An aqueous suspension of the synthetic clay Laponite undergoes a transition from a liquid-like ergodic state to a glass-like nonergodic arrested state. In an observation that closely resembles the dynamical slowdown observed in supercooled liquids, the phenomenon of kinetic arrest in Laponite suspensions is accompanied by a growth in the $alpha$-relaxation time with increasing sample aging time, $t_{w}$. The ubiquitous dynamic slowdown and fragile behavior observed in glass forming liquids approaching the glass transition is typically ascribed to the growth in the size of distinct dynamical heterogeneities. In this article, we present the characterization of the dynamical heterogeneities in aging colloidal Laponite clay systems by invoking the three-point dynamic susceptibility formalism. The average time-dependent two-point intensity autocorrelation and its sensitivity to the control parameter $t_{w}$ are probed in dynamic light scattering experiments. Distributions of relaxation time scales deduced from Kohlrausch-Williams-Watts equation widen with increasing $t_{w}$ signifying the heterogeneous dynamic slowdown. A suitable formalism to calculate three-point correlation function is employed for aging colloidal suspension where the main control parameter is $t_{w}$. The calculated three-point dynamic susceptibility exhibits a peak, with the peak height increasing with evolving $t_{w}$. The number of dynamically correlated particles is seen to initially increase with increasing $t_{w}$ at a fast rate, before eventually slowing down close to the non-ergodic transition point.This observation is in agreement with reports on supercooled liquids. Our study confirms the growth of dynamical heterogeneities in suspensions of Laponite, thereby shedding new light on the fragile supercooled liquid-like dynamics of aging suspensions of these anisotropic, charged, colloidal clay nanoparticles.
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