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Soft materials, such as gels and colloidal glasses, often exhibit different rheological properties at bulk and microscopic scales as a result of their complex microstructure. In this study, we have used multiple particle tracking microrheologies to explore how rheological properties vary with probe size in an aqueous dispersion of Laponite®, a “model drilling fluid” and discotic colloidal clay that forms an aging colloidal gel under appropriate conditions. We have shown that the microrheological properties are dependent on the probe particle size, implying that the dispersion is heterogeneous across different length scales. Probing at smaller length scales results in the observation of lower viscoelastic moduli and a delay in gelation time. We have also proposed a microstructural explanation for these phenomena: as the material ages, a porous network structure develops that traps larger probe particles, while smaller probes generally have more time to diffuse relatively unhindered through pores and more weakly gelled regions. In support of this hypothesis, we observed that the probe dynamics develop significant spatial heterogeneity as the system ages. Analysis of these heterogeneities for different probe sizes indicates a microstructural length scale in the system that is similar to the length scales measured previously by light scattering . In light of these results, it would be interesting to further investigate the microstructural heterogeneities and their associated length scales with two-point microrheology. With this method, the viscoelastic moduli could be explored as a function of probe separation, although we reserve this study for future work. In addition to heterogeneities, we find that as the system ages the probe particles exhibit correlations between successive displacements, which has been reported to be evidence of microstructural confinement. However, by analyzing trajectories of a Brownian particle in a continuum Kelvin–Voigt material, we find that correlations between successive probe displacements are more directly related to the apparent local elasticity. We propose that a better measure of the microstruc- tual confinement is the length scale at which deviations from a simple linear scaling are observed in these successive correlations. An interesting problem for future work would be to determine the corresponding correlations for probes diffusing in a Newtonian fluid confined by solid walls, which provides a simple model of a porous microstructure. Finally, motivated by the observed probe-size dependence of rheological properties and the proposed microstructural description, we identify a concentration–probe-size superposition, obtaining approximate scalings for the observed gelation time as a function of probe size and Laponite® concentration.

The results form this study will aid in the understanding of the structure and rheology of aqueous Laponite® dispersions. Furthermore, the methods used here may also find broader general application to other structured complex fluids and gels. The methods are particularly suitable for analyzing materials that serve different functions at different length scales, and that as a result must have different rheological properties across length scales. Possible examples include the cell cytoskeleton, which provides structural stabil- ity on the length scale of the entire cell, but must also allow macromolecules and vesicles to diffuse within the pores. Finally, the results of this study show that multiple particle tracking can provide insight into the structure of evolving materials, even when the system is inhomogeneous at the probe length scale.