Rouse Modes of Self-avoiding Flexible Polymers

TL;DR

This study investigates the Rouse modes of self-avoiding flexible polymers using lattice-based Monte Carlo simulations, revealing high statistical independence of modes and deriving key scaling properties and dynamics of the polymers.

Contribution

It provides an approximate analytical expression for mode correlations and demonstrates how the anomalous dynamics of the middle monomer can be derived from force fluctuations.

Findings

Rouse modes are highly statistically independent in self-avoiding polymers

Derived scaling laws for end-to-end distance and correlation functions

Confirmed anomalous dynamics of the middle monomer

Abstract

Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to be statistically independent; nevertheless, we demonstrate that numerically these modes maintain a high degree of statistical independence. Based on high-precision simulation data we put forward an approximate analytical expression for the mode amplitude correlation functions for long polymers. From this, we derive analytically and confirm numerically several scaling properties for self-avoiding flexible polymers, such as (i) the real-space end-to-end distance, (ii) the end-to-end vector correlation function, (iii) the correlation function of the small spatial vector connecting two nearby monomers at the middle of a polymer, and (iv) the anomalous dynamics of the middle monomer. Importantly, expanding on our recent work on the theory of polymer translocation, we also demonstrate that the anomalous dynamics of the middle monomer can be obtained from the forces it experiences, by the use of the fluctuation-dissipation theorem.