Size-Dependent Reentrant Mobility of Polymers Driven in a Periodic Potential

Barrier-crossing problems of polymers have been extensively addressed to better elucidate complex phenomena widely ranged from biology to soft matter, such as polymer translocation and electrophoresis. Here we revisit a relevant problem, considering potential applications extended to electrodialysis and filtration of polymers, in which the polymers of various flexibilities and lengths selectively cross over spatially periodic energy barriers in three dimensions. To this end, we perform coarse-grained computer simulations in which an external force field (constant bias) drives the polymers as a general source of nonzero flux of the system. Depending on the period of the barrier (L) and the degree of polymerization (N), the polymer flux exhibits unusual reentrance tendencies, particularly found significant for self-avoiding and semi-flexible polymers. Interestingly, for semi-flexible polymers, we find a local enhancement of their mobility as a function of L and N, especially when N is comparable to L, which induces inchworm-like motions of the polymers in a steady state. This reentrant mobility of polymers is further rationalized by approximate theories in one dimension. The results may provide fundamental guidance for developing polymer filtration applications.