Topologically Driven Swelling of a Polymer Loop

Abstract

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.

6 pages, 4 figures, submitted to PNAS (USA) in Feb 2004

References in corpus (4)

• Equilibrium shapes of flat knots
• Average size of random polygons with fixed knot topology
• Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical polygons
• Tight and loose shapes in flat entangled dense polymers

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