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

Abstract

We revisit a model of semiflexible Gaussian chains proposed by Winkler 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 for the dynamic structure factor 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 we study the same dynamical functions previously presented. We discuss different approaches to check whether a polymer has constant or heterogeneous stiffness along its contour. Finally, we provide expressions for the Lagrangian multipliers for Gaussian chains with variable stiffness and bond length, as well as for chains with torsion-like interactions. Overall, this work presents a new insight into a well-known model for semiflexible chains and provides tools that can be exploited to explore a much broader class of polymers or compare the predictions of the model with simulations of coarse-grained semiflexible polymers.