Diffusion Coefficients of Coated Plasmonic Nanoparticles in Viscous Environment

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.