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Molecular Weight Distribution of Core Cross‐Linked Star Polymers
Author(s) -
Tobita Hidetaka
Publication year - 2017
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.201600037
Subject(s) - core (optical fiber) , star (game theory) , weight function , mathematics , fraction (chemistry) , distribution (mathematics) , molar mass distribution , combinatorics , polymer , physics , chemistry , statistics , chromatography , mathematical analysis , optics , nuclear magnetic resonance
The analytic formulas for the number‐ and weight‐average molecular weights (MWs) of the core cross‐linked star polymers (CCSPs) are proposed. In the arm‐first method, the number‐ and weight‐average MWs of the arms (M ¯ nAandM ¯ wA) and CCSPs (M ¯ nandM ¯ w ) can be determined experimentally. FromM ¯ nA,M ¯ n , and weight fraction of the arms w A (or the core, w C = 1− w A ), the number‐average number of the arms (f ¯ n ) and the number‐average core MW (M ¯ nC) can be determined. Because of the correlation between the core MW and the number of the arms, the general solution ofM ¯ wfor CCSPs presented requires attention to the nature of correlation. When the average and variance of the arm‐number distribution are linear function of core MW, the weight‐average number of the arms (f ¯ w ) and the weight‐average core MW (M ¯ wC) can be determined. The approximate estimation method forf ¯ wis also discussed.