Brownian dynamics simulation of the diffusion of rod-like nanoparticles in polymeric gels

Rod-like nanoparticles (RNPs) have been shown to diffuse faster than spherical ones in polymeric hydrogels, but the underlying physics is not well understood. We develop a 3D Brownian dynamics model to investigate this phenomenon, representing the gel as a random network of rigid fibers in water and incorporating both steric repulsion and adhesive interactions. In non-adhesive gels, RNP diffusivity increases monotonically with the aspect ratio while its hydrodynamic diameter is kept constant, in agreement with the predictions of an obstruction scaling (OS) model. However, our model predicts a much higher diffusivity than the OS model, by up to 5 times for higher aspect ratios. To rationalize this discrepancy, we demonstrate that RNPs experience a skewed pore-size distribution in favor of the larger pores; they spend more time in coarser regions of the gel than in denser regions. Moreover, the RNPs execute a meandering motion in the coarser regions with pronounced rotational and transverse diffusion. In contrast, in denser regions, restricted rotation results in predominantly longitudinal diffusion. This anisotropy in diffusion further elevates the translational diffusivity of RNPs. Our model also reveals a competition between the steric and adhesive interactions, where steric repulsion limits access to adhesion sites, and produces a diffusivity intermediate between the purely steric and purely adhesive cases. Overall, our results show an even greater advantage for RNPs, in terms of rapid diffusion in hydrogels, than previously anticipated by using the OS model.