Elastic Response of Entangled Polymers

Abstract

The free energy is obtained for a long flexible circular molecule confined in a plane and entangled with a random distribution of parallel straight lines placed perpendicular to this plane. Based on the Gauss linking number the problem of topological classification is solved by variational method. The internal pressure and the elastic modulus for tensile deformation are calculated explicitly as a simultaneous function of polymer length, the number of obstacles and the degree of entanglements.