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Updated: Feb 24, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Configurational entropy of randomly double-folding ring polymers
Pieter H W van der Hoek1, Angelo Rosa1, Elham Ghobadpour2
1SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.
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Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here, we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we introduce a scheme that allows us to define a "code" specifying how a ring wraps a randomly branching tree and calculate the number of admissible wrapping codes via a variant of Bertrand's ballot theorem. As a validation, we demonstrate that data from Monte Carlo simulations of an elastic lattice model of non-interacting tightly double-folded rings with controlled branching activity are in excellent agreement with exact expressions for branch-node and tree size statistics that can be derived from our expression for the ring entropy.
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