Kinetics of emulsion polymerization

The kinetic analysis here is based on quantitative considerations of the ideal emulsion polymerization systems which have been described qualitatively in the preceding sections. The treatment centers only around Stage I and Stage II (Fig. 6.15), as no general theory for stage HI is available. 

Assuming that radicals nucleate micelles at a constant rate v (i.e., number of radicals/cm aqueous phase/s), vdr particles will be generated in the period dr 

Clearly, no micelles can remain when At = asWs, where is the area occupied by unit weight of surfactant and Ws is the weight concentration of surfactant. Suppose this condition is reached at time tc, which then marks the end of Stage I, that is, 

Primary radicals are produced by thermal decomposition of the initiator I in the aqueous phase. In units of number of radicals/cm aqueous phase/s, the rate of radical generation, Rr, is 

Combining Eqs. (6.195) and (6.197) and solving for tc with the assumption that AtiiasWs) 1, one obtains 

Assuming that radicals nucleate micelles at a constant rate y (i e., number of radicals/cm aqueous phase/s), vdr particles will be generated in the period dr and the area A/ of all particles at time t will be given by the sum of the areas of all particles generated till time t. Thus from Eq. (6.193) one obtains (Smith and Ewart, 1948 Rudin, 1982)  

the number of particles per unit volume of aqueous phase, Np, at the end of Stage I is (Smith and Ewart, 1948)  

Conventional emulsion polymerization occurs in a three-phase system (polymer particles, aqueous phase, and monomer droplets) and polymerization may, in principle, occur in any phase. However, the concentrations of both monomer and radicals in the polymer particles are much higher than those in the aqueous phase (see below), and hence the extent of the polymerization in the aqueous phase is in most cases negligible. On the other hand, the concentration of the radicals in the monomer droplets is very low because the monomer droplets are not efficient at capturing the radicals formed in the aqueous phase. The polymerization in the polymer particles follows the same mechanisms as in bulk polymerization and the rate of polymerization per polymer particle Rpp is given by Eq. (1), where kp is the propagation rate constant [m mol s ], [M] the concentration of monomer in the polymer particles [mol m ], h the average number of radicals per particle and Na Avogadro s number. 

The overall polymerization rate Rp takes into account the existence of many polymer particles in the system according to Eq. (2), where Np is the number of polymer particles in the reactor, and V the volume of the reactor. 

In order to calculate the polymerization rate, [Mi], n and Np should be available. 

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Dispersion polymerization involves an initially homogeneous system of monomer, organic solvent, initiator, and particle stabilizer (usually uncharged polymers such as poly(A-vinyl-pyrrolidinone) and hydroxypropyl cellulose). The system becomes heterogeneous on polymerization because the polymer is insoluble in the solvent. Polymer particles are stabilized by adsorption of the particle stabilizer [Yasuda et al., 2001], Polymerization proceeds in the polymer particles as they absorb monomer from the continuous phase. Dispersion polymerization usually yields polymer particles with sizes in between those obtained by emulsion and suspension polymerizations—about 1-10 pm in diameter. For the larger particle sizes, the reaction characteristics are the same as in suspension polymerization. For the smallest particle sizes, suspension polymerization may exhibit the compartmentalized kinetics of emulsion polymerization. 

Quantitative Analysis and Kinetics of Emulsion Polymerization by Smith and Ewart... 

Continuous emulsion polymerization processes are presently employed for large scale production of synthetic rubber latexes. Owing to the recent growth of the market for polymers in latex form, this process is becoming more and more important also in the production of a number of other synthetic latexes, and hence, the necessity of the knowledge of continuous emulsion polymerization kinetics has recently increased. Nevertheless/ the study of continuous emulsion polymerization kinetics hasf to datef received comparatively scant attention in contrast to batch kinetics/ and very little published work is available at present/ especially as to the reactor optimization of continuous emulsion polymerization processes. For the theoretical optimization of continuous emulsion polymerization reactors/ it is desirable to understand the kinetics of emulsion polymerization as deeply and quantitatively as possible. 

The Effect of Nonreactive Additives on the Kinetics of Emulsion Polymerization... 

