Linking single particle rearrangements to delayed collapse times in transient depletion gels

Weak depletion gels with particle radii of ∼200-500nm have been reported to display a time-dependent settling behaviour where an initially space spanning gel displays a catastrophic collapse after a characteristic period of time, defined as the delay time. Several experiments suggest that thermally activated particle rearrangements promote macroscopic gel coarsening, which ultimately triggers the rapid collapse. The delay time is found to be a sensitive function of the colloid volume fraction and polymer concentration. We have performed systematic experiments on the silica-decalin-polystyrene depletion system to explore how colloid volume fraction, polymer concentration, particle radius and ratio of polymer radius of gyration to particle radius influence the delayed collapse time of transient gels. We employ a recently developed activated barrier-hopping theory to make predictions of the timescales over which colloids can escape localized states as a function of system parameters. Our study shows that, within experimental uncertainty, delay times follow an exponential dependence on a composite variable that is a function of the three controllable system variables, which is very similar to that predicted for the thermally activated local rearrangement timescales. This provides support for the hypothesis that thermally activated particle motions are a rate-limiting step in determining the timescale for the initiation of catastrophic collapse of transient gels. In addition, the model explains why transient gel formation is found to be absent in weak depletion gels as particle sizes are reduced.