Thermodynamics and kinetics of a three-arm star polymer translocating through a nanopore

In this work, voltage-driven translocation of uniformly charged long linear and three-arm star polymers through narrow nanopores is investigated. Langevin dynamics simulation is performed using a coarse-grained model of the polymer and a semi-implicit representation of the nanopore. The mean translocation time of a linear polymer is found to be inversely proportional to the applied voltage over a wide range of voltages. In contrast, the mean translocation time of a three-arm star polymer of the same molecular weight exhibits a pronounced deviation from this scaling relation below a threshold voltage. The threshold voltage is found to be nearly independent of the molecular weight of the polymer but depends on the size of the nanopore and salt concentration. Metadynamics simulation is used to estimate the free energy landscape for the translocation of the three-arm star polymer. Below the threshold voltage, the free energy exhibits a pronounced second barrier resulting from an entropic contribution and electrostatic interactions between segments of the trailing arm inside the nanopore. A Fokker-Planck model developed using the estimated free energy accurately predicts the deviation from the scaling relation below the threshold voltage and shows a remarkable agreement with the Langevin dynamics simulation results using a voltage-independent fitting parameter. The agreement between the theory and the Langevin dynamics simulation results is seen for different nanopore radii, molecular weights of the polymer, and salt concentrations studied. A simple extension of the free energy landscape is suggested to predict translocation kinetics for higher molecular weights of the polymer without performing additional computationally expensive simulations.