Smith-Ewart theory, deviation from

That there is no generally acceptable model for the emulsion polymerization was emphasized by Min and Ray in their extensive discussion of mathematical modeling of emulsion polymerizations [145]. They list five deviations of the emulsion polymerization of vinyl acetate from the Smith-Ewart theory, which may be a bit different from the points made by Nomura and co-workers [143] and by Friis and Hamielec [144]. These points are as follows ... 

As discussed above, the well-known Smith-Ewart theory predicts that the number of particle nuclei per unit volume of water generated at the end of Interval I (Np,i) is proportional to the 0.6 power of the surfactant concentration and to the 0.4 power of the initiator concentration [Eq. (3.3)]. Accordingly, the rate of polymerization in Interval II (Rp Np, ) is expected to behave in an identical fashion. These predictions very often form the basis of a test used to verify the validity of the Smith-Ewart theory in emulsion polymerization. The early experimental results mostly obtained from emulsion polymerization of styrene were reported to be in reasonable agreement with the theory under adequate conditions. However, deviations between the experimental data and the Smith-Ewart theory were also observed [13,50,51]. 

Sutterlin [46] studied the effect of the polarity of various monomers (styrene, acrylate ester monomers, and methacrylate ester monomers see Table 3.1) on the particle nucleation mechanisms involved in emulsion polymerization. When the surfactant concentration is above its CMC, the emulsion polymerization of styrene follows the Smith-Ewart theory (Npj 5o ) except those experiments with relatively low levels of surfactant. The exponent x in the relationship Npj So decreases with increasing monomer polarity when the surfactant concentration is above its CMC. This trend is attributed to the increased tendency of agglomeration of particle nuclei with monomer polarity. The emulsion polymerizations of less polar monomers deviate significantly from the Smith-Ewart theory (x 0.6) if the surfactant concentration is reduced to a level just below its CMC. This implies that some mechanisms other than micellar nucleation (homogeneous nucleation or coagulative nucleation) must operate in these emulsion polymerization systems. 

Capek and Chudej [87] studied the emulsion polymerization of styrene stabilized by polyethylene oxide sorbitan monolaurate with an average of 20 monomeric units of ethylene oxide per molecule (Tween 20) and initiated by the redox system of ammonium persulfate and sodium thiosulfite. It is interesting to note that the constant reaction rate period is not present in this polymerization system. The maximal rate of polymerization is proportional to the initiator and surfactant concentrations to the -0.45 and 1.5 powers, respectively. The final number of latex particles per unit volume of water is proportional to the initiator and surfactant concentrations to the 0.32 and 1.3 powers, respectively. In addition, the resultant polymer molecular weight is proportional to the initiator and surfactant concentrations to the 0.62 and -0.97 powers, respectively. Some possible reaction mechanisms may explain the deviation of the polymerization system from the classical Smith-Ewart theory. Lin et al. [88] investigated the emulsion polymerization of styrene stabilized by nonylphenol polyethoxylate with an average of 40 monomeric units of ethylene oxide per molecule (NP-40) and initiated by sodium persulfate. The rate of polymerization versus monomer conversion curves exhibit two nonsta-tionary reaction rate intervals and a vague constant rate period in between. 

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. 

Polymerization of styrene in an emulsion polymerization has been shown to follow a kinetics scheme as first described by Smith and Ewart. When the vinyl monomer is not a good solvent for the polymer (l.e. acrylonitrile or vinyl acetate) large deviations from Sraith-Ewart Theory kinetic predictions are observed. 

Since the solubility of vinyl acetate is 2.1% at 50°C and 3.5% at 70°C [15], deviations from the Smith-Ewart treatment are not entirely surprising. The water solubility of vinyl acetate was one of the significant factors in the deviation from the conventional theory of emulsion polymerization. Another factor is the reactivity of the vinyl acetate radicals toward other materials present in the system such as the surfactants. 

The kinetic behavior of emulsion polymerization is greatly affected by radical desorption from polymer particles. This has been shown by Dgelstad et al. (1969)> Litt et al. (1970), Harada et nl. (1971), Friis and Nyhagen (1973), and Nomura et al (1971). It is believed that the deviation of the kinetic behavior of the emulsion polymerization of water-soluble monomers such as vinyl acetate and vinyl chloride from the Smith and Ewart (1949) Case 2 kinetic theory is mainly due to dominant desorption of... 

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