Eur. Phys. J. E (2006) 19: 461-469
https://doi.org/10.1140/epje/i2006-10003-7

Regular Article

Smoothening transition of a two-dimensional pressurized polymer ring

School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

^* e-mail: hdiamant@tau.ac.il

Received: 16 January 2006
Accepted: 9 February 2006
Published online: 10 April 2006

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 ∼ 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〉 ∼ 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〉 ∼ N ^3/2. For p ≫ p _c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.