A Mathematical Approach to the Ring-Chain Equilibria of (Co)polymers for Chemical Recycling

Closed-loop chemical recycling of polymers to their constituent monomers and subsequent repolymerization is a promising strategy for plastic recycling. Within this field, aliphatic polyesters and polycarbonates are often highlighted, and the thermodynamics that describe the ring-opening polymerization (ROP) equilibria have become a common metric to assess their chemical recyclability. The ring-chain equilibria (RCE) extend the recyclability of polymers further than described by ROP, by including larger rings that broaden the thermodynamic landscape. In this work, the equilibrium concentration of monomer units present in any ring ([O]eq) that form in the RCE is calculated from a modified Jacobson–Stockmayer equation based on random walk statistics. The equation was experimentally validated and used to study and predict RCE thermodynamics of different aliphatic lactones in homo- and comonomer systems. A term to account for polymer chain-end architecture was introduced to allow for accurate calculation of comonomer systems. For complex systems with many different monomers, a method that calculates [O]eq based on average ring size was developed, and with a decreased average ring size, a larger [O]eq was obtained. The knowledge gained in this work enables the prediction and study of (co)polymer recyclability through the RCE, without the need for their experimental synthesis.