Polymer translocation out of planar confinements

Polymer translocation in three dimensions out of planar confinements is studied in this paper. Three membranes are located at z = − h , z = 0 and z = h 1 . These membranes are impenetrable, except for the middle one at z = 0, which has a narrow pore. A polymer with length N is initially sandwiched between the membranes placed at z = − h and z = 0 and translocates through this pore. We consider strong confinement (small h ), where the polymer is essentially reduced to a two-dimensional polymer, with a radius of gyration scaling as R g (2D) ∼ N ν 2D ; here, ν 2D = 0.75 is the Flory exponent in two dimensions. The polymer performs Rouse dynamics. On the basis of theoretical analysis and high-precision simulation data, we show that in the unbiased case h = h 1 , the dwell time τ d scales as N 2+ν 2D , in perfect agreement with our previously published theoretical framework. For , the situation is equivalent to field-driven translocation in two dimensions. We show that in this case τ d scales as N 2ν 2D , in agreement with several existing numerical results in the literature. This result violates the earlier reported lower bound N 1+ν for τ d for field-driven translocation. We argue, on the basis of energy conservation, that the actual lower bound for τ d is N 2ν and not N 1+ν . Polymer translocation in such theoretically motivated geometries thus resolves some of the most fundamental issues that have been the subject of much heated debate in recent times.