Dynamics of end-to-end loop formation: A flexible chain in the presence of hydrodynamic interaction

Based on the Wilemski–Fixman approach [G. Wilemski, M. Fixman, J. Chem. Phys. 60 (1974) 866], we show that, for a flexible chain in θ solvent, hydrodynamic interaction treated with a pre-averaging approximation makes ring closing faster if the chain is not very short. We also show that the ring closing time for a long chain with hydrodynamic interaction in θ solvent scales with the chain length (N) as N1.5, in agreement with the previous renormalization group calculation based prediction by Freidman and O’Shaughnessy [B. Friedman, B. O’Shaughnessy, Phys. Rev. A 40 (1989) 5950].