Title
Effect of knotting on the shape of polymers
Department/School
Mathematics
Date
10-10-2008
Document Type
Article
Keywords
knotting, polymers, shape of polymers, knots
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.
Published in
Macromolecules
Citation/Other Information
Rawdon, E. J., Kern, J. C., Piatek, M., Plunkett, P., Stasiak, A., & Millett, K. C. (2008). Effect of Knotting on the Shape of Polymers. Macromolecules, 41(21), 8281–8287. https://doi.org/10.1021/ma801389c