Cyclization in Linear Step-Growth Polymerizations.

Intramolecular cyclization is a pervasive yet often ignored factor in step-growth polymerizations (SGPs), particularly under dilute conditions. While experimental studies have confirmed the significant impact of concentration on cyclization, the lack of deep theoretical understanding has limited the ability to guide reaction design and predict the polymer structure. In this work, we adopt a reverse-engineering strategy to extract cyclization-related equations from experimental data using a classical A2 + B2 step-growth polymerization system. By combining analytical derivations with symbolic regression, a machine learning technique for generating closed-form expressions, we obtain explicit formulas for cyclization probability, degree of cyclization, degree of linear polymerization, and molecular weights as functions of monomer conversion and reaction concentration. These expressions capture the dynamic nature of cyclization and demonstrate excellent agreement with experimental results across a broad concentration range. Our work provides a new quantitative framework to incorporate cyclization into SGP theory and offers practical tools for predicting molecular structures and properties under real-world conditions.