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“In‐out” recursive probability modeling of branched step‐growth polymerizations
Author(s) -
Miller Douglas R.,
Sarmoria Claudia
Publication year - 1998
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10217
Subject(s) - materials science , polymer science
This paper presents the derivation of mathematical formulae for molecular and network parameters of branched step‐growth polymerizations. Weight‐average molecular weight, gel point, and weight fractions of soluble, pendant and elastically‐effective material in a gel are derived. The direct “in‐out” recursive analysis of Macosko and Miller is applied to four general step‐growth polymerization systems. The method is introduced using the simple case of A f homopolymerization. Two new systems are then modeled; a homopolymerization of A f B g monomers with 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 before, but we give a new and complete presentation here to show the generality of the “in‐out” analysis. We also survey some additional polymer 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 silicone rubber system and a segmented polyurethane network system. Appendices present the small amount of elementary probability theory and polymer distribution theory needed to support the analysis. This paper serves as an introduction to the “in‐out” method; after reading this paper, the reader should be able to apply the “in‐out” method to many step‐growth polymer systems.