Step‐growth polymerized systems of general type "AfiBgi" : generating functions and recurrences to compute the MSD

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Abstract

General step-growth polymerization systems of order 2 are considered, i.e. systems of type "AfiBgi". We describe an algorithmic method to calculate the molecular size distribution (MSD). Input to the algorithm is the "recipe": a list of the monomers involved stating their A and B functionalities and their molar amounts, and the degree of conversion. Output is the MSD and its moments. Three main steps lead from input to output: (i) setting up a polynomial equation for the generating function that generates the MSD, (ii) transforming this polynomial equation to a differential equation, and (iii) transforming the latter one further to a recurrence equation. The recurrence yields the MSD and is of constant order. Keywords: branched polymers; molecular modeling; molecular weight distribution
Original languageEnglish
Pages (from-to)248-259
Number of pages12
JournalMacromolecular Theory and Simulations
Volume24
Issue number3
DOIs
Publication statusPublished - 2015

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