Computing phase equilibria by parallel excluded volume tempering

Abstract

We present a Monte Carlo scheme for the computation of phase equilibria at high densities. At these high densities, all conventional simulation techniques that rely on insertions and deletions of particles, e.g., the Gibbs ensemble technique, will have problems because the acceptance probability for these moves is very low. Furthermore, the efficiency of these methods strongly depends on the complexity of the system, e.g., degree of polymerization and branching of the components. Our new method is based upon simulating a path of independent systems in the grand-canonical ensemble. Each system has a slightly different interaction potential, ranging from a full excluded volume potential to an ideal gas, as well as different imposed chemical potentials of each component. This path is constructed in such a way that the average number of molecules of a specific component per system is constant along the path. To sample all systems of the path efficiently, we apply a parallel tempering procedure to exchange configurations of two adjacent systems. The advantage of these exchanges is that, for the full excluded volume system, one does not have to rely on particle insertions and deletions in this system to sample the full phase space, but rather on particle insertions and deletions in systems with soft interactions. Without excluded volume interactions, the acceptance of insertions is independent of molecular size and shape; hence our method does not suffer from the problems of the conventional methods. We have tested our method for very simple systems (Lennard-Jones particles) and found exact agreement with Gibbs ensemble simulations. For these simple systems the conventional techniques to compute phase equilibria are much more efficient. However, we expect that for long chain molecules this situation will be reversed.