Smith-Ewart nucleation model

The Smith-Ewart nucleation models are based on free-radical partitioning between particles and micelles until all the surfactant is adsorbed on the surface of nucleated particles. The batch reaction nucleation model for this simple system is given by Equation (8.4),... 

Two weaknesses of the Smith-Ewart nucleation model are (1) particles are formed even when no micelles are present and (2) more water-soluble monomers do not fit the theory. 

While vinyl acetate is normally polymerized in batch or continuous stirred tank reactors, continuous reactors offer the possibility of better heat transfer and more uniform quality. Tubular reactors have been used to produce polystyrene by a mass process (1, 2), and to produce emulsion polymers from styrene and styrene-butadiene (3 -6). The use of mixed emulsifiers to produce mono-disperse latexes has been applied to polyvinyl toluene (5). Dunn and Taylor have proposed that nucleation in seeded vinyl acetate emulsion is prevented by entrapment of oligomeric radicals by the seed particles (6j. Because of the solubility of vinyl acetate in water, Smith -Ewart kinetics (case 2) does not seem to apply, but the kinetic models developed by Ugelstad (7J and Friis (8 ) seem to be more appropriate. 

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. 

The rate of particle nucleation is assumed, as in the Smith-Ewart model, to be proportional to the amount of free surfactant... 

This nucleation/emulsifier utilization phenomena is one reason why batch kinetics and product characteristics are difficult to extrapolate from batch reactor to continuous stined-tank systems. A comparison of Equations (8.4) and (8.10) illustrates this in a quantitative manner for Smith-Ewart Case 2 kinetics. It should be noted that both formulation and operational variables (such as ) can influence nucleation and polymerization rates differently in the two reactor systems — even for the same kinetic model. One can change some aspects of this potential disadvantage of a CSTR by use of a small particle size seed in the feed stream or by placing a continuous tubular reactor upstream of the CSTR. These techniques can remove the nucleation phenomena tom the CSTR system which can then be used exclusively to grow the seed particles. 

Computer simulation results show a typical plot of the particle nucleation rate (dNpIdt) as a function of time (t), as shown schematically in Figure 3.4. It is shown that the rate of particle nucleation increases to a maximum and then decreases toward the end of the particle formation period. The dashed line in Figure 3.4 is obtained by assuming the ceasing of particle nucleation at when the total particle surface area is equal to that covered by the surfactant molecules present in the polymerization system (i.e., <2 = 0 when t > ti). The time at which particle nucleation ceased can be estimated by the relationship h = 0.53[asSol(2flcj [I])] established in the Smith-Ewart model (see Section 3.1.1). Reasonable agreement between the model predictions with practical values of parameters and experimental data obtained from the emulsion polymerization of styrene was achieved. 

Sajjadi [47] developed two mechanistic models for the particle nucleation process involved in the semibatch emulsion polymerization of styrene under the monomer-starved condition. In the first model, Smith-Ewart theory was extended to take into account the particle nucleation under the monomer-starved condition. The number of latex particles per unit volume of water is proportional to the surfactant concentration, the rate of initiator decomposition, and the rate of monomer addition, respectively, to the 1.0,2/3, and -2/3 powers. The second model considers the aqueous phase polymerization kinetics and its effect on the efficiency of free radical capture by the monomer-swollen micelles. This model is capable of predicting some features of the particle nucleation process. 

The time-dependent behavior of emulsion polymerization arises due to variation in monomer concentration, changes in the number of polymer particles Nt, or both. We have aheady observed that N, changes due to nucleation in stage I of emulsion polymerization and this normally ends at about 10-15% conversion. However, when the monomer-to-water ratio MIW) is high or the monomer is more than sparingly soluble, the constancy of N, cannot be assiuned up to conversions as large as 50%. If the monomer droplets are sufficiently small, they also become the loci of particle formation and, in such circumstances, the Smith-Ewart theory is inadequate to explain the experimental phenomena. We now present the outline of a mathematical model of emulsion polymerization that is... 

The quantitative description of particle nucleation is perhaps the most difficult problem of emulsion polymerization kinetics. Equation 5 is the well known relationship derived by Smith and Ewart (10) for their Case 2 Model. 

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