Smith-Ewart Case 2 kinetics

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. 

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. 

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. 

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. 

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. 

The prediction of polymerization rate is necessary if one is to design a commercial reactor. If Smith-Ewart Case 2 kinetics can be applied, the problem is identical to predicting the particle concentration, N, since the rate of pol3mierization is directly proportional to the number of particles. We have seen earlier that, in this case, there are striking differences between batch reactors and CSTR s. These differences seem to be less pronounced for systems in which the transport of free radicals out of particles is more important. This important area of kinetic modeling is the topic of the next portion of this paper. 

Smith-Ewart Case 2 kinetics [1] has been widely used to calculate the rate of polymerization (Rp) ... 

These assumptions then lead to a scenario that, at any moment, the monomer-swollen polymer particles contain either only one free radical (active) or none (idle). Under these circumstances, a value of n equal to 0.5 is achieved for the polymerization systems that follow the Smith-Ewart Case 2 kinetics. In addition, the concentration of monomer in the polymer particles does not vary to any extent with the progress of polymerization in the presence of monomer droplets. As a result, a steady polymerization rate is attained during Interval II. Furthermore, the polymerization kinetics is strictly controlled by the population of polymer particles available for consuming monomer. Smith-Ewart Case 2 kinetics has been successfully applied to emulsion polymerizations of relatively water-insoluble monomers such as styrene and butadiene. 

It is generally accepted that the number of latex particles per unit volume of water, the average number of free radicals per particle (n = 0.5), and the concentration of monomer in the particles are constant for emulsion polymerization systems that follow the ideal Smith-Ewart Case 2 kinetics. As a result, a constant reaction rate period can be observed during emulsion polymerization. Monomer molecules must be transferred from the gigantic monomer droplets to the growing submicron latex particles to supply the reaction. A dynamic balance between the rate of consumption of monomer in the latex particles and the rate of diffusion of monomer molecules from the monomer droplets to the particles may thus be established, and this results... 

Rgure 5.4. A schematic lepiesentation of typical polymerization rate as a function of monomer conversion profiles for (a) conventional emulsion polymerization (Interval II Smith-Ewart Case 2 kinetics), (b) miniemulsion polymerization, and (c) microemulsion polymerization. The distinct intenrals of the polymerization processes are also included in these plots. 

Chern [42] developed a mechanistic model based on diffusion-controlled reaction mechanisms to predict the kinetics of the semibatch emulsion polymerization of styrene. Reasonable agreement between the model predictions and experimental data available in the literature was achieved. Computer simulation results showed that the polymerization system approaches Smith-Ewart Case 2 kinetics (n = 0.5) when the concentration of monomer in the latex particles is close to the saturation value. By contrast, the polymerization system under the monomer-starved condition is characterized by the diffusion-con-trolled reaction mechanisms (n > 0.5). The author also developed a model to predict the effect of desorption of free radicals out of the latex particles on the kinetics of the semibatch emulsion polymerization of methyl acrylate [43]. The validity of the kinetic model was confirmed by the experimental data for a wide range of monomer feed rates. The desorption rate constant for methyl acrylate at 50°C was determined to be 4 x 10 cm s ... 

---