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)) similar to N-nu 2D; here, nu(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 tau(d) scales as N2+nu 2D, in perfect agreement with our previously published theoretical framework. For h(1) = infinity, the situation is equivalent to field-driven translocation in two dimensions. We show that in this case tau(d) scales as N-2 nu 2D, in agreement with several existing numerical results in the literature. This result violates the earlier reported lower bound N1+nu for tau(d) for field-driven translocation. We argue, on the basis of energy conservation, that the actual lower bound for tau(d) is N-2 nu and not N1+nu. 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.