Nomura (25) investigated the effect of carbon tetrabromide, carbon tetrachloride and long chain mercaptans on the kinetics of emulsion polymerization of styrene. In the case of CBr and CCl the effect on the polymerization was attributed to desorption of the small chain transferred radicals. Similar results were obtained by Napper et al (26). Nomura also observed that the long chain mercaptan (n- dodecyl mercaptan) did not affect the number of particles and the rate, presumably due to the water-insolubility of the chain transferred radicals. 

Emulsion polymerization takes place over a number of steps, where various chemical and physical events take place simultaneously during the process of particle formation and growth. Figure 1 depicts the generally accepted scheme for the kinetics of emulsion polymerization. 

After the nucleation period, three types of kinetic processes determine the kinetics of emulsion polymerization radical entry, radical desorption, and polymer chain formation in the polymer particles. The kinetics of emulsion polymerization are fully described by the following five dimensionless parameters ... 

The assumption of the significance of emulsifier adsorption capability to the kinetics of emulsion polymerization was suggested in our paper (6), for polar monomers, and by Roe (7) and Robb (8 for styrene. Paxton (2) demonstrated that the adsorption area occupied by a molecule of a given emulsifier (Ha-dodecyl benzyl sulphooate) on the surface of polymethylmethac-rylate latex particles, is 1.31 (nm), and so exceeds by a factor of 2.3 a similar area on the surface of polystyrene latex, equal to 0.33(n>n). ... 

After Smith and Ewart ( ), we define the kinetics of emulsion polymerization in terms of the recurrence formula,... 

The kinetic schemes described in this chapter apply to free-radical polymerizations in bulk monomer, solution, or in suspension. Suspension polymerizations ([Section 10.4.2.(iii)]) involve the reactions of monomers which are dispersed in droplets in water. These monomer droplets contain the initiator, and polymerization is a water-cooled bulk reaction in effect. Emulsion systems also contain water, monomer and initiator, but the kinetics of emulsion polymerizations are different from those of the processes listed above. Chapter 8 describes emulsion polymerizations. 

From a fundamental point of view it is interesting to speculate on tbe differences that could exist between the kinetics of emulsion polymerization initiated by y radiation and those of a conventional chemical initiator with, for example, potassium persulfate. At dose rates jiving a free radical flux comparable to those achieved with chemical initiation any differences... 

Equations, which are also applicable to suspension, solution, and bulk polymerization, form an extension of the Smith-Ewart rate theory. They contain an auxiliary parameter which is determined by the rate of initiation, rate constant of termination, and volume of the porticles. The influence of each variable on the kinetics of emulsion polymerization is illustrated. Two other variables are the number of particles formed and monomer concentration in the particles. Modifications of the treatment of emulsion polymerization are required by oil solubility of the initiator, water solubility of the monomer, and insolubility of the polymer in the monomer. 

The kinetics of emulsion polymerization is complex, involving a large number of species and at least two phases. The first quantitative approach to emulsion polymerization kinetics led to extensions by many others.The important events to consider are 1) the free-radical reactions of chain formation initiation, propagation, chain transfer, and termination and 2) the phase transfer events that control particle formation radical entry into particles from the aqueous phase, radical exit into the aqueous phase, radical entry into micelles, and the aqueous phase coil-globule transition. In free-radical emulsion polymerization, the fundamental steps are shown schematically in Fig. 1... 

Smith WV, Ewart RH. Kinetics of emulsion polymerization. J Chem Phys 1948 16 592-599. 

Kato S, Noguchi J, Nomura M. Kinetics of emulsion polymerization of methyl methacrylate using poly(methyl methacrylate-co-methacrylic acid) as polymeric emulsifier. Polym Mat Sci Eng 1999 80 552—553. 

The kinetics of emulsion polymerization reactions are complex because of the numerous chemical and physical phenomena that can occur in the multicomponent, multiphase mixture. A large amount of literature exists on kinetics problems. The general references listed at the end of this chapter contain many important papers. The review paper by Ugelstad and Hansen (11) is a comprehensive treatment of batch kinetics. The purpose of the remainder of this chapter is to present the general kinetics problems and some of the published results. The reader should use the references cited earlier for a more detailed study. 

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