Gibbs Ensemble Monte Carlo Technique Research Articles

The Vapor-Liquid Phase Diagram of Pure Methane Using Temperature-Dependent Interaction Parameters: A Monte Carlo Simulation

Adopting temperature-dependent interaction parameters in the Lennard-Jones potential, the vapor-liquid phase diagram of methane was produced using NVT Gibbs Ensemble Monte Carlo technique. Published second virial coefficient data were used to fit a simple two-parameter temperature-dependent model for the interaction parameters. The simulations were carried out in the temperature range 120-190 K. The critical density and temperature were evaluated using Ising-scaling model. Using the temperature-dependent interaction parameters in the simulation has reduced the root mean square deviation by 94.7% compared to the temperature-independent interaction parameters. The evaluated critical temperature was enhanced using temperature-dependent interaction parameters, whereas the simulations using temperature-independent interaction parameters predict a better critical density value

Prediction of the Temperature Dependence of the Surface Tension Of SO2, N2, O2, and Ar by Monte Carlo Molecular Simulations

We report Monte Carlo simulations of the liquid-vapor interface of SO(2), O(2), N(2), and Ar to reproduce the dependence of the surface tension with the temperature. Whereas the coexisting densities, critical temperature, density, and pressure are very well reproduced by the two-phase simulations showing the same accuracy as the calculations performed using the Gibbs ensemble Monte Carlo technique (GEMC), the performance of the prediction of the variation of the surface tension with the temperature depends on the magnitude of the electrostatic and repulsive-dispersive interactions. The surface tension of SO(2) is very well reproduced, whereas the prediction of this property is less satisfactory for O(2) and N(2), for which the average intermolecular electrostatic interactions are several orders smaller than the dispersion interactions. For argon, we observe significant deviations from experiments. The representation of the surface tension of argon in reduced units shows that our calculations are in line with the existing surface tensions of the Lennard-Jones fluid in the literature. This underlines the difficulty of reproducing the temperature dependence of the surface tension of argon with interactions only modeled by the Lennard-Jones pair potential.

A numerical test of a high-penetrability approximation for the one-dimensional penetrable-square-well model

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-Hückel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behaviors of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by the Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.

Simulation of water clusters in vapour, alkanes and polyethylenes

The Gibbs Ensemble Monte Carlo (GEMC) technique has been used to study the clustering of water in vapour, alkanes and polyethylene, where the water clusters are in equilibrium with liquid phase water. The effect of an external electric field and ionic impurities on the clustering of water in the hydrocarbons (alkanes and polyethylene) has also been studied. The simulations of water clustering in polyethylene were made more efficient by using a connectivity altering osmotic Gibbs ensemble method. It was found that trends in the size distribution of water clusters in the hydrocarbons are similar to those found in the pure vapour, but that fewer and smaller clusters are formed as the length of the hydrocarbon chain increased. Also, large external electric fields decrease the solubility of water in hydrocarbons, whereas the presence of ionic species dramatically increases the solubility.

The effects of chain length, embedded polar groups, pressure, and pore shape on structure and retention in reversed-phase liquid chromatography: Molecular-level insights from Monte Carlo simulations

Particle-based simulations using the configurational-bias and Gibbs ensemble Monte Carlo techniques are carried out to probe the effects of various chromatographic parameters on bonded-phase chain conformation, solvent penetration, and retention in reversed-phase liquid chromatography (RPLC). Specifically, we investigate the effects due to the length of the bonded-phase chains (C 18, C 8, and C 1), the inclusion of embedded polar groups (amide and ether) near the base of the bonded-phase chains, the column pressure (1, 400, and 1000 atm), and the pore shape (planar slit pore versus cylindrical pore with a 60 Å diameter). These simulations utilize a bonded-phase coverage of 2.9 μ mol/m 2and a mobile phase containing methanol at a molfraction of 33% (about 50% by volume). The simulations show that chain length, embedded polar groups, and pore shape significantly alter structural and retentive properties of the model RPLC system, whereas the column pressure has a relatively small effect. The simulation results are extensively compared to retention measurements. A molecular view of the RPLC retention mechanism emerges that is more complex than can be inferred from thermodynamic measurements.

