Vapor-liquid and vapor-solid phase equilibria for united-atom benzene models near their triple points: the importance of quadrupolar interactions

Gibbs ensemble Monte Carlo simulations were used to calculate the vapor-liquid and vapor-solid coexistence curves for benzene using two simple united-atom models. An extension of the Gibbs ensemble method that makes use of an elongated box containing a slab of the condensed phase with a vapor phase along one axis was employed for the simulations of the vapor-solid equilibria and the vapor-liquid equilibria at very low reduced temperatures. Configurational-bias and aggregation-volume-bias Monte Carlo techniques were applied to improve the sampling of particle transfers between the two simulation boxes and between the vapor and condensed-phase regions of the elongated box. An isotropic united-atom representation with six Lennard-Jones sites at the positions of the carbon atoms was used for both force fields, but one model contained three additional out-of-plane partial charge sites to explicitly represent benzene's quadrupolar interactions. Both models were fitted to reproduce the critical temperature and density of benzene and yield a fair representation of the vapor-liquid coexistence curve. In contrast, differences between the models are very large for the vapor-solid coexistence curve. In particular, the lack of explicit quadrupolar interactions for the 6-site model greatly reduces the energetic differences between liquid and solid phases, and this model yields a triple point temperature that is about a factor of 2 too low. In contrast, the 9-site model predicts a triple point of benzene at T = 253 +/- 6 K and p = 2.3 +/- 0.8 kPa in satisfactory agreement with the experimental data (T = 278.7 K and p = 4.785 kPa).     

Critical properties of aluminum

Gibbs ensemble Monte Carlo calculations are performed using a validated embedded-atom potential to obtain the vapor-liquid coexistence curve for elemental aluminum in good agreement with available experimental data up to the boiling point. These calculations are then extended to make a reliable prediction of the critical temperature, pressure, and density of Al, which have previously been known only with very large uncertainties. This demonstrates the ability of modern simulations to predict fundamental physical properties that are extremely difficult to measure directly.     

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.     

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.     

Investigation of the phase behavior of an embedded charge protein model through molecular simulation

The phase behavior of an embedded-charge model for lysozyme developed by Carlsson and co-workers (J. Phys. Chem. B 2001, 105, 9040) is investigated using grand canonical transition matrix Monte Carlo simulation. Within this model, protein-protein interactions are approximated through a combination of hard-sphere repulsion, isotropic hydrophobic attraction, and screened electrostatic interactions through a series of embedded point charges located at the positions of charged amino acid groups within lysozyme. Liquid-liquid phase diagrams are constructed for a wide range of solution conditions and compared with experimental data. Our results indicate that the model is generally capable of describing qualitative trends in the evolution of protein phase behavior with variation of pH and ionic strength. From a quantitative perspective, model estimates for both the change in critical temperature with variation of the solution conditions and the critical concentration do not agree with experimental results. We find the width of model coexistence curves to be independent of solution conditions and narrow relative to experimentally obtained phase envelopes. Connections between the value of the second virial coefficient evaluated at the critical temperature and the location of the liquid-liquid phase envelope are also examined.     

Effects of three-body intermolecular interactions on the nematic—paranematic phase diagram

An extension of the Maier—Saupe theory of the nematic—isotropic transition in liquid crystals, which incorporates three-body intermolecular interactions into the effective single-particle pseudopotential, is presented. Numerical calculations based on this theory are performed to investigate the effect of these three-body interactions on the nematic—isotropic transition in zero field, on the nematic—paranematic coexistence curve in the presence of an applied field, and on the mean field nematic—paranematic critical point. The zero field results are in good agreement with experimental measurements.     

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.     

