Redefining Gelation with Polymer Growth Dimensionality: A Monad‐Based Criterion Quantifying Cyclization Effects

ABSTRACT Conventional gelation theories have long faced challenges in accounting for the effects of cyclization, a persistent issue in polymerization kinetics. To address this, we introduce a kinetic framework focused on the evolution of structural units (monads), which balances mathematical simplicity with the retention of critical structural information. Analytical solutions for monad distribution functions (MDFs) are derived. A novel concept, polymer growth dimensionality (PGD, D P ) derived from MDF, is introduced to quantify monads' connectivity. By defining gelation at D P = 1, the newly developed gelation criterion reproduces the classical gel points of Carothers and Flory–Stockmayer for various self‐ and cross‐condensation systems. The identification of two additional crossover points at D P = 2 and 3, corresponding to the formation of 2D and 3D network structures, respectively, represents an extension of conventional gelation theory. Furthermore, as primary cyclization reactions occur at the monad level, their impact on gelation can be theoretically quantified, addressing a longstanding challenge. Our monad‐based PGD offers a simplified, parallel, and expanded toolkit for gelation analysis.