Extensions to Miller Macosko Theory and Validation by Means of Stockmayer's Equation - Cameron, Colin (Macromolecular theory and simulations, 2025)
The recursive method of Miller and Macosko for calculating the average properties of linear and non‐linear A + B step‐growth polymers is extended to give formulae for the site‐ and weight‐average functionality, and the site‐average mass of a polymerising mixture at any extent of conversion of functional groups. These parameters are necessary for the calculation of the weight average molecular weight of polymer systems. All derived formulae are fully validated using the output of Stockmayer's equation, by means of two examples, one branched and one linear step growth polymer, which are then combined in a second stage to show the application of the new expressions to polymeric reactants in the pre‐gel state, without the need for analytical expressions for chain length or functionality distributions. This second stage is also validated using Stockmayer's equation. The new formulae apply to any co‐reactive chemistries used in step polymerization. In linear A 2 + B 2 step polymerization, processed to less than complete reaction, use of these new recursive relations yields a new, simpler method to identify the abundance of chains with minority A groups at both ends, chains with one A group and one B group, and chains with majority B groups at both ends.