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.
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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