Dynamics of end to end loop formation for an isolated chain in viscoelastic fluid

TL;DR

This paper theoretically analyzes how a linear polymer's end-to-end looping dynamics are affected by a viscoelastic fluid environment, revealing faster looping times at shorter chain lengths and complex scaling behavior.

Contribution

It introduces a fractional memory kernel-based Rouse model to study polymer looping in viscoelastic fluids, providing new insights into the dynamics compared to Newtonian fluids.

Findings

Looping time is faster in viscoelastic fluid for short chains.

No clear scaling law for looping time with chain length in viscoelastic fluid.

Reversal of trend in looping times occurs at a certain chain length.

Abstract

We theoretically investigate the looping dynamics of a linear polymer immersed in a viscoelastic fluid. The dynamics of the chain is governed by a Rouse model with a fractional memory kernel recently proposed by Weber et al. (S. C. Weber, J. A. Theriot, and A. J. Spakowitz, Phys. Rev. E 82, 011913 (2010)). Using the Wilemski-Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)) formalism we calculate the looping time for a chain in a viscoelastic fluid where the mean square displacement of the center of mass of the chain scales as t^(1/2). We observe that the looping time is faster for the chain in viscoelastic fluid than for a Rouse chain in Newtonian fluid up to a chain length and above this chain length the trend is reversed. Also no scaling of the looping time with the length of the chain seems to exist for the chain in viscoelastic fluid.