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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.00407 |
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| _version_ | 1866909933955448832 |
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| author | Sarode, Bhavesh R. Katkar, Harshwardhan H. |
| author_facet | Sarode, Bhavesh R. Katkar, Harshwardhan H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free Energy and Diffusivity in the Fokker-Planck Theory of Polymer Translocation Sarode, Bhavesh R. Katkar, Harshwardhan H. Soft Condensed Matter 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. |
| title | Free Energy and Diffusivity in the Fokker-Planck Theory of Polymer Translocation |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2512.00407 |