Emulsion polymerization models

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. 

The Emulsion Polymerization Model (EPM) described in this paper will be presented without a detailed discussion of the model equations due to space limitations. The complete set of equations has been presented in a formal publication (Richards, J. R. et al. J. AppI. Poly. Sci . in press). Model results will then be compared to experimental data for styrene and styrene-methyl methacrylate (MMA) copolymers published by various workers. 

Ahmed, S. M. et al. In Polymer Colloids II Fitch, R.M.,Ed. Plenum Press New York, 1980 p 265. Prindle, J. C Ray, W. H., "Emulsion Polymerization Model Development for Operation Below the CMC" 1987 AIChE Annual Meeting. New York... 

Thomas and Webb (129), using an emulsion polymerization model, calculated k2 from Rp and the number of particles. Their value at room temperature was 2 x 104 1 m-1l-1, in good agreement, perhaps fortuitously, with Dainton and Eaton (49). This treatment assumes that the monomer water ratio at the particle is the same as in the continuous phase. If allowance were made for adsorption of monomer this value of k2 would fall to approach more closely the level observed in DMF. 

Fig. 18 Comparison of the calculated weight fraction distribution with Cf=Cfp=5xlO and Xc=0.5. For the emulsion polymerization model, the total number of polymerized monomeric units in a polymer particle Hp=4x 10, which is equal to the size of a dried polymer particle...

The earliest mathematical model of emulsion polymerization was that of Smith and Ewart [1-3], and was based on the Harkins [4-6] mechanistic understanding of emulsion polymerization (see Sections 4.3 and 4.4). This model was applicable only to a batch polymerization in which all formulation components were added at the start of the reaction. Modifications to this basic understanding were made by Gardon [7] in his model. A good review of emulsion polymerization modelling is provided by Penlidis et al. [8]. 

An important step in tire progress of colloid science was tire development of monodisperse polymer latex suspensions in tire 1950s. These are prepared by emulsion polymerization, which is nowadays also carried out industrially on a large scale for many different polymers. Perhaps tire best-studied colloidal model system is tliat of polystyrene (PS) latex [9]. This is prepared with a hydrophilic group (such as sulphate) at tire end of each molecule. In water tliis produces well defined spheres witli a number of end groups at tire surface, which (partly) ionize to... 

Process Modeling. The complexity of emulsion polymerization makes rehable computer models valuable. Many attempts have been made to simulate the emulsion polymerization process for different monomer systems (76—78). 

A kinetic model for the particle growth stage for continuous-addition emulsion polymerization has been proposed (35). Below the monomer... 

Continuous emulsion polymerization systems are studied to elucidate reaction mechanisms and to generate the knowledge necessary for the development of commercial continuous processes. Problems encountered with the development of continuous reactor systems and some of the ways of dealing with these problems will be discussed in this paper. Those interested in more detailed information on chemical mechanisms and theoretical models should consult the review papers by Ugelstad and Hansen (1), (kinetics and mechanisms) and by Poehlein and Dougherty (2, (continuous emulsion polymerization). 

New methods of emulsion polymerization, particularly the use of swelhng agents, are needed to produce monodisperse latexes with a desired size and surface chemistiy. Samples of latex spheres with uniform diameters up to 100 pm are now commercially available. These spheres and other mono-sized particles of various shapes can be used as model colloids to study two- and three-dimensional many-body systems of very high complexity. 

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

The verification of EPM on the well characterized styrene and styrene-MMA polymerizations has allowed us to use the same model structure to obtain fundamental insights into emulsion polymerizations involving other monomers of significant importance to Du Pont. 

DetaUed Modeling of Multicomponent Emulsion Polymerization Systems... 

Research on the modelling, optimization and control of emulsion polymerization (latex) reactors and processes has been expanding rapidly as the chemistry and physics of these systems become better understood, and as the demand for new and improved latex products increases. The objectives are usually to optimize production rates and/or to control product quality variables such as polymer particle size distribution (PSD), particle morphology, copolymer composition, molecular weights (MW s), long chain branching (LCB), crosslinking frequency and gel content. 

The derivation and development of a mathematical model which is as general as possible and incorporates detailed knowledge from phenomena operative in emulsion polymerization reactors, its testing phase and its application to latex reactor design, simulation, optimization and control are the objectives of this paper and will be described in what follows. 

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). 

Two of the most comprehensive discussions of these models were presented by Min and Ray (5) and by Poehlein and Dougherty (6). Min and Ray (5) gave a very general model framework which should be capable of modelling most emulsion polymerization systems. Of course, decisions must be made on the relative importance of the various phenomena occurring in a particular system. Other, more recent efforts on the modelling of emulsion reactors include the ones of Table I. Further details can also be found in (30). 

TABLE I. Recent Work on the Modelling of Emulsion Polymerization Reactors... 

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. 

A valid mechanistic model can be very useful, not only in that it can appreciably add to our process understanding, but also in that it can be successfully employed in many aspects of emulsion polymerization reactor technology, ranging from latex reactor simulation to on-line state estimation and control. A general model framework has been presented and then it was shown how it can be applied in a few of these areas. The model, being very flexible and readily expandable, was further extended to cover several monomer and comonomer systems, in an effort to illustrate some of its capabilities. 

---