Dynamical Transitions in a Dragged Growing Polymer Chain

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.