Resolving Long-Range Spatial Correlations in Jammed Colloidal Systems Using Photon Correlation Imaging

We introduce a new dynamic light scattering method, termed photon correlation imaging, which enables us to resolve the dynamics of soft matter in space and time. We demonstrate photon correlation imaging by investigating the slow dynamics of a quasi-two-dimensional coarsening foam made of highly packed, deformable bubbles and a rigid gel network formed by dilute, attractive colloidal particles. We find the dynamics of both systems to be determined by intermittent rearrangement events. For the foam, the rearrangements extend over a few bubbles, but a small dynamical correlation is observed up to macroscopic length scales. For the gel, dynamical correlations extend up to the system size. These results indicate that dynamical correlations can be extremely long-ranged in jammed systems and point to the key role of mechanical properties in determining their nature.

Figure 1

Schematic view of the low-angle, space-resolved light scattering apparatus.

Figure 2

Dynamic activity maps; the bars correspond to 2 mm. The color code indicates, in units of standard deviations $\sigma$, the fluctuations of the local $c_I$ with respect to its temporal average. (a) Brownian particles ($\tau =0.2\mathrm{s}$, $\tau /{\tau }_r=0.0048$); (b) foam ($\tau =3\mathrm{s}$, $\tau /{\tau }_r=0.021$); (c),(d) colloidal gel ($\tau =500\mathrm{s}$, $\tau /{\tau }_r=0.1$) during a rearrangement event and a quiescent period, respectively.

Figure 3

Instantaneous degree of correlation $c_I(t,\tau ,\mathbf{r})$, normalized by its standard deviation $\sigma (\tau ,\mathbf{r})$, measured at three different locations in the sample, as a function of reduced time $t/{\tau }_r$ (for the sake of clarity, the curves are offset along the vertical axis and only a limited portion of the data is shown). Data have been corrected for instrumental noise as explained in Ref. 23. For each sample, curves are labeled by the distance in millimeters with respect to the location for the black curve. Top: Brownian particles (the labels 0, 0.075, and 3.8 refer to the traces from bottom to top); middle: foam; bottom: colloidal gel. For all samples, $\tau /{\tau }_r$ is as in Fig. 2.

Figure 4

Spatial correlation of the dynamics for diluted Brownian particles (${\tilde{G}}_4$, blue squares), for a foam ($G_4$, orange triangles), and for a colloidal gel ($G_4$, black circles). The lines are stretched exponential fits to the decay of $G_4$, yielding $\xi =0.6$ and 16.4 mm for the foam and the gel, respectively. For all samples, $\tau /{\tau }_r$ is as in Fig. 2.