The effect of depletion layer on diffusion of nanoparticles in solutions of flexible and polydisperse polymers

Abstract

We introduce a model of diffusion of nanoparticles in solutions of flexible, polydisperse polymers. The model takes into account the effect of depletion layer with soft boundaries. The presence of depletion layer leads to nonlinear dependence of the mean square displacement (MSD) on time. Our model may be an alternative choice for the study of those experimental systems where the crossover between subdiffusion and normal diffusion is observed. Its advantage is mathematical simplicity: it allows easy identification of the crossover times and distances, which are here associated with the depletion layer thickness. The soft boundaries of the depletion layer, generated by the flexible and polydisperse polymers, are here approximated by two shells enclosed one in another, which may be interpreted as approximations of polymer density profiles around the probe. We show a very good agreement of the model with dynamic light scattering (DLS) measurements of diffusion of nanoparticles in solutions of polyethylene glycol (PEG).