First-principles calculation of particle formation in emulsion polymerization: pseudo-bulk systems

Kinetic behavior in emulsion polymerization can be conveniently assigned as either ‘zero-one’ or ‘pseudo-bulk’. Sufficiently small particles in emulsion polymerizations obey zero-one kinetics, where entry of a radical into a particle which contains a growing radical leads to instantaneous termination. Pseudo-bulk kinetics applies to particles in which more than one free radical can co-exist for a significant period; while this is commonly applicable to large particles for any monomer, it also applies to very small particles for monomers which propagate very rapidly, such as acrylates. A methodology is developed to enable particle sizes and rates to be calculated for systems in which pseudo-bulk kinetics are important during particle formation. This takes account of all significant reactions involving radical species in the water and particle phases, including the chain-length dependence of the termination rate coefficient. A ‘cross-over radius’ rco is used to describe the particle size where termination of radicals within the particles is no longer instantaneous. The model is applied to the emulsion polymerization of butyl acrylate. All parameters are available from the literature, except for rco and kp1, the rate coefficient for propagation of a monomeric radical formed from transfer. These were determined from experiments on seeded emulsion polymerizations of this monomer, involving the steady-state rate with chemical initiator and non-steady-state rate in a system initiated by γ radiolysis, after removal from the radiation source (‘relaxation’ mode). Particle sizes and rates in unseeded butyl acrylate emulsion polymerizations at 50 °C, over a range of concentrations of persulfate as initiator and sodium dodecyl sulfate as surfactant, are predicted by the model with acceptable accuracy.