Smith-Ewart-Harkins theory

Waterborne free radicals first polymerize with monomer molecules dissolved in the continuous aqueous phase. This would result in an increase in the hydrophobicity of oligomeric radicals. When the critical chain length is 

Based on the above reaction scheme and the assumptions that (a) a monomer-swollen micelle can be successfully converted into a particle nucleus via the capture of a free radical in the continuous aqueous phase, (b) the volumetric growth rate for particle nuclei (p = dvpidt, where Vp is the volume of a particle nucleus) is constant, (c) desorption of free radicals out of the particle does not occur, and (d) the amount of surfactant molecules dissolved in the continuous aqueous phase and adsorbed on the monomer droplet surfaces is insignificant, the rate of formation of particle nuclei is then equal to the rate of generation of free radicals in the continuous aqueous phase. 

Particle nucleation stops immediately after the depletion of monomer-swollen micelles, and the corresponding time is represented by the symbol h. At h, the volume of a particle nucleus generated at time x (Vp,i) is p(h - x) and the corresponding particle surface area ( p,i) of this nucleus is then [(47r) 3p] (ti - x) / Thus, the total particle surface area at h(Ap,i)isJ[(47r/ 3p] ti-xf 2fkd X )dx (integrated from 0 to h) = f [(4n) 3p] 2/krf[I])rf which is equal to UsSo. The parameter as is the particle surface area occupied by unit weight of the adsorbed surfactant, and 5o is the weight of surfactant initially present in the polymerization system. In 

Considering a more realistic scenario that the existing particle nuclei may also compete with monomer-swollen micelles in capturing free radicals, the rate of particle nucleation then becomes 

In comparison with Eq. (3.3), a smaller population of latex particles (Np,i) is obtained from Eq. (3.5) due to the competitive absorption of free radicals. 

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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 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). 

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. 

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. 

The concise Harkins-Smith-Ewart theory [9-16] delicately describes the key characteristics of emulsion polymerization. However, the difference in colloidal properties (e.g., composition, size, surface charge density, and particle surface area occupied by the adsorbed surfactant) between the monomer-swollen micelles and particle nuclei was not taken into account in the derivation of Eq. (3.4). The probability for micelles or particle nuclei to capture oligomeric radicals in the continuous aqueous phase is simply assumed to be proportional to their total oil-water interfacial area. 

Nomura and co-workers [20] studied the competitive absorption of free radicals by micelles and particle nuclei. In addition to the basic assumptions made in the Harkins-Smith-Ewart theory, the bimolecular termination reac-... 

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. 

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... 

Harkins, Smith-Ewart and Related Theories 4.4.2 Garden s version of the Smith-Ewart theory... 

Other Mechanistic Aspects.—Stannett et al have reported on the kinetics of the emulsion polymerization of styrene initiated by irradiation with cobalt-60 y-rays. The conclusion is reached that Smith-Ewart Case 2 kinetics are obeyed if the reaction system is such that compliance with Smith-Ewart Case 2 would be expected were initiation effected by the thermal decomposition of potassium persulphate. The efficiency of utilization of the radicals produced by radiolysis of the aqueous phase appears to be in the range 0.3—0.5. Chatterjee, Banerjee, and Konar have investigated the molecular weight of polystyrene produced by emulsion polymerization at low monomer concentration, and compared their observations with the predictions of the theories of Harkins, Smith-Ewart, and Gardon. These workers have also investigated the dependence of rate of polymerization upon monomer concentration in the emulsion polymerization of styrene. Arai, Arai, and Saito" have studied the persulphate-initiated surfacant-free emulsion polymerization of methyl methacrylate, and have proposed a model for the reaction. 

Dunn, A.S. Harkins, Smith-Ewart and related theories, in Emulsion Polymerisation and Emulsion Polymers (Lovell, P.A., El-Asser, M.S., eds.), Wiley, New York, 1997, Chpt 4,... 

The major reasons for the divergence of theory (Harkins Smith Ewart) and practice, involve the much lower degrees of conversion of the experiments on which the academic studies were based, and the much higher concentrations of surfactant (and their method of addition) commonly employed commercially. The latter play a major role in effecting the behaviour of the micelles and the critical micelle concentration (CMC) both factors on which the classical theories were built. 

In academia, these developments were closely paralleled by increasing understanding of the mechanistic and, subsequently, kinetic theories. Among these, the Harkins and Smith-Ewart theories are the most prominent and important. The Harkins theory has already been mentioned in the citation from Hohenstein and Mark (1946). It appeared in a series of publications between 1945 and 1950 (Harkins, 1945, 1946, 1947,1950 Harkins et al, 1945). Harkins interest was chiefly the role of surface-active substances in emulsion polymerisation. The Harkins theory is therefore a qualitative theory, but it is often looked upon as the starting point of all modern theories of emulsion polymerisation (Figure 1.1). The essential features of the theory are as follows (Blackley, 1975) ... 

Harkins did not explicitly state how the water soluble initiator would be able to initiate the monomer swollen, and therefore oil-rich , soap micelles. This detailed mechanism was somewhat unclear at the time (maybe stiU is), but it has been assumed that the initial polymerisation takes place within the aqueous phase. How these polymers (oligomers) would be capable of going into the micelles was not discussed. Harkins based his theory both on earlier opinions, as described above, and on experimental evidence. Building on the Harkins theory, the Smith-Ewart theory, which appeared in 1948, was a major leap forward in emulsion polymerisation. This is described further in Section 1.2.2. 

Definitely the most important theory in emulsion polymerisation is the Smith-Ewart theory. This theory was first pubhshed in 1948 (Smith Ewart, 1948) and since then has been the subject of continuing discussion and refinement. The theory is based on the Harkins mechanisms and then tries to predict the rate of reaction and its dependence upon the concentrations of the main components of the system. The rate of reaction is considered to be equal to the total rate of polymerisation in the nucleated soap micelles, which then have been converted to polymer particles. There is no polymerisation in the aqueous phase or in the monomer drops. The total rate can then be set equal to the rate in each polymer particle, multiplied by the number of particles ... 

The quantitative theory is therefore centred on predicting (a) the number of particles nucleated and (b) the rate of polymerisation in each particle. The Smith-Ewart theory operates in the three intervals of the polymerisation process, and defines three cases for the kinetics. The intervals correspond to the three stages in the Harkins theory Interval I is the nucleation stage where micelles are present and the particle number increases Interval II corresponds to the stage when the particle number is constant and free monomer drops are also present Interval III is the last part of the polymerisation when the monomer drops have disappeared. Smith and Ewart developed an expression for the particle number created by nucleation in the soap micelles that is stiU considered essentially correct, within its limits (meaning that monomers, surfactants and generally conditions can be found when the Smith-Ewart theory is not correct and that our understanding today is more detailed). The expression for the particle number, N, is... 

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. 

Their recipe of polymerization is reproduced in Table I, and Figure 1 shows the rate of polymerization, Rp, plotted against SLS concentration in the mixed surfactants. In that plot, the concentration of SLS was expressed in parts of SLS/5-parts BC-840/100 parts styrene. Based on this study, Kamath ( 8) proposed that particle-nucleation in his system was controlled by micellar nucleation mechanism following Harkins and Smith-Ewart s theory. 

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