Polymer-induced phase separation and crystallization in immunoglobulin G solutions

We study the effects of the size of polymer additives and ionic strength on the phase behavior of a nonglobular protein-immunoglobulin G (IgG)-by using a simple four-site model to mimic the shape of IgG. The interaction potential between the protein molecules consists of a Derjaguin-Landau-Verwey-Overbeek-type colloidal potential and an Asakura-Oosawa depletion potential arising from the addition of polymer. Liquid-liquid equilibria and fluid-solid equilibria are calculated by using the Gibbs ensemble Monte Carlo technique and the Gibbs-Duhem integration (GDI) method, respectively. Absolute Helmholtz energy is also calculated to get an initial coexisting point as required by GDI. The results reveal a nonmonotonic dependence of the critical polymer concentration rho(PEG) (*) (i.e., the minimum polymer concentration needed to induce liquid-liquid phase separation) on the polymer-to-protein size ratio q (equivalently, the range of the polymer-induced depletion interaction potential). We have developed a simple equation for estimating the minimum amount of polymer needed to induce the liquid-liquid phase separation and show that rho(PEG) (*) approximately [q(1+q)(3)]. The results also show that the liquid-liquid phase separation is metastable for low-molecular weight polymers (q=0.2) but stable at large molecular weights (q=1.0), thereby indicating that small sizes of polymer are required for protein crystallization. The simulation results provide practical guidelines for the selection of polymer size and ionic strength for protein phase separation and crystallization.

The phase diagram of the Lennard-Jones fluid using temperature dependent interaction parameters

The forces of interaction between argon atoms can be described by the Lennard-Jones potential model. It is hypothesised that the use of temperature dependent interaction parameters, instead of using temperature independent interaction parameters, may lead to improvement in the prediction of the vapour–liquid coexistence curve. Published second virial coefficient data were used to fit a simple two-parameter temperature dependent model for the collision diameter and well depth. Vapour–liquid coexistence curve for argon was simulated in the NVT Gibbs ensemble Monte Carlo technique. The simulations were carried out using each of the temperature independent and temperature dependent parameters in the temperature range: 110–148 K. The critical temperature and density were determined using the Ising-scaling model. The results using temperature dependent parameters produce, overall, a more accurate phase diagram compared to the diagram generated using temperature independent interaction parameters. The root mean square deviation is reduced by 42.1% using temperature dependent interaction parameters. Also, there was no significant difference between the results obtained using temperature dependent interaction parameters and the highly accurate and computationally demanding phase diagrams based on three body contributions.

Solubility of Carbon Dioxide in Aqueous Solutions of Methanol. Predictions by Molecular Simulation and Comparison with Experimental Data

The solubility of carbon dioxide in pure methanol, and in aqueous solutions of methanol, was computed using the Gibbs ensemble Monte Carlo (GEMC) technique for 313, 354, and 395 K at pressures up to 9 MPa. Three solvent mixtures (of methanol and water) with methanol mole fractions of 10, 50, and 75 mole percent (in the gas-free solvent mixture) were studied. The Monte Carlo simulations were conducted in an isothermal-isobaric ensemble applying effective pair potentials for the pure components from literature. Common mixing rules without any adjustable binary interaction parameters were used to describe the interactions between the mixture components. Overall, a good agreement between simulation results and recently published experimental data is achieved.

Phase coexistence in heterogeneous porous media: A new extension to Gibbs ensemble Monte Carlo simulation method

The effect of confinement on phase behavior of simple fluids is still an area of intensive research. In between experiment and theory, molecular simulation is a powerful tool to study the effect of confinement in realistic porous materials, containing some disorder. Previous simulation works aiming at establishing the phase diagram of a confined Lennard-Jones-type fluid, concentrated on simple pore geometries (slits or cylinders). The development of the Gibbs ensemble Monte Carlo technique by Panagiotopoulos [Mol. Phys. 61, 813 (1987)], greatly favored the study of such simple geometries for two reasons. First, the technique is very efficient to calculate the phase diagram, since each run (at a given temperature) converges directly to an equilibrium between a gaslike and a liquidlike phase. Second, due to volume exchange procedure between the two phases, at least one invariant direction of space is required for applicability of this method, which is the case for slits or cylinders. Generally, the introduction of some disorder in such simple pores breaks the initial invariance in one of the space directions and prevents to work in the Gibbs ensemble. The simulation techniques for such disordered systems are numerous (grand canonical Monte Carlo, molecular dynamics, histogram reweighting, N-P-T+test method, Gibbs-Duhem integration procedure, etc.). However, the Gibbs ensemble technique, which gives directly the coexistence between phases, was never generalized to such systems. In this work, we focus on two weakly disordered pores for which a modified Gibbs ensemble Monte Carlo technique can be applied. One of the pores is geometrically undulated, whereas the second is cylindrical but presents a chemical variation which gives rise to a modulation of the wall potential. In the first case almost no change in the phase diagram is observed, whereas in the second strong modifications are reported.

Capillary Condensation in a Geometrically and a Chemically Heterogeneous Pore: A Molecular Simulation Study

A computer simulation study has been carried out, using an extended Gibbs ensemble Monte Carlo technique, to examine the influence of so-called geometric and chemical disorder on the thermodynamic behavior of simple fluids confined in porous media. The technique allows the equilibrium coexistence of gas and liquid phases to be calculated in a single run. The phase diagram of Lennard-Jones fluid has been calculated in a perfectly cylindrical pore as a reference. Some disorder is then introduced in the porous material, first by spatially modifying the external potential of the initially cylindrical pore, to imitate the geometric disorder of a more realistic pore (undulation, constrictions, etc.) and second by modulating the amplitude of the same initially cylindrical potential to reproduce the energetic disorder of realistic pores due to chemical variations along it. It is shown that the chemical disorder has a much stronger effect on the phase diagram of the confined fluid. The complete adsorption/desorption isotherms are also calculated to help in understanding the large effects of chemical disorder.

Molecular simulation of vapor–liquid equilibria of toxic gases

In this paper, we derived the potential parameters for three toxic gases, hydrogen sulfide, phosgene and nitrous oxide, modeled by the effective Stockmayer potential model proposed by Gao et al. [Fluid Phase Equilib. 137 (1997) 87]. The vapor–liquid equilibria (VLE) of these substances have been extensively investigated over a wide range of temperatures by the Gibbs ensemble Monte Carlo (GEMC) technique. The simulated saturated densities and pressures are in good agreement with experimental data. The critical properties obtained by regression of the simulated data also agree well with the experimental values. The present work demonstrates that the effective Stockmayer potential can describe well the toxic gases concerned.

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.

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.

Closed-loop phase equilibria of a symmetrical associating mixture of square-well molecules examined by Gibbs ensemble Monte Carlo simulation

A closed loop of liquid-liquid immiscibility for a simple model binary symmetrical mixture of square-well monomers with a single short-ranged interaction site has been recently observed using the Gibbs ensemble Monte Carlo technique [L. A. Davies, G. Jackson, and L. F. Rull, Phys. Rev. Lett. $82,$ 5285 (1999)]. This model system has unfavorable mean-field interactions between unlike components which leads to phase separation at intermediate temperatures; the addition of a directional bonding site leads to association and miscibilty of the system at low temperatures. In this work we present a detailed study of the effect of a variation in pressure and of the strength of the bonding interaction on the phase equilibria of such a model system by Gibbs ensemble simulation. The phase diagram is dominated by regions of liquid-liquid immiscibility which are bounded at high temperatures by an upper critical solution temperature and by a lower critical solution temperature (LCST) for specific values of the pressure and association strength. This closed-loop region is seen to increase in size as the pressure of the system is increased. For weak bonding interaction strengths the system does not possess a LCST and is seen to exhibit regions of two-phase vapor-liquid coexistence which are separated from the region of liquid-liquid immiscibility by a three-phase line. The phase equilibria of the same model system is also determined using the statistical associating fluid theory as adapted for potentials of variable range; the theory provides a good description of the closed-loop immiscibility and other features of the phase diagram.

