Brownian Dynamics simulations of aging colloidal gels

Colloidal gel aging is investigated using very long runs of brownian dynamics simulations. The Asakura Oosawa description of the depletion interaction is used to model a simple colloid polymer mixture. Several regimes are identified during gel formation. The Intermediate scattering function displays a double decay characteristic of systems where some kinetic processes are frozen. The $\beta$ relaxation at short times is explained in terms of the Krall-Weitz model for the decorelation due to the elastic modes present. The $\alpha$ relaxation at long times is well described by a stretched exponential, showing a wide spectrum of relaxation times for which the $q$ dependence is $\tau_{\alpha} = q^{-2.2}$, lower than for diffusion. For the shortest waiting times, a combination of two stretched exponentials is used, suggesting a bimodal distribution. The extracted relaxation times vary with waiting time as $\tau_{\alpha}=\tau_w^{0.66}$, slower than the simple aging case. The real space displacements are found to be strongly non-Gaussian, correlated in space and time. We were unable to find clear evidence that the gel aging was driven by internal stresses. Rather, we hypothesise that in this case of weakly interacting gels, the aging behaviour arises due to the thermal diffusion of strands, constrained by the percolating network which ruptures discontinuously. Although the mechanisms differ, the similarity of some of the results with the aging of glasses is striking.