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Monte Carlo Simulations of Atom Transfer Radical (Homo)polymerization of Divinyl Monomers: Applicability of Flory–Stockmayer Theory
It
is well known that free radical (co)Âpolymerization of multivinyl
monomers (MVMs) leads to insoluble gels even at a low monomer conversion,
and the gelation point can be predicted by Flory–Stockmayer
theory (F–S theory) based on two assumptions: (1) equal reactivity
of all vinyl groups and (2) the absence of intramolecular cyclization.
This theory has been experimentally studied and verified with conventional
free radical (co)Âpolymerization (FRP) of several MVMs (e.g., divinylbenzene,
DVB). However, it is still debatable whether this theory is applicable
for the polymerization of MVMs using reversible deactivation radical
polymerization (RDRP) approaches, such as atom transfer radical polymerization
(ATRP). Herein, Monte Carlo simulations using two statistical modelsî—¸with
cyclization (<b>w.c.</b>) and without cyclization (<b>wo.c.</b>, corresponding to F–S theory)and dynamic lattice
liquid (DLL) models were conducted to study ATRP of divinyl monomers.
The simulated gel points using <b>w.c.</b> and <b>wo.c.</b> models were compared with those obtained from ATRP experiments,
from calculation using F–S theory, and from simulations using
DLL models. The molecular weights, dispersity, and extent of intermolecular/intramolecular
cross-linking were calculated as a function of double bond and cross-linker
conversion. The results demonstrated that the gel points obtained
from both <b>w.c.</b> and <b>wo.c.</b> models were lower
than the values from DLL models and experiments. This indicates that
F–S theory cannot be used to accurately predict the polymerization
of divinyl monomers via ATRP. Our study shows that the limitation
of F–S theory in predicting ATRP reaction of divinyl monomers
is not only due to neglecting intramolecular cyclization but also
due to spatial restrictions which can cause the reactivity and accessibility
of vinyl groups becoming nonequivalent in ATRP of divinyl monomers