Tumbling and Deformation of Isolated Polymer Chains in Shearing Flow

Abstract

Using Brownian dynamics simulations of polymer chains over a wide range of resolution, we find universal scaling laws for polymer coil dimensions and tumbling time. At high shear rates γ̇, the coil thickness in the gradient direction becomes independent of chain length, scaling as NK0γ̇–1/4, where NK denotes the numbers of Kuhn steps, and the tumbling time scales as NKγ̇–3/4, correcting scaling laws presented in prior studies. We find this to be a consequence of the formation of loops whose length is limited by the time required to stretch them and derive scaling laws from a balance of convection and diffusion of monomers. We find that, in the absence of hydrodynamic interaction (HI) and excluded volume (EV), for wormlike chains, the shrinkage in chain stretch observed at ultrahigh shear rates is pushed out to arbitrarily high shear rates if the chain is resolved increasingly finely below the persistence length. Finally, scaling laws in the presence of excluded volume and hydrodynamic interactions are derived that are expected to be valid for long chains at high shear rates.