Kinetic Smith-Ewart Case

Continuous stirred-tank reactors can behave very differently from batch reactors with regard to the number of particles formed and polymerization rate. These differences are probably most extreme for styrene, a monomer which closely follows Smith-Ewart Case 2 kinetics. Rate and number of particles in a batch reactor follows the relationship expressed by Equation 13. 

We now report on some experiments using seeded emulsion polymerization of styrene in which conditions were carefully chosen to ensure that Smith-Ewart Case 2 kinetics (6) would obtain throughout, in the absence of chain transfer/radical desorption effects. Various hydrocarbons were investigated for their effects on kinetics of polymerization and equilibrium swelling of the latex particles. 

The effects of the (water-soluble) initiator concentration on the polymerization of polymer-stabilized miniemulsion are shown in Table 2. An increase in the initiator concentration does not change the number of particles, but does increase the rate of polymerization. This is due to an increase in the number of radicals per particle. However, the number of radicals per particle ranged from just 0.5 to 0.8, indicating that the kinetics (after nucleation) are still essentially Smith Ewart Case II. The number of particles was found to be proportional to the initiator concentration raised to the power of 0.002 0.001. Macroemulsion polymerizations, in contrast, show a dependence of 0.2 and 0.4 for methyl methacrylate and styrene, respectively [141]. The fact that the exponent approaches zero indicates that all or nearly all of the droplets are being nucleated. 

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

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. 

It should be obvious that the simple concepts of Smith-Ewart Case II kinetics could not be expected to explain the complex phenomena outlined above. Another... 

Another feature of the Smith-Ewart theory is that the reaction rate at the end of the nudeation perind is expected to he higher than in the steady state because n is higher than the steady-state value of O.S (Smith-Ewart Case 2 kinetics). There is little experimental evidence for such a maximum in rate (Ugelstad and Hansen, 1976), and this discrepancy may be explained by more details about the radical absorption rates in micelles and particles. Before any further discussion of particle-formation mechanisms, it therefore seems logicaHo review the mechanisms responstUe for radical absewption. 

This corresponds to Smith-Ewart Case II kinetics and is applicable to styrene emulsion polymerization under normal conditions. On the other hand, when radical desorption from the particles is dominant (i.e., o = ) Eq.(IOS) lesdsto... 

Acres and Dalton (1963a) also studied the emulsion polymerization of methyl methacrylate initiated by Co y radiation using a recording dilatometer. Only the conversion-time curves were measured with constant dose rate, varying monomer concentration, and with constant monomer concentration at different dose rates. Except at the lowest monomer concentration a clear gel effect was observed, with linear rates up to that point. The linenr rates increased with increasing monomer concentration up to about 0.4 mol/liter and then leveled oif. The dependence of the rate, before the gel effect, on the dose rate was 0.4 and, unlike their findings with styrene, not dependent on the monomer concentration. Their results were consistent with those of Hummel ei al. that methyl methacrylate follows, with y radiation, the generally accepted Smith-Ewart Case 2 kinetics except for the marked gd effect. 

Araki et at. (1967, 1969) carried out a more systematic study of the kinetics and other features of the y-iniliated emulsion polymerization of vinyl acetate using sodium lauryl sulfate as the emulsifier. This system had been thoroughly investigated with potassium persulfate as the initiator (Litt et cL. 1960,1970). Some post ei cts have been observed with vinyl acetate, particularly above 50% conversion (Friis, 1973 Sunardi, 1979). These effects had been used by Allen cr at. (1960,1962) for the possible synthesis of block and graft polymers and will be described later in this chapter. The half-life of the radicals in a vinyl acetate latex polymerization was determinad by Hummel et at. (1969) as 0.8 min at 53.8% conversion. Araki et fll. (1967, 1969) determined all the normal rate dependencies and included some seeded latex studies. Their results and those of other investigators are summarized in Table II together with those found with potassium persulfate initiation and those predicted by the Smith-Ewart Case 2 theory. The... 

Radical termination. Free-radical termination reactions are very fast reactions. The combination of reaction speed and the small reactor volume (i.e., the polymer particle) alters the kinetic model in some cases. The simplest model (Smith-Ewart Case 2) is based on the assumption that instant termination occurs when a free radical enters a particle that already contains an active radical. As the particles become larger and/or the radical mobility decreases because of the gel effect, the termination rate becomes slower. 

The kinetics, as defined by the average number of macroradicals per particle (n) must not be significantly larger than one. This implies that if n is low (Smith-Ewart case I or II kinetics) the system is considered an emulsion . Similarly, if n is very large, on the order of 102 6, the polymerization is kinetically a suspension. The categorization of Smith-Ewart case III kinetics will be discussed in the following section of this paper. 

A polymerization with n very large (102-6) indicating suspension-like (bulk polymerization) kinetic behavior, and a particle nucleation mechanism residing outside the monomer droplets, which delineates an emulsion process. Smith-Ewart case III systems are examples of this type of behavior provided they have evolved from case I and/or case II polymerization at low conversions, which is common. 

