Langevin Dynamics of a Polymer with Internal Distance Constraints

TL;DR

This paper introduces a rigorous method for analyzing the Langevin dynamics of ideal polymer chains with internal distance constraints, providing exact solutions for systems with crosslinks modeled as harmonic potentials.

Contribution

It develops a formal, exact approach to model polymer dynamics with internal constraints, extending previous Lagrangian multiplier methods with a resolvent and spectral density matrix framework.

Findings

Derived exact expressions for the resolvent and spectral density matrix.

Analyzed monomer diffusion near a single crosslink within the Rouse model.

Provided a full solution to the constrained polymer dynamics problem.

Abstract

We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the potential approaches infinity (hard crosslinks). The crosslinks are assumed to exist between arbitrary pairs of monomers. Formally exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusional behavior of monomers in the vicinity of a single crosslink within the framework of the Rouse model. The same problem has been studied previously by Warner (J. Phys. C: Solid State Phys. {\bf 14}, 4985, (1981)) on the basis of Lagrangian multipliers. Here we derive the full, hence exact, solution to the problem.