Generalized Langevin equation for a tagged monomer in a Gaussian semiflexible polymer

TL;DR

This paper derives a generalized Langevin equation for a tagged monomer in a Gaussian semiflexible polymer, revealing how bending rigidity influences its non-Markovian diffusion behavior across all timescales.

Contribution

The study provides a novel derivation of the GLE for a tagged monomer in a semiflexible polymer, including the detailed analysis of the memory kernel and its effects.

Findings

Derived the GLE governing monomer motion with a focus on the memory kernel.

Analyzed the impact of bending rigidity on non-Markovian dynamics.

Calculated the mean-squared displacement consistent with known limits.

Abstract

In this study, we present a comprehensive analysis of the motion of a tagged monomer within a Gaussian semiflexible polymer model. We carefully derived the generalized Langevin Equation (GLE) that governs the motion of a tagged central monomer. This derivation involves integrating out all the other degrees of freedom within the polymer chain, thereby yielding an effective description of the viscoelastic motion of the tagged monomer. A critical component of our analysis is the memory kernel that appears in the GLE. By examining this kernel, we characterized the impact of bending rigidity on the non-Markovian diffusion dynamics of the tagged monomer. Furthermore, we calculated the mean-squared displacement of the tagged monomer using the derived GLE. Our results not only show remarkable agreement with previously known results in certain limiting cases but also provide dynamic features over the entire timescale.