Particle formation Smith-Ewart

The Smith-Ewart theory has been modified by several researchers [13,20-24]. These researchers argued against the Smith-Ewart theory that (1) the particle formation also occurs in the absence of micellar structure, (2) the predictions on particle number with the Smith-Ewart theory are higher relative to actual case. 

In that publication a dependence of the shape of the rate-time function on such parameters as initial monomer concentration, emulsifier concentration, and dose rate was shown for the methyl acrylate system. The behavior of this system tentatively was explained by assuming a strong gel effect even at low conversions, of prolonged particle formation, and some kind of interparticle radical termination—all factors which are included neither in the Harkins view nor in the classical Smith-Ewart theory. 

The emulsion polymerization of vinyl hexanoate has been studied to determine the effect of chain transfer on the polymerization kinetics of a water-insoluble monomer. Both unseeded and seeded runs were made. For unseeded polymerizations, the dependence of particle concentration on soap is much higher than Smith-Ewart predictions, indicating multiple particle formation per radical because of chain transfer. Once the particles have formed, the kinetics are much like those of styrene. The lower water solubility of vinyl hexanoate when compared with styrene apparently negates its increased chain transfer, since the monomer radicals cannot diffuse out of the particles. 

Vinyl caproate in emulsion polymerization behaves like styrene in most respects. The rate is first order in monomer. In the range of 1015 to 10"16 particles/cc, it depends on Np to the 0.75 power. This is higher than that for styrene in this range, Rp oc Np°5, indicating that there is less diffusion into the aqueous phase for vinyl caproate. However, the mechanism of particle formation for vinyl caproate may not fit the Smith-Ewart mechanism because of the high chain transfer rate to monomer. 

In the case of more water-soluble monomers and (amphiphilic) macromonomers, the Smith-Ewart [16] expression does not satisfactorily describe the particle nucleation. The HUFT [9,10] theory, however, satisfactorily describes the polymerization behavior or the particle nucleation of such unsaturated hydrophilic and amphiphilic monomers. The HUFT approach implies that primary particles are formed in the aqueous phase by precipitation of oligomer radicals above a critical chain length. The basic principals of the HUFT theory is that formation of primary particles will take place up to a point where the rate of formation of radicals in the aqueous phase is equal to the rate of disappearance of radicals by capture of radicals by particles already formed. Stabilization of primary particles in emulsifier-free emulsion polymerization may be achieved if the monomer (or macromonomer) contains surface active groups. Besides, the charged radical fragments of initiator increases the colloidal stability of the polymer particles. 

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

Observation (i) above can be understood in terms of droplet nucleation and the lack of competition between nucleation and growth. A mechanistic understanding of observation (ii) above was provided by Samer and Schork [64]. Nomura and Harada [136] quantified the differences in particle nucleation behavior for macroemulsion polymerization between a CSTR and a batch reactor. They started with the rate of particle formation in a CSTR and included an expression for the rate of particle nucleation based on Smith Ewart theory. In macroemulsion, a surfactant balance is used to constrain the micelle concentration, given the surfactant concentration and surface area of existing particles. Therefore, they found a relation between the number of polymer particles and the residence time (reactor volume divided by volumetric flowrate). They compared this relation to a similar equation for particle formation in a batch reactor, and concluded that a CSTR will produce no more than 57% of the number of particles produced in a batch reactor. This is due mainly to the fact that particle formation and growth occur simultaneously in a CSTR, as suggested earlier. 

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. 

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. 

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. 

Smith and Ewart (1948) proposed two idealized situations for the formation of polymer particles, assuming that (i) particle nucleation occurs in monomer-swollen emulsifier micelles, (ii) the volumetric growth rate of a particle is constant in the interval of particle formation, and (iii) radicals do not desoib from a panicle. 

Models for emulsion polymerization reactors must account for particle formation and particle growth. If these two phenomena can be handled in a satisfactory manner one can predict the polymerization rate, the number of particles formed, and the particle size distribution. The model presented below was first developed by Gershberg and Longfield (1961). It is based on the concepts developed for batch reactors by Smith and Ewart (1948) in their Case 2 model. 

