Smith-Ewart theory derivations

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. 

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. 

Based on the Smith-Ewart theory [1], Stockmayer [3] derived the following equations to calculate the steady value of n when desorption of free radicals out of the latex particles is insignificant (i.e., kdes = 0). 

The kinetic mechanism of emulsion polymerization was developed by Smith and Ewart [10]. The quantitative treatment of this mechanism was made by using Har-kin s Micellar Theory [18,19]. By means of quantitative treatment, the researchers obtained an expression in which the particle number was expressed as a function of emulsifier concentration, initiation, and polymerization rates. This expression was derived for the systems including the monomers with low water solubility and partly solubilized within the micelles formed by emulsifiers having low critical micelle concentration (CMC) values [10]. 

Smith and Ewart in the U.S.A [128], Haward in Britain [129], Yurzhenko and Kolechova in the U.S.S.R. [130], and later in a different way Fikentscher et al. in F.R.G. [131] derived a kinetic scheme of emulsion polymerization explaining most experimental evidence known at that time. Their theory is recognized as valid to this day, and it forms the basis of more modern developments. 

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