The small-scale rheology of Carbopol ETD 2050, a polymer gel with a yield stress, is studied as a function of polymer concentration by measuring the diffusion of submicron-sized spherical fluorescent particles suspended in gel. Dynamic light scattering is used to determine the mean-squared displacement (of the particles as a function of lag time t. Fluorescence microscopy is used to track the particle trajectories directly, from which and the van Hove correlation function are determined. From our results we calculate the microrheological viscous and elastic moduli of the material. The two techniques cover complementary ranges of tau and and give results that agree well. The microrheological moduli are substantially smaller than the bulk values as determined by conventional shear rheometry. The bulk viscoelastic behavior is dominated by the elastic modulus, while at low enough concentrations and high enough frequencies the microrheological response is predominantly viscous. These results will be discussed in the context of the gel structure.

Particle-tracking methods are used to study gelation in a colloidal suspension of Laponite clay particles. We track the motion of small fluorescent polystyrene spheres added to the suspension, and obtain the micron-scale viscous and elastic moduli of the material from their mean-squared displacement. The fluorescent spheres move subdiffusively due to the microstructure of the suspension, with the diffusive exponent decreasing from close to one at early times to near zero as the material gels. The particle-tracking data show that the system becomes more heterogeneous on the microscopic scale as gelation proceeds. We also determine the bulk-scale moduli using small-amplitude oscillatory shear rheometry. Both the macroscopic and microscopic moduli increase with time, and on both scales we observe a transition from a primarily viscous fluid to an elastic gel. We find that the gel point, determined as the time at which the viscous and elastic moduli are equal, is length-scale dependent--gelation occurs earlier on the bulk scale than on the microscopic scale.

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