Statistical mechanics of temporary polymer networks

The statistical theory of temporary polymer networks developed in parts I and II of this work is closed by a discussion on dynamical effects, including comparison with experiments. After a short review of the theory developed in parts I and II we discuss the situation in which a prescribed velocity gradient is imposed on the physical system formed by the temporary network and the solvent. The dynamical equation for the 2nd moments (derived from a generalized bead-spring model) contains the configuration-dependent transition probability, which depends on the second moments in a complex way. An approximate solution of these equations is obtained from a computer program. It shows the experimentally observed behavior, in particular the stress overshoot maximum after a sudden start of the flow.The derivation of the above equations contains simplifying assumptions which, however, leave the essential physics intact. The most important assumptions concern the relaxation time approach and the decay and formation processes. These were supposed to be dilute enough to break up the many-junction processes into one-junction processes. Both assumptions are analogous to frequently used assumptions in Boltzmann's kinetic theory.