Rheokinetic effects

The manufacture of products by reactive molding results in the superposition of interrelated chemical and physical phenomena. These include polymerization, crystallization, vitrification, heat transfer, rheokinetic effects, changes in the physical properties and volume of a material injected into a mold. It is quite natural that special experimental methods are required to study and control the complex processes which take place in molds. 

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. 

However, rheokinetic effects cause the develproducts accumulate on the walls and in the axial zone the flow is accelerated, i.e. the feed rate of the reactants increases. As a result, the Vf = U,. equilibrium is violated, the front line is distmted and its central part is displaced towards the ouq ut. Consequently, the temperatiure becomes lower, the rate of combustion dr<, and the feed—combustion equilibrium is violated still more. Also, the frcmt region is cooled down and is transferred out of the tube. Therefore, for a rheokinetic liquid (polymerizing medium with a sharp viscosity growth), a low-temperature condition for the process is the only steady-state solution. The polymerization front normal to the flow can exist only as an unsteady state and this solution is unstable. 

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. 

For the case where complete conversion is reached (i.e., p -> 1 when the reaction time is sufficiently long), the following rheokinetic equation, which assumes a self-acceleration effect, is... 

The occurrence of self-acceleration during curing of epoxy resins and epoxy-based compounds was proven by rheokinetic and calorimetric methods.53 This phenomenon can be treated formally in terms of an induction period (when the reaction is very slow in the initial stage of a process), followed by a constant rate. However, it seems preferable to use a single kinetic equation incorporating the self-acceleration effect to describe reaction as a whole. Such a kinetic equation contains only a limited number of constants (K and co in Eq. (2.33)) and allows easy and unambiguous interpretation of their dependencies on process factors. 

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. 

Thus, a combination of the given results indicates that rheokinetic phenomenology of curing of reactive compounds takes into account the mechanisms of both chemical reactions and phase paration occurring as a result of chemical conversion. As a consequence, a self-acceleration effect exists in the processes of curing of oligomers irrespective of a specific mechanism of the reaction. 

An analysis has shown that the characteristic feature of rheokinetics of curing with phase separation is the presence of a self-acceleration effect. Therefore, the rheokinetic equation of curing includes a multiplier, which describes the variations of the reaction rate. However, in some cases interesting deviations from this general rule are observed. 

Rheokinetic analysis shows that rheokinetic equations su ested to describe changes in viscosity and elastic modulus reflect the characteristics of this process. Therefore, the nature of the viscosity increase up to the gel point is defined not only by a variation of the molecular structure of the material but sometimes also by the effect of formation of a new phase (microgel) from particles of a cured product. 

Rheokinetic phenomenology of curing of oligomers is linked with the phase structure and covers a wide circle of thermoset materials. A self-acceleration effect is characteristic for some of them and if molecular mobility is limited conversion may be incomplete. 

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... 

Proceeding from the estimates of possible viscosity variations caused by non-Newtonian effects and rheokinetic phenomena, it is obvious that the effect of non-Newtonian factors on flow regularities always plays a minor role as a correction factor. The case, when the non-Newtonimi behavior affects qualitatively shear flow, for example, if a reactant acquires the abiUty to slip along e wall of a channel, will be discussed in detail later. 

R tly, theoretical investigatimis were carried out of the effect of hydrocfynamics of polymerizing liquids [Pg.132]

We think that it is an urgent matter to solve concrete problems taking into accoimt all possible peculiarities different empirical relationships (rheological, kinetic), different geometry, various types of representing boundary conditions, organization of heat and mass transfer, etc. The absence of investigations of the effect of non-Newtonian properties of a liquid on the flow mechanisms of rheokinetic media seems to be a gap in the field of theoretical analysis. 

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 effects of cure temperature and amount of catalyst on the rheokinetical behavior of an MF resin can be followed using dynamical mechanical techniques (127), and time-temperature-transformation (TTT) cure diagrams can be constructed using the results of these methods (127-129) (see Dynamic Mechanical Analysis). 

These results show that the evolution of the system in the course of its formation seem to be important from the point of view of understanding the real kinetic conditions of IPN formation and phase separation. Rheokinetic data allow us to study various structural states (from a rheological point of view) in different time periods of the reaction. Of course, the discussion given here is over-simphfied because it is difficult to separate pure kinetic effects that influence the viscosity and viscoelastic behavior from effects connected to simultaneously proceeding microphase separation. 

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