Abstract
When the size of a polymerization locus is smaller than a few hundred nanometers, such as in miniemulsion polymerization, each locus may contain no more than one key-component molecule, and the concentration may become much larger than the corresponding bulk polymerization, leading to a significantly different rate of polymerization. By focusing attention on the component having the lowest concentration within the species involved in the polymerization rate expression, a simple formula can predict the particle diameter below which the polymerization rate changes significantly from the bulk polymerization. The key component in the conventional free-radical polymerization is the active radical and the polymerization rate becomes larger than the corresponding bulk polymerization when the particle size is smaller than the predicted diameter. The key component in reversible-addition-fragmentation chain-transfer (RAFT) polymerization is the intermediate species, and it can be used to predict the particle diameter below which the polymerization rate starts to increase. On the other hand, the key component is the trapping agent in stable-radical-mediated polymerization (SRMP) and atom-transfer radical polymerization (ATRP), and the polymerization rate decreases as the particle size becomes smaller than the predicted diameter.
Highlights
The rate of polymerization, Rp in free-radical polymerization is represented by: Rp “ kp rMsrR‚ s (1)where kp is the propagation rate constant, [M] is the monomer concentration, and [R‚ ] is the active radical concentration.At the same monomer concentration, the polymerization rate is higher for larger radical concentration, [R‚ ]
To roughly estimate the threshold diameter what we want to determine is the approximate value of the average number of radical generating species (RGS) molecules in a particle, which could be represented by: pAverage number of RGS molecules in a particleq “ n p1 ́ φact q where n represents the average number of radicals in a particle when no reversible-addition-fragmentation chain-transfer (RAFT) agent is used, i.e., in the conventional free-radical miniemulsion polymerization, and φact is the average time fraction of the active period, which is defined explicitly by: φact “
For conventional free-radical polymerization, the threshold particle diameter below which the polymerization rate becomes faster than the corresponding bulk polymerization was derived from the polymerization rate expression, Rp = kp [R‚ ][M]
Summary
The rate of polymerization, Rp in free-radical polymerization is represented by: Rp “ kp rMsrR‚ s (1). A dp to extremely small radical concentration [R‚ ] in the order of 10 ́8 to 10 ́6 mol/L in usual free-radical where n is the average number of radicals in a particle, N A is the Avogadro constant, vp is the polymerization, as schematically represented by (a) bulk polymerization, where red dots particle volume, and dp is the particle diameter. Simple formulas to quantitatively predict the particle diameter below which the polymerization rate becomes much different from the bulk polymerization are elucidated, based on the high single-molecule concentration in a small particle. The effect of high single-molecule concentration on the polymerization rate is reorganized, starting from the conventional free-radical polymerization. Readers may find the other interesting aspects of the related topic in refs [2,6,7,8,9,10]
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