关键词: 缩聚反应, 数均聚合度, 基团数比, 平均官能度

Abstract: To address the pedagogical challenge of calculating the number-average degree of polymerization $\left(\overline{X_n}\right)$ in polycondensation reactions, this study systematically derives and analyzes the formulas involved in two distinct calculation approaches for different polycondensation systems. The functional group molar ratio ($r$) method proves exclusively applicable to linear polycondensation. For $\mathrm{aAa}+\mathrm{bBb}+\mathrm{Cb}$ and $\mathrm{aRb}+\mathrm{Cb}$ systems, the monofunctional Cb must first be converted to an equivalent bifunctional monomer with matching endcapping effects before determining $r$. When b groups are in excess, Cb's end-capping effect corresponds to bBb; conversely, with excess a groups, it mirrors aRb. The average functionality ($\bar{f}$) method demonstrates broader applicability, suitable for both linear and crosslinked polycondensation systems, with $\bar{f}$ being directly calculable from its definition. The integration of rigorous formula derivations with practical application examples has yielded significant improvements in teaching outcomes.

Key words: Polycondensation reaction, Number-average degree of polymerization, Molar ratio of functional groups, Average functionality