Smith/Ewart theory

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

A well-known emulsion polymerization kinetic model can be developed based on the following assumptions  

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. 

Case 2 des ajvp ktjvp (no desorption and fast termination) 

Case 3 JNp ktjvp (fast absorption and slow termination) 

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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... 

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). 

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. 

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. 

As mentioned earlier, this paper will stress homogeneous nucleation not only because of its applicability to a broad range of monomers and to systems both aqueous and organic, but also because several features are applicable to systems undergoing heterogeneous nucleation and which were not considered in the original Smith-Ewart theory. To begin with, a brief historical review is in order. 

The prediction of the MWD of emulsion polymers proved to be a relatively intractable problem even after the advent of the Harkins-Smith-Ewart theory. Perhaps the most successful early attack on the problem was that of Katz, Shinnar and Saidel (2). They considered only two microscopic events entry and bimolecular termination by combination. Their theory resulted in a set of partial integrodifferential equations, whose numerical solution provided the lower moments of the molecular weight distribution function. Other attempts to predict the MWD of emulsion polymers include those of Parts and Wat ter son (3 ), Sundberg and Eliassen (4), Min and Ray (5) and Gardon (6). 

Gordon, J.L. (1968) Emulsion polymerisation. 1. Recalculation and extension of Smith-Ewart theory. /. Polym. Sci. Al, 6(3PA1), 623. 

The basic prerequisities of the Smith-Ewart theory are equal dimensions of all polymer-monomer particles, and their constant growth rate... 

Equation (58) indicates that an increase in initiatior concentration will not enhance the rate of polymerization. It can be used for estimating the molecular mass of the polymer assuming, of course, the absence of transfer. The ratio N/q corresponds to the mean time of polymer growth and molecular mass is equal to the product of the number of additions per unit time and the length of the active life time of the radical, kpN/e. An increase in [I] also means a higher value of q, and thus a shortening of the chains. As in Phase II, the polymerized monomer in the particles is supplemented by monomer diffusion from the droplets across the aqueous phase a stationary state is rapidly established with constant monomer concentration in the particle. The rate of polymerization is then independent of conversion (see, for example the conversion curves in Fig. 7). We assume that the Smith-Ewart theory does not hold for those polymerizations where the mentioned dependence is not linear [132], The valdity of the Smith-Ewart theory is limited by many other factors. 

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. 

The above cited information showed unanimously that, in a mixed-surfactant system of emulsion polymerization, the composition of the mixed surfactant affects the rate of polymerization. Since by Harkins-Smith-Ewart theory, rate of polymerization is proportional to the total number of particles in the system, composition of mixed surfactants seems to affect the efficiency of nucleation. 

Therefore, the nonlinear relationship between rate of polymerization and the total surfactant concentration, as shown in Figure 2, was believed to be caused by a change in micellar size. Thus, the purpose of the present study was to verify the validity of the concept of micellar size effect in emulsion polymerization kinetics. Furthermore, although the Harkins-Smith-Ewart theory of micellar nucleation was proposed in 1948, and has found widespread application ever since, its validity is still challenged even for the case of polymerization of styrene ( ). If micellar... 

Equation (5) or (5b) is the highly important deduction of Harkins-Smith-Ewart theory. Its validity has been fully confirmed for many cases of polymerization (19). Furthermore, although it is difficult to determine the nvimber of particles, Np, accurately (19) this simple relationship has been used to determine the absolute value of the rate constant, kp, satisfactorily for the polymerization of butadiene and isoprene by Smith (20) and by Morton et al.(21). Conditions where the rate of polymerization is not proportional to the number of particles are where Trommsdorff s effect (22-24) or Gordon s unsteady state (25) principles apply. However, the existence of linear portions of the conversion-time plots proves the absence of these principles in this system. 

Table I shows that the diameters of the polymers from styrene are approximately twice as large as those from 1,4-DVB, and in all experiments with 1,4-DVB at least 6 times more particles have been formed than with styrene. The maximum diameters of spherical particles from 1,4-DVB which can be obtained, are about 500 A. Larger particles are mostly irregularly shaped (see 4.2) whereas in the case of styrene, latex particles of 2000 A and more may be prepared easily. These differences may be explained by a discussion of the SMITH-EWART theory ( ). According to this theory the number N of latex particles formed in the emulsion polymerization of styrene is given by...

The Harkins-Smith-Ewart theory predicts that the number of polymer particles formed, N, will be proportional to and This is observed for some batch polymerizations, as mentioned. In general, N oc 5, but the value of the exponent depends on the range of soap concentrations and the monomer solubility in water. This topic is of more academic than practical interest, however, because most useful polymerizations are not batch operations. 

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... 

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