Universal monomer dynamics of a two dimensional semi-flexible chain

TL;DR

This paper develops a unified scaling theory for monomer dynamics in dilute semiflexible polymers in 2D, revealing crossover behaviors and scaling laws validated by molecular dynamics simulations, with implications for biopolymer studies.

Contribution

The paper introduces a comprehensive scaling theory for monomer dynamics in 2D semiflexible polymers, unifying stiff and flexible regimes with validated simulation evidence.

Findings

Identifies crossover from stiff to flexible behavior at MSD ~ l_p^2.

Shows MSD scaling laws for different regimes, including t^{3/4} and Rouse-like.

Validates theory with molecular dynamics simulations across various persistence lengths.

Abstract

We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 \nu / (1+ 2\nu)} where \nu is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D=2 dimensions where \nu=3/4. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates.