Precise Simulation of Near-critical Fluid Coexistence

TL;DR

This paper introduces a new simulation method to accurately determine liquid-gas coexistence densities near critical points without prior criticality knowledge, revealing pressure mixing effects and confirming Ising universality.

Contribution

A novel, unbiased finite-size scaling approach to derive coexistence densities from grand canonical simulations without prior criticality information.

Findings

Achieved density measurements within 1-2% of critical density.

Confirmed Ising universality class for the models studied.

Revealed pressure mixing effects and quantified Yang-Yang ratios.

Abstract

We present a novel method to derive liquid-gas coexisting densities, $\rho^{\pm}(T)$, from grand canonical simulations (without knowledge of $\Tc$ or criticality class). The minima of $ Q_{L}\equiv< m^{2} >_{L}^{2}/< m^{4}>_{L}$ in an $L$$\times$$L \times$$L$ box with $m = \rho - <\rho>_{L}$ are used to generate recursively an unbiased universal finite-size scaling function. Monte Carlo data for a hard-core square-well fluid and for the restricted primitive model electrolyte yield $\rho^{\pm}$ to $\pm 1$-2% of $\rhoc$ down to 1 part in $10^4$-$10^3$ of $\Tc$ (and confirm well Ising character). Pressure mixing in the scaling fields is unequivocally revealed and indicates Yang-Yang ratios $R_{\mu} = -0.04_{4}$ and $0.2_{6}$ for the two models, respectively.