We study translocation dynamics of a driven compressible semi-flexible chain consisting of alternate blocks of stiff ($S$) and flexible ($F$) segments of size $m$ and $n$ respectively for different chain length $N$ in two dimension (2D). The free par
ameters in the model are the bending rigidity $kappa_b$ which controls the three body interaction term, the elastic constant $k_F$ in the FENE (bond) potential between successive monomers, as well as the segmental lengths $m$ and $n$ and the repeat unit $p$ ($N=m_pn_p$) and the solvent viscosity $gamma$. We demonstrate that due to the change in entropic barrier and the inhomogeneous viscous drag on the chain backbone a variety of scenarios are possible amply manifested in the waiting time distribution of the translocating chain. These information can be deconvoluted to extract the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe bio-molecules, such as DNA, RNA and proteins.
We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs)
of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 u / (1+ 2 u)} where u is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D=2 dimensions where u=3/4. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates.
