Experimental Verification of Rapid, Sporadic Particle Motions by Direct Imaging of Glassy Colloidal Systems

We analyze data from confocal microscopy experiments of a colloidal suspension to validate predictions of rapid sporadic events responsible for structural relaxation in a glassy sample. The trajectories of several thousand colloidal particles are analyzed, confirming the existence of such rapid events responsible for the structural relaxation of significant regions of the sample, and complementing prior observations of dynamical heterogeneity. Thus, our results provide the first direct experimental verification of the emergence of relatively compact clusters of mobility which allow the dynamics to transition between the large periods of local confinement within its potential energy surface, in good agreement with the picture envisioned long ago by Adam and Gibbs and Goldstein.

Figure 1

(a) Distance matrix ${\Delta }^2(t^{\prime },t^{\prime \prime })$ for portion $\xi =1$. The gray level corresponds to values of ${\Delta }^2(t^{\prime },t^{\prime \prime })$ that are given to the right of the figure. Units are $\mu {\mathrm{m}}^2$. Inset: for the analysis, we followed the colloidal particles that were initially ($t=0$) within the boundaries of rectangular prisms: $\xi =6$ (blue, the complete system), magenta, green, yellow, orange and $\xi =1$ (red, smallest region), respectively. All $\xi$ have the same depth $L_z$. Colloidal particles are not shown. (b) Averaged squared displacement ${\delta }^2(t,\theta )$ for all $\xi$. Each series (analysis over each $\xi$) is shifted by $0.5\mu {\mathrm{m}}^2$ respect the former one. For comparison we included the corresponding average values of ${\delta }^2(t,\theta )$ over all times, $⟨{\delta }^2(t,\theta )⟩$ (dashed colored lines, also shifted). The value of $\theta$ is 72 s. Inset: $\gamma =|{\delta }_{\xi }^2(5706\mathrm{s},\theta )-⟨{\delta }^2(t,\theta ){⟩}_{\xi }|/{\sigma }_{\xi }$ vs $\xi$, where $\sigma$ is the standard deviation in ${\delta }^2$ and 5706 s is the time of the largest average squared displacement. Subscript $\xi$ means that the function was evaluated for molecules in $\xi$. A maximum for $\xi =2$ is observed. (c) The function $m(t,\theta )$ for $\xi =1$ and its average value over all times (dashed black line).

Figure 2

Similar to Fig. 1a, but for $\varphi =0.46$ and for a (rectangular prism) region of approximately the size of $\xi =1$. At this $\varphi$, $N(1)=44$ and $t^{*}=300\mathrm{s}$.

Figure 3

Radial probability distribution functions $P(r)$ for $\xi =2$ and $\theta =72\mathrm{s}$. The black curve is $4\pi r^2{G}_s(r,\theta )$, the self-part of the van Hove function, and the gold curve is a Gaussian with the same value of $⟨r^2(\theta )⟩$. The crossing point of these two curves at $r\approx 0.23\mu \mathrm{m}$ is used as a threshold to identify the democratically moving particles. The blue and magenta curves are the average of $4\pi r^2{\widehat{G}}_s(r,t,t+\theta )$ for different values of $t$ in which the system is inside a MB (see text for details), and a transition (TR) from $t=5706\mathrm{s}$ to $t+\theta$.

Figure 4

Position of democratic particles for: (left) a MB-MB transition from $t=5706\mathrm{s}$ to $t+\theta$ and (right) $t=7290\mathrm{s}$ to $t+\theta$ inside a MB. The data are for $\xi =2$, $\theta =72\mathrm{s}$, $\varphi =0.56$.