The nonmetal-metal transition and phase separation in the europium-ammonia system

The coexistence curve of EuNH₃ solutions has been determined by visual observation and electron paramagnetic resonance (EPR). A nonmetal-metal transition is evident in EuNH₃ solutions, and the miscibility gap is the most pronounced among the metal-ammonia (MNH₃) systems that have been studied. The critical concentration and temperature are 1.30 mole% metal and 321 K, respectively. The coexistence curve has a parabolic shape within close vicinity of the critical point, which strongly suggests the existence of long-range interactions and cluster formation. EPR spectra indicate that the cation-electron interactions in these solutions are weak, so that the valence-electron concentration in MNH₃ solutions is probably the primary factor in determining the nature of the nonmetal-metal transition. The coexistence curve and associated critical parameters for EuNH₃ solutions are compared to those obtained for other MNH₃ solutions.     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

Density inhomogeneity and diffusion behavior of fluids in micropores by molecular-dynamics simulation

The density profiles and the diffusion behavior of fluid argon confined in micropores were studied by molecular-dynamics simulations. The effects of pore size (width), temperature and number density on the density profiles and the self-diffusion coefficients in micropores were simulated with pore widths from 0.6 to 4.0 nm. The density profiles are greatly affected by the pore size. Strong inhomogeneities in the channel direction and vapor-liquid phase separation in the micropores were observed when initial conditions were chosen in the coexistence region of the fluid. The self-diffusion coefficient in the channel direction in the pores was found to be much lower than in the bulk, and decreasing with decreasing pore size, decreasing temperature, and increasing density.     

An advanced Gibbs-Duhem integration method: theory and applications

The conventional Gibbs-Duhem integration method is very convenient for the prediction of phase equilibria of both pure components and mixtures. However, it turns out to be inefficient. The method requires a number of lengthy simulations to predict the state conditions at which phase coexistence occurs. This number is not known from the outset of the numerical integration process. Furthermore, the molecular configurations generated during the simulations are merely used to predict the coexistence condition and not the liquid- and vapor-phase densities and mole fractions at coexistence. In this publication, an advanced Gibbs-Duhem integration method is presented that overcomes above-mentioned disadvantage and inefficiency. The advanced method is a combination of Gibbs-Duhem integration and multiple-histogram reweighting. Application of multiple-histogram reweighting enables the substitution of the unknown number of simulations by a fixed and predetermined number. The advanced method has a retroactive nature; a current simulation improves the predictions of previously computed coexistence points as well. The advanced Gibbs-Duhem integration method has been applied for the prediction of vapor-liquid equilibria of a number of binary mixtures. The method turned out to be very convenient, much faster than the conventional method, and provided smooth simulation results. As the employed force fields perfectly predict pure-component vapor-liquid equilibria, the binary simulations were very well suitable for testing the performance of different sets of combining rules. Employing Lorentz-Hudson-McCoubrey combining rules for interactions between unlike molecules, as opposed to Lorentz-Berthelot combining rules for all interactions, considerably improved the agreement between experimental and simulated data.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

Vapor-liquid interfacial properties of rigid-linear Lennard-Jones chains

We have obtained the interfacial properties of short rigid-linear chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapour-liquid interface. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janec?ek [J. Phys. Chem. B 110, 6264-6269 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 4, and 5 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtain density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The surface tension has been scaled by critical properties and represented as a function of the difference between coexistence densities relative to the critical density.     

Line of percolation in supercritical water

The percolation transition of the hydrogen-bonded clusters of molecules is investigated in supercritical water by Monte Carlo computer simulations. Simulations have been performed at four thermodynamic state points located above the supercritical extension of the vapor-liquid coexistence curve on the p-T phase diagram and at four state points located below this curve. It is found in a temperature range of a few hundred Kelvin that the extension of the vapor-liquid coexistence curve separates the supercritical thermodynamic states in which the water molecules form infinite hydrogen-bonded clusters from those in which the hydrogen-bonded clusters are isolated oligomers. However, the difference between the size of the hydrogen-bonded clusters at thermodynamic states located at the two sides of the extension of the coexistence curve is found to decrease with increasing temperature, and the present results suggest that this difference is likely to vanish at high enough temperatures.     

