Polymer translocation induced by adsorption

We study the translocation of a flexible polymer through a pore in a membrane induced by its adsorption on \trans side of the membrane. When temperature $T$ is higher than $T_c$, the adsorption-desorption transition temperature, attractive interaction between polymer and membrane plays little role in affecting polymer conformation, leading to translocation time that scales as $\tau\sim L^3$ where $L$ is the polymer contour length. When $T < T_c$, however, the translocation time undergoes a sharp crossover to $\tau\sim L^2$ for sufficiently long polymers, following the second order conformational (adsorption) transition. The translocation time is found to exhibit the crossover around $T=T_c'$, which is lower than $T_c$ for polymers shorter than a critical length($N<N_c$).