Relationship between Gel Mesh and Particle Size in Determining Nanoparticle Diffusion in Hydrogel Nanocomposites

The diffusion of poly(ethylene glycol) methyl ether thiol (PEGSH)-functionalized gold nanoparticles (NPs) was measured in polyacrylamide gels with various cross-linking densities. The molecular weight of the PEGSH ligand and particle core size were both varied to yield particles with hydrodynamic diameters ranging from 7 to 21 nm. The gel mesh size was varied from approximately 36 to 60 nm by controlling the cross-linking density of the gel. Because high-molecular-weight ligands are expected to yield more compressible particles, we expected the diffusion constants of the NPs to depend on their hard/soft ratios (where the hard component of the particle consists of the particle core and the soft component of the particle consists of the ligand shell). However, our measurements revealed that NP diffusion coefficients resulted primarily from changes in the overall hydrodynamic diameter and not the ratio of particle core size to ligand size. Across all particles and gels, we found that the diffusion coefficient was well predicted by the confinement ratio calculated from the diameter of the particle and an estimate of the gel mesh size obtained from the elastic blob model and was well described using a hopping model for nanoparticle diffusion. These results suggest that the elastic blob model provides a reasonable estimate of the mesh size that particles "see" as they diffuse through the gel. This work brings new insights into the factors that dictate how NPs move through polymer gels and will inform the development of hydrogel nanocomposites for applications such as drug delivery in heterogeneous, viscoelastic biological materials.