The Role of Gel Mesh and Particle Size in Predicting Nanoparticle Diffusion in Hydrogel Nanocomposites

The diffusion of poly(ethylene glycol) methyl ether thiol (PEGSH) capped gold nanoparticles (NPs) was measured in polyacrylamide gels of various crosslinking densities. The molecular weight of the PEGSH capping ligand and the crosslinking density of the gel were both varied, yielding particles with hydrodynamic diameters between 7 and 21 nm and gels with theoretical mesh sizes of approximately 16 to 44 nm. While we expected the diffusion constants of the NPs to depend on their core:ligand ratios, since high molecular weight ligands are expected to yield more compressible particles, our measurements revealed that the diffusion instead resulted primarily from changes in the overall hydrodynamic diameter. Across all particles and gels, we found that the diffusion was best 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. These results suggest that this model is the effective pore size that the particles "see" as they diffuse through the gel. This work brings new insights into the mechanisms by which NPs move through polymer gels, and will inform development of hydrogel nanocomposites for applications such as of drug delivery in heterogenous, viscoelastic biological materials.