Chain Length Dependence of Chemically Controlled Reactions in Polymerization

Chemically controlled reactions in polymerization processes are traditionally assumed to have chain-length-independent rate coefficients. However, this work challenges that assumption by using multiscale modeling to demonstrate that chemically controlled polymer-polymer reactions can exhibit significant chain length effects. Taking reversible addition-fragmentation chain transfer (RAFT) polymerization as a case study, we compare the chain length convergence of the reaction entropy for two processes: the addition of a growing polymer radical to a simultaneously growing polymeric RAFT agent, and the analogous reaction involving a low molecular weight RAFT agent. While the latter reaches equilibrium within 10 monomer additions, the former shows delayed convergence, with effects persisting to degrees of polymerization (DP) of 100 or more. A similar trend was observed in the Diels-Alder step-growth polymerization, where rapid convergence occurred when one chain length was fixed and short, but markedly slower convergence was observed when both reacting chain lengths increased simultaneously. These results reveal that entropy contributions, which scale logarithmically with chain length, lead to significant chain length dependence in the equilibrium constants (Keq). Because these effects arise from fundamental entropic considerations rather than specific features of the reacting species, they are expected to manifest broadly in the kinetics and thermodynamics of other chemically controlled polymer-polymer reactions. Our findings provide a mechanistic basis for resolving discrepancies in experimental estimates of fragmentation rate coefficients, shedding light on debate surrounding rate retardation in RAFT systems. More broadly, this work underscores the importance of chain length effects in the kinetics and thermodynamics of chemically controlled polymer-polymer reactions.