A semimicroscopic model to describe nonmonotonic stress relaxation of associative polymer networks

Recent experiments on associative polymer networks revealed a nonmonotonic stress relaxation after cessation of preshear. A temporal increase in the stress at intermediate times is observed before full relaxation of the stress occurs. Motivated by what is expected to occur on a molecular level, we propose equations of motion for the network stress and the concentration of cross-links. These equations lead to an explicit expression for the time dependence of the stress, which quantitatively reproduces experimental nonmonotonic stress relaxation curves for two different types of associative polymer systems. Our mathematical model involves a time scale for the recovery of cross-links, a Maxwell-type time scale for the final stress relaxation, for the relative number of cross-links that survives the preshear period, and the initial stress right after cessation of preshear. The numerical results for these parameters obtained from the comparison with experiments allow for a further interpretation of the underlying mechanisms on a molecular level depending on the type of associative polymer.