Universal bond correlation function for two-dimensional polymer rings

¹ Department of Physics, Kyushu University 33 - Fukuoka 812-8581, Japan
² PRESTO, Japan Science and Technology Agency (JST) - 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
³ Laboratoire de Physique de la Matière Vivante, Ecole Polytechnique Fédérale de Lausanne (EPFL) CH-1015 Lausanne, Switzerland
⁴ Yukawa Institute for Theoretical Physics, Kyoto University - Kyoto 606-8502, Japan

^a sakaue@phys.kyushu-u.ac.jp
^b hwada@yukawa.kyoto-u.ac.jp

Received: 4 June 2010
Accepted: 8 September 2010

Abstract

The bond orientational correlation function (BCF) of a semiflexible ring polymer on a flat surface is studied theoretically. For a stiff chain, we give an exact analytic form of BCF with perturbation calculations. For a chain sufficiently longer than its persistence length, the conventional exponential decay vanishes and a long-range order along the chain contour appears. We demonstrate that the bond orientational correlation satisfies the scaling properties, and construct an interpolating formula for its universal curve that encompasses the short- and large-distance behaviors. Our analytical findings are confirmed by extensive Langevin dynamics simulations, and are in excellent agreement with recent experimental data obtained from DNA molecules imaged by atomic force microscopy without any fitting parameters.