title: Scattering functions of knotted ring polymers.
abstract: We discuss the scattering function of a Gaussian random polygon with N nodes under a given topological constraint through simulation. We evaluate the form factor PK(q) of a Gaussian polygon of N = 200 having a fixed knot K for some different knots such as the trivial, trefoil, and figure-eight knots. Here the Gaussian polygons with different knots K have distinct values of the mean-square radius of gyration, R2(G,K). We obtain the Kratky plots of the form factors--i.e., the plots of (qR(G,K))2PK(q) versus qR(G,K)--for the different topological constraints and discuss nontrivial large-q behavior as well as small-q behavior for the scattering functions. We also find that the distinct values of R2(G,K) play an important role in the large-q and small-q properties of the Kratky plots.
authors.affiliation: Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan. miyuki@degway.phys.ocha.ac.jp
authors.forename: Miyuki K
authors.initials: MK
authors.lastname: Shimamura
authors.forename: Kumiko
authors.initials: K
authors.lastname: Kamata
authors.forename: Akihisa
authors.initials: A
authors.lastname: Yao
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Deguchi