Smith and Ewart theory

The Smith and Ewart theory (the S-E theory) describes the basic concept of emulsion polymerization. Its main points are briefly reviewed here. Smith and Ewart showed that the rate of emulsion polymerization, which proceeds exclusively in the polymer particles, is given by... 

We will first discuss the modeling of the second stage of emulsion polymerization, because most of the polymerization occurs in this stage. One of the simplest (and oldest) models existing is that of Smith and Ewart. This model was the first to explain gross experimental observations. It may be added that the Smith and Ewart theory assumes that primary radicals (SO4 ) can enter into the polymer particles. Although we have already explained that this is not possible because of thermodynamic constraints, it is an important simplifying assumption of this theory. 

SMITH AND EWART THEORY FOR STATE II OF EMULSION POLYMERIZATION [1,2]... 

Example 7.2 The Smith and Ewart theory for emulsion polymerization yields the average number of radicals per particle as 0.5. Experimental results for vinyl chloride give the following [10] ... 

Example 7.3 In the Smith and Ewart theory, we define state i of the polymer particles the same as the niunber of polymerizing fi"ee radicals within it. Experimentally, it has been demonstrated that the polymer particles have a particle size distribution (PSD), which caimot be obtained through this theory. Assume that within the reaction mass, particles have either 0 or 1 growing radicals and develop necessary relations that give the PSD [11]. 

One of the assumptions in the Smith and Ewart theory is that no new polymer particles are generated in the second stage of emulsion polymerization. The rate of polymerization per particle has been experimentally measured in the... 

Emulsion Polymerization. Emulsion SBR was commercialised and produced in quantity while the theory of the mechanism was being debated. Harkins was among the earliest researchers to describe the mechanism (16) others were Mark (17) and Elory (18). The theory of emulsion polymerisation kinetics by Smith and Ewart is still vaUd, for the most part, within the framework of monomers of limited solubiUty (19). There is general agreement in the modem theory of emulsion polymerisation that the process proceeds in three distinct phases, as elucidated by Harkins (20) nucleation (initiation), growth (propagation), and completion (termination). 

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]. 

Considerable work has been done to understand emulsion homopolymerization from a mathematical modeling viewpoint beginning with Smith and Ewart (i) in 1948. Significant contributions to homopolymerization theory have been recently added by the models of workers such as Min and Ray (2.), Rawlings and Ray ( ,), Hansen and Ugelstad (2), Gilbert and Napper (A), and Feeney et al.(8-9). For other work in the field the reader is directed to the review of Penlidis et al. (2.). ... 

The increase in iV, and therefore in the rate as well, with initial soap concentration is thus explained. Quantitative results agree approximately with the predicted three-fifths power dependence. The prediction of an increase in polymerization rate with also has been confirmed by experiments at variable initiator concentrations.t Most important of all, the actual number of particles N calculated from Eq. (35) agrees within a factor of two with that observed. It is thus apparent that the theory of emulsion polymerization developed by Harkins and by Smith and Ewart has enjoyed spectacular success in accounting for the unique features of the emulsion polymerization process. 

The micelles are present at a concentration of about lO per ml of liquor and each micelle contains around 100 monomer molecules. In contrast, the number of monomer droplets is only about 10 ° per ml. Thus, despite the larger volume of monomer droplets, the micelles offer a very much larger surface area. A radical formed in the aqueous phase will thus encounter a monomer-filled micelle much more often than a monomer droplet. Therefore, the polymerization takes place practically only in the micelles and not in the monomer droplets. The monomer consumed in the micelles is replaced by diffusion from the monomer droplets through the aqueous phase. According to the theories of Harkins and of Smith and Ewart, the kinetic course of an emulsion polymerization is divided into three intervals At first some of the micelles increase rapidly in size as the polymerization advances and are transformed into so-called latex particles, containing both monomer and polymer. These are still very much smaller than the monomer droplets and have an initial diameter of about 20-40 pm, corresponding to about... 

On the other hand, a number of qualified investigations on the emulsion polymerization initiated by chemical catalysts and on the experimental verification of the quantitative theory of Smith and Ewart were performed by van der Hoff (14) and Gerrens et ah (4,6). The high experimental standard of these papers in determining the kinetic data is rarely met by papers on the gamma-induced emulsion polymerization. 

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. 

