Kinetic Acceleration and the Stoichiometric Limit Dictate the Behavior of Reactivity-Enhanced Step-Growth Polymerization

For nearly a century, the Carothers equation and Flory’s equal-reactivity assumption have governed our fundamental understanding of step-growth polymerization, dictating that (ultra)high-molecular-weight polymers strictly demand stoichiometric equivalence. However, the recent emergence of reactivity-enhanced step-growth polymerization, known as nonstoichiometric polycondensation, contradicts this classical paradigm by producing (ultra)high-molecular-weight polymers under stoichiometric imbalances. Herein, we resolve this empirical paradox by deriving an elegant, closed-form algebraic expression, Xn(α, r, p), based on the steady-state approximation. This compact formula explicitly quantifies how the degree of polymerization (Xn) is co-determined by kinetic acceleration factor (α), stoichiometric ratio (r), and monomer conversion (p). Through rigorous mathematical derivation, we explicitly decouple the polymerization behavior into kinetic acceleration and stoichiometric limits. The resulting formulation elucidates their intricate interplay, revealing how the former systematically delays molecular end-capping to circumvent classical stoichiometric limitations. Counterintuitively, we demonstrate that the optimal critical stoichiometry is not a fixed constant, but a dynamic trajectory continuously evolving with time or monomer conversion—overturning the long-held assumption of a static optimum. The predictions of our framework are validated against previously experimental observations, successfully resolving the stoichiometric paradox. Ultimately, this theoretical framework not only reshapes our understanding of step-growth polymerization by moving beyond the classically stoichiometry-dominated paradigm, instead revealing a profound synergistic interplay between kinetics and stoichiometry but also provides a solid foundation to rationally design and synthesize advanced polymeric materials.