Detailed dynamics of discrete Gaussian semiflexible chains with arbitrary stiffness along the contour

TL;DR

This paper provides exact analytical solutions for the dynamics of discrete Gaussian semiflexible chains with arbitrary stiffness, extending previous models and validating results with simulations, offering new tools for studying complex polymer behavior.

Contribution

The paper derives exact algebraic expressions for dynamical observables of semiflexible Gaussian chains and generalizes the model to chains with spatially varying stiffness.

Findings

Excellent agreement between analytical results and Brownian dynamics simulations

Generalization to chains with linearly varying stiffness along the contour

New insights into the dynamics of heterogeneous semiflexible polymers

Abstract

We revisit a model of semiflexible Gaussian chains proposed by Winkler \textit{et al}, solve the dynamics of the discrete description of the model and derive exact algebraic expressions for some of the most relevant dynamical observables, such as the mean-square displacement of individual monomers, the dynamic structure factor, the end-to-end vector relaxation and the shear stress relaxation modulus. The mathematical expressions are verified by comparing them with results from Brownian dynamics simulations, reporting an excellent agreement. Then, we generalize the model to linear polymer chains with arbitrary stiffness. In particular, we focus on the case of a linear polymer with stiffness that changes linearly from one end of the chain to the other, and study the same dynamical functions previously presented. We discuss different approaches to check whether a polymer has constant or heterogeneous stiffness along its contour. Overall, this work presents a new insight for a well known model for semiflexible chains and provides tools that can be exploited to compare the predictions of the model with simulations of coarse grained semiflexible polymers.