Molecular simulation in a pseudo grand canonical ensemble

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.

Simulation of phase transitions in fluids

This review provides a discussion of recent techniques for simulation of phase equilibria of complex fluids. Monte Carlo methods are emphasized over molecular dynamics methods. We describe recent developments, such as the use of expanded-ensemble, tempering, or histogram reweighting techniques. Our discussion of such developments is aimed at a general audience and is intended to provide an overview of the main advantages and limitations of each particular technique. References are provided to allow interested readers to identify and trace back most recent applications of a particular simulation technique. We conclude with general guidelines regarding selection of suitable simulation methods for particular problems and systems of interest.

Temperature and density extrapolations in canonical ensemble monte carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.