Title
Shapes of knotted cyclic polymers
Department/School
Mathematics
Date
4-20-2009
Document Type
Article
Keywords
knot theory, knotted cyclic polymers
Abstract
Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots. This paper is a shorter, revised version of the article Ref. [12]. For more details, see Ref. [12].
Volume
92
Issue
1
Published in
Bussei Kenkyu
Citation/Other Information
Rawdon, E. J., Kern, John C., Plunkett, P., Piatek, M., Stasiak, A., and Millett, K. (2009). Shapes of knotted cyclic polymers. Bussei Kenkyu 92(1), 32-37. https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/169124.