Computer Simulation of Fractionation in Bidisperse Liquid Crystals

We present evidence of fractionation at the isotropic-nematic transition in a bidisperse liquid crystal system, using the Gibbs ensemble Monte Carlo technique[1] and the generalised Gay-Berne potential[2]. Using a 50:50 mixture of prolate molecules with identical breadths but different length to breadth ratios, fractionation was observed which shows qualitative agreement with the coexistence behaviour predicted by mean field theory[3]

Some aspects of the Methodology in Gibbs Ensemble Monte Carlo Simulations in Connection with a Model Fluid of C60

Conventional and new versions of the Gibbs ensemble Monte Carlo technique existing for one-component systems were applied for the determination of the vapour-liquid coexistence in the model fluid of C60. Employing exact long range corrections for the model, no significant particle number dependence of the simulation results was found. The results confirm that a liquid phase may exist for this model.

Monte Carlo simulation of high-pressure phase equilibria in aqueous systems

We have used Gibbs ensemble and histogram-reweighting Monte Carlo techniques to obtain the phase behavior of water and aqueous mixtures at high pressures. These calculations are relevant for the design of high-pressure separation processes, such as supercritical fluid extraction and supercritical water oxidation. In particular, we have obtained the phase behavior of several simple point charge models of water, as well as polarizable versions of these models. None of the models studied reproduce the experimentally observed phase behavior and critical parameters of water. The binary mixture water/carbon dioxide at high pressures has also been studied. Good agreement for this mixture has been obtained without use of any adjustable parameters for the mixture interactions, thus suggesting that the predictive power of molecular-based methods is greater than that of purely phenomenological approaches, even when using imperfect pure component intermolecular potential models.

Effective Intermolecular Potential for Fluid Hydrogen Sulfide

A recently developed version of the Gibbs ensemble Monte Carlo technique is used for the determination of vapor−liquid equilibria of potential models for hydrogen sulfide. By fitting to experimental saturation properties of the substance, an optimized effective pair potential is parametrized on the basis of an existing four-site model of Lennard-Jones plus point charge type. The new model reproduces well also the critical properties and the structural characteristics of the substance.

Vapor–liquid coexistence of quasi-two-dimensional Stockmayer fluids

A quasi-two-dimensional (2D) Stockmayer model is developed in which the center of mass of the molecule is confined on a plane while the dipole of the molecule can rotate freely in three dimensional space. This model entails essential characteristics of systems such as dipolar molecules physisorbed on a solid surface, or a Langmuir monolayer consisting of short-chain molecules with a dipolar tail. The Gibbs ensemble Monte Carlo technique is employed to determine the vapor–liquid equilibria of the model fluids. An Ewald sum for this quasi-2D model is formulated to account for the long-range dipolar interactions. Three systems with different reduced dipole moments were studied. The critical point of each system is determined by fitting the vapor–liquid coexistence data to a 2D scaling law and the rectilinear law. We find that in general the critical temperature of the system is reduced due to the confinement and is sensitive to the strength of the dipole moment, whereas the critical density is not. The effect of reducing the dispersion part of potential on the vapor–liquid equilibria is also studied. We find the dispersion potential reduction leads to a lower critical temperature and a higher in-plane part of molecular dipole moment; however, because the reduced critical temperature is relatively small compared with that of a 3D system, disappearance of the critical point is not observed in the quasi-2D SM system within practical scope of the simulation.

Direct Evaluation of Solid–Liquid Equilibria by Molecular Dynamics Using Gibbs-Duhem Integration

An application of the Gibbs-Duhem integration [D. A. Kolke, J. Chem. Phys., 98, 4149 (1993)] for the direct evaluation of solid–liquid equilibria by molecullar dynamics is presented. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence at one coexistence point, simultaneous but independent constant pressure-constant temperature colecular dynamics simulations of each phase are caried out in succession along saturation lines. In each simulation, the saturated pressure is adjusted to satisfy the Clapeyron equation, a first-order nonlinear differential equation that prescribes how the pressure must change with the temperature to maintain coexistence. The Clapeyron equation is solved by the predictor–corrector method. Running averages of enthalpy and density of each phase are used to evaluate the right-hand side of the Clapeyron equation. The Gibbs-Duhem integration method is applied to a two-centre Lennard-Jones system with elongation 0.67. The starting coexistence point is determined as the point of intersection of solid and liquid isotherm in the pressure vs chemical potential plane.