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Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

Emir Haleva·Haim Diamant
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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, $p_c \sim N^{-1}$, 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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Emir Haleva, Haim Diamant. 2006-01-17. Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring. https://doi.org/10.1140/epje%2Fi2006-10003-7

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