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 $N<N_0$.

arXiv comment10 pages, 5 figures, supplementary tex file and datafile

References in corpus (5)

• Critical exponents for random knots
• Topologically Driven Swelling of a Polymer Loop
• Equilibrium size of large ring molecules
• Average size of random polygons with fixed knot topology
• Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical polygons

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• Probability Theory of Random Polygons from the Quaternionic Viewpoint
• The symplectic geometry of closed equilateral random walks in 3-space
• A Fast Direct Sampling Algorithm for Equilateral Closed Polygons
• Abundance of unknots in various models of polymer loops
• Knot probabilities in equilateral random polygons
• Testing the physics of knots with a Feringa nanoengine
• A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
• Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent