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 $⟨r^2\left(\tau \right)⟩$ of the particles as a function of lag time $\tau$. Fluorescence microscopy is used to track the particle trajectories directly, from which $⟨r^2\left(\tau \right)⟩$ 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 $⟨r^2\left(\tau \right)⟩$ 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.

• Received 20 January 2006

DOI:https://doi.org/10.1103/PhysRevE.73.041405