Non-monotonous translocation time of polymers across pores

Polymers confined in corrugated channels, i.e. channels of varying amplitude, display {multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization $N$}. We propose a theoretical effective free energy for linear polymers based on a Fick-Jacobs approach. We validate the predictions against numerical data, obtaining quantitative agreement for {the effective free energy, the diffusion coefficient and the Mean First Passage Time}. Finally, we employ the effective free energy to compute the polymer lengths $N_{min}$ at which the diffusion coefficient presents a minimum: we find a scaling expression that we rationalize with a blob model. Our results could be useful to design porous adsorbers, that separate polymers of different sizes without the action of an external flow.