Brownian versus Newtonian devitrification of hard-sphere glasses

In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014)]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.

Figure 1

$X$ vs time for ten independent trajectories for MD (left column) and BD (right column) at $\varphi =0.610$ [(a) and (c)] and 0.613 [(b) and (d)], as indicated in the figures. Six of the runs at 0.610 are from Ref. [30].

Figure 2

$\text{MSD}/{\sigma }^2$ (in blue, top line), $X$ (in black, middle curve), and $N_{\mathrm{av}}/N$ (in red, bottom curve) vs time for (a) an MD trajectory and (b) a BD one, each at $\varphi =0.613$.

Figure 3

(a) Mean crystallinity jump $X$ at different $\varphi$ for MD (black circles) and BD (red squares); (b) time needed to crystallize $20\%$ of the system as a function of $\varphi$. $60\%$ of data at 0.610 and all data at 0.612 and 0.614 are from Ref. [30].

Figure 4

Black arrows: Displacement vectors of avalanche particles represented in $xyz$. Red dots: Solidlike particles. (a) MD, (b) BD. Both at $\varphi =0.613$.

Figure 5

Ratio between the Newtonian and the Brownian times required for a particle to diffuse its own diameter (MSD $={\sigma }^2$) as a function of packing fraction. Red circles: Our calculations for $\varphi <{\varphi }_g$ (${\varphi }_g=0.586$ [30]). Solid line: Linear fit to the red circles. Dashed line: Linear extrapolation to the packing fractions where we have studied devitrification (green circles). Error bars have been computed performing ten independent runs.