Trapped Entanglements in Rubbers. A Unification of Models

An expression for the contribution of trapped entanglements to stress in a cross-linked polymer network is obtained using a slip-link model. This is intended as a simplified alternative to the replica calculation (Ball et al.), and is a more exact treatment of the "hoop" model (Adolf) and a generalization of the "belt-loop" model (Kosc). We discuss the relationship between slip-link and tube models and consider under what circumstances the two ideas are equivalent.