Reaction loci size effect on reversible deactivation radical polymerization rate

The effect of reaction loci size on the rate of reversible deactivation polymerization (RDRP) in dispersed media such as miniemulsion polymerization is estimated theoretically and some threshold diameters where the rate starts to increase/decrease significantly are proposed [1]. According to one of the threshold diameters, a simple experimental method to discriminate between two controversial kinetic models for reversible addition-fragmentation chain-transfer (RAFT) polymerization is proposed and demonstrated experimentally [2,3]. The rate of successful RDRP (Rp) can be expressed as Rp = kp [M] K [RGS]/[Trap], where kp is the propagation rate constant and [M] the monomer concentration, K the equilibrium constant for the reversible activation, [RGS] the concentration of the radical generating species (RGS), which generates radicals by the reversible activation, and [Trap] the concentration of the trapping agent. In a radical polymerization in dispersed media, such as in miniemulsion polymerization, only a molecule of RGS or the trapping agent in a dispersed reaction locus (such as a polymer particle or a miniemulsion droplet) may make its concentration in a dispersed reaction locus larger than that for bulk polymerization if the size of the dispersed reaction locus is less than a certain size, which is called “Single Molecule Concentration (SMC) effect”. In the case of successful stable free radical polymerization such as nitroxide-mediated polymerization and atom-transfer radical polymerization, [Trap] \u3c [RGS] and SMC effect for the trapping agent is significant. Thus, the rate of the polymerization is expected to be proportional to the 3rd power of the diameter of the dispersed reaction loci if the diameter is less than a threshold diameter Dp,SMC = {6/(p NA [Trap]bulk)}1/3, where NA is Avogadro\u27s number and [Trap]bulk is the trapping agent concentration for the corresponding bulk polymerization. In the case of successful RAFT polymerization, RGS is an intermediate (radical), which is generated by addition of active radical to the trapping agent (RAFT agent), and [RGS] \u3c [Trap]. Thus, the rate of the polymerization is expected to be inversely proportional to the 3rd power of the diameter of the dispersed reaction loci if the diameter is less than a threshold diameter Dp,SMC = {6 n (1-fA)/(p NA [RGS]bulk)}1/3, where n is the average number of radicals per dispersed reaction locus for the corresponding non-RDRP polymerization in the dispersed media, [RGS]bulk is the RGS concentration for the corresponding bulk polymerization, and fA is the time fraction of the active period, represented by fA = K/(K+[Trap]). Two controversial models for rate retardation by addition of RAFT agent were proposed. One is so-called intermediate termination (IT) model, which assumes bimolecular termination of intermediate radicals with active radicals (intermediate termination) [4]. The other is so-called slow fragmentation (SF) model, which assumes by far lower rate constant for fragmentation of intermediate radicals and no intermediate termination [5]. The threshold diameter Dp,SMC calculated with IT model for typical RAFT styrene polymerization with dithiobenzoate shows that a significant polymerization rate increase is predicted for the diameter smaller than 200-300nm. On the other hand, a large intermediate concentration ([RGS]bulk) in SF model leads to an extremely small threshold diameter, which shows that it is impossible to make the polymerization rate faster in miniemulsion polymerization. Thus two models can be discriminated by comparing the rates of the RAFT miniemulsion and bulk polymerization. The rate of miniemulsion polymerization of styrene with benzyl dithiobenzoate [4] or 2-cyano-2-propylbenzoditioate [5] with miniemulsion droplets average diameter around 100nm is by far higher than the corresponding RAFT bulk polymerization, and increased with the decrease in the miniemulsion droplet average diameter [5], and the experimentally-measured time-conversion curves agree fairly well with those simulated with IT model with reaction rate constants proposed in literature, which demonstrates the applicability of IT model for RAFT polymerization of styrene with dithiobenzoates