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 $R_g^{\text{tinytext}(2D)}\sim N^{{\nu }_{\text{tinytext}2D}}$; here, ${\nu }_{\text{tinytext}2D}=0.75$ 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 $N^{2+{\nu }_{\text{tinytext}2D}}$, in perfect agreement with our previously published theoretical framework. For $h_1=\mathrm{\infty }$, the situation is equivalent to field-driven translocation in two dimensions. We show that in this case ${\tau }_d$ scales as $N^{2{\nu }_{\text{tinytext}2D}}$, 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.