Polydispersity
quantifies the breadth of polymer molecular weight distribution, making
it an important and frequently quoted chain microstructural property
for characterization. An explicit expression of such an important
variable is desirable for ease of calculation, correlation with experiment
data, and/or parameter estimation. A review of published literatures
shows that great efforts have been put forth by many researchers to
derive these equations for various polymerization mechanisms. In atom
transfer radical polymerization (ATRP), polydispersity depends on
three factors: monomer conversion, number of monomer addition per
activation/deactivation cycle, and amount of dead chains. The existing
expressions available in the literature only account for, at most,
two of these three factors, with the contribution from dead chains
commonly neglected. This assumption results in polydispersity monotonically
decreasing with conversion, which is often not observed in experiments.
In this work, a new equation for polydispersity, which accounts for
contributions of all the three aforementioned factors, is proposed.
The validity of assumptions involved in the derivation is evaluated
by comparing the polydispersity profiles to those simulated by the
method of moments. In addition, this new equation is used to correlate
several experiment data sets for verification, namely from ATRP of
2-hydroxyethyl methacrylate, methyl methacrylate, and N-isopropylacrylamide, showing better agreement than the existing
equation. Although the equation derived here is strictly applicable
to homogeneous (bulk and solution) normal ATRP, with further effort
it may be extended to other types of ATRP as well as NMP and RAFT
systems.
si‐RAFT polymerization is widely used for surface modification. However, how the surface radicals terminate requires further elucidation. A kinetic model is developed for si‐RAFT via the R group approach. The model describes the molecular weight of grafted polymers as well as polymer layer thickness and various chain concentrations. It is shown that surface/surface radical termination plays an important role. The termination is facilitated by the migration of surface radicals through “hopping” and “rolling” mechanisms. “Hopping” occurs through activation/deactivation cycles between surface and solution chains, dependent on the RAFT concentration in solution. “Rolling” occurs through transfers between surface/surface chains, dependent on the grafting density at surface.
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