On the Limits of Analogy Between Self-Avoidance and Topology-Driven Swelling of Polymer Loops

Abstract

The work addresses the analogy between trivial knotting and excluded volume in looped polymer chains of moderate length, $N<N_0$, where the effects of knotting are small. A simple expression for the swelling seen in trivially knotted loops is described and shown to agree with simulation data. Contrast between this expression and the well known expression for excluded volume polymers leads to a graphical mapping of excluded volume to trivial knots, which may be useful for understanding where the analogy between the two physical forms is valid. The work also includes description of a new method for the computational generation of polymer loops via conditional probability. Although computationally intensive, this method generates loops without statistical bias, and thus is preferable to other loop generation routines in the region $N<N_0$.

10 pages, 5 figures, supplementary tex file and datafile

Cited by in corpus (6)

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• Testing the physics of knots with a Feringa nanoengine
• Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent
• A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting