Coagulative nucleation theory

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

The debate as to which mechanism controls particle nucleation continues. There is strong evidence the HUFT and coagulation theories hold tme for the more water-soluble monomers. What remains at issue are the relative rates of micellar entry, homogeneous particle nucleation, and coagulative nucleation when surfactant is present at concentrations above its CMC. It is reasonable to assume each mechanism plays a role, depending on the nature and conditions of the polymerization (26). 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

As an even more explicit example of this effect Figure 6 shows that EPM is able to reproduce fairly well the experimentally observed dependence of the particle number on surfactant concentration for a different monomer, namely methyl methacrylate (MMA). The polymerization was carried at 80°C at a fixed concentration of ammonium persulfate initiator (0.00635 mol dm 3). Because methyl methacrylate is much more water soluble than styrene, the drop off in particle number is not as steep around the critical micelle concentration (22.) In this instance the experimental data do show a leveling off of the particle number at high and low surfactant concentrations as expected from the theory of particle formation by coagulative nucleation of precursor particles formed by homogeneous nucleation, which has been incorporated into EPM. 

According to the aggregative and coagulative nucleation mechanisms which have been derived originally from the homogeneous nucleation theory of Fitch and Tsai [128], the most important point in the reaction is the instant at which colloidally stabilized particles form. After this point, coagulation between similar-sized particles no longer occurs, and the number of particles present in the reaction is constant. As shown in Fig. 6, the dispersion copolymerization with macromonomers is considered to proceed as follows. (1) Before polymerization, the monomer, macromonomer, and initiator dissolve completely into the... 

The basic principle of this nucleation theory is that the formation of primary particles takes place up to the point where the rate of formation of the radicals in the aqueous phase is equal to the rate of their disappearing via capture of radicals by swollen micelles-if present-initially and by particles already formed (Figure 2, [14]), and via coagulation. 

The general accepted theory for explaining the particle formation is based on fiindamental mechanisms of nucleation, growth and coagulation. According to the classical nucleation theory the rate of formation of a nucleus with critical size is... 

According to the micellar theory [6, 7] the rate of polymerization (in the stationary interval 2) is proportional to the 0.4 power of the concentration of initiator and the 0.6 power of the concentration of emulsifier [4]. It was later shown by Roe [23], Fitch [22,25, 67] and Hansen and Ugelstad [18] that this behavior is also consistent with homogeneous nucleation. Indeed, identical exponents can be predicted by virtually any mechanism which assumes that (1) coagulation does not occur, (2) nucleation ceases when the surface area of the latex particles is equal to the total surface area capable of being occupied by the emulsifier molecules, and (3) the rate of production of free radicals is uniform. Here, determination of exponents for [I] and [E] fails to discriminate between competing micellar and homogeneous nucleation theories. 

Sutterlin [46] studied the effect of the polarity of various monomers (styrene, acrylate ester monomers, and methacrylate ester monomers see Table 3.1) on the particle nucleation mechanisms involved in emulsion polymerization. When the surfactant concentration is above its CMC, the emulsion polymerization of styrene follows the Smith-Ewart theory (Npj 5o ) except those experiments with relatively low levels of surfactant. The exponent x in the relationship Npj So decreases with increasing monomer polarity when the surfactant concentration is above its CMC. This trend is attributed to the increased tendency of agglomeration of particle nuclei with monomer polarity. The emulsion polymerizations of less polar monomers deviate significantly from the Smith-Ewart theory (x 0.6) if the surfactant concentration is reduced to a level just below its CMC. This implies that some mechanisms other than micellar nucleation (homogeneous nucleation or coagulative nucleation) must operate in these emulsion polymerization systems. 

At the beginning of the chapter it is shown that the usual models for coagulation and nucleation presented in Chapters 7 and 10 arc special cases of a more general theory for very small particles. An approximate criterion is given for determining whether nucleation or coagulation is rate controlling at the molecular level. The continuous form of the GDE is then used to derive balance equations for several moments of the size distribution function. 

When a fast chemical reaction or a rapid quench leads to the formation of a high density of condensable molecules, panicle formation may take place either by homogeneous nucleation, an activated process, or by molecular "coagulation a process in which nearly all collisions are successful. What determines which of these processes controls In principle, this problem can be analyzed by solving the GDE for the discrete distribution discussed in the previous section. An approximate criterion proposed by Ulrich (1971) for determining whether nucleation or coagulation is the dominant process is based on the critical particle diameter d that appears in the theory of homogeneous nucleation (Chapter 9)... 

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