Analytical Solution of Free Radical Polymerization: Derivation and Validation

An elegant, simple, and exact analytical solution (AS) was obtained for a large range of elementary steps with practical importance in free radical polymerization. The AS matches excellently with the numerical solution for the four cases of monomer–polymer systems studied ranging from the slowest to the fastest. It works equally well for different initiators, different initiator and monomer concentrations, presence or absence of solvent, various solvent volume fractions, and different temperatures. It also matches quite well with experimental data reported in the literature. This AS is not only in line with previous published solutions but also extends their applicability in a natural way. Overall, the conceptual correctness as well as predictive capabilities of the derived AS are established beyond doubt. This AS has the potential to be used in various practical applications such as model based process control, CFD simulations, and so forth

Analytical Solution of Free Radical Polymerization: Applications- Implementing Gel Effect Using CCS Model

This article presents the implementation of the Chiu, Carratt, and Soong (CCS) gel/glass model in an analytical solution (AS) derived for the free radical polymerization under isothermal condition. This implantation allows AS to be applicable for the whole range of conversion thus making it more useful for practical applications. The results were compared with numerical solution (NS) as well as with experimental data for two different monomers: styrene (St) and methyl methacrylate (MMA). MMA with chain transfer agent was also used for this purpose. The results were found to be in good agreement with both NS and experimental data. NS with and without quasi-steady state assumption were also found to be in good agreement with each other for the entire range of conversion. As constant time step was used, the effect of stiffness on AS during gel effect was visible at low temperature compared to higher temperature

Analytical Solution of Free Radical Polymerization: Applications- Implementing Gel Effect Using AK Model

In this work, gel/glass/cage effects using the Achillias and Kiparissides (AK) model has been incorporated in the analytical solution (AS) obtained in our previous work. The AK model is based on the Chiu, Carratt, and Soong (CCS) model and free volume theory. The results of AS matched quite well with the numerical solutions as well as with the experimental data for methyl methacrylate (MMA). Various variables like termination kinetic coefficient, initiator efficiency, macroradicals concentration profile matched with the established published results. The work clearly demonstrates that AS is sufficiently flexible to accommodate gel/glass/cage effects explicitly although it was not primarily derived for these conditions. This extends the practical usage of AS for the whole range of conversion under isothermal conditions

Coil Flow Inversion as a Route To Control Polymerization in Microreactors

Linear and branched polymers of 2-(dimethylamino)­ethyl methacrylate (PDMAEMA) were synthesized in flow by atom transfer radical polymerization (ATRP) and self-condensing vinyl copolymerization adapted to ATRP, respectively, in capillary type stainless steel coiled tube (CT) microreactors. Coil flow inversion (CFI) was introduced to achieve better mixing and narrower residence time distributions during polymerization. This strategy was adopted to improve control over macromolecular characteristics and polymer architecture. Polydispersity index (PDI), as an overall indicator of control over polymerization, was significantly lower for CFI in the case of linear PDMAEMA, 1.39 compared to 1.53 for CT. For branched polymers containing up to 10 mol % of inimer, a reduced PDI was also obtained for CFI microreactor. As for the branching efficiency, it was found to follow the following trend CFI > CT > batch reactor