Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

Details Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

2006-01-16

arxiv.org/abs/cond-mat/0601345v2

Eur. Phys. J. E 19, 461 (2006)

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 8 figures

Scientific paper

10.1140/epje/i2006-10003-7

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, $p_c \sim N^{-1}$, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as $ \sim N$, to a smooth state with $\sim N^2$. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which $\sim N^{3/2}$. 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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