The Effect of Ligand Shell Density on the Diffusion of Nanoparticles in Hydrogel Nanocomposites

The diffusion of poly(ethylene glycol) methyl ether thiol (PEGSH) functionalized gold nanoparticles (NPs) with different ligand densities was measured in polyacrylamide hydrogels to investigate how the NP ligand density affects the diffusion coefficient . The NP core size was held constant, and the NPs were functionalized with mixtures of high molecular weight ligands (either 1 or 2 kDa PEGSH) and short stabilizing ligands (254 Da PEGSH). The ligand density of the large ligand was varied between 1-107 ligands/NP and 0-54 ligands/NP for the 1kDa and 2 kDa functionalized NPs, respectively. The hydrodynamic diameter (D_h) correspondingly increased from 8-12 nm and 8-15 nm for the 1 kDa and 2 kDa functionalized NPs. The diffusion coefficients of the NPs were then measured in gels with mesh sizes from 35-62 nm and decreased as a function of decreasing ligand density. We found that the diffusion coefficients for particles with high ligand densities were well-predicted by the hopping model for diffusion in polymeric gels, but the diffusion coefficients for particles with low ligand densities were higher than predicted based on their D_h. These results suggest that NP ligand densities influence the diffusion process, and that D_h is not a good predictor of diffusion coefficient at low ligand densities. 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.