Nucleation in a simple model for protein solutions with anisotropic interactions

A lattice analog of density functional theory is used to explore the structural and thermodynamic properties of critical nuclei in mixtures of particles with attractive anisotropic interactions. Protein molecules are assumed to occupy the sites on a regular cubic lattice, with effective directional interactions that mimic hydrogen bonding and the solvation forces induced by water. Interaction parameters are chosen to qualitatively reproduce the phase behavior of protein solutions. Our model predicts that critical nuclei of the solidlike phase have nonspherical shapes, and that their specific geometry depends on the nature of the anisotropic interactions. Molecules tend to align in distinctive ways in the core and in the interfacial region of these critical clusters, and the width and structure of the interface are highly affected by the presence of a metastable fluid-fluid critical point. Close to the critical region, the height of the barrier to nucleation is strongly reduced; this effect is enhanced by increasing the anisotropy of the intermolecular interactions. Unlike systems with short-range isotropic interactions, nucleation in our model is initiated by highly ordered clusters in which the order-disorder transition is confined to the interfacial region.     

Scaled equations for the coexistence curve,the capillary constant and the surface tension of n-alkanes

A review of experimental data of several fluids shows that their coexistence curve follows a power law in reduced temperature at the approach of the critical point, with an universal exponent equal to 0.325, their capillary constant a power law with an universal exponent equal to 0.925 and their surface tension a power law with an universal exponent equal to 1.26. In the critical region, the concept of two-scale-factor universality was used to predict the density difference amplitude, the capillary constant amplitude, and the surface tension amplitude between near critical vapor and liquid phases. A comparison with amplitudes determined from experimental data is given. In order to extend this universality all along the liquid–gas coexistence curve from the triple point to the critical point for n-alkanes, a mean field approximation was used far away from T_C. We show that the density difference, the capillary constant and the surface tension can be calculated with a reasonable accuracy by generalized scaled equations adding only two empirical constants. A comparison between calculated and experimental data is presented.     

Integral equation study of a Stockmayer fluid adsorbed in polar disordered matrices

Based on replica integral equations in the (reference) hypernetted chain approximation we investigate the structural features and phase properties of a dipolar Stockmayer fluid confined to a disordered dipolar matrix. The integral equations are applied to the homogeneous high-temperature phase where the system is globally isotropic. At low densities we find the influence of dipolar interactions between fluid (f) and matrix (m) particles to be surprisingly similar to the previously investigated effect of attractive isotropic (fm) interactions: the critical temperature of the vapor-liquid transition decreases with increasing (fm) coupling, while the critical density increases. The anisotropic nature of the dipolar (fm) interactions turns out to play a more dominant role at high fluid densities where we observe a pronounced sensitivity in the dielectric constant and a strong degree of local orientational ordering of the fluid particles along the local fields generated by the matrix. Moreover, an instability of the dielectric constant, which is a precursor of ferroelectric ordering occurring both in bulk Stockmayer fluids and in fluids in nonpolar matrices, is observed only for very small dipolar (fm) couplings.     

Simulating fluid-phase equilibria of water from first principles

Efficient Monte Carlo algorithms and a mixed-basis set electronic structure program were used to compute from first principles the vapor-liquid coexistence curve of water. A water representation based on the Becke-Lee-Yang-Parr exchange and correlation functionals yields a saturated liquid density of 900 kg/m3 at 323 K and normal boiling and critical temperatures of 350 and 550 K, respectively. An analysis of the structural and electronic properties of the saturated liquid phase shows an increase of the asymmetry of the local hydrogen-bonded structure despite the persistence of a 4-fold coordination and decreases of the molecular dipole moment and of the spread of the lowest unoccupied molecular orbital with increasing temperature.     

The phase behavior of two-dimensional symmetrical mixtures

Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles. We discuss the interplay between the demixing transition in a liquid and the freezing in detail. Phase diagrams for several systems characterized by different parameters describing interactions in the system are presented. It is explicitly demonstrated that different scenarios involving demixing and freezing transitions, described in our earlier paper [A. Patrykiejew and S. Soko?owski, Phys. Rev. E, 81, 012501 (2010)], are possible. In one class of systems, the λ-line representing a continuous demixing transition in a liquid phase starts at the liquid side of either the vapor-liquid or liquid-solid coexistence. The second class involves the systems in which the λ-line begins at the liquid side of the vapor-liquid coexistence, in the lower critical end point, and then terminates at the liquid side of the liquid-solid coexistence, in the upper critical end point. It is also shown that in such systems the solid phase may undergo a demixing transition at the temperature above the upper critical end point.