We present a rheology study of associating polymers. The associating polymers are telechelic, composed of a water-soluble backbone (polyethylene oxide) terminated by hydrophobic moieties (C16H33). In aqueous solutions, these polymers self-assemble to form micellar structures. Above a critical concentration, approximately 1 wt % of polymer, bridging between the micelles forms a transient network. Traditionally, the viscoelastic response of these polymeric solutions has been described using the Maxwell model. In this work we measure the viscoelastic properties over an extended frequency range (0.01–6000 Hz) using microrheology, and show that at high frequencies the rheology behaves as the square root of the oscillation frequency. To fit the data, we use a combination of the Maxwell model and the Rouse model. The Maxwell model accounts for the hydrophobic associations between the polymeric micelles, and the Rouse model accounts for the microscopic dynamics of the individual micelles.
Fig. Diagram of the forces on a colloidal particle in an oscillating optical trap embedded in a viscoelastic medium.
Fig. (A) The real and imaginary parts of the complex shear modulus for a 0.75 wt % aqueous solution of Mn=67.6 kg/mol telechelic PEO probed by a 1.6 mm diameter silica probe particle with the oscillating optical tweezers technique. The solid line indicates the viscous contribution from the solvent, G”=hsw, where hs=0.01 P, the viscosity of water at room temperature. (B) The real part of the complex shear modulus for a 2.5 wt % aqueous solution of Mn=67.6 kg/mol telechelic PEO probed by a 1.6 mm diameter silica probe particle. The dark gray symbols represent the imaginary part of the complex shear modulus as measured by a bulk rheology technique.
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