ENTANGLED POLYMER RINGS IN 2D AND CONFINEMENT

The statistical mechanics of polymer loops entangled in the two-dimens ional array of randomly distributed obstacles of infinite length is di scussed. The area of the loop projected onto the plane perpendicular t o the obstacles is used as a collective variable in order to re-expres s a (mean-field) effective theory for the polymer conformation. It is shown explicitly that the loop undergoes a collapse transition to a ra ndomly branched polymer with R proportional to lN(1/4).