Bridging Macroscopic\nDiffusion and Microscopic Cavity\nEscape of Brownian and Active Particles in Irregular Porous Networks

While irregular and geometrically complex pore networks\nare ubiquitous\nin nature and industrial processes, there is no universal model describing\nnanoparticle transport in these environments. 3D super-resolution\nnanoparticle tracking was employed to study the motion of passive\n(Brownian) and active (self-propelled) species within complex networks,\nand universally identified a mechanism involving successive cavity\nexploration and escape. In all cases, the long-time ensemble-averaged\ndiffusion coefficient was proportional to a quantity involving the\ncharacteristic length scale and time scale associated with microscopic\ncavity exploration and escape (<i>D</i> ∼ <i>r</i><sup>2</sup>/<i>t</i><sub>trap</sub>), where\nthe proportionality coefficient reflected the apparent porous network\nconnectivity. For passive nanoparticles, this coefficient was always\nlower than expected theoretically for a random walk, indicating reduced\nnetwork accessibility. In contrast, the coefficient for active nanomotors,\nin the same pore spaces, aligned with the theoretical value, suggesting\nthat active particles navigate “intelligently” in porous\nenvironments, consistent with kinetic Monte Carlo simulations in networks\nwith variable pore sizes. These findings elucidate a model of successive\ncavity exploration and escape for nanoparticle transport in porous\nnetworks, where pore accessibility is a function of motive force,\nproviding insights relevant to applications in filtration, controlled\nrelease, and beyond.