Analytical Solution of Free Radical Polymerization: Applications- Implementing Gel Effect Using CCS Model Dhiraj K. Garg, †,§ Christophe A. Serra,* ,‡,§ Yannick Hoarau, † Dambarudhar Parida, § M. Bouquey, ‡,§ and R. Muller ‡,§ † Laboratoire des Sciences de l’Ingé nieur, de l’Informatique et de l’Imagerie (ICUBE), Universite ́ de Strasbourg (UdS), F-67000 Strasbourg, France ‡ Universite ́ de Strasbourg (UdS), E ́ cole Europe ́ enne de Chimie, Polyme ̀ res et Mate ́ riaux (ECPM), 25 rue Becquerel, F-67087 Strasbourg Cedex 2, France § Institut Charles Sadron (ICS) - UPR 22 CNRS, 23 rue du Loess, F-67034 Strasbourg Cedex 2, France * S Supporting Information ABSTRACT: 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 con- version 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. ■ INTRODUCTION During any chemical reaction, certain physical phenomena always draw attention and diffusion is one of them. In bulk or concentrated solution polymerization, diffusion plays a very sig- nificant role especially at higher conversions. Therefore, signi- ficant reaction steps like termination, propagation and initiation could become diffusion controlled as the reaction proceeds. As the conversion increases, the viscosity of the reaction mixture also increases. This increase of viscosity decreases the transla- tional diffusion of macroradicals. Thus, the termination of radical chains decreases as one radical need to approach another radical for terminating by combination or by disproportionation. Once in the proximity, the alignment of the radical segments is char- acterized by segmental diffusion. The overall decrease in termi- nation of macroradicals leads to the so-called Trommsdorff effect or gel effect 1 which is accompanied by an increase in the reaction rate. It may happen even in isothermal conditions. This has highly detrimental effects on the product quality, reactor safety and reactor operability. As the reaction continues the viscosity increases almost ex- ponentially. This decreases the species diffusivity even further so that even the monomer is now almost restricted to its place. If the reactor is operating below the glass temperature of the polymer and going for higher conversion, the reaction mixture glassifies. Thus, the reaction freezes at the conversion below completion. This effect is called glass effect. 1 This leads to incomplete usage of monomer and initiator and they remain within the product. They, thus, can act as impurities to cause adverse reactions when the polymer produced is used as final product without further processing. In the tubular flow reactor, the residence time is infinite near the walls due to no-slip flow condition at the wall surface. Thus, glass type product formation can takes place on the inner walls of the tubular reactor when the reactor operating temperature is less than the glass temperature of the polymer. This decreases the area for flow and hence increases the pre- ssure drop across the reactor. Under severe condition, it can even lead to the blockage of the tube reactor thus making it inoperable. So it becomes necessary either to operate at temperatures higher than the glass temperature of the polymer or diluting the reaction mixture using the inert solvent so as to keep the glass temperature of the mixture below the operating temperature. When the radicals are formed upon initiator decomposition, they need to reach monomer molecules to form the primary radicals. But due to several mechanisms, induced by impurities and chemical species like solvent present in the reaction mixture, many radicals are destroyed or consumed before reaching and reacting with monomer. Thus, only a fraction of radicals formed are able to form these primary radicals. The probability of an initiator radical to reach monomer decreases with increasing Received: June 19, 2014 Revised: August 27, 2014 Article pubs.acs.org/Macromolecules © XXXX American Chemical Society A dx.doi.org/10.1021/ma501251j | Macromolecules XXXX, XXX, XXX-XXX