Modeling Controlled/Living Radical Polymerization Kinetics: Bulk and Miniemulsion

A first‐principle model for the controlled/living radical polymerization (CLRP) is discussed. The polymerization rate of CLRP is conveniently represented by a simple relationship, R p ∝ [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, D p,SMC below which R p starts to decrease significantly compared with the corresponding bulk polymerization, and $R_{{\rm p}} \,{\propto} \,D_{{\rm p}}^{3} $ for D p  <  D p,SMC . For the particle sizes somewhat larger than D p,SMC , the statistical variation in the number of trapping agents can make R p larger. A simple equation to estimate the D p,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 R p is larger than for bulk polymerization, may be observed for D p,SMC  <  D p  <  D p,Fluct . On the other hand, many reversible‐addition‐fragmentation chain transfer polymerizations conform to the condition [ Interm ] ≪ [ Trap ], and R p is controlled by [ Interm ]. If [ Interm ] in a particle under the zero‐one condition is larger than for bulk polymerization, R p 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, D p,ZIM below which R p increases significantly compared with the bulk polymerization, and $R_{{\rm p}} \,{\propto} \,D_{{\rm p}}^{{-} 3} $ for D p  <  D p,ZIM .