Emulsion polymerization population balances

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

Population Balance Approach. The use of mass and energy balances alone to model polymer reactors is inadequate to describe many cases of interest. Examples are suspension and emulsion polymerizations where drop size or particle distribution may be of interest. In such cases, an accounting for the change in number of droplets or particles of a given size range is often required. This is an example of a population balance. 

The population balance equations are very general and may be applied to batch, semicontinuous, and continuous emulsion polymerizations. Furthermore, both seeded and ab initio polymerizations are comprehended by Eq. (5) in all (or part) of the three commonly considered polymerization intervals. The following sections show how the different possibilities are reflected in different functional forms of the elements of the matrices O and K and of the vector c. It should be remembered, however, that certain conceivable situations are not comprehended by Eq. (5) for example, if the monomer molecules are not freely exchanged between the latex particles so that the monomer concentration inside each latex particle is determined by its growth history. 

Because of the large number of mechanistic processes opo-ative in emulsion polymerizations, complete theories for the PSD are necessarily complex. Nevertheless, they can be formulated by a population balance approxch. Much remains to he done, however, to clarify the basic colloid science that underpins the nucleation process in Interval I. The experimental challenge in evaluating the predictions of the theory for PSDs resides not only in the attainment of agreement with experiment but also in showing that such agreement is not merely fortuitous but arises from the correct mechanistic scheme. Considerable experimental work will be required to establish the validity of mechanistic assumptions for any particular monomer. 

An example of the use of the population balance method to predict reaction in particulate systems is presented in the work of Min and Ray (M16, M17). The authors developed a computational algorithm for a batch emulsion polymerization reactor. The model combines general balances, individual particle balances, and particle size distribution balances. The individual particle balances were formulated using the population balance... 

Most kinetic studies focus on batch emulsion polymerization. These studies enable estimation of important polymer properties. Only recently, the control of particle size and MWD described by population balance models has been achieved. The differences between emulsion polymerization and copolymerization... 

Penlidis, A. Macgregor, J.F. Hamielec, A.E. Mathematical-modeling of emulsion polymerization reactors—a population balance approach and its applications. ACS Symp. Ser. 1986, 313, 219-240. 

Crowley, T.J. Meadows, E.S. Kostoulas, E. Doyle, F.J. Control of particle size distribution described by a population balance model of semibatch emulsion polymerization. J. Process. Control 2000, 10 (5), 419-132. 

Continuous Emulsion Polymerization.—A useful discussion of theories of continuous emulsion polymerization and review of experimental data has been published recently by Poehlein and Dougherty. Thompson and Stevens have developed a population-balance approach to the modelling of continuous emulsion polymerization reactions. They base their approach upon the Smith-Ewart recursion formula, and allow for both radical desorption from, and finite rate of termination within, reaction loci. Cauley et aU have also attempted to model a continuous emulsion polymerization by means of a population balance, the assumed reaction system being such that bimolecular termination of radicals occurs instantaneously within reaction loci. The effect of flow regime on the continuous emulsion polymerization of styrene in a tubular reactor is the subject of a paper by Rollin et... 

Unzueta and Forcada [93] developed a mechanistic model for the emulsion copolymerization of methyl methacrylate and n-butyl acrylate stabilized by mixed anionic and nonionic surfactants, which was verified by the experimental data. This model is based on the mass and population balances of precursor particles and the moments of particle size distribution. It is sensitive to such parameters as the composition of mixed surfactants and the total surfactant concentration. A competitive particle nucleation mechanism is incorporated into the model to successfully simulate the evolution of particle nuclei during polymerization. 

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