Comprehensive molecular dynamics study of the dynamical properties of a dense binary hard-sphere mixture

Abstract

We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, $\varphi \approx 0.357-0.582$. The self-diffusivity, $D$, and shear viscosity, $\eta$, are computed using an efficient implementation of the Einstein--Helfand method. The finite-size effects in $D$ scale as $1/N^{\alpha }$, with $\alpha$ increasing from approximately $1/3$ to $3/4$ with increasing $\varphi$, whereas those in $\eta$ are negligible except for $\varphi \gtrsim 0.554$, where they scale as $1/N$. The data are then extrapolated to the thermodynamic limit to obtain $D_{\infty }$ and ${\eta }_{\infty }$. Both coefficients show a super-Arrhenius dependence on $\varphi$ for dense states, accompanied by a breakdown of the Stokes--Einstein relation. Although both $D_{\infty }(\varphi )$ and ${\eta }_{\infty }(\varphi )$ data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, ${\varphi }_0$, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between $\eta$ and the structural relaxation time, ${\tau }_{\alpha }$ , to not hold for this system. For $\varphi \gtrsim 0.570$, the van Hove self-correlation function $G_s(r,\tau )$ exhibits a spatial exponential decay at intermediate times, $\tau$, signaling dynamic heterogeneity. The characteristic decay length scales as $\lambda \sim {\tau }^{\nu }$, with $\nu \approx 1/3$, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, ${\chi }_4(\tau )$, and its peak time, ${\tau }_4$. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.