Polymerization Kinetics in Viscous Drops

Free radical polymerization kinetics has received much attention and many aspects of the process are well understood (see Chapter 4). Most academic investigations have been carried out in idealized conditions where the extent of monomer conversion is low. The classical expression for the rate of polymerization (Rp), in a single-phase reaction, is Eq. (13), where kp is the propagation rate coefficient, Cm is monomer concentration, J i is the initiation rate and kt is the termination rate coefficient [63]. 

If radicals are generated by the thermal decomposition of an added initiator then, at steady-state conditions, Eq. (14) applies, where / is an efficiency factor, kj is the initiator decomposition rate coefficient and C is the initiator concentration. 

Chain termination is often diffusion-controlled and the value of kj diminishes substantially as the polymer concentration increases. At high polymer concentrations, kp decreases also [64]. The reduction in kt leads to an increase in the polymerization rate, a phenomenon often described as a gel effect . 

Although most workers agree that the chain termination reaction is diffusion-controlled, reliable quantitative relationships between the rate coefficients and measurable properties of the reaction medium are not generally available. Radical diffusion can depend on solution viscosity, polymer volume fraction and polymer molecular weight. The latter three entities are interrelated in complicated ways meaningful experiments, which may relate them to the rate coefficients, are not easy to devise [65]. However, Brooks et al. showed that effects of viscosity changes on polymerization rate could be distinguished from the effects of polymer volume fraction [66]. In some cases, the value of / may also depend on polymer content [67]. 

The value of kj can often be determined independently but traditional steady-state experiments give values for kp/k - and do not provide separate values for kp and kt. This restriction becomes a problem for reactor modeling because, in the presence of polymer, both kp and kt diminish (even in isothermal conditions). 

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