Smith-Ewart kinetics

The kinetics of a polymerisation refers to the rate at which the polymerisation occurs (397). In emulsion polymerisation, the fundamental polymerisation kinetics theory is that of Smith and Ewart (377, a. 13). They proposed a theoretical framework in which monomer-swollen polymer particles are entered by radicals at a constant rate (radical flux). The radicals may desorb from the particle, terminate with one another, or initiate polymerisation within the particles. Through mathematical analysis, the average number 

In the first situation (Case 1), where the particles are small or the monomer is substantially water-soluble, and desorption of radicals from the particle is likely, n is very low, and polymerisation is slow. In the second situation. Case 11, radical exit is negligible. When a radical enters a particle, polymerisation occurs until a second radical enters, and both are instantaneously terminated (zero-one kinetics). Under these conditions, n is equal to V2. In the third situation. Case III, the particles are large enough that two or more radicals may coexist within the same particle without 

Through a surfactant balance. Smith and Ewart determined that the rate of polymerisation is proportional to the surfactant concentration to the 0.6 power, and to the initiator concentration to the 0.4 power. Smith used styrene as monomer and sodium dodecyl sulfate as surfactant in his experiments demonstrating the concept. In practice, most monomer/surfactant systems deviate from the ideal Smith-Ewart kinetics. However, equation (1) is rigorous for all emulsion polymer systems  

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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... 

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. 

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. 

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... 

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 order to apply these equations, the kinetics of polymerization must be known (Rp in Equation 10). Fitch and Tsai assumed homogeneous kinetics (22) for their MMA polymerizations, based on the earlier results of Fitch, Prenosil and Sprick (19) and of Baxendale et al. (8). Such an assumption is probably not valid for other monomers, especially those less water-soluble than MMA. In such cases the non-steady-state modification of the Smith-Ewart kinetics (9d) may be applied, or a direct numerical calculation of the distribution of radicals among particles by means of Equation 7 may be made. 

While vinyl acetate is normally polymerized in batch or continuous stirred tank reactors, continuous reactors offer the possibility of better heat transfer and more uniform quality. Tubular reactors have been used to produce polystyrene by a mass process (1, 2), and to produce emulsion polymers from styrene and styrene-butadiene (3 -6). The use of mixed emulsifiers to produce mono-disperse latexes has been applied to polyvinyl toluene (5). Dunn and Taylor have proposed that nucleation in seeded vinyl acetate emulsion is prevented by entrapment of oligomeric radicals by the seed particles (6j. Because of the solubility of vinyl acetate in water, Smith -Ewart kinetics (case 2) does not seem to apply, but the kinetic models developed by Ugelstad (7J and Friis (8 ) seem to be more appropriate. 

The "ideal" concept of emulsion polymerization was built on the assumption that the monomer was water insoluble and that in the absence of chain transfer, the number average degree of polymerization, Xj can be related to the rate processes of initiation and propagation by the steady-state relationship Xjj = 2 Rp/Rj. Since Ri and Rp are both constant and termination is assumed to be Instantaneous during the constant rate period described by Smith-Ewart kinetics, the above equation predicts the generation of constant molecular weight polymer. Data has been obtained which agrees with Smith-Ewart but there is... 

Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

State with no entrance effects or radial velocity components body forces are neglected axial heat conduction is small compared to radial conduction Region I of Smith-Ewart kinetics (i.e., when micelles are first forming) is neglected and the initiator concentration is constant. The model may be summarized as ... 

A computer model, based on Smith-Ewart kinetics and the continuity equations predicts experimental conversion data, except at low conversions. 

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

The Smith-Ewart kinetic theory of emulsion polymerization is simple and provides a rational and accurate description of the polymerization process for monomers such as styrene, butadiene, and isoprene, which have very limited solubility in water (less than 0.1%). However, there are a number of exceptions. For example, as we indicated earlier, large particles (> 0.1 to 0.5 cm diameter) may and can contain more than one growing chain simultaneously for appreciable lengths of time. Some initiation in, followed by polymer precipitation from the aqueous phase may occur for monomers with appreciable water solubility (1 to 10%), such as vinyl chloride. The characteristic dependence of polymerization rate on emulsifier concentration and hence N may be altered quantitatively by the absorption of emulsifier by these particles. Polymerization may actually be taking place near the outer surface of a growing particle due to chain transfer to the emulsifier. 

Smith-Ewart kinetics n. Emulsion polymerization kinetics describing the initiator that dissociates into free radicals, which can either travel into the micelle and start a polymerization directly (Smith-Ewart-Harkins theory) or react first with an emulsifier molecule, under transfer, forming an emulsifier radical, which then starts the polymerization (Medvedev theory). 

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. 

Figure 4.2. Schematic representation of the Smith-Ewart kinetics Cases 1-3.

Figure 4.3. Schematic representation of the iog (n) versus iog (a) protiie tor a typicai emuision polymerization system. The three iimiting cases of the Smith-Ewart kinetic modei are aiso indicated in this plot.

Figure 4.4. Schematic representation of the log (n) versus log (a) profiles with different values of m(mi = 0 (Smith-Ewart kinetics Case 2) < m2 < /TI3 < m ) for a typical emulsion polymerization system.

The emulsion polymerization of vinyl acetate (to homopolymers and copolymers) is industrially most important for the production of latex paints, adhesives, paper coatings, and textile finishes. It has been known that the emulsion polymerization kinetics of vinyl acetate differs from those of styrene or other less water-soluble monomers largely due to the greater water solubility of vinyl acetate (2.85% at 60°C versus 0.054% for styrene). For example, the emulsion polymerization of vinyl acetate does not follow the well-known Smith-Ewart kinetics and the polymerization exhibits a constant reaction rate even after the separate monomer phase disappears. The following observations have been reported for vinyl acetate emulsion polymerization [78] (a) The polymerization rate is approximately zero order with respect to monomer concentration at least from 20% to 85% Conversion (b) the polymerization rate depends on the particle concentration to about 0.2 power (c) the polymerization rate depends on the emulsifier concentration with a maximum of 0.25 power (d) the molecular weights are independent of all variables and mainly depend on the chain transfer to the monomer (e) in unseeded polymerization, the number of polymer particles is roughly independent of conversion after 30% conversion. 

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