Smoothening transition of a two-dimensional pressurized polymer ring |
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Authors: | E Haleva H Diamant |
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Institution: | (1) School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv, Israel |
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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,
pc ∼ N-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N2. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is
found, in which 〈A〉 ∼ N3/2. For p ≫ pc we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state. |
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Keywords: | 36 20 Ey Macromolecules and polymer molecules: Conformation (statistics and dynamics) 05 40 Fb Random walks and Levy flights 64 60 -i General studies of phase transitions |
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