Smith-Ewart model

It was found that the maximum rate of polymerization occurred at (NRe)e 5000. This shift in (NRe) corresponds to the shift of the laminar turbulent transition in a helically coiled tube as reported by White ( ). Further, no plugging of this reactor, under any conditions of operation, was noticed. The reaction mechanism appears to be very close to the Smith-Ewart model, although conversions were not always a3 complete as expected. 

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. 

Emulsion polymerization first gained industrial importance during World War II when a crash research program in the United States resulted in the production of styrene-co-butadiene [SBR] synthetic rubber. The Harkins-Smith-Ewart model [5-6] summarized the results of early research, which focussed on this and similar systems. Current thinking is not entirely in accord with this mechanism. It is still worthwhile to review it very brielly here, however, because it is still widely referenced in the technical literature and because some aspects of the model provide valuable insights into operating procedures. 

Strictly speaking, the Smith-Ewart model applies only to the batch polymerization of a completely water-insoluble monomer in the presence of micellar soap. (The terms soap, suifactanf, and emulsifier are used interchangeably in this technology.) Its predictions do in fact apply neatly to the case of styrene. Tlie polymerization reaction, after the induction period, can be classified conveniently into three stages, as shown schematically in Fig. 8-2. 

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

The ocxiventional model for describing the mechanism of emulsion polymerization was used as a starting point Qrigincilly proposed by Harkins / it was made more quantitative by Stnith and Ewart u) and has recently been exta )ded by Garden While there is much controversy over the applicability of the Smith-Ewart model/ and many systems have been found in vhich it does not apply/ the properties of the present system/ particularly the low solubility of the major monomer in water/ seemed favorable for its use ... 

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. 

The Smith-Ewart model describes satisfactorily the polymerization of styrene, isoprene, and methyl methacrylate for these systems, it can be used to predict the size of the latex particles and the corresponding molar masses. In contrast, it is unsuited for the case of monomers partially water-soluble or polymers insoluble in their monomer—that is, polymerization of vinyl chloride and vinyl acetate. It accounts neither for the fact that styrene can be polymerized in absence of surfactant nor for the fact that free radicals (RM ) can equally penetrate into a micelle or in an already formed particle during the initial phase. 

Case C This situation corresponds to the Smith-Ewart second idealized situation for particle formation and to the Gershberg model... 

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. 

At higher values of m, specifically, and where m is increased to 0.10 and tt = 0.02 radical distribution calculations show that 2% of occupied particles contain 2 radicals while. 02% contain 3 radicals or more. This is outside the range of validity of Smith and Ewart s Case I model but is well described by Ugelstad s model for vinyl chloride polymerization wherein the Smith-Ewart recursion formula is solved by considering only latex particles Nq, Ni, and N2. 

Figure 12. Calculated h vs. measured particle volume, showing deviation from the simplified Smith-Ewart Case I model at large particle volumes...

The results have been interpreted along the lines of a modified Smith-Ewart Case I kinetic model. 

Stevens and Funderburk (5 ) presented theoretical models for particle size distributions based on Smith-Ewart Case II and several other particle growth theories. They concluded that the Smith-Ewart Case II theory containing the Stockmayer modification fit CSTR data for styrene better than other models. 

Although theoretical models seem to be quite adequate for styrene emulsion polymerization in either batch reactors or CSTR s, such is not the case with other monomers like vinyl acetate, methyl acrylate, methyl methacrylate, vinyl chloride, etc. One of the early papers to discuss scane of the important mechanisms involved with these other moncaners was written by Priest ( ). He studied the emulsion polymerization of vinyl acetate and identified most of the key mechanisms involved. Priest s paper has been largely overlooked, however, perhaps because of the success of the Smith-Ewart approach to styrene. 

This dependency is quite different from the predictions of theoretical models based on Smith-Ewart Case II kinetics and also different from styrene data (Equation 1), ... 

Steady-state conversions for VA and MMA polymerizations in a CSTR do not agree with reactor models based on Smith-Ewart Case II kinetics. This is not surprising since such a model does not consider many important phenomena. The particle-formation component of the Smith-Ewart Case II model is based on a simple mathematical relation which assumes that the rate of formation of new particles is proportional to the ratio of free (dissolved or in micelles) surfactant to total surfactant. This equation is based on the earlier concept of particle formation via free radical entry into micelles. 

Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

State with no entrance effects or radial velocity components body forces are neglected axial heat conduction is small compared to radial conduction Region I of Smith-Ewart kinetics (i.e., when micelles are first forming) is neglected and the initiator concentration is constant. The model may be summarized as ... 

A computer model, based on Smith-Ewart kinetics and the continuity equations predicts experimental conversion data, except at low conversions. 

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

Equation (5) reduces to the Smith-Ewart equation [Eq. (2)] if c is sef equal to zero and if both sides of Eq. (5) are integrated between <7 = 0 and cr = oo. This reduction further requires the assumption that all rate coefficients forming the elements of Q are independent of population balance Eq. (5) are considerably more general in scope than the Smith-Ewart equation because the inclusion of the size parameter enables the formalism to model the particle formation process, as well as both the kinetics and the evolution of the PSD. 

The basic tenet of the Smith-Ewart Case 2 particle growth model is that each particle will contain an active free radical one half of the time. Thus, the average number of free radicals per particle is 0.5. The rate of polymerization is given by... 

The Smith-Ewart Case 2 model for the number of particles formed in a batch reaction is given by... 

If a continuous process is to he used for commercial production, a similar small-scale reactor system should he utilized in this second stage of product development. There are a number of reasons for this recommendation. The earher discussion of the difference between batch reactors and CSTRs lists some of these reasons, if, for example, engineering data are to he obtained for design of a commercial unit, the variable relation ps might be quite different for the different reactors. The Smith-Ewart CSTR model predicts a linear relationship between or N and the surfactant concentration [5]. The same mechanistic model for a batch reactor predicts a 0.6 power relationship between Rp or N and... 

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