Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Simple statistical thermodynamic model of the heteroaggregation and gelation of dispersions and emulsions

The heteroaggregation behaviour of mixtures of equal-sized particles (type A+type B) exhibiting short-ranged attractive interactions is investigated using the sticky hard-sphere model. The average cluster size is calculated as a function of the total particle volume fraction, the binary mixture composition, and the A-B stickiness interaction parameter τ(AB)(-1). We show that a value of τ(AB)(-1)=10(2), equivalent to an attractive well depth of ～5kT in a realistic continuous pair potential, leads to a state of heteroaggregation just below the gelation threshold of the equimolar mixture of volume fraction 0.1. We discuss the conditions under which the assumptions of this statistical thermodynamic model are satisfied experimentally, with particular reference to recent data on the heteroaggregation behaviour of protein-stabilized emulsions and latex particle dispersions.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Electrolytes in a nanometer slab-confinement: ion-specific structure and solvation forces

We study the liquid structure and solvation forces of dense monovalent electrolytes (LiCl, NaCl, CsCl, and NaI) in a nanometer slab-confinement by explicit-water molecular dynamics (MD) simulations, implicit-water Monte Carlo (MC) simulations, and modified Poisson-Boltzmann (PB) theories. In order to consistently coarse-grain and to account for specific hydration effects in the implicit methods, realistic ion-ion and ion-surface pair potentials have been derived from infinite-dilution MD simulations. The electrolyte structure calculated from MC simulations is in good agreement with the corresponding MD simulations, thereby validating the coarse-graining approach. The agreement improves if a realistic, MD-derived dielectric constant is employed, which partially corrects for (water-mediated) many-body effects. Further analysis of the ionic structure and solvation pressure demonstrates that nonlocal extensions to PB (NPB) perform well for a wide parameter range when compared to MC simulations, whereas all local extensions mostly fail. A Barker-Henderson mapping of the ions onto a charged, asymmetric, and nonadditive binary hard-sphere mixture shows that the strength of structural correlations is strongly related to the magnitude and sign of the salt-specific nonadditivity. Furthermore, a grand canonical NPB analysis shows that the Donnan effect is dominated by steric correlations, whereas solvation forces and overcharging effects are mainly governed by ion-surface interactions. However, steric corrections to solvation forces are strongly repulsive for high concentrations and low surface charges, while overcharging can also be triggered by steric interactions in strongly correlated systems. Generally, we find that ion-surface and ion-ion correlations are strongly coupled and that coarse-grained methods should include both, the latter nonlocally and nonadditive (as given by our specific ionic diameters), when studying electrolytes in highly inhomogeneous situations.     

On the use of multiple interpolation functions in scaled particle theory to improve the predictions of the properties of the hard-sphere fluid

We present a modification to a previously proposed method of adapting scaled particle theory (SPT) to an arbitrary hard-sphere equation of state that satisfies a large number of exact SPT conditions, including thermodynamic consistency. By introducing a set of functions to interpolate the density of hard-spheres centers at the cavity surface, a broad range of hard-sphere properties, in particular the planar surface tension and related properties, are predicted with high accuracy as compared to simulation data. Similarly accurate results are obtained when this modified interpolation scheme is incorporated into a self-consistent version of SPT, i.e., an equation of state is a predicted output of the method. Hence, SPT is now able to closely match the surface thermodynamic properties of the hard-sphere fluid either without using any adjustable parameters or by simply setting the pressure and chemical potential via a reliable equation of state. We also consider other interpolation schemes, some of which better represent certain exact relations that can be derived within SPT. The limited success of these more rigorous approaches provides insights into the various trade-offs between the simplicity and rigor of the chosen interpolation method, as well as the accuracy of the results, that arise in any (inexact) version of SPT.     

Surface tension and capillary waves at the nematic-isotropic interface in ternary mixtures of liquid crystal, colloids, and impurities

In mixtures of thermotropic liquid crystals with spherical poly(methyl methacrylate) particles, self-supporting networklike structures are formed during slow cooling past the isotropic-to-nematic phase transition. Experimental results support the hypothesis that a third component, alkane remnants slowly liberated from the particles, plays a crucial role. A theoretical model, based on the phenomenological Landau-de Gennes, Carnahan-Starling, and hard-sphere crystal theories, is developed to describe the continuous phase separation in a ternary nematic-impurity-colloid mixture. The interfacial tension and the dispersion relation of the surface modes of the nematic-isotropic interface are determined. The colloids decrease the interfacial tension and the damping rate of surface waves, whereas impurities act in an opposite way. This should strongly influence the formation of abovementioned networklike structures and could help explain some of their rheological properties.     

