Dragging a polymer in a viscous fluid: steady-state and transient

TL;DR

This paper investigates the steady-state and transient dynamics of a single polymer pulled by a constant force in a viscous fluid, combining analytical models and scaling arguments to reveal force-dependent behaviors and protocol-sensitive transient responses.

Contribution

It provides a comprehensive analysis of polymer stretching dynamics under force, incorporating realistic effects like finite extensibility and hydrodynamics, and highlights protocol-dependent transient behaviors.

Findings

Exact solutions for the Rouse model of polymer stretching.

Scaling predictions for force-dependent friction constants.

Transient friction evolution depends on experimental protocol.

Abstract

We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual macromolecules, which offers a paradigm research for probing far-from-equilibrium responses of long flexible biological polymers. We first analyze the Rouse model for the Gaussian chains for which the exact analytical results can be obtained. More realistic features such as the finite extensibility, the excluded volume and the hydrodynamic interactions are taken into account with the help of the scaling argument, which leads to various nontrivial predictions such as the stretching-force-dependent friction constants. We elucidate (i) generalized dynamical equations of state describing extension/friction laws in steady-state and (ii) the tension propagation laws in the transient process. We point out that the time evolutions of the dynamic friction in the transient process crucially depend on the experimental protocol, i.e., either constant force or velocity ensemble, which might be detectable in experiments using giant DNAs and chromosomes.