Microrheology of model quasi-hard-sphere dispersions

Abstract

We examine if a microrheological interpretation of probe diffusion in model dispersions dominated by excluded-volume interactions and hydrodynamics captures the underlying viscoelastic relaxation mechanisms reasonably accurately. Standard dynamic light scattering is used to measure mean-squared displacements (MSDs) of visible probe particles in a refractive-index-matched model hard-sphere dispersion [poly(methyl methacrylate) particles in cycloheptyl alcohol]. The loss and storage moduli of the dispersion are extracted as functions of frequency ω from the measured MSDs. We suggest a semiempirical modification of the generalized Stokes–Einstein relation to convert the MSD to the viscoelastic modulus G*(ω). The results show a volume-fraction-dependent plateau G∞ at high frequencies in the storage modulus consistent with the domination of lubrication stresses. Viscoelasticity sets in at volume fractions φ above 0.2, and for 0.2≲φ≲0.45 the ratio of the mean viscoelastic relaxation time 〈τ〉 to the Peclet time ...