Acceleratory reaction

When k (0.01) k2 (0.0005) as shown in the middle simulation, the rate of degradation remains constant from about 400 sec. to 2000 sec. and represents zero order kinetics over most of the degradation. At relative values of k. and k2 of 1 to 20 and 20 to 1 the initial and final portions of these degradations are characteristic of acceleratory reactions. When ratios are 1 to 100 and 100 to 1, the acceleratory characteristics are not seen and the reactions are truly first order and zero order. The upper simulation shows a typical acceleratory reaction in which k- = k2 = 0.0008. An alpha-time plot for the data of the upper simulation gives the typical S-shaped curve of an acceleratory reaction. 

Curve C is characterized by the rapid onset of an acceleratory reaction and no induction period is found. Any initial small evolution of gas will probably be obscured by onset of the main reaction. Such behaviour is found in the decompositions of iron(II) and iron(III) oxalates [91]. 

Young [56] described a somewhat different pattern of kinetic behaviour for decomposition of the same salt. Again, there was an initial reaction of a surface impurity (about 2%) by a first-order process (f, = 121 kJ mol ). The subsequent acceleratory reaction, perhaps delayed by the initial process, was fitted by the power law (n = 3). This is attributed to the growth of a constant number of nuclei present at time, tg, and, because the nimiber of such nuclei is slightly temperature dependent, the value of E, for interface advance is 209 kJ moT . The mechanism of reaction was not developed fiulher. 

The acceleratory reaction, as mentioned previously, is usually attributed to the development of metal nuclei, M , which form after sufficient decomposition has occurred ... 

The absence of an acceleratory reaction, caused by filtering the 180 nm line from the spectrum of a mercury lamp, was discussed in the previous section. Observations for NaN3, however, conflict, some showing an acceleratory reaction and some not showing one. The differences may be due to an impurity or... 

It has already been established that (1) PVC decomposes in the temperature range 220-240°C to the extent of 60 to 90% by an acceleratory reaction in which the time to reach the maximum rate depends upon the chain length, (2) the initiation reaction is separate from the zip reaction and is very much dependent upon the presence of hydrogen chloride, and (3) the unzipping reaction is not stopped even by long exposure to the atmosphere. 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the... 

Fig. 1. Generalized a—time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory) B, induction period C, acceleratory period D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate) E, deceleratory (or decay) period and F, completion of reaction.

The strongly acceleratory character of the exponential law cannot be maintained indefinitely during any real reaction. Sooner or later the consumption of reactant must result in a diminution in reaction rate. (This behaviour is analogous to the change from power law to Avrami—Erofe ev equation obedience as a consequence of overlap of compact nuclei.) To incorporate due allowance for this effect, the nucleation law may be expanded to include an initiation term (kKN0), a branching term (k N) and a termination term [ftT(a)], in which the designation is intended to emphasize that the rate of termination is a function of a, viz. 

Having identified the kinetic relation applicable to the data for a particular reaction by the general techniques outlined in the preceding paragraph, it is necessary to confirm linearity of the appropriate plot of the function f(a) against time. The special problems which relate to the induction period, the acceleratory and the deceleratory regions are conveniently considered separately. 

Kinetic analyses during the acceleratory stage of reaction, therefore, may necessitate corrections to both variables, (a — a0) and/or (t — f0)> and the plots used to identify the rate equation may be insensitive. Again, the importance of microscopic or other independent observations, is obvious. 

While it is generally true to state that reaction rates increase with temperature, such a qualitative statement is not specific enough to be useful and in some circumstances can be incorrect, e.g. at high a values when the deceleratory character of the reaction may be sufficiently great to offset the acceleratory effect of a slow temperature rise. 

Dehydroxylation of the clay mineral kaolinite [71,626—629] is predominantly deceleratory and sensitive to PH2o (Table 11). Sharp and co-workers [71,627] conclude that water evolution is diffusion controlled and that an earlier reported obedience to the first-order equation is incorrect. A particularly critical comparison of a—time data is required to distinguish between these possibilities. Anthony and Garn [629] detected a short initial acceleratory stage in the reaction and concluded that at low Ph2o there is random nucelation, which accounts for the reported... 

Hofer et al. [671] observed that the decompositions of Ni3C and Co2C (the iron compounds melt) obeyed the zero-order equation for 0.3 < a < 0.9 (596-628 K and E = 255 kJ mole-1) and 0.2 < a < 0.75 (573-623 K and E = 227 kJ mole-1), respectively. The magnitudes of the rate coefficients for the two reactions were closely similar but the nickel compound exhibited a long induction period and an acceleratory process which was not characteristic of the reaction of the cobalt compound. Decomposition mechanisms were not discussed. 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

The kinetic observations reported by Young [721] for the same reaction show points of difference, though the mechanistic implications of these are not developed. The initial limited ( 2%) deceleratory process, which fitted the first-order equation with E = 121 kJ mole-1, is (again) attributed to the breakdown of superficial impurities and this precedes, indeed defers, the onset of the main reaction. The subsequent acceleratory process is well described by the cubic law [eqn. (2), n = 3], with E = 233 kJ mole-1, attributed to the initial formation of a constant number of lead nuclei (i.e. instantaneous nucleation) followed by three-dimensional growth (P = 0, X = 3). Deviations from strict obedience to the power law (n = 3) are attributed to an increase in the effective number of nuclei with reaction temperature, so that the magnitude of E for the interface process was 209 kJ mole-1. 

The decomposition kinetics of mercury fulminate [725] are significantly influenced by ageing, pre-irradiation and crushing these additional features of reaction facilitated interpretation of the observations and, in particular, the role of intergranular material in salt breakdown. Following a slow evolution of gas ( 0.1%) during the induction period, the accelerator process for the fresh salt obeyed the exponential law [eqn. (8)] when a < 0.35. The induction period for the aged salt was somewhat shorter and here the acceleratory process obeyed the cube law [eqn. (2), n = 3] and E = 113 kj mole-1. 

Singh and Palkar [726] identified an initial deceleratory reaction in the decomposition of silver fulminate. This obeyed first-order kinetics (E = 27 kJ mole-1) and overlapped with the acceleratory period of the main reaction, which obeyed the power law [eqn. (2), n = 2] with E = 119 kj mole-1. The mechanism proposed included the suggestion that two-dimensional growth of nuclei involved electron transfer from anion to metal. 

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