Active diffusion and barrier crossing in a semi-flexible polymer network

Particle diffusion in a polymer network is an important and widely studied subject which provides basic knowledges on transport dynamics inside a gel or drug delivery. However, understanding the motion of active self-propelled particles in such networks is particularly challenging, as their activity drives the system out of equilibrium, leading to the breakdown of the fluctuation-dissipation theorem. Here, we address this problem by explicitly constructing a soft matter complex of active particles and a semi-flexible polymer network and by performing Langevin dynamics simulation of this system. We systematically investigate the trapped-and-hopping diffusion of active tracers for varying the mesh-to-particle size ratio, Péclet number, and bending stiffness of the polymer network. Notably, when the particle size is comparable to the mesh size, the mean trapped time follows an exponential law with respect to the bending stiffness, with an activity-dependent slope. In addition to the simulation study, we develop an analytical theory of the active Kramers' escaping dynamics in a harmonic potential. Our findings provide new insights into the complex interplay between polymer stiffness, tracer size, and particle activity, offering implications for microrheology involving active particles. Also, our results may offer insights into the biological processes such as motor-driven cargo transport in the cytoskeletal networks or movements of E. coli in mucus gels.