Stick, Slide, or Bounce: Charge Density Controls Nanoparticle Diffusion.

The diffusion and interaction dynamics of charged nanoparticles (NPs) within charged polymer networks are crucial for understanding various biological and biomedical applications. Using a combination of coarse-grained molecular dynamics simulations and experimental diffusion studies, we investigate the effects of the NP size, relative surface charge density (ζ), and concentration on the NP permeation length and time. We propose a scaling law for the relative diffusion of NPs with respect to concentration and ζ, highlighting how these factors influence the NP movement within the network. The analyses reveal that concentration and ζ significantly affect NP permeation length and time, with ζ being critical, as critical as concentration. This finding is corroborated by controlled release experiments. Further, we categorize NP dynamics into sticking, sliding, and bouncing regimes, demonstrating how variations in ζ, concentration, and NP size control these behaviors. Through normalized attachment time (NAT) analyses, we elucidate the roles of electrostatic interactions, steric hindrance, and hydrodynamic forces in governing NP dynamics. These insights provide guidance for optimizing NP design in targeted drug delivery and advanced material applications, enhancing our understanding of NP behavior in complex environments.