Diffusion Coefficients of Coated Plasmonic Nanoparticles in Viscous Environment

Abstract The Stokes‐Einstein relationship (SER) is not valid anymore in polymeric solutions for nanoparticles. It is thus important to characterize their diffusion properties to get a finer understanding of their behavior and to better tune their attributes for biomedical applications. The diffusion of gold and silver nanoparticles with citrate, hyaluronic acid, methyl‐polyethylene glycol, and antibody‐polyethylene glycol coatings is studied in hyaluronic‐based viscous solutions. The diffusion coefficient D is estimated from the Brownian motion thanks to a cost‐effective side‐illumination device. It is determined that the nanoparticles (hydrodynamic radius r _h : 30–135 nm) diffuse up to 4–5 times faster than expected using the SER with a macroscopic viscosity from 1 to 30 mPa·s. It is shown that the adapted Huggins equation is a good model to describe the diffusion behavior of nanoparticles using an effective viscosity η _eff given by where where E is the polymer correlation length, R _h the polymer hydrodynamic radius and η _s the solvent viscosity. The values of k and a are given and allow to obtain D with an error of 10–20%. The impact of chemical interactions on the model parameter values are also highlighted, especially due to electrostatic interactions between the polymer and the nanoparticles.