Length scale dependence of dynamical heterogeneity in a colloidal fractal gel

Abstract

We use time-resolved dynamic light scattering to investigate the slow dynamics of a colloidal gel. The final decay of the average intensity autocorrelation function is well described by $g\_2(q,τ)-1 \sim \exp[-(τ/τ\_\mathrm{f})^p]$, with $τ\_\mathrm{f} \sim q^{-1}$ and $p$ decreasing from 1.5 to 1 with increasing $q$. We show that the dynamics is not due to a continuous ballistic process, as proposed in previous works, but rather to rare, intermittent rearrangements. We quantify the dynamical fluctuations resulting from intermittency by means of the variance $χ(τ,q)$ of the instantaneous autocorrelation function, the analogous of the dynamical susceptibility $χ\_4$ studied in glass formers. The amplitude of $χ$ is found to grow linearly with $q$. We propose a simple --yet general-- model of intermittent dynamics that accounts for the $q$ dependence of both the average correlation functions and $χ$.