Step-Growth Polymerizing Systems of General Type 'AfiBgi': Calculating the Bivariate (Molecular Size) x (Number of Branch Points) Weight Distribution Using Generating Functions and Recurrences

摘要

This study considers step-growth polymerizing systems of general type "AfiBgi" whereby one or more of the reacting monomer species bear at least three reactive groups. The random polymerization process will lead to a population of polymer molecules in which the individual molecules may differ widely with respect to degree of polymerization and number of branch points. This study presents an algorithmic method to calculate the statistical distribution of weight over these two molecular properties. The method uses bivariate generating functions, recurrences, and integer arithmetic.