Ratchet effect of self-propelled colloids in an asymmetric periodic potential

We report a systematic study of barrier-crossing dynamics of self-propelled particles (SPPs) across a periodic ratchet potential U0(x), which is fabricated on a ratchet-microgroove-patterned polydimethylsiloxane substrate. From the measured steady-state probability density function P(x; F0) of the SPPs with different self-propulsion forces F0, we find that the escape dynamics of slow-rotating SPPs over the asymmetric ratchet potential can be well described by an activity-dependent potential, U±(x; F0) ≃ U0(x) ∓ aF0x, for the forward (+) and backward (-) moving particles with aF0 being the amplitude of their self-propulsion force projected along the x axis. By a thorough analysis of a large volume of the SPP trajectories obtained from both the spatially symmetric and asymmetric potentials, we delineate two experimental conditions under which the ratchet effect of SPPs is realized without involving a time-dependent rectification, and directed particle transport with a steady flux is observed. This work thus provides an effective statistical approach to describe the non-equilibrium transport of SPPs across ratchet potentials.