How tension propagates for a driven semi-flexible chain while translocating through a nano-pore

Driven translocation of a stiff chain through a nano-pore is studied using Langevin dynamics in two dimension (2D). We observe that for a given chain length $N$ the mean first passage time (MFPT) $\langle \tau \rangle$ increases for a stiffer chain and the translocation exponent $\alpha$ ($\langle \tau \rangle \sim N^\alpha$) satisfies the inequality $2\nu < \alpha < 1+\nu$, where $\nu$ is the equilibrium Flory exponent for a given chain stiffness. We calculate the residence time of the individual monomers and observe that the peak position of the residence time $W(m)$ as a function of the monomer index $m$ shifts at a \textit{lower} $m$-value with \textit{increasing chain stiffness $\kappa_b$}. Finally, we provide qualitative physical explanation for dependence of various quantities on chain stiffness $\kappa_b$ by using ideas from Sakaue's tension propagation(TP) theory [Phys. Rev. E {\bf 76}, 021803 (2007)] and its recent implementation into a Brownian dynamics tension propagation (BDTP) scheme for a finite chain by Ikonen et al. [J. Chem. Phys. {\bf 137}, 085101 (2012); Phys. Rev. E {\bf 85}, 051803 (2012)]for a semi-flexible chain.