Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation

TL;DR

This study uses computer simulations combining Monte Carlo and Molecular Dynamics to analyze the critical behavior of a symmetrical binary fluid, confirming theoretical and experimental predictions for critical exponents and transport properties near the liquid-liquid critical point.

Contribution

It introduces a combined simulation approach to accurately determine critical exponents and transport coefficients in a binary fluid near criticality, validating universality class predictions.

Findings

Critical exponents match 3D Ising universality class.

Shear viscosity and mutual diffusion show expected critical behavior.

Self-diffusion coefficient remains unaffected by critical fluctuations.

Abstract

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $T<T_c$ and at the critical concentration, $x_c=1/2$, for $T>T_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.