Abstract
The effect of the preservation of the topology of the entanglement in systems of polymer loops which are part of a gel is investigated. A simple two-state invariant of this topology is implemented in the preservation of the state of linking of sets of loops. We compute the free energy of a network by making use of a variational principle and thereby to go beyond the limit of phantom chains. We compute the contribution due to entanglements to the reduced stress of the network.
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