  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.
