(240d) Population Balances for Full-Chain Constitutive Models of Living Polymers

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 “fast breaking” 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 work on the use of population balances in full-chain constitutive models of living polymers. This work provides a systematic method for constructing living polymer models by appending population balance equations to the stress relaxation dynamics as described by existing non-linear differential constitutive models of stress relaxation phenomena in polymeric materials. We consider results for reptation, contour length fluctuations (CLF), chain retraction, and Rouse relaxation. Finally, when considering a ‘fast breaking’ limit of the full non-linear model, we combine all of the preceding results together and show that the resultant leading-order equations (which we call the STARM model) simplify dramatically and are suitable for computational fluid dynamics applications.