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Step‐Growth Polymerized Systems of General Type “AfiBgi”: Generating Functions and Recurrences to Compute the MSD
Author(s) -
Hillegers L. Tom,
Slot Johan J. M.
Publication year - 2015
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201400091
Subject(s) - polynomial , constant (computer programming) , mathematics , differential equation , type (biology) , function (biology) , degree (music) , generating function , monomer , order (exchange) , polymerization , mathematical analysis , computer science , chemistry , physics , ecology , organic chemistry , finance , evolutionary biology , economics , biology , programming language , polymer , acoustics
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.