Scaling between structural relaxation and particle caging in a model colloidal gel

In glassy dynamics, the rattling of particles in a cage formed by their neighbors is typically limited to a length scale of the order of the particle diameter but is nevertheless strongly coupled to the overall structural arrest of the system (solidification). Furthermore, the rattling amplitude and the structural relaxation time have been recently shown to follow the same scaling form in various polymer melts and supercooled liquids. In this paper we analyze from this perspective for the first time the glassy dynamics emerging from the formation of a persistent network in a model colloidal gel at very low density. The structural relaxation time of the gel network is compared with the mean squared displacement at short times, corresponding to the localization length associated to the presence of energetic bonds. Interestingly, we find that the same type of scaling as for the dense glassy systems holds. Our findings elucidate the strong coupling between the cooperative rearrangements of the gel network and the single particle localization in the structure, and support the general nature of the scaling proposed.