Diffusing wave spectroscopy has been used to investigate the thermally driven displacement of colloidal particles dispersed in solutions of associating polymers (APs). The effect of varying colloidal probe size on the measured particle displacements is studied in particular. Recent theories of microrheology are examined in light of the observed effects. The associating polymer used in this research was a linear polyethylene oxide (PEO) chain (molecular weight 35 000 g/mole) with a ${\mathrm{Cl}}_{14}$ aliphatic group appended to each end of the PEO. Above a critical concentration, the associating polymers display linear viscoelasticity consistent with the Maxwell model. The concentration of aqueous AP solutions was varied from 0.25 to 4.0 wt. %. At low concentration of APs, the mean square displacement of the colloidal beads was indistinguishable from simple Brownian diffusion in the aqueous solvent. However, at concentrations greater than 0.5 wt. %, the mean square displacement differed from simple diffusion in a way that was found to be consistent with the Maxwell model linear viscoelasticity (LVE) of the AP solutions. Significantly, for the most concentrated solutions, as the probe particle size was varied from 0.3 to 2.2 μm, the observed mean square displacement deviated substantially from the generalized Stokes-Einstein behavior predicted by microrheological theories. Our experiments showed that these deviations could not be attributed to specific physicochemical interactions at the probe-matrix interface, since observed mean square displacements were independent of different probe surface chemistries studied. Moreover, this particle size effect was not observed in semidilute, high molecular weight PEO solutions (molecular weight $4.0\times {10}^6\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}).\mathrm{}$ We concluded that possible effects of AP network compressibility and AP depletion at the probe surface could not account for the observed particle size effects. We examined recent reports of the structural heterogeneity in AP solutions for their possible connection to our observation of the breakdown of the generalized Stokes-Einstein equation for this system. Numerical conversion of the microscopic results to the linear viscoelastic moduli, $G^{\prime }\left(\omega \right)$ and $G^{″}\left(\omega \right),$ by means of a constrained regularization method (CONTIN), demonstrates that the experiments with larger probe particles are most consistent with the single-mode Maxwell model LVE observed by macroscopic mechanical rheology.

• Received 7 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.061504