A more detailed fundamental study was reported by Hummel et al. (1962 Hummel, 1963). Using a sensitive recording dilatometer of their own design they could follow the variation of tbe rate of polymerization with time and conversion. There was an abrupt rise in the rate for tbe first few percent conversion attributed to particle formation. There followed a constant rate period up to about 30% when the free monomer phase disappeared. An increase in rate to a maximum was then observed, ascribed to tbe gel effect, followed by a steady decrease in rate due to monomer depletion and slower diffusion of the monomer to the active sites in the highly viscous particles. The particle sizes were rather small, about 500 A diameter, compared with those often obtained with chemical initiation (e.g., Zimmt, 1959). This presumably explains the comparatively close adherence to the simple Smith-Ewart picture up to the appearance of the gel effect. 

Because of its overriding importance in determining the rate of emulsion polymerization, the factor discussed first is the number of particles formed. The mechanism of particle formation described above has been treated quantitatively by Smith and Ewart (58) on the basis of some simplifying assumptions. The most important of these is that a soap molecule occupies the same interfacial area whether it forms part of a micelle or is adsorbed on the polymer-water interface— i.e., during the period of particle formation, the total surface area of micelles plus polymer particles is constant. 

It is obvious that in the theoretical treatment sketched above, S, the amount of soap, refers to the amount of micellar soap. If in a polymerization mixture a soap is used with a relatively high critical micelle concentration (C.M.C.), it is necessary to correct for the amount of soap which is molecularly dissolved and does not contribute to particle formation, at least in the mechanism considered by Smith and Ewart. Consequently, the number of particles and hence the rate of polymerization decrease sharply with increasing C.M.C., as was observed by Staudinger (59), who reported initial polymerization rates of 0.041, 0.12, and 0.225% per minute for reactions in 3% solutions of potassium caprate, laurate, and stearate, where the C.M.C.s are about 2.1, 0.60, and 0.17%, respectively. 

Our assumption of prolonged particle formation during the emulsion polymerization of MA can explain the course of v r in mixtures with high emulsifier concentration. For proving this assumption it would be necessary to measure the change in particle number during the course of the emulsion polymerization of MA this has not yet been done. The results of our work on the y-induced emulsion polymerization of MA cannot be interpreted in terms of the Smith-Ewart theory in its simple form (33). Therefore one cannot expect that v r is independent of the monomer-water ratio or proportional to [E] - or to [initator] - (dose rate and initator concentration can be substituted). A quantitative interpretation of the y-induced emulsion polymerization of MA cannot yet be formulated, because of the complexity of the phenomena involved. To make this possible, considerable further work on this subject has to be done. The dependence of on [M] - ... 

This observation seems to be in line with the Smith-Ewart concepts. The adsorption of surfactants on the surfaces of latex particles influences the capture by the particles of low-molecular-weight polymers formed in the aqueous solution. This in turn affects the reaction kinetics and the formation of new particles. The number of free radicals per particle, which is usually considered to be constant during the major phases of an emulsion polymerization, seems to vary considerably during the polymerization of vinyl acetate [139]. 

Equations 10.1 and 10.4 show that the number of polymer particles is crucial in determining both the rate and degree of polymerization. The mechanism of polymer particle formation indicates clearly that the number of polymer particles will depend on the emulsifier, its initial concentration (which determines the number of micelles), and the rate of generation of primary radicals. Smith and Ewart have shown that... 

C. M. Miller, Particle formation and growth during styrene oil-in-water miniemul-sion polymerization, PhD dissertation, Lehigh University, 1994 W. V. Smith and R. H. Ewart, /. Chem. Phys., 16, 592 (1948)... 

After the emulsion of the monomer phase in the water phase and the presence of the emulsifier micelles established, the pol3mierization is initiated by the addition of initiator. According to the theories proposed by Harkins and Smith and Ewart, conventional emulsion pol)nnerization mechanism occurs into three intervals including the initial (particle formation or nucleation) stage, the particle growth stage and the completion stage. 

For most emulsion systems, the rate of polymerization is controlled by the rate of entry and exit of free radicals to and from polymer particles, not by the rate of monomer diffusion to the polymerization sites. The entry of radicals into the polymer particles has been treated as a collisional process [14] as well as a diffusional process [15] and a colloidal process [16]. Nomura et al [17] pointed out that radical desorption from the polymer particles and micelles plays an important role in particle formation and numerous examples of deviations from the Smith-Ewart kinetic model have been attributed to radical desorption. 

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