Universal monomer dynamics of a two-dimensional semi-flexible chain

Abstract

We present a unified scaling theory for the dynamics of monomers for dilute solutions of semi-flexible 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 with time due to bending motions, and the Rouse-like regime where ν 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 , and show that a crossover from stiff to flexible behavior occurs at a MSD of order (at a time proportional to ). A second crossover (to diffusive motion) occurs when the MSD is of order R2. Large-scale molecular-dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D = 2 dimensions where . Our results should be valuable for understanding the dynamics of DNA (and other semi-flexible biopolymers) adsorbed on substrates.