Tube models for rubber-elastic systems

In the first part of the paper, we show that the constraining potentials in troduced to mimic entanglement effects in Edwards' tube model and Flory's c onstrained junction model are diagonal in the generalized Rouse modes of th e corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model f or the confinement of long paths in polymer networks which is partially due to cross-linking and partially due to entanglements. Our model describes a nontrivial crossover between the Warner-Edwards and the Heinrich-Straube t ube models. We present results for the macroscopic elastic properties as we ll as for the microscopic deformations including structure factors.