Harkins’ theory

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 Harkins theory of nuclear structure was formulated before the discovery of the neutron, but predicted the existence of this particle. An atom was described in terms of a mass number, P, that specihes the number of protons in a nucleus, an atomic number Z, that specihes the number of extranuclear electrons and the number of nuclear electrons, N. Another fundamental quantity was dehned as the isotopic number... 

The essence of Harkins theory is that all atomic nuclei are built up from (j-particles and clusters H,, of hydrogen atoms, with x = 0,1, 2, 3 to yield mass numbers of An, An — 2, 4n 1, together with charge compensating... 

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]. 

The system initially consists of water, a practically water-insoluble monomer, an emulsifier, and a water-soluble initiator (see Figure 20-10). The emulsifier forms a great number of micelles above the critical micelle concentration. The micelles solubilize monomer, which causes them to swell. Another fraction of the monomer forms monomer droplets of about 1000 nm diameter. The initiator 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... 

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. 

Figure 1.1 Cartoon of an emulsion polymerisation b lsed on the Harkins theory. Ingredients are monomer, surfactant, and initiator. The surfactant forms micelles and the initiator is soluble in water. This snapshot is taken during Interval I, when particles are being formed and monomer is present both as free droplets, in aqueous solutions, in micelles and in already formed polymer particles. The surfactant is distributed as dissolved molecules, in micelles, adsorbed on polymer particles and on monomer droplets (to a lesser degree).

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... 

As mentioned in Section 1.2.2, the Harkins theory states that no, or at least very little, polymerisation takes place in the monomer droplets. This is essentially correct, and the reason is that the number of monomer droplets compared to the particles nucleated from micelles is of many orders of magnitude lower. This does not mean that the monomer droplets are not initiated, however, and in many processes, a few extra large particles maybe observed. Also, monomer suspension polymerisation is often the source of reactor fouling. Many believe that these large particles are the leftovers of the monomer drops that are probably all initiated, but contribute very little to the overall conversion because of the peculiar compartmentalisation kinetics. It might be thought then, that if the monomer drops could be made smaller and thus more numerous, they might be more important in the nucleation process. This has indeed been shown to be the case. 

Unsaturated polyesters for laminates Debye, light scattering of polymer solutions Flory, viscosity of polymer solutions Harkins, theory of emulsion polymerization Weissenberg, normal stresses in polymer flow Silicones... 

---