Kinetics, nucleation induction period

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

Breck (1) was the first to investigate the reaction in the hydrothermal formation of zeolites. He found that there is always some delay before crystallization starts. This so-called induction period can be reduced by raising the temperature or alkalinity of the reaction batch (2). As Sand (8) reported in 1968 in connection with the formation of mordenite, the nature of the Si02 material also has a decisive influence on the reaction and the nature of the zeolite crystals. The induction period as a nucleation phase is discussed by Domine and Quobex (4) in connection with kinetic investigations relating to mordenite formation. 

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 reaction of this solid [48] was the first [133] example of Smith-Topley behaviour recognized and studies of this rate process have continued. Flanagan and Kim [133] showed that irradiation decreased the induction period to dehydration and the rate of water evolution rapidly reached a maximum value which was maintained between 0 < nr < 0.4. Water evolution was more rapid than that found for unirradiated salt and the value of , was decreased. Irradiation damage to the crystal promoted nucleation and there was rapid initial establishment of a constant area of reaction interface (the contracting volume equation approximates to zero-order kinetics at low values of nr). There was also evidence [134] that preirradation aided recrystallization during vacuum dehydration. 

While several reactions exhibit sigmoid ar-time relationships, including an induction period, such kinetic behaviour does not necessarily imply the occurrence of a nucleation and growth mechanism, but could be a consequence of initial impurity removal, or the necessity for the generation of an appropriate intermediate. 

The kinetics of decomposition of nickel formate [6,7] are sensitive both to the experimental conditions [8] and the reactant structure, ar-time curves for the isothermal decomposition (about 450 K) are usually [8], though not invariably [9], sigmoid and there is microscopic evidence [6] that reaction proceeds through nucleation and growth. The induction period [6] and the shape of the subsequent acceleratory process [8] are influenced by the rapidity with which product water vapour is removed from the vicinity of the reactant. Data fit the Prout-Tompkins equation with , about 100 kJ mol". ... 

Nickel carbide is not stable at steam reforming conditions. The nucleation of the carbon whisker takes place when the concentration of carbon dissolved in the nickel crystal is higher than that at equilibrium. This is reflected by the kinetics (3). After an induction period, the carbon growth proceeds with constant rate (Fig. 1) (8,9). The rate of dissociation depends strongly on type of hydrocarbon with olefins and acetylene being the most reactive (9). 

The crystallization process often follows the mechanism of three-dimensional growth of nuclei after an induction period. Amorphous forms of the same compound made by different methods can have different physical stabilities due to kinetic differences of the crystal nucleation and growth processes [31]. When evaluating the physical stability of amorphous systems, the properties of the crystalline counterpart should also be considered regarding the enthalpic driving force for crystallization and activation energy for nucleation [32]. 

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