Translocation Time through a Nanopore with an Internal Cavity Is Minimal for Polymers of Intermediate Length

The translocation of polymers through nanopores with large internal cavities bounded by two narrow pores is studied via Langevin dynamics simulations. The total translocation time is found to be a nonmonotonic function of polymer length, reaching a minimum at intermediate length, with both shorter and longer polymers taking longer to translocate. The location of the minimum is shown to shift with the magnitude of the applied force, indicating that the pore can be dynamically tuned to favor different polymer lengths. A simple model balancing the effects of entropic trapping within the cavity against the driving force is shown to agree well with simulations. Beyond the nonmonotonicity, detailed analysis of translocation uncovers rich dynamics in which factors such as going to a high force regime and the emergence of a tail for long polymers dramatically change the behavior of the system. These results suggest that nanopores with internal cavities can be used for applications such as selective extraction of polymers by length and filtering of polymer solutions, extending the uses of nanopores within emerging nanofluidic technologies.

Figure 1

Schematic of the nanopore with a large internal cavity and smaller pores on both the cis and trans side. The polymer is depicted as being stuck within the cavity.

Figure 2

Time evolution of $N_{\text{cis}}$, $N_{\text{cavi}}$, and $N_{\text{trans}}$, shown in blue, red, and green respectively, for an example successful translocation event. The vertical lines show transitions between the states described in the text. The schematics illustrate the polymer behavior described in the text.

Figure 3

Numerical measurements of five metrics defined in the text. Panel (a) shows $t_{\text{trans}}$, (b) $t_{\text{stuck}}$, (c) $t_{\text{exit}}$, (e) $N_{\text{stuck}}$, (f) $N_{\text{exit}}$, and all of these are plotted against chain length, $N$. Panel (d) contains schematics illustrating the exit phase for medium-length chains (d1,d2) and long chains (d3–d5).

Figure 4

Comparison between numerical measurements of the chain length $N$ that minimizes $t_{\text{stuck}}$, shown as markers, and the values predicted by the free-energy model, shown as dotted lines. The solid blue line indicates chains with $R_G=r_{\text{eff},\text{cavi}}$. The black line indicates the highest monomer density for which the model should hold [43].