Entangled Polymer Rings in 2D and Confinement
  The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$. 
Matthias Otto and Thomas A. Vilgis (MPI fuer Polymerforschung, Mainz)