Smith-Ewart treatment

Since the solubility of vinyl acetate is 2.1% at 50°C and 3.5% at 70°C [15], deviations from the Smith-Ewart treatment are not entirely surprising. The water solubility of vinyl acetate was one of the significant factors in the deviation from the conventional theory of emulsion polymerization. Another factor is the reactivity of the vinyl acetate radicals toward other materials present in the system such as the surfactants. 

Among the observable facts it was found that there is no significant effect of the concentration of emulsifier on this system. Therefore, the implication is that the polymerization initially takes place exclusively in the aqueous phase [136]. The resulting polymer particle precipitates as it forms [134]. In this case we may assume, that only a microscopic phase-separation takes place. The polymer particles which form adsorb emulsifier fiom the aqueous environment and remain dispersed. Then the particles may absorb more monomer somewhat in the manner called for by the Smith-Ewart theory. Of course, other dissolved vinyl acetate monomer molecules may continue to be polymerized in aqueous solution, thus accounting for the increase in the number of particles as the polymerization proceeds to high conversion. The classical Smith-Ewart treatment states that the number of particles is determined by the surfactant to monomer ratio and, in effect remains constant throughout the process. 

The ideal case of the Smith-Ewart treatment actually proposes a rather elegant method for obtaining the absolute value of the propagation rate constant from emulsion polymerization systems, as shown in Eq. (2.26), where N is the number of particles per imit volume ... 

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... 

AU discussions of particle nudeation start with the Smith-Ewart theory in which Smith and Ewart (1948) in a quantitative treatment of Harkins micellar theory (Harkins, 1947, 1950) managed to obtain an equation for the particle number as a function of emulsifier concentration and initiation and polymerization rates. This equation was developed mainly for systems of monomers with low water solubility (e.g., styrene), partly solubilized in micelles of an emulsifier with low critical micelle concentration (CMC) and rseeited to work well for such systems (Gerrens, 1963). Other authors have, however, argued against the Smith-Ewart theory on the grounds that (i) particles are formed even if no micelles are present, (ii) the equation for the... 

Equations, which are also applicable to suspension, solution, and bulk polymerization, form an extension of the Smith-Ewart rate theory. They contain an auxiliary parameter which is determined by the rate of initiation, rate constant of termination, and volume of the porticles. The influence of each variable on the kinetics of emulsion polymerization is illustrated. Two other variables are the number of particles formed and monomer concentration in the particles. Modifications of the treatment of emulsion polymerization are required by oil solubility of the initiator, water solubility of the monomer, and insolubility of the polymer in the monomer. 

General quantitative treatment (Smith-Ewart) of the foregoing theory (35)... 

Other recent contributions to this aspect of the subject include those of Brooks and Qureski and Brooks. The former of these papers is concerned with the distribution and desorption of free radicals during the emulsion polymerization of styrene. The latter gives a simplified treatment of the type of problem which has been dealt with by Birtwistle and Blackley, and the Napper group in essence, the Brooks treatment involves truncation of the infinite series of Smith-Ewart differential difference equations. 

The kinetic mechanism of emulsion polymerization was developed by Smith and Ewart [10]. The quantitative treatment of this mechanism was made by using Har-kin s Micellar Theory [18,19]. By means of quantitative treatment, the researchers obtained an expression in which the particle number was expressed as a function of emulsifier concentration, initiation, and polymerization rates. This expression was derived for the systems including the monomers with low water solubility and partly solubilized within the micelles formed by emulsifiers having low critical micelle concentration (CMC) values [10]. 

The physical picture of emulsion polymerization is based on the original qualitative picture of Harkins [1947] and the quantitative treatment of Smith and Ewart [1948] with subsequent contributions by other workers [Blackley, 1975 Casey et al., 1990 Gao and Penlidis, 2002 Gardon, 1977 Gilbert, 1995, 2003 Hawkett et al., 1977 Piirma, 1982 Poehlein, 1986 Ugelstad and Hansen, 1976]. Table 4-1 shows a typical recipe for an emulsion polymerization [Vandenberg and Hulse, 1948]. This formulation, one of the early ones employed for the production of styrene-1,3-butadiene rubber (trade name GR-S), is typical of all emulsion polymerization systems. The main components are the monomer(s), dispersing medium, emulsifier, and water-soluble initiator. The dispersing medium is the liquid, usually water,... 

The foundations of emulsion polymerization were described originally by Harkins [39]. The first theoretical treatment was proposed by Smith and Ewart [40]. The theory was later modified to some extent by O Toole [41] and more fundamentally by Garden [42], who proposed an unsteady-state mechanism for the concentration of free radicals in the emulsion particles. Tauer [43], Gilbert [44] and Lovell and El-Aasser [45] have produced recent reviews. 

Noting that in the treatments by Smith and Ewart, by Stockmayer, and by OToole the fate of the desorbed radicals was not necessarily spedfied. 

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. 

The value of n in Eq. (6.230) is of critical importance in determining the rate of polymerization in stage II. Three cases — designated 1, 2, 3 — corresponding, respectively, to n < 0.5, n = 0.5, and n > 0.5 can be distinguished based on the work of Smith and Ewart [69] and others [70-74]. The kinetic treatment given above conforms to Case 2 (n = 0.5), which is the predominant behavior for emulsion polymerizations. It occurs when desorption of radicals does not occur or is negligible compared to the... 

The original theory of emulsion polymerization is based on the quahtative picture of Harkins (1947) and the quantitative treatment of Smith and Ewart (1948). The essential ingredients in an emulsion polymerization system are water, a monomer (not miscible with water), an emulsifier, and an initiator which produces free radicals in the aqueous phase. Monomers for emulsion polymerization should be nearly insoluble in the dispersing medium but not completely insoluble. A slight solubility is necessary as this will allow the transport of monomer from the emulsified monomer reservoirs to the reaction loci (explained later). 

A number of questions need to be resolved from the qualitative description of emulsion polymerization given in the previous section. For example, it is necessary to consider whether the diffusion of monomers to the polymer particles is high enough to sustain polymerization given the low solubdity of monomer in the aqueous phase. It is also important to know the average radical concentration in a polymer particle. Also, the validity of the assumption that only the monomer-polymer particles capture the radicals generated by the initiator needs to be established convincingly. The answers to these questions were pro vided by Smith and Ewart and this forms the basis for the quantitative treatment of the steady-state portion of emulsion polymerization. 

The physical picture of emulsion polymerization is based originally on the qualitative picture of Harkins [18] and the quantitative treatment of Smith and Ewart [19], followed by other contributions. Gilbert shaped the qualitative and quantitative picture of the emulsion polymerization process as it is now generally accepted [16]. The main components of an emulsion polymerization recipe are the monomer(s), dispersing medium (usually water), surfactant and initiator. 

Diene Polymerization. Simultaneously with the resolution of the question of the crosslinking reaction in emulsion polymerization of dienes, it became possible to evaluate the rate constants of the polymerization reaction itself. This was, of course, primarily due to the definitive analysis of the kinetics of emulsion polymerization by Ewart and Smith. By a careful study of various "recipes" used in the emulsion copolymerization of butadiene-styrene, it was found that certain low-temperature systems obeyed Case II of the Ewart-Smith treatment, i. e.,... 

The Smith and Ewart-Stockmayer-O Toole treatments [48-50] (see Chapter 4) that are widely used to calculate the average number of free radicals per particle (n) are based on the assumption that the various components of the monomer-swollen latex particles (e.g., monomer, polymer, free radicals, chain transfer agent, etc.) are uniformly distributed within the particle volume. A latex particle in emulsion homopolymerization of styrene involves uniform distribution of monomer and polymer within the particle volume except perhaps for a very thin layer near the particle surface. In the case of free radicals, this uniform distribution would only hold in a stochastic sense. However, as illustrated in Eq. (8.1), free radicals are not distributed uniformly in the latex particles when water-soluble initiators are used to initiate the free radical polymerization. The assumption of uniform distribution of free radicals in the latex particles would be valid only if the particles are very small or chain transfer reactions are the dominate mechanism for producing free radicals. If such a nonuniform free radical distribution hypothesis is accepted, the very basis of the Smith and Ewart-Stockmayer-O Toole methods might be questioned. Despite this potential problem, the Stockmayer-O Toole solutions for the average number of free radicals per particle have been used for kinetic studies of many emulsion polymerization systems. The theories seem to work reasonably well and have been tested extensively with monomers such as styrene. 

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