Nonlinear Concentration Dependence of the Collective Diffusion Coefficient of TiO2 Nanoparticle Dispersions

Aqueous dispersions of titania nanoparticles are shown to yield collective diffusion coefficients in dynamic light-scattering measurements that depend nonlinearly on particle concentration under dilute conditions. From theory, one expects a linear dependence for monodisperse systems except for strongly interacting charged particles in low ionic strength media. Angularly resolved dynamic light-scattering measurements reveal that aggregates are present, which explains the collective diffusion coefficient tending to lower values in the dilute limit than the Stokes-Einstein diffusion coefficient of the nanoparticles. A simple theoretical model based on mixtures of charged nanoparticle spheres and small amounts of larger-sized neutral or weakly charged spheres, modeling the presence of aggregates, is applied and shown to yield predictions in qualitative accord with the experimental trends. In particular, the downward curvature of the collective diffusion coefficient on diluting the system arises in the model from nanoparticles being driven into close proximity to the larger particles by electrostatic interactions. Similar experimental trends observed in silica dispersions suggest that the behavior is not an isolated finding. This study clearly shows that a small number of larger aggregates dramatically change the measured value of the collective diffusion coefficient; thus, care must be exercised when characterizing nanoparticles with dynamic light scattering.