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A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers Bearing A and B Coreactive Groups
Author(s) -
Hillegers L. Tom,
Blokhuis Aart,
Slot Johan J. M.
Publication year - 2012
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.201200027
Subject(s) - computation , monomer , polymerization , polymer , order (exchange) , distribution (mathematics) , set (abstract data type) , mathematics , degree of polymerization , type (biology) , combinatorics , molar mass distribution , statistical physics , materials science , polymer chemistry , physics , algorithm , mathematical analysis , computer science , nuclear magnetic resonance , ecology , finance , economics , biology , programming language
General step‐growth polymerization systems of order 2 are considered, i.e., systems of type “Af i Bg i ”, and a fast algorithmic method is presented to compute, at a given degree of conversion, the MSD and the MWD. The complete distribution is calculated; not just statistical averages of the polymer population such as $\overline {M} _{{\rm n}} $ or $\overline {M} _{{\rm w}} $ . For the computation of the low‐ and intermediate size/weight parts of the distribution curves, a set of recurrence relations is used. The high‐molecular size/weight parts of the curves (right tails) are computed using an accurate approximation derived from generating functions. In a previous paper, we applied our method to general order‐1 systems, i.e., systems of type “Af i ”.