Abstract
This study extends Flory's 1941 foundational work on three-dimensional step-growth polymerization (SGP) with trifunctional branching units. Flory laid the groundwork for understanding polymer size distribution back then, however, he did not fully explore the polydispersity and/or average degree of polymerization in A(2) + A(3) and A(2) + A(3) + B(2) types of systems. As the demand for advanced three-dimensional polymer materials grows, a more comprehensive theoretical framework is required. In this work, new analytical expressions are derived for the number-average (X (n)), weight-average (X (w)) degree of polymerization, and polydispersity (Đ) of trifunctional branched polymers through Flory's probability method. Additionally, we introduce the concept of Branch Unit Distribution (BUD), which has not been previously investigated. This new theoretical concept is validated through comparison with both experimental results and Monte Carlo simulations. Our findings provide new insights into the internal structure of three-dimensional branched polymers, offering valuable guidance for future design and development of novel materials from SGPs.