Batch initiation, nucleation phase

All quantitative theories based on micellar nucleation can be developed from balances of the number concentrations of particles, and of the concentrations of aqueous radicals. Smith and Ewart solved these balances for two limiting cases (i) all free radials generated in the aqueous phase assumed to be absorbed by surfactant micelles, and (ii) micelles and existing particles competing for aqueous phase radicals. In both cases, the number of particles at the end of Interval I in a batch macroemulsion polymerization is predicted to be proportional to the aqueous phase radical flux to the power of 0.4, and to the initial surfactant concentration to the power of 0.6. The Smith Ewart model predicts particle numbers accurately for styrene and other water-insoluble monomers. Deviations from the SE theory occur when there are substantial amounts of radical desorption, aqueous phase termination, or when the calculation of absorbance efficiency is in error. 

Batch miniemulsion polymerization of MMA using PMMA as the costabilizer was carried out with SLS as the surfactant and KPS as the initiator. Solids content was kept at -30%. A low surfactant level was used with the miniemulsions to ensure droplet nucleation. The initiator concentration of the polymer-stabilized miniemulsion polymerizations was varied from 0.0005 to 0.02 Mjq, based on the total water content. An aqueous phase retarder, (sodium nitrite) or an oil-phase inhibitor (diphenylpicrylhydrazol [DPPH]), was added to both the miniemulsions and the macro emulsions prior to initiation. Particle numbers and rates of polymerization for both systems were determined. 

The relatively large monomer droplets (generally 2-5ym in diameter) have too small a surface area to capture radicals from the aqueous phase and therefore serve as reservoirs for the diffusion of monomer through the aqueous phase to the pol3onerizing oligomeric radicals, micelles, or polymer particles. Despite the unfavorable statistical probabilities, however, some monomer droplets capture radicals and polymerize to form microscopic or near-microscopic particles (14), and some of these particles which are entirely separate from the main particle size distribution are formed in most batch polymerizations. Polymerization in monomer droplets becomes much more significant when the size of the emulsion droplets is decreased. The use of ionic emulsifier-fatty alcohol mixtures (13) and, later, ionic emulsifier-alkane mixtures (15), allows the preparation of 0.1-0.2ym size styrene monomer droplets, which compete favorably with initiation in micelles and in the aqueous phase as the mechanism of particle nucleation. The mechanism of formation of these "mini-emulsions" has been attributed to the very low solubility of the fatty alcohols and alkanes in water (16) or to the formation of crystalline complexes between the ionic emulsifiers and fatty alcohols (17) the two mechanisms are not mutually exclusive. Thus this mechanism pertains only to special systems. 

Determination of the optimal temperature (or supersaturation) trajectory for a seeded batch crystallizer is a well studied problem. This is a dynamic optimization or optimal control problem. The process performance is determined by the crystal size distribution and product yield at the final time. For uniformity of shape and size in the crystals in a seeded batch crystallization process, it is essential to ensure that the nucleation phenomena occurs to the minimum and mostly the seeded crystals grow to the desired size at a certain rate. If nucleation occurs in the initial phase, then there is a possibility that the nucleated crystal will compete with the seeded ones, thus if the phenomena is of late growth, then nucleation in the earlier phase is preferred. Thus, depending upon the process operation, many types of objective functions have been proposed [4]. 

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