We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of a propagating front of tensile force along the chain backbone, suggested by Sakaue [Phys. Rev. E 76, 021803 (2007); Phys. Rev. E 81, 041808 (2010); Eur. Phys. J. E 34, 135 (2011)]. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation: trumpet, stem-trumpet, etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasistatic approximation), we derive an equation of motion for the tensile front position $X\left(t\right)$. We show that the scaling law for the average translocation time $\langle \tau \rangle$ changes from $\langle \tau \rangle \sim N^{2\nu }/f^{1/\nu }$ to $\langle \tau \rangle \sim N^{1+\nu }/f$ (for the free-draining case) as the dimensionless force ${\tilde{f}}_R=a{N}^{\nu }f/T$ (where $a$, $N$, $\nu$, $f$, and $T$ are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by molecular-dynamics simulation. Data from our computer experiment indicate indeed that the translocation scaling exponent $\alpha$ grows with the pulling force ${\tilde{f}}_R$, albeit the observed exponent $\alpha$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations that are neglected in the quasistatic approximation.

• Received 27 August 2011

DOI:https://doi.org/10.1103/PhysRevE.85.041801