Bhavesh R. Sarode | Searcharxiv

arXiv2026

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.

cond-mat.soft↗

arXiv2025

Free Energy and Diffusivity in the Fokker-Planck Theory of Polymer Translocation

We revisit the Fokker-Planck based theory of driven polymer translocation through a narrow nanopore. A bead-spring model of a uniformly charged polyelectrolyte chain translocating through a semi-implicit model of a nanopore embedded in a membrane are used to gain insights into the underlying free energy landscape and kinetics of translocation. The free energy landscape is predicted using metadynamics simulation, an enhanced sampling method. A direct comparison with the theoretical free energy formulation proposed in the literature allows us to introduce a modification related to the entropic contribution in the theory. Additional classical Langevin dynamics simulation runs are performed to obtain the translocation time distribution for polymers of lengths $N$ driven by voltages $V$ through nanopores of radii $r_p$. In agreement with earlier reports, a scaling of the mean translocation time $\langle τ_\text{LD} \rangle \sim N^α/V$ is observed, with $α\sim 1.40 - 1.48$ depending on the nanopore size. Fitting the mean first passage time given by the Fokker-Planck theory, $\langle τ_\text{FP}\rangle$,to simulation results helps gain insights into the diffusivity $k_\text{FP}$ used in the theory. We report a scaling of $k_\text{FP}\sim N^β$. The $r_p-$dependent values of the exponent $β$ significantly deviate from the Rouse theory prediction of $β= -1$ for center-of-mass diffusivity of a polymer chain.

cond-mat.soft↗