Free-energy barrier for electric-field-driven polymer entry into nanoscale channels

Free-energy barrier for entry of a charged polymer into a nanoscale channel by a driving electric field is studied theoretically and using molecular dynamics simulations. Dependence of the barrier height on the polymer length, the driving field strength, and the channel entrance geometry is investigated. Squeezing effect of the electric field on the polymer before its entry to the channel is taken into account. It is shown that lateral confinement of the polymer prior to its entry changes the polymer length dependence of the barrier height noticeably. Our theory and simulation results are in good agreement and reasonably describe related experimental data.

Figure 1

Schematic of a polymer under the electric field of strength $E_o$ behind a channel of diameter $d$ in a wall. (a) The polymer can be viewed as a 2D chain of blobs of size $L_I$. (b) A polymer which is also confined laterally by a cylinder of diameter $D$. The polymer can be considered as a chain of blobs closely packed inside a cylinder of height $L_{\mathit{II}}$. (c) A segment of the polymer entered to the channel inside which the electric field is of strength $E_i$.

Figure 2

(a) $\beta$ in $L\propto N^{\beta }$ and $\gamma$ in $R_{\parallel }{L}^{\frac{1}{4}}\propto N^{\gamma }$ versus the polymer length. With increasing $N$ crossover from values corresponding to case I to those of case II can be seen. (b), (c) Simulation results for polymer entry barrier and fitted functions of the theory for cases I and II. Coefficients $a=3.02$, $b=1.50$, and $c=0.32$ are fitting parameters. Considering the scaled axes of these figures, agreement between simulation and theory can be seen. Insets: entry barriers versus $E^{-1}$ and fitted lines.

Figure 3

Logarithm of capture time versus $\Delta V$ extracted from referenced articles (symbols) and fitted equation of our theory, Eq. (4) (solid lines). All the data sets are from polymer translocation experiments through the $\alpha$-hemolysin channel. As it can be seen, all data sets are followed well by the suggested function. Fit parameters are shown in Table .