Nucleation first-order kinetic model

Many high-pressure reactions consist of a diffusion-controlled growth where also the nucleation rate must be taken into account. Assuming a diffusion-controlled growth of the product phase from randomly distributed nuclei within reactant phase A, various mathematical models have been developed and the dependence of the nucleation rate / on time formulated. Usually a first-order kinetic law I =fNoe fi is assumed for the nucleation from an active site, where N t) = is the number of active sites at time t. Different shapes of the... 

The dehydration of kaolinite has been the subject of several kinetic studies and Brett et al. [1] summarize the salient features of the mechanisms proposed for the sequence of reactions by which kaolinite is converted to mullite (920 to 1370 K). The first step, water loss, is most satisfactorily described by a two-dimensional diffusion equation. Brindley et al. [57] proposed this model from isothermal kinetic measurements (670 to 810 K) and reported a marked increase of in a maintained pressure of water vapour. Anthony and Gam [58] concluded that random nucleation is rate limiting at low pressures of water vapour and that this accounts for reports of first-order kinetic behaviour. Increase in the rate of nucleation, as the (HjO) is increased, is ascribed to a proton transfer mechanism, and acceleration of the growth process may result from contributions due to the onset of the reverse reaction. 

The SECM theory for the first-order process was developed [66a] and applied to dissolution of the (100) face of copper sulfate single crystal, while the second-order kinetic model was shown to describe well the dissolution of potassium ferrocyanide trihydrate [66c]. By considering a dislocation-free crystal surface on which dissolution sites are only nucleated above a certain critical value of the undersaturation, one can also model an oscillatory dissolution process [66b]. In all cases, the change in geometry caused by dissolution of the substrate and electrodeposition at the tip was neglected. 

Under hydrothermal conditions (150-180 °C) maghemite transforms to hematite via solution probably by a dissolution/reprecipitation mechanism (Swaddle Olt-mann, 1980 Blesa Matijevic, 1989). In water, the small, cubic crystals of maghemite were replaced by much larger hematite rhombohedra (up to 0.3 Lim across). Large hematite plates up to 5 Lim across were produced in KOH. The reaction conditions influenced both the extent of nucleation and crystal morphology. The transformation curve was sigmoidal and the kinetic data in water and in KOH fitted a first order, random nucleation model (Avrami-Erofejev), i.e. 

State may be incorrect in complex rate processes where there is reactant melting, (iii) Commercial software for kinetic analysis sometimes restricts coverage to reaction orders, and the wider range of rate equations (Table 3.3.) is simply not considered, (iv) Some specific reaction models have the same form as reaction orders. For example, random nucleation within a large number of small crystals can be regarded as formally identical with a first-order reaction. 

As illustrated in Fig. 10, the concentration of FeO(g) increases rapidly at the flame front, with a similar rate of increase for each precursor feed rate. This is followed by a decrease in the FeO(g) concentration due to the conversion of the vapor to the particle phase. The two processes of precursor oxidation (FeO(g) formation) and that of particle formation (FeO(g) consumption) take place simultaneously however, the profiles indicate that the precursor oxidation is the faster of the two initially. This behavior is expected since one might approximate the FeO(g) formation rate to be (pseudo) first order with respect to the precursor concentration due to the excess oxygen, while the consumption (at least at early times) will be proportional to the square of the FeO(g) concentration resulting from FeO(g) dimerization. An analysis of this type has been performed by expressing the particle formation or nucleation rate as a kinetic process (6,11-13) details of which are presented in this paper in the section on modeling. 

First theoretical interpretations of Me UPD by Rogers [3.7, 3.12], Nicholson [3.209, 3.210], and Schmidt [3.45] were based on an idealized adsorption model already developed by Herzfeld [3.211]. Later, Schmidt [3.54] used Guggenheim s interphase concept" [3.212, 3.213] to describe the thermodynamics of Me UPD processes. Schmidt, Lorenz, Staikov et al. [3.48, 3.57, 3.89-3.94, 3.100, 3.214, 3.215] and Schultze et al. [3.116-3.120, 3.216] used classical concepts to explain the kinetics of Me UPD and UPD-OPD transition processes including charge transfer, Meloiy bulk diffusion, and nucleation and growth phenomena. First and higher order phase transitions, which can participate in 2D Meads phase formation processes, were discussed controversially by various authors [3.36, 3.83, 3.84, 3.92-3.94, 3.98, 3.101, 3.110-3.114, 3.117-3.120, 3.217-3.225]. 

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