Ranking knots of random, globular polymer rings

Abstract

An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.

4 pages, 5 figures

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Cited by in corpus (13)

• The entropic cost to tie a knot
• Interplay between writhe and knotting for swollen and compact polymers
• Universality in the diffusion of knots
• Topological signatures of globular polymers
• Minimal knotted polygons in cubic lattices
• Knot Probabilities in Random Diagrams
• BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices
• Knotted globular ring polymers: how topology affects statistics and thermodynamics
• Elastic Lattice Polymers
• Lattice Knots in a Slab
• Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
• Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings
• Writhe-induced knotting in a lattice polymer