Smith-Ewart

The Smith-Ewart expression (eq. 1) accurately predicts the particle number for hydrophobic monomers like styrene and butadiene (21), but fails to predict the particle number (22) for more hydrophilic monomers like methyl methacrylate and vinyl acetate. A new theory based on homogeneous particle... 

Stage II Growth in Polymer Particles Saturated With Monomer. Stage II begins once most of the micelles have been converted into polymer particles. At constant particle number the rate of polymerization, as given by Smith-Ewart kinetics is as follows (27) where is the... 

During Stages II and III the average concentration of radicals within the particle determines the rate of polymerization. To solve for n, the fate of a given radical was balanced across the possible adsorption, desorption, and termination events. Initially a solution was provided for three physically limiting cases. Subsequentiy, n was solved for expHcitiy without limitation using a generating function to solve the Smith-Ewart recursion formula (29). This analysis for the case of very slow rates of radical desorption was improved on (30), and later radical readsorption was accounted for and the Smith-Ewart recursion formula solved via the method of continuous fractions (31). 

The Smith-Ewart kinetics described assume homogeneous conditions within the particle. An alternative view, where monomer polymerizes only on the surface of the particle, has been put forth (35) and supported (36). The nature of the intraparticle reaction environment remains an important question. 

Emulsion Polymerization. Emulsion and suspension reactions are doubly heterogeneous the polymer is insoluble in the monomer and both are insoluble in water. Suspension reactions are similar in behavior to slurry reactors. Oil-soluble initiators are used, so the monomer—polymer droplet is like a small mass reaction. Emulsion polymerizations are more complex. Because the monomer is insoluble in the polymer particle, the simple Smith-Ewart theory does not apply (34). 

Mechanisms. Because of its considerable industrial importance as well as its intrinsic interest, emulsion polymerization of vinyl acetate in the presence of surfactants has been extensively studied (75—77). The Smith-Ewart theory, which describes emulsion polymerization of monomers such as styrene, does not apply to vinyl acetate. Reasons for this are the substantial water solubiUty of vinyl acetate monomer, and the different reactivities of the vinyl acetate and styrene radicals the chain transfer to monomer is much higher for vinyl acetate. The kinetics of the polymerization of vinyl acetate has been studied and mechanisms have been proposed (78—82). 

The Smith-Ewart theory predicts = K [I. The rate of polymerization of vinyl acetate is virtually independent of emulsifier concentration,... 

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. 

Based on the Smith-Ewart theory, the number of latex particles formed and the rate of polymerization in Interval II is proportional with the 0,6 power of the emulsifier concentration. This relation was also observed experimentally for the emulsion polymerization of styrene by Bartholomeet al. [51], Dunn and Al-Shahib [52] demonstrated that when the concentrations of the different emulsifiers were selected so that the micellar concentrations were equal, the same number of particles having the same size could be obtained by the same polymerization rates in Interval II in the existence of different emulsifiers [52], The number of micelles formed initially in the polymerization medium increases with the increasing emulsifier concentration. This leads to an increase in the total amount of monomer solubilized by micelles. However, the number of emulsifier molecules in one micelle is constant for a certain type of emulsifier and does not change with the emulsifier concentration. The monomer is distributed into more micelles and thus, the... 

Treatments (Smith-Ewart,79 pseudo-bulk77) have been devised which allow for the possibility of greater than one radical per particle and for the effects of chain length dependent termination. Further discussion on these is provided in the references mentioned above.77 751... 

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. 

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. 

Data of Siitterlin (22.). Figure 4 shows that EPM is also able to predict the classical Smith-Ewart (2) dependence of the particle number on initiator concentration at high levels of added surfactant (sodium dodecylsulfate =... 

In the second case, a wide difference In time scales between the terms determining the active chain distribution (p, k and c) and all the other terms (accumulation and volume growth) Is apparent. Again, we can neglect the "slow" terms In equation 10, thus obtaining the classical steady-state Smith-Ewart equation for the particles with a particular volume v ... 

In an emulsion polymerization, the reaction mixture is initially heterogeneous due to the poor solubility of the monomer in the continuous phase. In order for a reaction to take advantage of the desirable Smith-Ewart kinetics [96], the monomer and initiator must be segregated with the initiator preferentially dissolved in the continuous phase and not the monomer phase. Because of the kinetics of an emulsion polymerization, high molecular weight polymer can be produced at high rates. The polymer which results from an emulsion polymerization exists as spherical particles typically smaller than one pm in diameter. However, due to the high solubility of most vinyl monomers in C02, emulsion polymerization in C02 probably will not be a very useful process for commercially important monomers. 

According to the classical Smith-Ewart mechanism [85], the number of particles, N, is related to the emulsifier concentration, E, by... 

SMILES (Simplified Molecular Input Line Systems), 6 3-6 Smith, Adam, 24 364 Smith—Ewart kinetics, 14 715 Smith-Ewart recursion formula, 14 715 Smith-Ewart theory, 25 571, 572 VDC polymerization and, 25 697... 

Improvement and Development of the Harkins-Smith-Ewart Theory... 

Gardon employed new parameters in terms of the number of particles and checked the Harkins-Smith-Ewart theory qualitatively in l%3 (9). 

The very informative semilogarithmic plot of over-all reaction rate vs. time was first published by Bartholome et al. (4, 6). Looking at the reaction rate-time curves given below one can see that even for the styrene system, which was shown to follow Smith-Ewart kinetics the best... 

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. 

Vinylidene chloride and chloroprene (Figures 7 and 8) under the given conditions produce curves which more or less resemble the styrene curve. Vinylidene chloride especially shows a long period of a rather constant reaction rate. By the theory of Harkins and Smith-Ewart this would be interpreted as a period of constant particle number and of constant monomer concentration at the reaction site—i.e., the monomer-polymer particles. The first assumption seems justified (15). The second assumption of constant monomer concentration at the reaction site can be true only in a modified sense because poly (vinylidene chloride) is insoluble in its monomer, and the monomer-polymer particles in this system therefore have a completely different structure as compared with the monomer-polymer particles in the styrene system. 

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 accordance with the Smith-Ewart theory, the nucleation of particles takes place solely in the monomer-swollen micelles which are transformed into polymer particles [16]. This mechanism is applicable for hydrophobic (macro)mon-omers (see Scheme 2). The initiation of emulsion polymerization is a two-step process. It starts in water with the primary free radicals derived from the water-soluble initiator. The second step occurs in the monomer (macromonomer)-swollen micelles by entered oligomeric radicals. 

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