1110.5763 (J. L. A. Dubbeldam et al.)

Forced translocation of a polymer: dynamical scaling vs. MD-simulation    [PDF]

J. L. A. Dubbeldam, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

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
propagating front of tensile force along the chain backbone, suggested recently
by T. Sakaue. 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 quasi-static approximation), we
derive an equation of motion for the tensile front position $X(t)$. We show
that the scaling law for the average translocation time $<\tau>$ changes from
$<\tau> \sim N^{2\nu}/f^{1/\nu}$ to $<\tau> \sim N^{1+\nu}/f$ (for the
free-draining case) as the dimensionless force ${\widetilde f}_{R} = a N^{\nu}f
/T$ (where $a$, $N$, $\nu$, $f$, $T$ 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 (MD) simulation. Data from our computer experiment indicates indeed
that the translocation scaling exponent $\alpha$ grows with the pulling force
${\widetilde f}_{R}$) albeit the observed exponent $\alpha$ stays
systematically smaller than the theoretically predicted value. This might be
associated with fluctuations which are neglected in the quasi-static
approximation.

View original: http://arxiv.org/abs/1110.5763