Smoothening transition of a two-dimensional pressurized polymer ring.

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 <A> approximately N, to a smooth state with <A> 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 <A> 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.