This is a general categorization, including examples of Smith-Ewart Case I kinetics [14-lQ Case II kinetics (n — 1/2) and Case III kinetics [17,18]. 

A pseudo-bulk system is one in which the compartmentalized nature of the locus of polymerization has no effect on any kinetic property (rate, molar mass or particle size distributions). A system in which n is appreciably greater than 0.5 will always be pseudo-bulk there are so many radicals in a particle that the polymerization will be indistinguishable from the equivalent bulk one. However, a system with a low value of n can also be pseudo-bulk, if (for example) radical desorption results in the desorbed radical suffering no other fate except to re-enter another particle [1,3]. It is then apparent that the polymerization process will not see the walls between particles. Because pseudo-bulk kinetics can occur in systems where n 0.5, a pseudo-bulk system is different from the Smith-Ewart Case 3. 

The simplest kinetic model for batch emulsion polymerization is due to Smith and Ewart [1] (see Sections 4.4.1 and 4.9). The Smith-Ewart Case 2 model is based on the following rate equation ... 

A population balance approach can be used to derive a similar expression for a steady-slate CSTR. Equation (8.3) still applies to this reactor but a new relationship for N must be developed. The particle size distribution for Smith-Ewart Case 2 kinetics in a CSTR is given by... 

Miiny important systems, however, do not follow Smith-Ewart Case 2 kinetics n can be less than 0.5 if free radicals can diffuse from the particles into the aqueous phase. This radical transport is believed to follow chain transfer reactions to small molecules such as monomers, solvent, added chain transfer agents and even emulsifier. The resulting radicals are sufficiently mobile so that a fraction of them can diffuse out of the particles thus causing n to be less than 0.5. 

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. 

Smith-Ewart Case 2 kinetics is based on the assumption that n = 0.5 which leads to volumetric particle growth independent of size or dv/dt = n., during Eiterval II. The volume growth of polymer in the particles may remain constant during Interval III if = 0.5, but the overall particle size will decrease because of the conversion of monomer to polymer which is more dense. 

A priori, it seems logical to apply the accepted concepts of conventional emulsion polymerization (with water-soluble initiators) to inverse emulsions using oil-soluble initiators. In fact, only few attempts have been made to apply the Smith-Ewart theory [26,36-38]. The determination of n is difficult here because of the ill-defined stages of the reaction, the unusual kinetics and the broad particle size distribution. The kinetic studies of Vanderhoff et al. [26,29] and Visioli [37] are examples of applying the Smith-Ewart theory to the polymerization of acrylamide and p-vinylbenzenesulfonate in xylene initiated with benzoyl peroxide. The data unexpectedly followed Smith-Ewart Case 1 (n 0.S). It was postulated that radicals were generated in, or enter particles pairwise due in the enhanced water solubility of the benzoyl peroxide by the presence of monomo-. 

Finally, the role of the impurities caimot be neglected. Indeed, a study performed by Hubingen and Reichert [36] with an hi y purified emulsifier (pentaerytiiritol myristate) led to a zero dependence of Rp on [E]. The kinetic data ft wed Smith-Ewart Case 1 (n 0.S) with the initiation stq in the inverse micelles. The final latex particles had a narrow distribution, contrary to those obtained in other stu hes (see Section 21.3.4). 

To calculate the rate of emulsion pol3unerization (J p) of relatively water-insoluble monomers such as st3rrene and butadiene. Smith Ewart case 2 kinetics has been widely used [40] ... 

Other Mechanistic Aspects.—Stannett et al have reported on the kinetics of the emulsion polymerization of styrene initiated by irradiation with cobalt-60 y-rays. The conclusion is reached that Smith-Ewart Case 2 kinetics are obeyed if the reaction system is such that compliance with Smith-Ewart Case 2 would be expected were initiation effected by the thermal decomposition of potassium persulphate. The efficiency of utilization of the radicals produced by radiolysis of the aqueous phase appears to be in the range 0.3—0.5. Chatterjee, Banerjee, and Konar have investigated the molecular weight of polystyrene produced by emulsion polymerization at low monomer concentration, and compared their observations with the predictions of the theories of Harkins, Smith-Ewart, and Gardon. These workers have also investigated the dependence of rate of polymerization upon monomer concentration in the emulsion polymerization of styrene. Arai, Arai, and Saito" have studied the persulphate-initiated surfacant-free emulsion polymerization of methyl methacrylate, and have proposed a model for the reaction. 

For a given solids content under Smith-Ewart Case 3 kinetics, it is inversely proportional to the number of polymer particles, and hence the polymerization rate is independent of the number of polymer particles if aqueous-phase termination is negligible. Otherwise, the polymerization rate increases with Np. 

For Smith-Ewart Case 3, the number of radicals per particle is large and the kinetics approaches bulk polymerization. In this case, the concentration of radicals in the polymer particles is given by Eq. (19) and the molecular weight is mainly controlled by chain transfer and bimolecular termination. The rate of generation of polymer of length m in particles with i radicals is given by Eq. (46). 

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