This research deals with the theory of rubber elasticity, a property that is unique to polymers. Specifically, it deals with the role of topological constraints, in the form of molecular- chain entanglements, on the mechanical properties of crosslinked rubber networks. In one approach, the equilibrium entanglements will be modeled in a mean-field manner, by subjecting all of the segments of each network chain to some type of confinement that is transverse to the direction of the chain. This is the so- called "tube model." In another approach, nonequilibrium entanglement effects will be modeled in terms of a process involving multiple barriers represented by the discrete entanglements along the contour of dangling chains and unattached chains.
