Comprehensive molecular dynamics study of the dynamical properties of a dense binary hard-sphere mixture
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, $\phi \approx 0.357-0.582$. 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 $\phi$, whereas those in $\eta$ are negligible except for $\phi \gtrsim 0.554$, 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 $\phi$ for dense states, accompanied by a breakdown of the Stokes--Einstein relation. Although both $D_{\infty}(\phi)$ and $\eta_{\infty}(\phi)$ data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, $\phi_0$, 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 $\phi\gtrsim 0.570$, 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.