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Updated: Jul 31, 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
Smoothening transition of a two-dimensional pressurized polymer ring
1School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
Abstract:
We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p(c) approximately N(-1), the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as approximately N, to a smooth state with approximately N(2). The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which approximately N(3/2). For p >> p(c) we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.
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