The Role of Computer Simulation in Studying Fluid Phase Equilibria

Vapor-liquid equilibrium and thermodynamic properties of saturated argon and krypton from Monte Carlo simulations using ab initio potentials

Vapor-liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using ab initio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal-isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor-liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art ab initio pair and nonadditive three-body potentials and quantum effects are accounted for.

Thermodynamics of liquid and fluid mixtures from the kinetic Monte Carlo viewpoint

In this study a binary mixture is modelled in a uniform simulation cell at various temperatures using an extended version of the grand canonical kinetic Monte Carlo (GC-kMC) method. The main goal of this study is to consider the thermodynamic properties of binary liquids, gases, and gas-liquid mixtures from a more general point of view than that applied to the particular case of vapour-liquid equilibrium when the pressure and partial chemical potentials in coexisting phases are the same. Particular attention is paid to thermodynamic functions such as chemical potentials, Gibbs free energy and entropy. For the pair potential of unlike molecules a more universal scheme is proposed in comparison with the Lorentz-Berthelot combining rule. The approach is tested on an Ar-Kr mixture in a wide range of temperatures. In all cases, the obtained values of chemical potentials, pressure and internal energy for the entire set of component densities and temperature fully satisfy the Gibbs-Duhem equation with a high degree of accuracy. For the case of vapour-liquid equilibrium, the developed approach made it possible to reproduce the experimental pressure-composition diagrams with the highest accuracy ever achieved in the literature. Despite the fact that the Ar-Kr mixture, according to Raoult's law, is close to an ideal system, it was found that the partial pressures in the liquid phase or in a dense supercritical gas mixture are non-linear functions of the composition, and the partial pressure of the heavier component (Kr) can even be negative.

Detecting Liquid-Liquid Phase Separations Using Molecular Dynamics Simulations and Spectral Clustering

A stringent test of the accuracy of empirical force fields is reproducing the phase diagram of bulk phases and mixtures. Exploring the phase diagram of mixtures requires the detection of phase boundaries and critical points. In contrast to most solid-liquid transitions, in which a global order parameter (average density) can be used to discriminate between two phases, some demixing transitions entail relatively subtle changes in the local environment of each molecule. In such cases, finite sampling errors and finite-size effects make the identification of trends in local order parameters extremely challenging. Here we analyze one such example, namely a methanol/hexane mixture, and compute several local and global structural properties. We simulate the system at various temperatures and study the structural changes associated with demixing. We show that despite a seemingly continuous transformation between mixed and demixed states, the topological properties of the H-bond network change abruptly as the system crosses the demixing line. In particular, by using spectral clustering, we show that the distribution of cluster sizes develops a fat tail (as expected from percolation theory) in the vicinity of the critical point. We illustrate a simple criterion to identify this behavior, which results from the emergence of large system-spanning clusters from a collection of aggregates. We further tested the spectral clustering analysis on a Lennard-Jones system as a standard example of a system with no H-bonds, and also, in this case, we were able to detect the demixing transition.

Direct Simulations of Phase Behavior of Mixtures of Oppositely Charged Proteins/Nanoparticles and Polyelectrolytes

We use direct simulations of particle-polyelectrolyte mixtures using the single chain in mean field framework to extract the phase diagram for such systems. At high charges of the particles and low concentration of polymers, we observe the formation of a coacervate phase involving the particles and polyelectrolytes. At low particle charges and/or high concentration of polymers, the mixture undergoes a segregative phase separation into particle-rich and polymer-rich phases, respectively. We also present results for the influence of particle charge heterogeneity on the phase diagram.

A simulation method for the phase diagram of complex fluid mixtures

The phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. The method is easy to implement and readily applied to any mixture of complex fluids.

Example of a Fluid-Phase Change Examined with MD Simulation: Evaporative Cooling of a Nanoscale Droplet

We carried out a series of molecular dynamics simulations in order to examine the evaporative cooling of a nanoscale droplet of a Lennard-Jones liquid. After thermally equilibrating a droplet at a temperature T_ini/T_t ≃ 1.2 (T_t is the triple-point temperature), we started the evaporation into vacuum by removing vaporized particles and monitoring the change in droplet size and the temperature inside. As free evaporation proceeds, the droplet reaches a deep supercooled liquid state of T/T_t ≃ 0.7. The temperature was found to be uniform in spite of the fast evaporative cooling on the surface. The time evolution of the evaporating droplet properties was satisfactorily explained with a simple one-dimensional phase-change model. After a sufficiently long run, the supercooled droplet was crystallized into a polycrystalline fcc structure. The crystallization is a stochastic nucleation process. The time and the temperature of inception were evaluated over 42 samples, which indicate the existence of a stability limit.

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.