On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface

The long-range corrections (LRCs) to the configurational energy have been taken into consideration in the Monte Carlo simulation of the vapor-liquid interface for a pure Lennard-Jones (LJ) fluid. The simulated bulk densities agree satisfactorily with those obtained from the Gibbs ensemble method, and the simulated surface tension values agree reasonably well with those reported in the literature for a larger number of molecules and a larger cut-off distance. To compare the influence of the potential forms on the simulation results, a truncated LJ potential, and a shifted and truncated LJ potential have been examined. Although the bulk densities and surface tensions calculated for different model fluids are strongly affected by the LRC, the different potentials essentially lead to similar density values and similar surface tension values when the respective calculated values are compared on the basis of a reduced temperature scale.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Communication: inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency.     

Sulfur hexafluoride's liquid-vapor coexistence curve, interfacial properties, and diffusion coefficients as predicted by a simple rigid model

We present here molecular-dynamics simulation results of the vapor-liquid coexistence curve, surface tension, and self-diffusion coefficients of sulfur hexafluoride. Sulfur hexafluoride is modeled as a rigid molecule, following the model proposed by Pawley [Mol. Phys. 43, 1321 (1981)]. Vapor-liquid coexistence curve and surface tension are obtained through direct molecular-dynamic simulations in the NVT ensemble. Simulation results are able to reproduce the qualitative shape of the vapor-liquid envelope. However, lower densities, a higher critical temperature, and an overestimated surface tension are obtained here. Those deviations are explained on the basis of the rigidity of the molecular model used. Self-diffusion coefficients are calculated from simulations in the NVE ensemble for different gas states at atmospheric pressure. The rigid model performs better for dynamical properties since simulation results provide very good agreement with available experimental data in this case.     

A theory of a curved vapor-liquid separation boundary: The lattice gas model

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.     

A Hard-Sphere Scheme Used to Model the Viscosity of Two Ternary Mixtures up to 100 MPa

Abstract

Recently, an extensive experimental study of two different ternary mixtures has been undertaken which aimed at showing the effect of composition, temperature and pressure on viscosity and density. The ternary mixture heptane + methylcyclohexane + 1-methylnaphtalene has been chosen as it can be, in some ways, a synthetic representation of a C₅₊ distillation fraction of a petroleum crude oil. The ternary mixture water + diacetone-alcohol + 2-propanol has the distinctive feature of involving components which have important interactions. The key issue of this study is the fairly high number of samples within the ternary diagram, as the first mixture is described by 45 compositions and the second one by 66 compositions. The viscosity of both mixtures have then been measured at three temperatures (303.15, 323.15, and 343.15K) and 6 pressures (0.1, 20,40,60,80 and 100 MPa) using a high pressure falling body viscometer which allowed to collect 1998 experimental data.

Our entire set of data have then been used to test the hard-sphere scheme developed by J. H. Dymond and M. J. Assael. This model has been developed in order to correlate simultaneously thermal conductivity, viscosity and self-diffusion coefficient data for a wide range of temperature and pressure and is derived from the hard-sphere theory.

We have only used the procedure to estimate viscosity and very good results (absolute average deviation equal to 2.3%) are obtained.     

Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials

A novel test-area (TA) technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface (the relation of Kirkwood and Buff [J. Chem. Phys. 17, 338 (1949)]). For particles interacting through discontinuous intermolecular potentials (e.g., hard-core fluids) this involves the determination of delta functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two (or more) systems with different interfacial areas (the method of Bennett [J. Comput. Phys. 22, 245 (1976)]), which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo (TAMC) simulations are compared with the data obtained with other techniques (e.g., mechanical and free-energy differences) for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo (TAMC) or molecular-dynamics (TAMD) algorithms for different types of interfaces (vapor-liquid, liquid-liquid, fluid-solid, etc.) of pure systems and mixtures consisting of complex polyatomic molecules.     

The influence of interactions between reagents on the excess in the rate of quenching reaction: molecular dynamics study

The influence of the interactions between reagents on the excess in the rate coefficient, Deltak, for the instantaneous reaction A+B-->C+B have been investigated by performing large scale molecular dynamics simulations for simple soft spheres. The simulation method has enabled us to determine the contributions to Deltak coming from A-B as well as B-B interactions. The simulations have shown that positive values of Deltak that appear both for the liquid and for the Brownian system [M. Litniewski, J. Chem. Phys. 123, 124506 (2005); 124, 114501 (2006)] result from B-B interactions. If B-B interactions were absent, Deltak was always negative. The influence of B-B interactions was about three times higher for the Brownian system than for the liquid. A qualitative explanation for the effect has been proposed basing on a simple model and analyzing the influence of B-B interactions on fluctuations in concentrations of reagents. The influence of A-B interactions was completely negligible except for the liquid at short times, for which the cancellation of A-B interaction noticeably decreased Deltak.