Investigation ofq-dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy

Abstract

We use time-resolved x-ray photon correlation spectroscopy to investigate the slow dynamics of colloidal gels made of moderately attractive carbon black particles. We show that the slow dynamics is temporally heterogeneous and quantify its fluctuations by measuring the variance chi of the instantaneous intensity correlation function. The amplitude of dynamical fluctuations has a nonmonotonic dependence on scattering vector q, in stark contrast with recent experiments on strongly attractive colloidal gels [Duri and Cipelletti, Europhys. Lett. 76, 972 (2006)]. We propose a simple scaling argument for the q-dependence of fluctuations in glassy systems that rationalizes these findings.

Beyond simple exponential correlation functions and equilibrium dynamics in x-ray photon correlation spectroscopy

“…The positions of the peak τ * as a function of Q and as a function of waiting time are shown in figures 5 and 6, respectively, illustrating this close correspondence between the maximum of the temporal heterogeneity and the correlation time. Similar correspondence has been observed for χ (Q, t) for several systems [31], [37]- [39], [49,73] and also for χ 4 , where the peak position is considered a measure of the persistence of spatial heterogeneities [63]- [66]. While the position of the peak in χ(Q, t) unsurprisingly follows this common trend, the magnitude of χ (Q, t) for the sheared depletion gel is significantly smaller than the variance characterizing the hyper-diffusive dynamics in dilute gels measured with DLS [31], reflecting the relatively smooth evolution in dynamics observed in figure 3.…”

“…While the position of the peak in χ(Q, t) unsurprisingly follows this common trend, the magnitude of χ (Q, t) for the sheared depletion gel is significantly smaller than the variance characterizing the hyper-diffusive dynamics in dilute gels measured with DLS [31], reflecting the relatively smooth evolution in dynamics observed in figure 3. However, the magnitude of χ(Q, t) in figure 7 is similar to the magnitudes seen for other dense colloidal systems with XPCS [37]- [39]. Given this small magnitude, we note that the results should be viewed with caution, particularly since the ageing of the system will lead to a variance in the instantaneous correlations irrespective of any dynamic heterogeneity.…”

“…Indeed, a power-law scaling relation between χ 4 and a corresponding temporal quantity similar to χ has been advanced to connect the spatial and temporal heterogeneity of collective dynamics in granular materials [63,65]. This connection thus opens up an opportunity with XPCS to make contact with recent key advances in the study of disordered, glassy and out-of-equilibrium materials through analysis of χ (Q, t), and several recent XPCS studies [37]- [39] of glassy colloidal systems have considered the behavior of χ(Q, t).…”

Self-assembly and cooperative dynamics of a model colloidal gel network

“…A q-dependent dynamical heterogeneity in colloidal gels has indeed been reported in recent light scattering experiments [15,60]. It is worth mentioning that the experiments do not show a peak in χ 4 associated to thermally induced fluctuations of the gel branches (i.e.…”

Dynamical Heterogeneity and Nonlinear Susceptibility in Supercooled Liquids with Short-Range Attraction

“…Indeed, as discussed by Chandler et al [15] (see also Refs. [27,28]), the k dependence of 4 k; t is a useful way to probe the various length scales associated with dynamical heterogeneity. The k dependence of 4 k; t should not be confused with that of S 4 k; t , which provides a four-point analog to the static structure factor and allows for the direct extraction of a length scale associated with cooperative heterogeneous motion.…”