Non-stationary kinetics

A number of publications purport to give values for the absolute propagation rate constant kp for the polymerization of isobutyl vinyl ether (Table 2). The values of Okamura et ah, are derived by techniques and arguments which are of doubtful validity [54a] and they seem much too small. Eley s value, derived from an analysis of non-stationary kinetics, is four orders of magnitude smaller than the kp deduced from studies of radiation... 

The solution of the first kind is stable and arises as the limit, t —> oo, of the non-stationary kinetic equations. Contrary, the solution of the second kind is unstable, i.e., the solution of non-stationary kinetic equations oscillates periodically in time. The joint density of similar particles remains monotonously increasing with coordinate r, unlike that for dissimilar particles. The autowave motion observed could be classified as the non-linear standing waves. Note however, that by nature these waves are not standing waves of concentrations in a real 3d space, but these are more the waves of the joint correlation functions, whose oscillation period does not coincide with that for concentrations. Speaking of the auto-oscillatory regime, we mean first of all the asymptotic solution, as t —> oo. For small t the transient regime holds depending on the initial conditions. 

The initial charge distributions, which were recognized as very important, were analyzed in more detail in a number of works [32]. The analysis was extended to multichannel ionization [179], and the role of the excitation lifetime was specified [25]. A few articles devoted to them were published by Murata and Tachiya [26,27]. Earlier these authors studied experimentally the non-stationary kinetics of fluorescence quenching, which was fitted numerically... 

Stationary and Non-Stationary Kinetics of the Photoinitiated Polymerization Yu.G. Medvedevskikh, A.R. Kytsya,... 

When the active centre concentrations change during propagation, the whole polymerization is non-stationary. Kinetically the process becomes more complicated and often even experimental control of the process becomes more difficult. On the other hand, a non-stationary condition can be utilized in studies of the elementary polymerization steps. To this end, the non-stationary phases of radical polymerizations are suitable, where outside these phases the process is essentially stationary [23-25]. Hayes and Pepper [26] called attention to the existence and solution of a simple non-stationary case caused by slower decay of rapidly generated cationic centres. In more complicated cases, exact analysis of the causes of a non-stationary condition is often beyond present possibilities. Information from the process kinetics is often not conclusive. It should be mentioned that, even when the condition d[Ac]/dt = 0 is strictly valid, polymerizations may be non-stationary, particularly in those cases when during propagation the more active form of the centres is slowly transformed to the less active form or vice versa. 

Any of Eqs. [8], [9] and [10] allow the determination of C and also of relevant rate constants in the simplest case defined above. Complications arise, when these rates are time-or polymer yield-dependent. C is seldom time-invariable formation and deactivation of active centers are quite often difficult to express by simple kinetic laws. Nevertheless, the fundamental Eq. [7] should be valid, and Ivanov et al. 35) and Ermakov and Zakharov 6> suggested its modified version applicable to the non-stationary kinetics of polymerization, if only transfer reactions occur. Supposing that kp, ktr, [M], and [X] are time-independent and substituting C by Rp/kp[M], equation ... 

In principle, the knowledge of the momentary concentrations of the active species is not necessary to determine the rate constants (cf. Fig. 14) because both kp and kj can be simultaneously determined by solving equations describing the non-stationary kinetics, as was shown for the cationic polymerization of sts rene by Peppra (partial solution) and for the polymerization of a-epichlorohydrin (complete kinetic solution). 

Table 18. Basie kinetic equations in non-stationary kinetics with chain transfer ... 

At a first glance, it is not so obvious that algebraic models can be used for the description of non-stationary kinetic processes where a description of changes in species concentration is required over time. The key lies in the replacement of the kinetic odes by difference equations ... 

Next, let us consider the non-stationary kinetics of the postpolymerization in the dark. Since, as was noted before, the contribution of the homophaseous process into the total process under the postpolymerization process should be insufficient, we analyzed only the kinetics in the interface layer assuming that w = In the dark period Vim = 0, and... 

Equations (7.40M7.43) thus obtained describe the non-stationary kinetics of methacrylate polymerization (postpolymerization) in the polymer-monomeric phase, taking into account the wide spectrum of characteristic times of the postpolymerization inside the micrograins in the polymer-monomeric phase. 

Results of investigations the stationary and non-stationary kinetics of monomers with one functional group showed that at conversions P > 0.5 two polymeric phases are coexisted, namely first is a monomer-polymeric solution with conversion Pb 0.5 saturated by a polymer, and the second one is solid solution of a monomer in the polymer with the conversion P = 0.8. That is why two films which are polymerized under UV-illumination on different surfaces, even at high general conversion, are easily conjuncted when compressed and after that the layer formed via the postpolymerization process becomes stronger. 

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