Entangled Polymer Rings in 2D and Confinement

Abstract

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 $R\propto l{N}^{\frac{1}{4}}$.

17 pages of Latex, 1 ps figure now available upon request, accepted for J.Phys.A:Math.Gen

References in corpus (2)

• Mean Area of Self-Avoiding Loops
• Numerical knot invariants of finite type from Chern-Simons perturbation theory

Cited by in corpus (3)

• The direct link model for polymer rings as a topological field theory and the second topological moment in dense systems
• Field Theory of N Entangled Polymers
• Topological Entanglement of Polymers and Chern-Simons Field Theory