A Unified Theory for Generalized Step-Growth Polymerization: From Flory’s Equal‑Reactivity to Kinetic Symmetry‑Breaking
- 1Hubei Key Laboratory for New Textile Materials and Applications
- 2Wuhan Textile University
Abstract
For nearly nine decades, Flory’s equal-reactivity hypothesis has universally underpinned the statistics of step-growth polymerization. However, modern monomers featuring rigid fused-ring architectures or catalytic bond-forming mechanisms routinely violate this core assumption. Consequently, the resulting molecular-weight anomalies have long been erroneously misattributed to side reactions or impurities, obscuring the underlying kinetic reality. Here, we resolve this theoretical blind spot by generalizing the AA + BB polycondensation into a strict analytical framework encompassing a kinetic enhancement parameter (𝛼). By exactly solving the infinitely coupled kinetic network, we derive closed-form expressions for the entire parameter space of stoichiometry (𝑟) and kinetics (𝛼), unveiling three macroscopic laws. First, a Terminal Dichotomy: on the A-deficient side (𝑟 < 1), the reaction undergoes "kinetic freezing," permanently archiving the kinetic 𝛼 -fingerprint within the end-cap inventory; conversely, on the A-excess side (𝑟 > 1 ), the system exhibits "𝛼 -amnesia," where terminal states are dictated solely by stoichiometry. Second, at the equimolar critical point (𝑟 = 1), the dispersity exhibits a profound singularity with non-commuting limits. Third, a Moving-Target Mechanism: while chain length grows monotonically with the feed ratio at fixed conversion, the optimal stoichiometry at a fixed reaction time migrates dynamically with 𝛼, allowing fast-asymmetric systems to achieve molecular weights nearly an order of magnitude higher than classical equimolar yields. Ultimately, this framework identifies a falsifiable end-group signature to reverse-engineer 𝛼 , transforming long-standing polycondensation anomalies into predictable, mathematically rigorously controllable levers for macromolecular design.
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BibTeX
@misc{tang2026unified,
title = {{A Unified Theory for Generalized Step-Growth Polymerization: From Flory’s Equal‑Reactivity to Kinetic Symmetry‑Breaking}},
author = {Qingquan Tang},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009468/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009468/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - A Unified Theory for Generalized Step-Growth Polymerization: From Flory’s Equal‑Reactivity to Kinetic Symmetry‑Breaking
AU - Qingquan Tang
PY - 2026
DA - 2026/09/25
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009468/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009468/v1
AB - For nearly nine decades, Flory’s equal-reactivity hypothesis has universally underpinned the statistics of step-growth polymerization. However, modern monomers featuring rigid fused-ring architectures or catalytic bond-forming mechanisms routinely violate this core assumption. Consequently, the resulting molecular-weight anomalies have long been erroneously misattributed to side reactions or impurities, obscuring the underlying kinetic reality. Here, we resolve this theoretical blind spot by generalizing the AA + BB polycondensation into a strict analytical framework encompassing a kinetic enhancement parameter (𝛼). By exactly solving the infinitely coupled kinetic network, we derive closed-form expressions for the entire parameter space of stoichiometry (𝑟) and kinetics (𝛼), unveiling three macroscopic laws. First, a Terminal Dichotomy: on the A-deficient side (𝑟 < 1), the reaction undergoes "kinetic freezing," permanently archiving the kinetic 𝛼 -fingerprint within the end-cap inventory; conversely, on the A-excess side (𝑟 > 1 ), the system exhibits "𝛼 -amnesia," where terminal states are dictated solely by stoichiometry. Second, at the equimolar critical point (𝑟 = 1), the dispersity exhibits a profound singularity with non-commuting limits. Third, a Moving-Target Mechanism: while chain length grows monotonically with the feed ratio at fixed conversion, the optimal stoichiometry at a fixed reaction time migrates dynamically with 𝛼, allowing fast-asymmetric systems to achieve molecular weights nearly an order of magnitude higher than classical equimolar yields. Ultimately, this framework identifies a falsifiable end-group signature to reverse-engineer 𝛼 , transforming long-standing polycondensation anomalies into predictable, mathematically rigorously controllable levers for macromolecular design.
ER -