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 dose rate dependence found in this study is 0.40, identical to that predicted from Smith-Ewart Case II theory. The Smith-Ewart prediction, however, arises from a nucleation step wherein... 

Figure 11. Solutions of the Smith-Ewart recursion equation for the case of no aqueom propagation or termination. Dotted line m = 0 (Smith-Ewart Case II). Curve 1 (m = 10 ) depicts typical styrene-like polymerization. Curve 2(m = 0.01) depicts radiation initiated emulsion polymerization of vinyl chloride. Curve 3 (m > 1.0) depicts chemically initiated emulsion polymerization of vinyl chloride.

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. 

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. 

The assumption of such a low efficiency as found by Hawkett, where the order of p i whh respect to [/] approaches 0.5 with increasing [/], seems to be in contradiction to both the absolute value of particles formed (both below and above the CMC) and even more so with the observed exponent in Eqs. (5) or (7) (i e.. 0.4). Also, it would seem to contradict the well-known fact that at hi values of [/] (ije., high o = 2kJ r]vJNkJ the rate of polymerization is proportional to even in Interval II (Smith-Ewart Case 3). 

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... 

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... 

The key assumption in the Smith-Ewart Case 2 theory can he stated mathematically by the simple expression n = O.S. The physical basis for this assumption involves several phenomena. First is the fact that free radicals react with one another to terminate polymerization very rapidly. Second, the latex particles, which are the reaction sites, are very small. Third, the... 

The effect of the additive on the rate will of course depend upon whether we operate in Interval II or 111, and moreover on v hether Smith-Ewart Case 1, 2, or 3 is operating. Figure 11 gives an example of experiments with seeded styrene polymerization with different amounts of hexadecane added. The value of Vi/vS is in this case - 20, the value of % is 0.08 and 0.16, respectively. 

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... 

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