Non-Fickian single-file pore transport

Single-file diffusion exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short porelike channels using a symmetric exclusion process with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux $\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\sim}1/{L}^{3}$, where $L$ is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with $\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\sim}1/L$. Longer systems are more often in a low-flux state, leading to the non-Fickian behavior.