Rheokinetic model

In this section, we will describe the application of the rheokinetic model to adiabatic and isothermal pultrusion by the RIP process. Adiabatic pultrusion is defined as a pultrusion... 

This chapter reviewed the chemistry of ring opening polymerization of cyclic monomers that yield thermoplastic polymers of interest in composite processing. In addition, this chapter focuses on the chemistry, kinetics, and rheology of the ring opening polymerization of caprolactam to nylon 6. Finally, these rheokinetics models are applied to the reactive injection pultrusion (RIP) process. 

The same authors who developed a rheokinetic model for polyurethane synthesis also proposed the following equation for the dependence ri(P,T) ... 

Figure 4.29. Comparison of velocity profiles (a), degrees of conversion (b) and MWD-H (c) for calculations carried out for a rheokinetic model with changes in of the velocity profile along the reactor (solid lines) and for an unchanging Poiseuille velocity profile (dashed lines). Values of the parameters in calculations Da/Da = 0.2 [A] = 0.7 mol%.

It has to be concluded that the polymerization of acrylates in water is different to its acid. A rheokinetics model to describe the complex behavior is not available, because this merged fit of (20.29) is not in compliance with the literature of rheokinetics. In the following discussion the focus is only on acrylic acid. 

It should be emphasized that in all these cases, combined or superimposed phenomena must be dealt with, viz. for stage IV, fluiddynamics, kinetics of polymerization, and rheokinetic changes caused by chemical reactions for stage V, polymerization kinetics, crystallization kinetics and heat transfer effects a thermomechanical problem in combination with crystallization kinetics. Construction of a mathematical model requires simultaneous solution of a set of equations in order to describe these related phenomena. 

A complete analysis of the role of the radial distributions of all the parameters that determine the flow through a tubular reactor during polymerization is a very complicated, and it is doubtful whether general solutions can be found. However, solutions can be obtained for various situations for a system with known kinetic and rheological properties, because we will be searching for specific details rather than for a general physical picture of the process. It is also possible to carry out a general analysis at certain simplified models, which nevertheless include the principal rheokinetic effects. 

Industrial equipment use for reactive processing is limited by the permissible injection pressure. The model being discussed can also be used to estimate the pressure drop necessary to fill the mold. The pressure changes during the filling process, and the time dependence of the pressure is determined by the rheokinetic properties of the reactive mixture and the dimensions... 

An identical mathematical description of the kinetics of curing of reactants different in chemical nature and that obtained on the basis of fundamentally different experimental methods allows us to assume that this apparent selfacceleration course of some rheokinetic parameters is common to the processes of formation of materials with a crosslinked structure. It should be emphasized once more that the self-acceleration" effect must not be identified with the self-catalysis of the reaction of interaction between epoxy monomers and diamines which is studied in detail on model compounds [116, 117]. For each particular curing process the self-acceleration effect is influenced by the mechanism of network formatic, namely, chemical self catalysis [118], the appearance of local inhomogeneities [120], the manifestation of gel eff t [78], parallel course of catalytic and noncatalytic reactions [68]. It is probably true that the phenomena listed above may in one form or another show up in specific processes and make their contribution into self-acceleration of a curing reaction. 

Malkin and Kulichikin (1991) initially reviewed the rheokinetics of cured polymers and highlighted the first empirical chemorheological models. They showed that for a simple homogeneous reaction with no diffusion limitations or gel effects for reacting epoxy-resin systems the chemoviscosity could be described by... 

The most important problem of rheokinetics remains the analysis of distribution of the residence times, especially for the stirred tank reactors. To develop a reasonable hydrodynamic model, which is physically proved and mathematically simple and takes into account the effect of a sharp viscosity growth is the main problem. 

The important problems include the control of polymerization reactors containing rheokinetic liquids. These problems have not been solved in many respects even for more simple situations. Both mathematical modelling and physical understanding of the process are the key problems [112]. 

In the third and last chapter the pre-reaction and nozzle design are the main part of the discussion. The optimization is first done theoretically with the combination of a kinetic and thermodynamic model from the literature with a novel rheokinetic approach. Tests of the pre-reaction nozzle are done without spraying in a dripping mode to verify the theoretical models. 

Until now the viscosity function has just been measured without a relationship to the kinetic of the reaction. The model of Malkin and KuUchiklim was introduced and their advantages and problems were discussed earlier. Nevertheless, a complete description of the rheokinetics is not the focus of this investigation. But a more detailed understanding in the relationship of viscosity and the polymerization is found, when stopping the progress of polymerization in the rheometer. In Fig. 20.18 results from stop test at certain stop times are shown. With the determination of the conversion at different stop times at different concentrations of acrylic acid, the... 

But it is also reconunended to do further investigations on the rheokinetics. Different monomers or solvents have to be analyzed in detail. Another interesting investigation is the analysis of the changing viscosity during drying. Additional information can support drying models of drops that consist of suspensions or emulsions. 

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