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Free‐Radical Polymerization with Long‐Chain Branching and Scission: Markovian Solution of the Weight‐Average Molecular Weight
Author(s) -
Tobita Hidetaka
Publication year - 2014
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.201400024
Subject(s) - branching (polymer chemistry) , polymerization , radical polymerization , polymer chemistry , bond cleavage , chemistry , kinetic chain length , chain transfer , eigenvalues and eigenvectors , monte carlo method , molecule , polymer , thermodynamics , mathematics , organic chemistry , physics , quantum mechanics , statistics , catalysis
Analytic solution for the weight‐average chain length in a matrix formula,P ¯ w = w s w + wF ( I − M ) − 1 s , is derived for free‐radical polymerization with simultaneous long‐chain branching and scission. Illustrative calculations are conducted for a batch polymerization. With bimolecular termination by combination, gelation could be observed. Assuming the same polymerization kinetics for branching and scission in the post‐gel period, the formed gel molecule could be degenerated into sol molecules again, i.e., degelation might occur. Both the gelation and degelation points are defined as the point when the largest eigenvalue of M is unity. The matrix formula is suitable to determine accurate values, while the Monte‐Carlo simulation can give much more detailed information. These two approaches are nicely complementary.