Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

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 $<A>\sim N$, to a smooth state with $<A>\sim N^2$. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which $<A>\sim N^{3/2}$. For $p>>p_c$ we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.

9 pages, 8 figures

References in corpus (1)

• Constrained dynamics of a polymer ring enclosing a constant area

Cited by in corpus (8)

• Collapse and folding of pressurized rings in two dimensions
• Critical swelling of particle-encapsulating vesicles
• Phase Transitions in Pressurised Semiflexible Polymer Rings
• Swelling of two-dimensional polymer rings by trapped particles
• Asymptotic Behavior of Inflated Lattice Polygons
• Swelling of particle-encapsulating random manifolds
• Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter
• Rigidity transitions in zero-temperature polygons