions added as a perturbation is discussed.

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.

Primitive models of patchy colloidal particles. A review

In this article I will review some recent studies of the phase behavior and of the self-assembly of patchy colloidal particles. These studies have been based on simple primitive models for colloid–colloid interactions, effectively extending to soft matter the seminal work of I. Nezbeda on associated fluids. I will discuss the possibilities offered by the study of the self-assembly of particles with limited valence in deepening our understanding of the onset of the liquid state, of the differences between gels and glasses and of the possible connection between physical and chemical gels. A review with 55 references.

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However, truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equation defined with a Gaussian-smoothed charge density. We apply LMF theory to 3 simple molecular systems that exhibit different aspects of the failure of a naïive application of spherical truncations-water confined between hydrophobic walls, water confined between atomically corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system, in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.

Toward a statistical mechanical theory for water: Analytical theory for a short-ranged reference system

Starting from a realistic Hamiltonian and making use of recent findings that the properties of associating fluids are determined primarily by short-ranged interactions, this methodology has been implemented using statistical mechanical approaches and thermodynamic perturbation theory for the TIP4P model of water. We focus on the short-range reference system for which an analytic expression for the Helmholtz free energy is derived. It is found that the model (reference system) exhibits, in addition to a faithful representation of the structure of water, the same features that are characteristic for real water, namely, (i) the temperature of the density maximum and its pressure dependence, including the inflection point at high pressures and (ii) the temperature minima of the constant pressure heat capacity and the coefficient of isothermal compressibility.

Slow dynamics in a primitive tetrahedral network model

We report extensive Monte Carlo and event-driven molecular dynamics simulations of the fluid and liquid phase of a primitive model for silica recently introduced by Ford et al. [J. Chem. Phys. 121, 8415 (2004)]. We evaluate the isodiffusivity lines in the temperature-density plane to provide an indication of the shape of the glass transition line. Except for large densities, arrest is driven by the onset of the tetrahedral bonding pattern and the resulting dynamics is strong in Angell's classification scheme [J. Non-Cryst. Solids 131-133, 13 (1991)]. We compare structural and dynamic properties with corresponding results of two recently studied primitive models of network forming liquids-a primitive model for water and an angular-constraint-free model of four-coordinated particles-to pin down the role of the geometric constraints associated with bonding. Eventually we discuss the similarities between "glass" formation in network forming liquids and "gel" formation in colloidal dispersions of patchy particles.

Molecular dynamics comparative study of Lennard-Jones -6 and exponential -6 potentials: application to real simple fluids (viscosity and pressure)

In this work, using molecular dynamics simulation, the viscosity (dynamic property) and the pressure (static property) of spherical fluid particles interacting through Lennard-Jones -6 and exponential -6 potentials are computed. Simulations are performed for going from 10 to 20 for the Lennard-Jones potential and from 12 to 22 for the exponential one. Six different thermodynamic states are tested that cover a large range of conditions, from sub- to supercritical temperature and from low to high density. To compare in a consistent manner the results for the various potentials tested, the simulations are carried out for the same set of reduced thermodynamic conditions (using the critical point). It is found that a perfect corresponding-states formulation is not possible between these potentials. Then, these potentials are applied on real simple fluids (argon, oxygen, nitrogen, methane, ethane, and one mixture, air) and the calculated viscosity and pressure values are compared with reference values. It appears that, using the appropriate , both potential families lead to a good accuracy in pressure and viscosity using the same set of molecular parameters for both properties, the average absolute deviations being always lower than 5% for the studied states. In addition, it is shown that the exponential potential results do not outperform the Lennard-Jones ones. Furthermore, for all compounds except for methane, the best results are obtained for the Lennard-Jones 12-6 and the exponential 14-6 potentials. This result partly explains why, despite no theoretical background, the Lennard-Jones 12-6 potential is so widely used. Finally, it is shown that a van der Waals one-fluid model performs extremely well for the studied mixture (air).

A general perturbation approach for equation of state development: Applications to simple fluids, ab initio potentials, and fullerenes

A new perturbation scheme based on the Barker-Henderson perturbation theory [J. Chem. Phys. 47, 4714 (1967)] is proposed to predict the thermodynamic properties of spherical molecules. Accurate predictions of second virial coefficients and vapor-liquid coexistence properties are obtained for a large variety of potential functions (square well, Yukawa, Sutherland, Lennard-Jones, Buckingham, Girifalco). New Gibbs ensemble Monte Carlo simulations of the generalized exp-m Buckingham potential are reported. An extension of the perturbation approach to mixtures is proposed, and excellent predictions of vapor-liquid equilibria are obtained for Lennard-Jones mixtures. The perturbation scheme can be applied to complex potential functions fitted to ab initio data to predict the properties of real molecules such as neon. The new approach can also be used as an auxiliary tool in molecular simulation studies, to efficiently optimize an intermolecular potential on macroscopic properties or match force fields based on different potential functions.

Effect of the Range of Interactions on the Properties of Fluids. 2. Structure and Phase Behavior of Acetonitrile, Hydrogen Fluoride, and Formic Acid

To complete the study on the effect of the long-range part of Coulombic interactions on properties of complex polar and associating fluids, we have investigated in detail three compounds with extreme features: acetonitrile for its unusually large dipole moment, hydrogen fluoride with very strong hydrogen bonding, and formic acid for its potential formation of different n-mers in liquid and gaseous phases. The effect of the long-range Coulombic interactions on both the structure and thermodynamics of the homogeneous phase, and on the vapor-liquid equilibria has been examined using the same decomposition of realistic potential models into a short-range part and a residual part as in the previous paper [Kettler, M.; et al. J. Phys. Chem. B 2002, 106, 7537-7546]. The present results fully confirm the previous findings that the properties of polar and associating systems are determined primarily by the short-range interactions regardless of their nature, i.e., contributions arising from the long-range interactions constitute only a small portion of the total properties, and thus that the short-range potential counterpart of full realistic models can be used as a convenient reference for a successful perturbation expansion.