Viscoelasticity of a colloidal gel during dynamical arrest: evolution through the critical gel and comparison with a soft colloidal glass

We consider gelation of colloidal particles in suspension after cessation of shear flow. Particle aggregation is driven by a temperature-tunable attractive potential which controls the growth of clusters under isothermal conditions. A series of frequency resolved time sweeps is used to systematically reconstruct the frequency dependent dynamic moduli as a function of time and temperature or attraction strength. The data display typical hallmarks of gelation with an abrupt transition from a fluid state into a dynamically arrested gel state after a characteristic gelation time $t_g$ that varies exponentially with temperature and serves to collapse the evolution of the system onto a universal curve. We observe the viscoelastic properties of the critical gel where we find that $G'(\omega)\approxeq G''(\omega)\sim \omega^{n_c}$ where $n_c=0.5$ in a narrow time window across all attraction strengths. We measure a dynamic critical exponent of $\kappa=0.25$ which is similar to that observed in crosslinked polymer gels. The approach to the critical gel is therefore governed by $\eta_0\sim-\epsilon^{-s}$ and $G_e\sim\epsilon^z$ with $s=z=2$ where $\epsilon=p/p_c-1$ is the distance to the gel point. Remarkably, the relaxation moduli of the near-critical gels are identical across the temperatures considered, with $G(t)\approx0.33t^{-0.5}$. This suggests an underlying strong similarity in gel structure in the regime of attraction strengths considered, despite the differences in aggregation kinetics. We contrast these findings with the behavior of a colloidal glass undergoing dynamical arrest where no critical state is observed and where the arrest time of the system displays a marked frequency dependence. These findings highlight the underlying structural differences between colloidal gels and glasses which are manifest in their dynamic properties in the vicinity of the liquid-to-solid transition.