Vapor–liquid and liquid–liquid phase equilibria of mixtures containing square‐well molecules by Gibbs ensemble Monte Carlo simulation

Efficient determination of solid-state phase equilibrium with the multicell Monte Carlo method

Building on our previously introduced multicell Monte Carlo (MC)^{2} method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^{2} method uses multiple cells, representing possible phases. Mass transfer between cells is modeled virtually by solving the mass balance equation after the composition of each cell is changed arbitrarily. However, searching for the minimum free energy during this process poses a practical problem. The solution to the mass balance equation is not unique away from equilibrium, and consequently the algorithm is in risk of getting trapped in nonequilibrium solutions. Therefore, a proper stopping condition for (MC)^{2} is currently lacking. In this work, we introduce a consistency check via a predictor-corrector algorithm to penalize solutions that do not satisfy a necessary condition for equivalence of chemical potentials and steer the system toward finding equilibrium. The most general acceptance criteria for (MC)^{2} is derived starting from the isothermal-isobaric Gibbs ensemble for mixtures. Using this ensemble, translational MC moves are added to include vibrational excitations as well as volume MC moves to ensure the condition of constant pressure and temperature entirely with a MC approach, without relying on any other method for relaxation of these degrees of freedom. As a proof of concept the method is applied to two binary alloys with miscibility gaps and a model quaternary alloy, using classical interatomic potentials.

INVESTIGATING BRIDGE-LIKE STRUCTURES IN A SQUARE-WELL BINARY MIXTURE USING NVT MONTE CARLO SIMULATION

Bridge-like structures have been reported in recent studies for a binary mixture with square well fluids in 2D and 3D using different techniques. In this paper, we present our NVT simulation results in 3D with symmetric additive water and oil-like molecules. We use Dirac's delta function defined using theta step function for evaluating pressure components and surface tension values. Our investigation reveals that though 3D NVT MC results are in qualitative agreement with the published results showing all the structures as bridge-like, complete wetting of the walls by the preferred component and micelle structures but the critical parameters as surface attraction strength significantly alter to lower values for PW and CW cases in comparison to the 2D MD cases. We have studied cases with pore width as H = 6.0, 8.0, and 10.0 at T = 0.70, 0.80, and 0.90 for εAB = 0.0, 0.25, 0.50, and 1.0. For all of the bridge cases ε Wall -A = -0.50 and λ wall -A = 1.0. For fluid–fluid interaction λ ff = 1.2 and 1.5 are taken with εAA = εBB = -1.0. Our pressure and surface tension values show clear signature of confinement effect and dependence on other parameters for the bridge cases but it is concluded that different structural transitions depend only on the predefined energetically favorable and unfavorable interfaces which in turn comes from the separation of the two walls and average initial density. Our density profiles confirm the evolved structures.

Binary fluid with attractions near a planar wall

It is well known that a mixture of big and small hard spheres next to a planar wall will exhibit segregation based on their size difference. The larger spheres will tend to locate next to the substrate because the overall system entropy loss per unit area is less. In the present study we determine the role of attraction between the small particles and the wall to displace the larger particles. Both fluids density-functional theory and discontinuous molecular dynamics simulations demonstrate that at a certain attractive potential, which is on the order of the thermal energy, the large particles can indeed be dislodged from the surface layer so the small particles are now the major surface component. Exploration of a range of parameters, including relative sphere size and concentration, as well as attractions between the small spheres in the bulk, shows that the phenomenon is quite robust.

Phase behavior of a symmetrical binary fluid mixture

We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.

Limitations of the rigid planar nonpolarizable models of water

We analyzed the ability of variants of the SPC/E and TIP4P types of water models to describe the temperature dependence of their second virial coefficients, liquid-vapor phase envelopes, and corresponding coexistence vapor pressure. We complete the characterization of the two most promising models by testing their adequacy to predict the structure of the 13 known crystalline phases of ice by (Parrinello-Rahman) isothermal-isobaric Monte Carlo simulations. While these models perform well for the description of properties to which their force fields were fitted (density, heat of vaporization, structure at the level of pair correlations), their transferability to the entire phase diagram is unsatisfactory, i.e., none could significantly mitigate the shortcomings of the original models. In fact, the most appropriate alternative appears to be the TIP4P-EW model, i.e., the recent reparametrization of the original TIP4P water model. Model parametrizations aimed at improving the description of ice behavior fail even in the description of the liquid phase.

Isomolar semigrand ensemble molecular dynamics: Development and application to liquid-liquid equilibria

An extended system molecular dynamics method for the isomolar semigrand ensemble (fixed number of particles, pressure, temperature, and fugacity fraction) is developed and applied to the calculation of liquid-liquid equilibria (LLE) for two Lennard-Jones mixtures. The method utilizes an extended system variable to dynamically control the fugacity fraction xi of the mixture by gradually transforming the identity of particles in the system. Two approaches are used to compute coexistence points. The first approach uses multiple-histogram reweighting techniques to determine the coexistence xi and compositions of each phase at temperatures near the upper critical solution temperature. The second approach, useful for cases in which there is no critical solution temperature, is based on principles of small system thermodynamics. In this case a coexistence point is found by running N-P-T-xi simulations at a common temperature and pressure and varying the fugacity fraction to map out the difference in chemical potential between the two species A and B (mu(A)-mu(B)) as a function of composition. Once this curve is known the equal-distance/equal-area criterion is used to determine the coexistence point. Both approaches give results that are comparable to those of previous Monte Carlo (MC) simulations. By formulating this approach in a molecular dynamics framework, it should be easier to compute the LLE of complex molecules whose intramolecular degrees of freedom are often difficult to properly sample with MC techniques.

Phase diagram of symmetric binary mixtures at equimolar and nonequimolar concentrations: a systematic investigation

We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As delta is increased in the interval 0<delta<1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical end point topology predicted by mean-field theory as delta approaches 1, at least up to delta=0.8, which is the largest value of delta investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.

Reentrant miscibility in fluids with spherical interactions

We have obtained the closed-loop fluid-fluid immiscibility in the phase diagram of a binary mixture with interactions with spherical symmetry. That topology appears when a short-range attractive interaction is considered between unlike pair molecules. We present "exact" results obtained from Monte Carlo simulation on different ensembles and results from the application of a first-order perturbation theory.