Calculation of number-average functionality and gel-point for stepwise polymerization

The number-average functionality is proposed a simplified equation which can be used to predict the reaction progress of the stepwise polymerization expediently. According to the equation, once the average functionality of one reactant ((f_b ) ̅, for example) is fixed, there will be a critical functionality of (f_a ) ̅. The reaction system has no risk to gel with the increase of component A if (f_a ) ̅ is below the critical functionality, while gelation will occur with the increase of component A if (f_a ) ̅ is higher than the critical functionality, and the gel point is the degree of reaction when (f_nb ) ̅ diverges to indefinitely large. The deduced equation is suitable for polymerization between R-An and R’-Bn, in which one of the components could be consumed completely, such as polyurethane, polyester, or other stepwise polymerization reactions. The equation can calculate the number-average functionality of polymer mixtures, especially for grafting or branched polymerization.