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

Abstract

We consider the 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 tg 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′(ω)≊G″(ω)∼ωnc, where nc = 0.5 in a narrow time window across all attraction strengths. We measure a dynamic critical exponent of κ = 0.25 which is similar to that observed in cross-linked polymer gels. The approach to the critical gel is therefore governed by zero-shear viscosity η0∼−ϵ−s and plateau modulus Ge∼ϵz with s = z = 2, where ϵ = p/pc − 1 is the distance to the gel point in appropriate reaction coordinates. Remarkably, the relaxation moduli of the near critical gels are identical across the temperatures considered, with G(t) ≈ 0.33 t−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.