Rheokinetics

Figure 1.12 Dual stream injection system for in situ rheokinetic study of anionic ring opening polymerization of caprolactam...

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 rheokinetics of polycaprolactam polymerizing in the monomer shows that below 50 percent conversion, the relative complex viscosity versus conversion of the nylon 6 homopolymerization is defined by the phenomenological equation ri / t]Q = exp(19.6 X), where // is the complex viscosity of nylon 6 anionically polymerizing in its monomer, 0 is the viscosity of caprolactam monomer, and X is fractional conversion. 

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. 

Incomplete conversion must also be covered by the rheokinetic equation. A possible version of such an equation is 54... 

In the most general case, curing of an epoxy-based compound can be accompanied not only by self-acceleration at the beginning of the process but also simultaneous slowing of the reaction in its final stage. Therefore the complete rheokinetic equation can be written as follows ... 

Studies of rheokinetics over the whole range of polyester curing is based (as for other materials) on a dynamic method, i.e., on measurements of the time dependence of the dynamic modulus at a fixed frequency, from which the time dependence of the degree of conversion (3(t). The observed dependence P(t) for polyester resins can be analyzed by an equation of the type used for other materials. Thus the following general equation was proposed for the kinetics of curing polyester and epoxy resins 69 72... 

The main rheokinetic problem consists of the determination of the time dependence of the degree of conversion (3(t) and the correlation between (3(t) and the changes in the rheological properties of the reactants. One possible kinetic function (3(t) was discussed in Section 2.2. In considering the rheological properties of the reactive medium, we can neglect non-Newtonian... 

Real examples illustrating different types of time dependences of viscosity, can be found elsewhere.52 It is worth mentioning that the rheokinetics of polymerization, even for a specific type of polymer (for example, polyurethane) depends on the composition, which determines both the kinetics of the process and the structure of the newly formed polymer. Clearly, the important factor is whether a linear or three-dimensional polymer is formed. In the first case, the viscosity increases... 

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

These equations must be supplemented by a kinetic equation for the time dependence of the degree of conversion P(t), and the dependence of the viscosity of a reactive mass on (3, temperature, and (perhaps) shear rate, if the reactive mass is a non-Newtonian liquid. The last two terms in the right-hand side of Eq. (2.89) are specific to a rheokinetic liquid. The first reflects the input of the enthalpy of polymerization into the energy balance, and the second represents heat dissipation due to shear deformation of a highly viscous liquid (reactive mass). 

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. 

One of most popular techniques for dynamic mechanical analysis is the torsion pendulum method. In a modification of this method designed to follow curing processes, a torsion bar is manufactured from a braid of fibers impregnated with the composition to be studied this is the so-called torsional braid analysis (TBA) method.61 62,148 The forced harmonic oscillation method has been also used and has proven to be valuable. This method employs various types of rheogoniometers and vibroreometers,1 9,150 which measure the absolute values of the viscoelastic properties of the system under study these properties can be measured at any stage of the process. The use of computers further contributes to improvements in dynamic mechanical analysis methods for rheokinetic measurements. As will be seen below, new possibilities are opened up by applying computer methods to results of dynamic measurements. 

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. 

As a first approximation, the several authors assumed a fixed constant parabolic velocity profile.193,194 However, this approach is generally inadequate for a rheokinetic liquid because, first, real velocity profiles have a very different shape (as will be demonstrated below), and second,... 

The investigation by Lynn and Huff201 was the first one in which the true velocity profiles during polymerization in a tubular reactor were determined. The idea of the dependence of the hydrodynamic field on the varying rheokinetics during a chemical reaction is quite fruitful and has... 

Figure 4.25. Profiles of axial velocities in the flow of a rheokinetic liquid through a tubular reactor. Row rate increases from (a) to (c). The dashed lines denote the boundary between the high-viscosity product (high degree of conversion) and the low-viscosity reactant (breaking through stream).

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