In living polymer systems, there is a complex relationship between reversible polymerization dynamics and stress relaxation processes, as reactions can reshape how stress is distributed across structures in a system. The interplay between reactions and stress relaxation is perhaps best understood for small deformations (linear rheology) of well-entangled and âfast breakingâ linear-chain polymers undergoing reversible scission. There, the classical work by Cates describes how reactions move slow-relaxing interior chain segments to end positions where stress relaxation is faster. Unfortunately, practical applications of living polymers often involve non-linear rheology and/or slow-breaking systems, where a more general modeling framework has remained incomplete and/or intractable.
In this talk, we present our recent progress on developing practical tools for modeling both the linear and non-linear rheology of living polymers that are not âfast breakingâ. We begin with linear rheology, where we show that a âshufflingâ approximation of the population balance terms dramatically simplifies the computational burden with no restriction on the breaking time. Linear rheology predictions are presented for single reptation, double reptation, and reptation with contour length fluctuations. Next, we systematically derive a âsingle-modeâ replacement to the full-chain representation of reptation, after which it becomes possible to retroactively estimate the error introduced by the earlier âshufflingâ approximation of the population balance terms. Finally, we scale up to a non-linear rheology model that further accounts for chain retraction and convective constraint release. The resultant equations (which we call the LRP-f model) can be solved efficiently, and are suitable for computational fluid dynamics calculations.
