Microscopic ergodicity breaking governs the emergence and evolution of elasticity in glass-forming nanoclay suspensions

We report a study combining x-ray photon correlation spectroscopy (XPCS) with in situ rheology to investigate the microscopic dynamics and mechanical properties of aqueous suspensions of the synthetic hectorite clay Laponite, which is composed of charged, nanometer-scale, disk-shaped particles. The suspensions, with particle concentrations ranging from 3.25 to 3.75 wt %, evolve over time from a fluid to a soft glass that displays aging behavior. The XPCS measurements characterize the localization of the particles during the formation and aging of the soft-glass state. The fraction of localized particles, ${f}_{0}$, increases rapidly during the early formation stage and grows more slowly during subsequent aging, while the characteristic localization length ${r}_{\mathrm{loc}}$ steadily decreases. Despite the strongly varying rates of aging at different concentrations, both ${f}_{0}$ and ${r}_{\mathrm{loc}}$ scale with the elastic shear modulus ${G}^{\ensuremath{'}}$ in a manner independent of concentration. During the later aging stage, the scaling between ${r}_{\mathrm{loc}}$ and ${G}^{\ensuremath{'}}$ agrees quantitatively with a prediction of naive mode coupling theory. Breakdown of agreement with the theory during the early formation stage indicates the prevalence of dynamic heterogeneity, suggesting the soft solid forms through precursors of dynamically localized clusters.