Mean‐Field Calculation of MZ for Randomly Branched Condensation Polymers

ABSTRACT The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of MZ via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents t...

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Bibliographic Details
Published inJournal of polymer science. Part B, Polymer physics Vol. 57; no. 21; pp. 1415 - 1422
Main Authors Odle, Roy, Mitchell, Joseph D., Bendler, John T.
Format Journal Article
LanguageEnglish
Published Hoboken, USA John Wiley & Sons, Inc 01.11.2019
Wiley Subscription Services, Inc
Subjects
Chain branching
characteristic molecular weight
Condensation polymerization
crosslinking
Gelation
GPC
Mathematical analysis
Mean field theory
percolation
Polymers
Recursive methods
SEC
sol–gel transition
static critical scaling
Stoichiometry
Z‐average molecular weight
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Summary:ABSTRACT The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of MZ via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents to control the chain length between branch points, multiple branching agents, and arbitrary stoichiometries. MZ closely approximates the largest branched polymer in the system and is therefore a key parameter describing static scaling behavior near the gel point. Nonuniversal static scaling of MZ is illustrated with examples from the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1415–1422 Though it was developed over 75 years ago, the Flory–Stockmayer (FS) percolation model is applicable to a wide variety of new gelation phenomena, including thermoreversible gels, hydrogels, and drug delivery systems. While avoiding the combinatorial complexity historically encountered, this article extends FS to a calculation of MZ that represents the largest molecular aggregate in the gelling system and is a key theoretical and characterization parameter. Asymptotic scaling behavior of the largest cluster near the gel point is shown to be masked by nonuniversal molecular details.
ISSN:0887-6266
1099-0488
DOI:10.1002/polb.24884