Acceleratory period

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.

Kinetic data for the decompositions of several metal hydrides are summarized in Table 12 to which the following information can be added. The acceleratory period in the decomposition of BeH2 (a < 0.35) is ascribed [673] to the random formation of metal nuclei followed by linear growth. The increase in rate consequent upon exposure to X-irradia-tion is attributed to enhanced nucleation. Grinding similarly increased the... 

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. 

Hill et al. [117] extended the lower end of the temperature range studied (383—503 K) to investigate, in detail, the kinetic characteristics of the acceleratory period, which did not accurately obey eqn. (9). Behaviour varied with sample preparation. For recrystallized material, most of the acceleratory period showed an exponential increase of reaction rate with time (E = 155 kJ mole-1). Values of E for reaction at an interface and for nucleation within the crystal were 130 and 210 kJ mole-1, respectively. It was concluded that potential nuclei are not randomly distributed but are separated by a characteristic minimum distance, related to the Burgers vector of the dislocations present. Below 423 K, nucleation within crystals is very slow compared with decomposition at surfaces. Rate measurements are discussed with reference to absolute reaction rate theory. 

This expression fitted the acceleratory period of the a—time curves, followed by first-order decay and E = 122 2 kJ mole-1. No disintegration of small crystals was observed but pre-irradiated crystals [909] shattered on completion of the induction period. X-ray diffraction studies [910] confirm the existence of strain during the formation of decomposition product. Addition of small amounts (5% by mass) of ZnO or Th02 accelerated the decomposition of AgMn04 at 388 K. Ti02 reduced the rate, while NiO and Co304 had no effect [911]. 

The addition of nickel formate to magnesium formate significantly reduced the decomposition temperature [1151]. The acceleratory period characteristic of the decomposition of pure Mg(HC02)2 was eliminated and the value of E was substantially diminished. For the double (Zn,Ba) and (Cu,Ba) formates, the rate of decomposition [1152] of the less stable component (Zn or Cu) was slower and that of the more stable component (Ba) more rapid than the values characteristic of pure preparations of these substances. 

The inflexion in curves (A) and ( ) occurs after a decomposition of about 30% of substance. The plots of the acceleratory period are approximately parabolic. The mechanism of the decomposition probably consists of nucleation of sub-grains at the edges and progression of the reaction into the grains with a non-coherent interface. 

Fig. 5.13 General form of curves relating the fraetion of C3S consumed to time in a paste. AB initial reaetion. BC induction period. CD acceleratory period. DE deceleratory period and continuing, slow reaction. Taylor et al. (T25).

At early ages, da/d/ increases markedly with w/s ratio above 0.7 (B56). Moderate variations in specific surface area have little effect on the length of the induction period, but with finer grinding, da/d/ during the acceleratory period increases (K20,O12,B56). The rate of reaction increases with temperature up to the end of the acceleratory period, but is much less affected thereafter (K21), suggesting a change from chemical to diffusion control. Introduction of defects into the CjS shortens the induction period (M53,F20,O12). 

The kinetics up to the middle of the acceleratory period are discussed in the following sections. Those of the later stages have been more thoroughly studied with cement (Section 7.7) and only some aspects are considered here. 

The rate of reaction in the induction and acceleratory periods is controlled by nucleation and growth of the C-S-H formed in the main reaction, the induction period ending when growth begins (S54,O13,F20,B63). 

Thus, first order kinetics and zero order kinetics appear as special cases of the more general kinetics which have been derived on the basis of the zipper mechanism. The zipper model does not invoke the steady state assumption but allows the number of producing sites to increase during the acceleratory period as more zip chains start production and to decrease during the de-celeratory period as more chains are terminating than are starting. 

In reactions of this type, the induction period, if any, may be too short to permit detection and, during this time, there is virtually instantaneous and dense nucleation across all active surfaces. The maximum reaction rate is attained at a low a and, thereafter, the ur-time curve is deceleratory. There is, thus, no sharp distinction between such kinetic behaviour and the later stages of the nucleation and growth processes discussed above. In some early work [42], the influence of slow nucleation and an acceleratory period was removed by artificial initiation of reaction (nucleation) across all surfaces, so that the kinetic analysis was simplified to the consideration of a process advancing inwards from all faces of a crystal of known size and geometry. 

The thermal decomposition of Hg(CNO)2 was studied by Bartlett et al. [70] who were particularly concerned with the effects of ageing, preirradiation and crushing on reaction kinetics. The acceleratory period for the fi esh reactant followed the exponential relation, whereas for the aged salt the acceleratoiy period was described by the cubic law ( = 3 and , = 113 Id mol" ). There was an initial small (< 0.4%) deceleratory evolution of gas. 

The kinetics of decomposition of AgMn04 in vacuum between 378 and 393 K [38] differ fi om the behaviour of KMn04 in that the acceleratory periods of the ar-time curves are described by the modified form of the Prout-Tompkins equation ... 

Many kinetic studies of the thermal decomposition of silver oxalate have been reported. Some ar-time data have been satisfactorily described by the cube law during the acceleratory period ascribed to the three-dimensional growth of nuclei. Other results were fitted by the exponential law which was taken as evidence of a chain-branching reaction. Results of both types are mentioned in a report [64] which attempted to resolve some of the differences through consideration of the ionic and photoconductivities of silver oxalate. Conductivity measurements ruled out the growth of discrete silver nuclei by a cationic transport mechanism and this was accepted as evidence that the interface reaction is the more probable. A mobile exciton in the crystal is trapped at an anion vacancy (see barium azide. Chapter 11) and if this is further excited by light absorption before decay, then decomposition yields two molecules of carbon dioxide ... 

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