Although there have been several references on the theory of emulsion polymerization kinetics, it is surprising that its commercial importance and multiphase kinetics have not generated more interest. Smith and Ewart (46) predicted a constant rate of polymerization per particle, based on initiation in the water phase and three ranges of radical concentration per particle. Van der Hoff (55) confirmed this for concentrations... 

Theory of emulsion polymerisation developed by Harkins and by Smith and Ewart... 

Smith and Ewart in the U.S.A [128], Haward in Britain [129], Yurzhenko and Kolechova in the U.S.S.R. [130], and later in a different way Fikentscher et al. in F.R.G. [131] derived a kinetic scheme of emulsion polymerization explaining most experimental evidence known at that time. Their theory is recognized as valid to this day, and it forms the basis of more modern developments. 

All quantitative theories based on micellar nucleation can be developed from balances of the number concentrations of particles, and of the concentrations of aqueous radicals. Smith and Ewart solved these balances for two limiting cases (i) all free radials generated in the aqueous phase assumed to be absorbed by surfactant micelles, and (ii) micelles and existing particles competing for aqueous phase radicals. In both cases, the number of particles at the end of Interval I in a batch macroemulsion polymerization is predicted to be proportional to the aqueous phase radical flux to the power of 0.4, and to the initial surfactant concentration to the power of 0.6. The Smith Ewart model predicts particle numbers accurately for styrene and other water-insoluble monomers. Deviations from the SE theory occur when there are substantial amounts of radical desorption, aqueous phase termination, or when the calculation of absorbance efficiency is in error. 

Polymerization of styrene in an emulsion polymerization has been shown to follow a kinetics scheme as first described by Smith and Ewart. When the vinyl monomer is not a good solvent for the polymer (l.e. acrylonitrile or vinyl acetate) large deviations from Sraith-Ewart Theory kinetic predictions are observed. 

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... 

The kinetic behavior of emulsion polymerization is greatly affected by radical desorption from polymer particles. This has been shown by Dgelstad et al. (1969)> Litt et al. (1970), Harada et nl. (1971), Friis and Nyhagen (1973), and Nomura et al (1971). It is believed that the deviation of the kinetic behavior of the emulsion polymerization of water-soluble monomers such as vinyl acetate and vinyl chloride from the Smith and Ewart (1949) Case 2 kinetic theory is mainly due to dominant desorption of... 

According to the theories of Smith and Ewart and of Garden, the effect of emulsifiers on the number of polymer latex particles fomied N (and hence on tbe rate of polymerization during Interval II) is determined by the area % which the emulsifier molecule occupies in a saturated monolayer at tbe polymer-water inteiface,... 

That the average number of radicals per particle should be about 1/2 can also be seen by considering that, on entry of a new radical into a very small particle containing one polymer particle, termination between the two radicals occurs after a time lapse very small compared with the time interval between successive entries of new radicals under the conditions usually prevalent in emulsion polymerization. Hence, the particle contains either one or no radical and the average number of radicals per particle is 1/2. This simple description was first given by Smith and Ewart (58) and will be referred to as the Smith-Ewart rate theory. It follows from n = 1/2 that [R ] = N/2N, ... 

According to the theory of Smith and Ewart [4] of the kinetics of emulsion polymerisation, the rate of propagation Rp is related to the number of particles N formed in a reaction by the equation. 

By assuming the [M]p can be determined by published methods, the problem of computing R is reduced to the prediction of and N. The value of N can be known if a latex seed is used in the reactor. Seeds are used in many scientific studies because the problem of predicting N is eliminated. If a seed is not employed N must be predicted by published correlations or measured. Smith and Ewart (6) published an early theory on particle nucleation that resulted in the relationship shown in Equation 7 ... 

Smith and Ewart (13a. 13b) quantified the Harkins theory by the equation R = k MpN/2 where Rp is the rate of propagation, kp is the rate constant for propagation, M is the monomer concentration in growing chain particles, and N the number of polymer particles per unit volume. If M is the constant, this equation is reduced to R = k N. Thus, the rate of emulsion polymerization should solely be a function of the number of polymer particles. In actuality, the reaction rate increases up to 20-25% conversion because of the increase in the number of growing radical chains then the rate steadies as does the number of polymer particles up to 70-80% conversion. Beyond this point, the rate drops off because of low monomer concentration. Thus, as Talamini (13c. 13d) has noted, available evidence indicates that emulsion polymerization of vinyl chloride does not resemble true emulsion polymerization as described by Smith and Ewart, but shows the general behavior of heterogeneous polymerization. 

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). 

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