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 $R^{\tinytext{(2D)}}_g \sim N^{\nu_{\tinytext{2D}}}$; here, $\nu_{\tinytext{2D}}=0.75$ is the Flory exponent in two dimensions. The polymer performs Rouse dynamics. Based on theoretical analysis and high-precision simulation data, we show that in the unbiased case $h=h_1$, the dwell-time $\tau_d$ scales as $N^{2+\nu_{\tinytext{2D}}}$, in perfect agreement with our previously published theoretical framework. For $h_1=\infty$, the situation is equivalent to field-driven translocation in two dimensions. We show that in this case $\tau_d$ scales as $N^{2\nu_{\tinytext{2D}}}$, in agreement with several existing numerical results in the literature. This result violates the earlier reported lower bound $N^{1+\nu}$ for $\tau_d$ for field-driven translocation. We argue, based on energy conservation, that the actual lower bound for $\tau_d$ is $N^{2\nu}$ and not $N^{1+\nu}$. Polymer translocation in such theoretically motivated geometries thus resolves some of the most fundamental issues that are the subjects of much heated debate in recent times.