IN-OUT RECURSIVE PROBABILITY MODELING OF BRANCHED STEP-GROWTH POLYMERIZATIONS

This paper presents the derivation of mathematical formulae for molecu lar and network parameters of branched step-growth polymerizations. We ight-average molecular weight, gel point, and weight fractions of solu ble, pendant and elastically-effective material in a gel are derived. The direct ''in-out'' recursive analysis of Macosko and Miller is appl ied to four general step-growth polymerization systems. The method is introduced using the simple case of A(f) homopolymerization. Two new s ystems are then modeled: a homopolymerization of A(f)B(g) monomers wit h two types of reactive groups, and an A(f)+B-g+C-h terpolymerization. The fourth system presented is a general A(f)+B-g copolymerization of polydispersed reactants; we have partially analyzed this system befor e, but we give a new and complete presentation here to show the genera lity of the ''in-out'' analysis. We also survey some additional polyme r systems that have been analyzed in the literature. Then, we discuss limitations of this modeling approach, the use of the models and their implementation in software. We give two numerical examples: a silicon e rubber system and a segmented polyurethane network system. Appendice s present the small amount of elementary probability theory and polyme r distribution theory needed to support the analysis. This paper serve s as an introduction to the ''in-out'' method; after reading this pape r, the reader should be able to apply the ''in-out'' method to many st ep-growth polymer systems.