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We consider gelation of colloidal particles in suspension after cessation ofshear flow. Particle aggregation is driven by a temperature-tunable attractivepotential which controls the growth of clusters under isothermal conditions. Aseries of frequency resolved time sweeps is used to systematically reconstructthe frequency dependent dynamic moduli as a function of time and temperature orattraction strength. The data display typical hallmarks of gelation with anabrupt transition from a fluid state into a dynamically arrested gel stateafter a characteristic gelation time $t_g$ that varies exponentially withtemperature and serves to collapse the evolution of the system onto a universalcurve. We observe the viscoelastic properties of the critical gel where we findthat $G'(\omega)\approxeq G''(\omega)\sim \omega^{n_c}$ where $n_c=0.5$ in anarrow time window across all attraction strengths. We measure a dynamiccritical exponent of $\kappa=0.25$ which is similar to that observed incrosslinked polymer gels. The approach to the critical gel is thereforegoverned 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, therelaxation moduli of the near-critical gels are identical across thetemperatures considered, with $G(t)\approx0.33t^{-0.5}$. This suggests anunderlying strong similarity in gel structure in the regime of attractionstrengths considered, despite the differences in aggregation kinetics. Wecontrast these findings with the behavior of a colloidal glass undergoingdynamical arrest where no critical state is observed and where the arrest timeof the system displays a marked frequency dependence. These findings highlightthe underlying structural differences between colloidal gels and glasses whichare manifest in their dynamic properties in the vicinity of the liquid-to-solidtransition.

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