Modeling Controlled/Living Radical Polymerization Kinetics: Bulk and Miniemulsion

Abstract

AbstractA first‐principle model for the controlled/living radical polymerization (CLRP) is discussed. The polymerization rate of CLRP is conveniently represented by a simple relationship, Rp ∝ [Intermediate]/[Trapping Agent], which highlights the important characteristics of various types of CLRPs. In stable free radical polymerization and atom‐transfer radical polymerization, the relationship, [Trap] ≪ [Interm] holds, and the polymerization rate is controlled by [Trap]. When the polymerization is conducted in nanosized particles, even a single trapping agent in a particle may lead to a larger [Trap] than for bulk polymerization. This single‐molecule‐concentration (SMC) effect theory leads to determine the particle diameter, Dp,SMC below which Rp starts to decrease significantly compared with the corresponding bulk polymerization, and $R_{{\rm p}} \,{\propto} \,D_{{\rm p}}^{3} $ for Dp < Dp,SMC. For the particle sizes somewhat larger than Dp,SMC, the statistical variation in the number of trapping agents can make Rp larger. A simple equation to estimate the Dp,Fluct‐value, below which the acceleration due to the fluctuation effect is predicted to occur, is presented. In conjunction with the SMC effect, an acceleration window, in which Rp is larger than for bulk polymerization, may be observed for Dp,SMC < Dp < Dp,Fluct. On the other hand, many reversible‐addition‐fragmentation chain transfer polymerizations conform to the condition [Interm] ≪ [Trap], and Rp is controlled by [Interm]. If [Interm] in a particle under the zero‐one condition is larger than for bulk polymerization, Rp can be increased significantly by reducing the particle size due to the zero‐one intermediate molecule (ZIM) effect. The ZIM effect theory leads to determine the particle diameter, Dp,ZIM below which Rp increases significantly compared with the bulk polymerization, and $R_{{\rm p}} \,{\propto} \,D_{{\rm p}}^{{-} 3} $ for Dp < Dp,ZIM. magnified image