Exploring Fluctuations and Phase Equilibria in Fluid Mixtures via Monte Carlo Simulation

TL;DR

This paper extends the virtual Gibbs ensemble Monte Carlo method to binary fluid mixtures, demonstrating its pedagogical and analytical utility through two models and providing open-source tools for educational use.

Contribution

It introduces an extended virtual GEMC method for binary mixtures, with algorithms, validation, and educational applications, including open-source Java programs.

Findings

Validated phase diagrams for fluid demixing.

Analyzed fluctuation dependence on system size.

Demonstrated pedagogical value in classroom settings.

Abstract

Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo (GEMC), which allows direct computation of phase coexistence curves of model fluids by assigning each phase to its own simulation cell. When one or both of the phases can be modeled virtually via an analytic free energy function [M. Mehta and D. A. Kofke, Molecular Physics 79, 39 (1993)], the GEMC method takes on new pedagogical significance as an efficient means of analyzing fluctuations and illuminating the statistical foundation of phase behavior in finite systems. Here we extend this virtual GEMC method to binary fluid mixtures and demonstrate its implementation and instructional value with two applications: (1) a lattice model of simple mixtures and polymer blends and (2) a free-volume model of a complex mixture of colloids and polymers. We present algorithms for performing Monte Carlo trial moves in the virtual Gibbs ensemble, validate the method by computing fluid demixing phase diagrams, and analyze the dependence of fluctuations on system size. Our open-source simulation programs, coded in the platform-independent Java language, are suitable for use in classroom, tutorial, or computational laboratory settings.