Size-Dependent Localization in Polydisperse Colloidal Glasses

We have investigated concentrated suspensions of polydisperse hard spheres and have determined the dynamics and sizes of individual particles using confocal microscopy. With increasing concentration, the dynamics of the small and large particles start to differ. The large particles exhibit slower dynamics and stronger localization. Moreover, as the particle size increases, the local volume fraction ${\varphi }_{\mathrm{loc}}$ also increases. In the glass state, the localization length significantly decreases beyond ${\varphi }_{\mathrm{loc}}\approx 0.67$. This suggests a link between local crowding and dynamical heterogeneities. However dynamical arrest of subpopulations seems not directly linked to a large value of ${\varphi }_{\mathrm{loc}}$, indicating the importance of collective effects.

Figure 1

Particle size distribution $P(R)$ for samples with different volume fractions $\varphi$, as indicated. Dashed black lines delimit the subpopulations of the 20% smallest and 20% largest particles, respectively, for the sample with $\varphi =0.61$

Figure 2

Mean squared displacement (MSD), $⟨\mathrm{\Delta }{r}^2(t)⟩$, as a function of delay time $t$ for samples with different volume fractions $\varphi$, as indicated. The MSDs are based on all particles (symbols), the 20% smallest (blue solid lines) and the 20% largest particles (red dashed lines). Inset: Squared localization length $L^2$, characterized by the MSD at the shortest observed delay time, $⟨\mathrm{\Delta }{r}^2(t_{\mathrm{i}}=3\mathrm{s})⟩$, as a function of the particle radius $R$ for the sample with $\varphi =0.61$. Vertical dashed lines indicate the 20% smallest and 20% largest particles, respectively (as in Fig. 1), and the horizontal lines the mean localization lengths of the smallest, all, and the largest particles, respectively (top to bottom).

Figure 3

Pair distribution functions for samples with different volume fractions (a) $\varphi =0.53$, (b) 0.54, (c) 0.55, (d) 0.58, (e) 0.59 and (f) 0.61. They are based on the arrangement of all particles around any particle, $g(r)$ (symbols), around one of the 20% smallest particles, $g_{\mathrm{s}}(r)$ (blue solid lines), and around one of the 20% largest particles, $g_{\mathrm{l}}(r)$ (red dashed lines). The vertical line indicates the average particle diameter $2⟨R⟩$.

Figure 4

(a) Projection of a $5\text{−}\mu \mathrm{m}$-thick and $51\times 51\mu {\mathrm{m}}^2$-wide slice of the sample with total volume fraction $\varphi =0.61$. All, the 20% smallest, and the 20% largest particles are shown (left to right). Particle radius $R$ and Voronoi volume $V$ are represented by the points’ sizes and colors (as indicated), respectively. (b) Voronoi volume $V$ and (c) local volume fraction ${\varphi }_{\mathrm{loc}}$ as a function of particle radius $R$. The solid lines represent power-law fits [56]. (d) Normalized squared localization length $⟨\mathrm{\Delta }{r}^2(t_{\mathrm{i}})⟩/⟨\mathrm{\Delta }{r}_0^2⟩$ as a function of ${\varphi }_{\mathrm{loc}}$. The vertical dashed line indicates ${\varphi }_{\mathrm{loc}}=0.67$. Data are shown for total volume fractions $\varphi =0.54$ (square), 0.58 (triangle), 0.59 (diamond), and 0.61 (circle).