Self-acceleration effect

Malkin s autocatalytic model is an extension of the first-order reaction to account for the rapid rise in reaction rate with conversion. Equation 1.3 does not obey any mechanistic model because it was derived by an empirical approach of fitting the calorimetric data to the rate equation such that the deviations between the experimental data and the predicted data are minimized. The model, however, both gives a good fit to the experimental data and yields a single pre-exponential factor (also called the front factor [64]), k, activation energy, U, and autocatalytic term, b. The value of the front factor k allows a comparison of the efficiency of various initiators in the initial polymerization of caprolactam [62]. On the other hand, the value of the autocatalytic term, b, describes the intensity of the self-acceleration effect during chain growth [62]. 

Experiments have confirmed that the pre-exponential factor Ko and the constant co, which characterizes the self-acceleration effect, both depend on the concentration of the catalytic complex, i.e., on the concentrations of the catalyst [C] and the activator [A]. On the basis of purely chemical... 

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. 

Various experiments show that in some cases the kinetics of curing cannot be described by a phenomenological equation of the n-th order at any reasonable values of n [113, 114]. In a number of cases, the kinetics of curing processes is adequately described by a phenomenological equation which takes into account the self-acceleration effect [115] ... 

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 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. 

Markovic and co-workers [13] investigated the effects of the phenol to formaldehyde ratio used for the preparation of novolac and the nature of methylene linkages on the curing behaviour of the novolac/HMTA system using rheological studies. Cure kinetics were described by a third-order phenomenological equation, which took into account the self-acceleration effect that arises from the chemical reaction and phase separation. The reaction rate was found to increase with an increase in phenol to formaldehyde ratio. For the same phenol to formaldehyde ratio, the reaction rate increased with an increase in o, o methylene linkages (Table 2.2). 

Since the early days of using PVC separators in stationary batteries, there has been a discussion about the generation of harmful substances caused by elevated temperatures or other catalytic influences, a release of chloride ions could occur which, oxidized to perchlorate ions, form soluble lead salts resulting in enhanced positive grid corrosion. Since this effect proceeds by self-acceleration, the surrounding conditions such as temperature and the proneness of alloys to corrosion as well as the quality of the PVC have to be taken carefully into account. 

Thus, the process of PAN transformation under the effect of IR radiation proceeds with considerable self-acceleration. The irradiation of uniaxially oriented PAN films gives a polymer with a distinct anisotropy of optical properties, dichroism in the visible spectral region in particular. Figure 8 presents dichroism curves [D =/(X)] at various angles (ip) between the polarization plane and the orientation axis. The same figure shows the dependence D =f(uniaxially oriented film. 

This function corresponds to the first order kinetic equation (first term on the right-hand side of the equation) and also reflects the effect of self-acceleration (second term on the right-hand side of the equation) the quantitative measure of this effect is the constant co. Thus the reaction rate is determined by two independent constants co and K. The fit of this equation to experimental data is illustrated in Fig. 2.4. The effect of self-acceleration in anionic polymerization of e-caprolactam was also discussed in other publications, 33 35 The kinetic equation of isothermal polymerization based on Eq. (2.13) can be written as... 

It is interesting to note the following rule applying to a homologous series of activators the higher the initial reaction rate (higher values of k) the smaller the effect of self-acceleration (lower values of m). A typical example demonstrating the pattern of kinetic curves for the systems with different activators listed in Table 2.1 is shown in Fig. 2.7. 

The treatment of kinetic effects in anionic polymerization of e-caprolactam in terms of selfacceleration is now quite conventional thus it is considered incorrect to use first- or second- order kinetic equations to describe the kinetics of this reaction, although this was attempted in some early publications. However, the analytical representation of the kinetic function f(P) need not be like Eq. (2.14). For example, the same qualitative effect was observed in one publication,36 which was described in other publications as self-acceleration. A different kinetic function was derived from the proposed set of elementary reactions ... 

A quantitative kinetic model of the polymerization of a-pyrrolidine and cyclo(ethyl urea) showed,43 that two effects occur the existence of two stages in the initiation reaction and the absence of an induction period and self-acceleration in a-pyrrolidine polymerization. It was also apparent that to construct a satisfactory kinetic model of polymerization, it was necessary to introduce a proton exchange reaction and to take into consideration the ratio of direct and reverse reactions. As a result of these complications, a complete mathematical model appears to be rather difficult and the final relationships can be obtained only by computer methods. Therefore, in contrast to the kinetic equations for polymerization of e-caprolactam and o-dodecalactam discussed above, an expression... 

It is interesting to note the following results cited in these publications. First, the sum of the exponents m + n = 2 which diminishes the number of arbitrary constants. Second, m and n do not depend on temperature (changes of both constants with temperature were mentioned only in74). Third, while ki and k2 are strongly temperature dependent functions, their ratio which characterizes the effect of self-acceleration is almost independent of temperature. This was also mentioned above in the discussion of self-accelerating kinetics equations for lactam polymerization. Values of the constants m and n according to the experimental data from several publications are listed below ... 

Dendrimers usually exhibit spherical (isotropic) shape. However, wedge-like dendrimer fragments ( dendrons ) that have been attached to linear polymers as side groups can be used to create anisotropic nanocylinders , leading to uncoiling and extension of the polymer chains. Synthetic macromolecules of this type can be visualized directly on surfaces and their contour length determined from the images. Unexpected acceleration effects in the self-encapsulated polymerization of dendron monomers used to prepare such polymers as well as the structural consequences of dendritic pieces of cake on linear polymer chains are discussed. 

Effect of Reaction Products. The reaction of HP-2 is self-accelerating and suggests autocatalysis by reaction products. The effect of two of the reaction products are given below. 

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