title: Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions.
abstract: This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T ∼ N(3/2)ln(N/b(2)), which differs from the case of the Rouse dynamics where T ∼ N(2). The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented.
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, Paris 75005, France.
authors.forename: N
authors.initials: N
authors.lastname: Levernier
authors.affiliation: Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-St. 3, D-79104 Freiburg, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Dolgushev
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, Paris 75005, France.
authors.forename: O
authors.initials: O
authors.lastname: Bénichou
authors.affiliation: Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-St. 3, D-79104 Freiburg, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Blumen
authors.affiliation: Laboratoire Ondes et Matière d'Aquitaine, University of Bordeaux, Unité Mixte de Recherche 5798, CNRS, F-33400 Talence, France.
authors.forename: T
authors.initials: T
authors.lastname: Guérin
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, Paris 75005, France.
authors.forename: R
authors.initials: R
authors.lastname: Voituriez