Dynamic emulsion polymerization model

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. 

Continuons emulsion polymerization is one of the few chemical processes in which major design considerations require the use of dynamic or unsteady-state models of the process. This need arises because of important problems associated with sustained oscillations or limit cycles in conversion, particle number and size, and molecular weight. These oscillations can occur in almost all commercial continuous emulsion polymerization processes such as styrene (Brooks et cl., 1978), styrene-butadiene and vinyl acetate (Greene et cl., 1976 Kiparissides et cl., 1980a), methyl methacrylate, and chloropene. In addition to the undesirable variations in the polymer and particle properties that will occur, these oscillations can lead to emulsifier concentrations too low to cover adequately the polymer particles, with the result that excessive agglomeration and fouling can occur. Furthermore, excursions to high conversions in polymer like vinyl acetate... 

To illustrate this approach we consider the emulsion polymerization of vinyl acetate in a sin e CSTR. The dynamic model given by Eqs. (56-60), and Eqs. (69) and (70) can he represented more concisely by the set of nonlinear differential equations... 

The dynamic model developed by Kiparissides et al M,2] and subsequently modified by Chiang and Thompson [ J] can predict the conversion, number of particles, particle diameters, etc., for the continuous emulsion polymerization of vinyl acetate. In this paper, the model is extended to predict molecular weight averages and long chain branching as well. 

Ciullo PA, Hewitt N (1999) The rubber formulary. Noyes, Norwich Coker K (2001) Modeling of chemical kinetics and reactor design. Gulf, Boston, MA Davis FJ (2004) Polymer chemistry a practical approach. Oxford University Press, Oxford Drobny JG (2001) Technology of fluoropolymers. CRC Press, Boca Raton, FL Durairaj RB (2005) Resorcinol chemistry technology and applications. Springer, Berlin Dutcher JR et al (eds) (2005) Soft materials structure and dynamics. Marcel Dekker, New York Erbil HY (2000) Vinyl acetate emulsion polymerization and copolymeiization with acrylic monomers. CRC Press, Boca Raton, FL... 

Pollock, M. J., MacGregor, J. F., and Hamielec, A. E. (1981) Continuous poly (vinyl acetate) emulsion polymerization reactors dynamic modeling of molecular weight and particle size development and application to optimal multiple reactor system design. Computer Applications in Applied Polymer Science, (ed. T. Provder), ACS, Washington, pp. 209-20. 

As discussed in depth earlier, the dynamic model completely describes the PSD for an emulsion polymerization process, given the current mechanistic knowledge. However, it is often convenient to represent the dishibution by one or more measurable parameters. Such parameters can include the number average radius, defined as... 

One can use the dynamic model of the emulsion polymerization to apply perturbations in the inputs u and record the model outputs y. The step response coefficients are then calculated as follows ... 

As mentioned above, the two most popular reaction mechanisms involved in the absorption of free radicals by the monomer-swoUen micelles and polymer particles are the diffusion- and propagation-controlled models. Nevertheless, liotta et al. [39] were inclined to support the colUsion-controlled model. A dynamic competitive particle growth model was developed to study the emulsion polymerization of styrene in the presence of two distinct populations of latex particles (i.e., bimodal particle size distribution). Comparing the on-line density and particle size data with model predictions suggests that absorption of free radicals by the latex particles follows the collision-controlled mechanism. 

One unique but normally undesirable feature of continuous emulsion polymerization carried out in a stirred tank reactor is reactor dynamics. For example, sustained oscillations (limit cycles) in the number of latex particles per unit volume of water, monomer conversion, and concentration of free surfactant have been observed in continuous emulsion polymerization systems operated at isothermal conditions [52-55], as illustrated in Figure 7.4a. Particle nucleation phenomena and gel effect are primarily responsible for the observed reactor instabilities. Several mathematical models that quantitatively predict the reaction kinetics (including the reactor dynamics) involved in continuous emulsion polymerization can be found in references 56-58. Tauer and Muller [59] developed a kinetic model for the emulsion polymerization of vinyl chloride in a continuous stirred tank reactor. The results show that the sustained oscillations depend on the rates of particle growth and coalescence. Furthermore, multiple steady states have been experienced in continuous emulsion polymerization carried out in a stirred tank reactor, and this phenomenon is attributed to the gel effect [60,61]. All these factors inevitably result in severe problems of process control and product quality. 

In all but the most basic cases of very dilute systems, with microstructural elements such as rigid particles whose properties can be described simply, the development of a theory in a continuum context to describe the dynamical interactions between structure and flow must involve some degree of modeling. For some systems, such as polymeric solutions, we require modeling to describe both polymer-solvent and polymer-polymer interactions, whereas for suspensions or emulsions we may have an exact basis for describing particle-fluid interactions but require modeling via averaging to describe particle-particle interactions. In any case, the successful development of useful theories of microstructured fluids clearly requires experimental input and a comparison between experimental data and model... 

The Kalman filter is an optimal estimator for the estimation of the states of a dynamic system from a set of measurements which are a subset of the set of states (or linear combinations of states). As such it can be used for noise filtering, estimation of unmeasured states, rectification of multiple sensors for the same property, and prediction of future values of states. Kalman filtering has been used in a number of polymerization applications including the estimation of copolymer composition during emulsion copolymerization [28]. One drawback to the Kalman filter is that it incorporates the process model into the filter structure. In many cases a simple observer will suffice. An observer requires model predictions of the process outputs, but the model is not incorporated into the observer structure. The process model can be updated without changing the observer [29]. 

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