Role of Ligand Shell Density in the Diffusive Behavior of Nanoparticles in Hydrogels

The diffusion coefficients of poly(ethylene glycol) methyl ether thiol (PEGSH)-functionalized gold nanoparticles (NPs) with different effective grafting densities were measured in polyacrylamide hydrogels. The NP core size was held constant, and the NPs were functionalized with mixtures of short oligomeric ligands (254 Da PEGSH) and longer (either 1 or 2 kDa PEGSH) ligands. The ratio of short and long ligands was varied such that the grafting density of the high-molecular-weight (MW) ligand ranged from approximately 1 to 100 high-MW ligands/NP. The diffusion coefficients of the NPs were then measured in gels with varying average mesh sizes. The measured diffusion coefficients decreased with higher MW ligand density. Interestingly, the diffusion coefficients for NPs with high effective grafting densities were well-predicted by their hydrodynamic diameters, but the diffusion coefficients for NPs with low effective grafting densities were higher than expected from their hydrodynamic diameters. These results suggest that crowding in the NP ligand shell influences the mechanism of diffusion, with lower grafting densities allowing ligand chain relaxations that facilitate movement through the gel. This work brings new insights into the factors that dictate how NPs move through hydrogels and will inform the development of models for applications such as drug delivery in complex viscoelastic biological materials.