Transition from collective to pairwise entanglements

Topological entanglements restrict the fluctuations of network strands and control the mechanical properties of high molecular weight polymer networks. Polymer entanglements have traditionally been modeled in two different ways, either using a collective mean-field confining potential that restricts fluctuations of network strands to confining tubes or by discrete pairwise interactions between chains. We discovered a connection between these two qualitatively different descriptions and proposed a method of obtaining affine length scale of deformed entanglement strand from the decay rate of the correlation function of bond vectors. Using this new method, we observed a cross-over from collective entanglements at weak network deformations to pairwise entanglements at strong deformations.