Double Transition Scenario for Anomalous Diffusion in Glass-Forming Mixtures

We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced difference in the species’ long-time dynamics. Anomalous, power-law-like diffusion of small particles arises that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport.

Figure 1

MD-simulated self-diffusion coefficients for small ($D_s$) and large particles ($D_l$) in a disparate-sized binary mixture. The solid line is a power-law fit $\propto ({\rho }_c-\rho {)}^{\gamma }$, where ${\rho }_c=2.23$ and $\gamma =2.1$. Inset: partial static structure factors $S_{\alpha \beta }(q)$ at two densities as functions of $q{\rho }^{-1/3}$. The dotted line is $S_{ss}(q)$ for noninteracting small particles at $\rho =2.19$.

Figure 2

Mean-squared displacements (MSD), $\delta r_{\alpha }^2(t)$ for the large (dotted lines) and small (solid lines) particles in the simulated binary mixture. Densities shown are $\rho {\sigma }_{ll}^3=2.0$, 2.296, and 4.215 for $\alpha =l$ and $\rho {\sigma }_{ll}^3=2.0$, 2.296, 2.654, 2.837, 3.257, 3.627, 3.906, and 4.215 for $\alpha =s$.

Figure 3

(a) Small-particle MSD with (solid lines) and without (dashed lines) interactions among small particles, densities as indicated. (b) Effective exponent $\mu (t)=d[\log \delta r_s^2(t)]/d(\log t)$.

Figure 4

Self-part of the van Hove correlation function $G_s(r,t)$ for small particles with (solid lines) and without (dashed lines) mutual interaction, plotted as probability distribution $4\pi r^2{G}_s(r,t)$ for times indicated, and at density $\rho =3.257{\sigma }_{ll}^{-3}$, as functions of $r=r/{\sigma }_{ll}$.

Figure 5

Mean-squared displacements $\delta r_{\alpha }^2(t)$ obtained from mode-coupling theory with MD-simulated $S(q)$. Solid (dashed) lines: small-particle MSD with (without) interactions between small particles, densities as labeled. Dotted lines: big-particle MSD for the highest density shown.