Grand canonical simulation of phase behaviour in highly size-asymmetrical binary fluids

Abstract

We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilises an expanded ensemble in which the insertion and deletion of large particles is accomplished gradually by traversing a series of states in which a large particle interacts only partially with the environment of small particles. Free energy barriers arising from interfacial coexistence states are surmounted with the aid of multicanonical preweighting, the associated weights being determined from the transition matrix. As an illustration, we present results for the liquid–vapour coexistence properties of a Lennard-Jones binary mixture having a 10 : 1 size ratio.

Keywords:

• size-asymmetric binary mixtures
• Monte Carlo simulation
• phase behaviour

Acknowledgements

It is a pleasure to contribute to this Special Issue of Molecular Physics celebrating the work of Professor Bob Evans. During his career, Bob has made numerous seminal contributions to liquid state theory, been a tireless champion of the field, and an inspiration to those in it. We wish him many rewarding years to come. This work was supported by EPSRC grant EP/F047800. Computational results were partly produced on a machine funded by HEFCE's Strategic Research Infrastructure fund.

Notes

Notes

1. Note that this volume fraction is notional in the sense that we use the value of σ as if it were a hard-core radius , where V is the system volume.

2. We note in passing that further efficiency gains accrue by reducing the cell side by a factor of 2 and summing over a greater number of cells, thereby reducing the volume to be searched by up to a factor of 2.

3. While certainly sufficient, this choice of weights is generally not optimal 34,35.

4. In practice, the initial estimate of w(N _l, n) can be obtained more rapidly by restricting the range of N _l that can be sampled in a given run. This is done by holding N _l inside a fixed window, . The results from different windows can be combined self consistently by simply merging the collection matrix from each.