Dynamical Transitions in a Dragged Growing Polymer Chain

TL;DR

This paper extends the Rouse model to non-stationary growing polymers, revealing two key dynamical transitions related to tension propagation and center-of-mass motion, with implications for various polymer types.

Contribution

It introduces a generalized Rouse model for growing polymers, identifying two critical dynamical transitions at specific growth rates.

Findings

Transition at α=1/2 affects tension propagation and chain shape

Transition at α=1 halts average center-of-mass motion

Model remains computationally efficient and analytically tractable

Abstract

We extend the Rouse model of polymer dynamics to situations of non-stationary chain growth. For a dragged polymer chain of length $N(t) = t^\alpha$, we find two transitions in conformational dynamics. At $\alpha= 1/2$, the propagation of tension and the average shape of the chain change qualitatively, while at $\alpha = 1 $ the average center-of-mass motion stops. These transitions are due to a simple physical mechanism: a race duel between tension propagation and polymer growth. Therefore they should also appear for growing semi-flexible or stiff polymers. The generalized Rouse model inherits much of the versatility of the original Rouse model: it can be efficiently simulated and it is amenable to analytical treatment.