Hydrodynamic Drag on Diffusing Nanoparticles for Size Determination

Size estimates of proteins and nanoparticles obtained from measured diffusivities using the Stokes-Einstein relation are typically twice the true size. We report here a new drag law obtained by allowing for the increase in shear viscosity near the surface of the particle and solving the Navier Stokes equations for viscous flow to leading order in this increase. This improvement in the description of the drag force permits accurate size measurements for particles with radii of a few nanometers. We discuss literature data on the hydrodynamic radii of CdSe quantum dots of known size, simulations of both nanoparticles and dendritic structures, and literature data on protein simulations. The experimental data agree well with the drag law that allows for a viscosity increase near the surface. We use the persistence time method to examine local changes in viscosity and so find independent confirmation of the expected increase in viscosity near the surfaces of simulated diffusing particles. Typical increases in shear viscosity near the surfaces of the diffusing particles are between 50 and 150% of its bulk value.