Rheokinetic methods

In the papers quoted above, the authors followed the crystallization kinetics from calorimetric data. From the point of view of rheokinetic methods discussed here, no less interesting is one more example of describing crystallization kinetics given in Fig. 26, where there is a comparison of experimental (obtained in Ref. [126]) and calculated by Eq. (18) time dependences of the relative elastic modulus of crystallization of cis-l,4-polybutadiene. A good agreement between experimental and calculated data implies the possibility of describing the crystallization kinetics, with the help of formulas of the type of Eq. (18). 

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. 

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 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. 

Among physicochemical methods for studying curing processes, rheokinetics is the closest to calorimetry, also yielding combined characteristics of the chemical dynamics of the process. Due to this, there was carried out a comparison of quantitative curing parameters obtained by rheological and calorimetric methods. 

The rheokinetic degree of conversion means a conversion dependent parameter measurwl by a rheological method. 

When the time changes are characterized by rheological methods the apparent autocatalytic shape of (t) may be generated by a non-linear dependence of the rheokinetic parameter on / . For instance, it can be shown that, if p is the storage modulus G, G is proportional to the concentration of elastically active... 

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. 

It should be noted that all investigations of flow stability of polymerizing liquids are few in number and have been carried out up till now only for unidimensional problems. The problem of stability of steady rheokinetic two-dimensional flows to local hydrodynamic perturbations has not been discussed in the literature yet. Obviously the problem can be solved (the solution is difficult from the technical point of view), for example, by numerical methods solving the problem on unsteady development of the flow of polymerizing mass directly after a forced local change of the profile of the flow velocity. 

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). 

In contrast to the later used specific viscosity, rjs is the viscosity of the diluted polymer solution and i/o is the viscosity of the pure solvent. With consideration of (20.24) Malkin developed a method to connect a measured viscosity diuing a polymerization with the kinetics of the reaction and called this method, rheokinetics [41]. The initial equation from 1980 is shown in (20.25). 

Finally the development of the shear viscosity diulng polymerization is calculated by (20.39), representing the result of the rheokinetics (compare Fig. 20.18 left) with an addend, that considers the temperature dependency of the viscosity of the aqueous acrylic acid solution. Equations (20.37) and (20.38) can also be calculated by the Runge-Kutta method, whereby (20.41) is calculated separately and with the resulting conversion of (20.39). 

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