How Long Does It Take to Pull an Ideal Polymer into a Small Hole?

Abstract

We present scaling estimates for characteristic times ${\ensuremath{\tau}}_{\mathrm{lin}}$ and ${\ensuremath{\tau}}_{\mathrm{br}}$ of pulling ideal linear and randomly branched polymers of $N$ monomers into a small hole by a force $f$. We show that the absorbtion process develops as sequential straightening of folds of the initial polymer configuration. By estimating the typical size of the fold involved into the motion, we arrive at the following predictions, ${\ensuremath{\tau}}_{\mathrm{lin}}(N)\ensuremath{\sim}{N}^{3/2}/f$ and ${\ensuremath{\tau}}_{\mathrm{br}}(N)\ensuremath{\sim}{N}^{5/4}/f$, and we also confirm them by the molecular dynamics experiment.