Intrinsic growth kinetics

For intrinsic growth kinetics C is the interfacial solution concentration of solute. The rate law may be expressed in terms of relative supersaturation, cr. 

Chain growth during the Fischer-Tropsch synthesis is controlled by surface polymerization kinetics that place severe restrictions on our ability to alter the resulting carbon number distribution. Intrinsic chain growth kinetics are not influenced strongly by the identity of the support or by the size of the metal crystallites in supported Co and Ru catalysts. Transport-limited reactant arival and product removal, however, depend on support and metal site density and affect the relative rates of primary and secondary reactions and the FT synthesis selectivity. 

Thus, whether a metal can be deposited by electroless deposition onto a silicon surface depends on the redox potential and its relative position to the band edges and on whether the silicon can be dissolved under those conditions. On the other hand, whether the deposition can be sustained to cover the entire surface area depends, on nucleation and growth kinetics of the deposits, the catalytic effect of the deposits on silicon dissolution and hydrogen evolution and the evolution of the morphology of the surface. The formation of a continuous and uniform metal film by electroless deposition is intrinsically difficult because a certain amount of bare silicon surface area is required for silicon dissolution in order to sustain the deposition. 

The parameter K is the carrying capacity of the system, at which the growth rate vanishes. If we nondimensionalize the system by measuring the density in terms of the carrying capacity, p = p/K, and rescale time by the intrinsic growth rate, t = rt, then we obtain again KPP kinetics ... 

The overall growth kinetics is thus second order and exhibits diffusion dependence, with intrinsic surface integration kinetics (not shown) being greater than second order implying a polynuclear growth mechanism. 

Conventionally used macrokinetic equations to model intrinsic FT kinetics essentially use adapted versions of Eq. (16.16a), which we find valid only within the polymerization model. It agrees with the assumption that the rate of chain growth is to be fast compared to formation. The effect of variation of k, which... 

Having discussed some equilibrium properties of a crystal, we now outline and contrast the bases of the growth theories which will be dealt with in more detail later. The theories may be broadly split into two categories equilibrium and kinetic. The former [36-42] explain some features of the lamellar thickness, however the intrinsic folding habit is not accounted for. Therefore, at best, the theory must be considered to be incomplete, and today is usually completely ignored. We give a brief summary of the approach and refer the interested reader to the original articles. The kinetic theories will be the topic of the remainder of the review. 

It is argued that the kinetics of the limited coalescence process is determined by the uncovered surface fraction 1 - t and by the rate of thinning (drainage) of the films formed between the deformable droplets [46,47], The homogeneous and monodisperse growth generated by limited coalescence is intrinsically different from the polydisperse evolution observed for surfactant-stabilized emulsions. As noted by Whitesides and Ross [48], the mere fact that coalescence halts as a result of surface saturation does not provide an obvious explanation of the very... 

The role of hydrate intrinsic kinetics has been more recently suggested to play a smaller role in hydrate growth in real systems than heat and mass transfer effects. In view of this, the discussion on the kinetics models is only briefly presented here. For a more thorough treatment, the reader is referred to the original references (Englezos et al., 1987a,b Malegaonkar et al., 1997). 

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