Emulsion Harkins-Smith-Ewart theory

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... 

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. 

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,... 

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 ... 

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). 

Nucleation in emulsion polymerization has been a matter of controversial discussion because for more than five decades no direct experimental data on the nucleation process were available. Discussions were mainly centered on the question of the role of emulsifying agents, in particular on the role of micelles as precursors of polymer particles. Micellar nucleation theory, as it was expressed by Smith-Ewart (77) on the baseis of ideas developed by William Harkins (78-80), states ... 

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 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... 

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. 

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

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). 

Many of the results of wartime research in the USA are reviewed by Harkins [43,50,51]. The quantitative development of the Harkins theory which still dominates most discussions of emulsion polymerization kinetics was published by Smith and Ewart in 1948 [52] with a first attempt at experimental verification by Smith [53]. 

After the emulsion of the monomer phase in the water phase and the presence of the emulsifier micelles established, the pol3mierization is initiated by the addition of initiator. According to the theories proposed by Harkins and Smith and Ewart, conventional emulsion pol)nnerization mechanism occurs into three intervals including the initial (particle formation or nucleation) stage, the particle growth stage and the completion stage. 

Classically, emulsion polymerizations involve monomers that are solvents for the homopolymer. Strictly speaking only these systems follow the theory of Harkins as quantified by Smith and Ewart. According to this theory, the propagation rate is a function of the number of polymer particles that are... 

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