Brownian motion of colloidal spheres in aqueous PEO solutions

The Brownian motion of colloidal spheres in aqueous poly(ethylene oxide) (PEO) solutions ranging in concentration from 0.2 to 15 wt % is measured with diffusing wave spectroscopy over more than 6 decades of time. The measured colloidal sphere mean-squared displacements are shown to satisfy the generalized Stokes-Einstein relation that relates the particle mean-squared displacement to the polymer solution shear modulus as the microrheological creep compliance calculated from the colloidal sphere Brownian motion was found to agree with that measured by mechanical rheometry. The microrheological zero shear viscosity concentration dependence for the entangled solution regime, η ∼ c ^4.7, is in agreement with that reported by others from mechanical rheometry measurements on polymergood solvent solutions and is stronger than the tube model prediction, η ∼ c ^3.9. Essentially the entire deviation between the predicted and measured entangled solution regime zero shear viscosity concentration dependence is accounted for in the difference between the predicted, τ ∼ c ^1.6, and measured, τ ∼ c ^2.3, terminal relaxation time concentration dependence as the predicted, G ∼ c ^2.3, and measured, G ∼ c ^2.4, plateau modulus scaling at the terminal relaxation time are in excellent agreement. A power-law viscoelastic "plateau" region is observed to persist to frequencies of at least 10 ⁵ s ^-1, thereby extending knowledge of polymer solution dynamics by nearly 3 decades of frequency. Interestingly, the high-frequency shear modulus was found to scale as G ∼ c ^4.5, not as G ∼ c ^2.3.