Accurate statistics of a flexible polymer chain in shear flow

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times tau of the polymer decays exponentially as approximately exp(-alphatau/tau_{0}) (where tau_{0} is the longest relaxation time). We show that for a Rouse chain this nontrivial constant alpha can be calculated in the limit of a large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of alpha approximately 0.324. We also derive exactly the distribution functions for the length and the orientational angles of the end-to-end vector R of the polymer.