Diffusing wave microrheology of highly scattering concentrated monodisperse emulsions

Abstract

Motivated by improvements in diffusing wave spectroscopy (DWS) for nonergodic, highly optically scattering soft matter and by cursory treatment of collective scattering effects in prior DWS microrheology experiments, we investigate the low-frequency plateau elastic shear moduli Gp0 of concentrated, monodisperse, disordered oil-in-water emulsions as droplets jam. In such experiments, the droplets play dual roles both as optical probes and as the jammed objects that impart shear elasticity. Here, we demonstrate that collective scattering significantly affects DWS mean-square displacements (MSDs) in dense colloidal emulsions. By measuring and analyzing the scattering mean free path as a function of droplet volume fraction φ, we obtain a φ-dependent average structure factor. We use this to correct DWS MSDs by up to a factor of 4 and then calculate Gp0 predicted by the generalized Stokes–Einstein relation. We show that DWS-microrheological Gp0 (φ) agrees well with mechanically measured Gp0 (φ) over about three orders of magnitude when droplets are jammed but only weakly deformed. Moreover, both of these measurements are consistent with predictions of an entropic–electrostatic–interfacial (EEI) model, based on quasi-equilibrium free-energy minimization of disordered, screened-charge–stabilized, deformable droplets, which accurately describes prior mechanical measurements of Gp0 (φ) made on similar disordered monodisperse emulsions over a wide range of droplet radii and φ. This very good quantitative agreement between DWS microrheology, mechanical rheometry, and the EEI model provides a comprehensive and self-consistent view of weakly jammed emulsions. Extensions of this approach may improve DWS microrheology on other systems of dense, jammed colloids that are highly scattering.