Fluid phase coexistence and critical behaviour from simulations in the restricted Gibbs ensemble

Abstract

The symmetrical restricted Gibbs ensemble (RGE) is a version of the Gibbs ensemble in which particles are exchanged between two boxes of fixed equal volumes. It has recently come to prominence because -- when combined with specialized algorithms -- it provides for the study of near-coexistence density fluctuations in highly size-asymmetric binary mixtures. Hitherto, however, a detailed framework for extracting accurate estimates of critical point and coexistence curve parameters from RGE density fluctuations has been lacking. Here we address this problem by exploiting an exact link between the RGE density fluctuations and those of the grand canonical ensemble. In the sub-critical region we propose and test a simple method for obtaining accurate estimates of coexistence densities. In the critical region we identify an observable that serves as a finite system size estimator for the critical point parameters, and present a finite-size scaling theory that allows extrapolation to the thermodynamic limit.

12 pages, 9 figures

References in corpus (1)

• Simulation of phase transitions in highly asymmetric fluid mixtures

Cited by in corpus (4)

• Transport Phenomena in Fluids: Finite-size scaling for critical behavior
• Monte Carlo cluster algorithm for fluid phase transitions in highly size-asymmetrical binary mixtures
• Simulation of Transport around the Coexistence Region of a Binary Fluid
• Monte Carlo methods for estimating depletion potentials in highly size-asymmetrical hard sphere mixtures