Simulation study of the polymer translocation free energy barrier.

Monte Carlo simulations are used investigate the properties of the free energy barrier associated with polymer translocation through a nanopore. We employ a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. Some calculations were carried out for nanopores connected to a spherical cavity at one or both ends. Attractive monomer-nanopore interactions and a linear driving force through the nanopore were also included in some calculations. The properties of the free energy functions for short polymers were studied upon variation in all of the key system parameters, including polymer length, the nanopore dimensions, the strengths of the attractive, and driving force interactions. The results were analyzed using a simple theoretical model, whose only free parameter is the confinement free energy per link for monomers inside the nanopore. Generally, the results are in excellent quantitative agreement with the model. One notable feature of the free energy functions is the presence of oscillations whose amplitude increases with decreasing pore radius. These oscillations are due to the nature of the variation with Q of the orientational entropy of bonds at the two edges of the pore. A simple model was constructed to account for dependence of the oscillation amplitude and period on the system parameters. We propose that the theoretical models developed here can be used to make quantitatively accurate predictions of translocation free energy functions for very long polymers using simulation data acquired for short polymers.