STRESS-RELAXATION IN LIVING POLYMERS - RESULTS FROM A POISSON RENEWAL MODEL

The problem of stress relaxation in entangled, reversibly breakable polymers (e.g., wormlike micelles) is considered. In the case where the dominant diffusive mode for the polymers is reptation, this problem has been treated in earlier numerical work by coupling the full reaction kinetics of scissions and recombinations to the dynamics of reptation (represented by a one-dimensional stochastic process). Here we study a simplified renewal model, which replaces the exact reaction kinetics by a Poisson jump process that neglects temporal correlations in the chain length experienced by a particular monomer or tube segment. Between jumps in chain length, the stress relaxation is presumed to follow that of an equivalent unbreakable chain. We apply the solution to the case of reptating flexible polymers and compare the resulting complex modulus with the earlier numerical treatments. It is found that agreement is very good. The renewal model is then used to analyze in detail, for the first time, the crossover to a rapid-scission regime in which chain diffusion between scission events is dominated by breathing modes. A third regime, in which the motion between scission events is Rouse-like, remains unsuitable for study with this model, for reasons that we explain. Various implications of the renewal model for the interpretation of experimental results are discussed. We also provide, explicit estimates for chain lengths in CTAC/NaSal/NaCl systems using experimental Cole-Cole plots.