Unfolding Kinetics of a Wormlike Chain under Elongational Flow.

Theo Odijk

doi:10.3390/polym9060190

Abstract

A simple theory of the unfolding kinetics of a semi-flexible polymer chain is presented in terms of a Kramers type picture for the energy of elongation. The hydrodynamic interactions are discussed in terms of slender body theory. It turns out that the elongation of the chain is basically linear in time and independent of the viscosity. The former prediction agrees with experiments on the stretching dynamics of DNA under planar elongational flow. Nevertheless, the theory overestimates the experimental rate by a significant amount for reasons that are unclear.

Highlights

An unconfined wormlike chain is well known to be characterized by its persistence lengthL p, demarcating the rigid rod limit from that of the fully flexible random coil
Though global hydrodynamic frictional properties of a rod are pinned by the contour length L, higher order modes are not
If we momentarily suppose hydrodynamic interactions may be neglected, we can use a powerful technique introduced by Kramers [33] for setting up theories for elongational flows

Summary

Introduction

An unconfined wormlike chain is well known to be characterized by its persistence length. Buckling of such rods in elongational flows is generally interpreted in terms of classic elasticity theory [2,3,4,5,6] Another relevant length scale besides the contour length is the persistence length [7,8,9,10,11,12], so slight effects by thermal motion could be discernible even for quite short rods. The extension of DNA in elongational flows was studied by Brownian dynamics simulations, including excluded-volume effects [28], but the two-parameter theory used could break down for wormlike chains, especially at high degrees of elongation. Hydrodynamic interactions are added on to logarithmic order in a slender body approximation

Slender Body Theory for Rods

Kramers-Type Theory for Unfolding Dynamics

Discussion

Concluding Remarks