Reaction-limited regime

Sec. 12.5 Eslimetion of Dftfusloo- and Reaction-Limited Regimes 12.5.1 Weisz-Prater Criterion for internai Diffusion... 

For the reaction-limited regime (section 7.3.1.2 above), Carr and Bowers [24] give the time constant as... 

Reaction limitation obtains if the rate coefficients of the surface reactions [(4), (5), (6)] are very low compared to the transport steps. Chemical reactions are thermally activated and rates of simple reactions follow Arrhenius behavior. Thus a plot of the logarithm of the deposition rate vs. 1/T is a straight line in the temperature range corresponding to the reaction-limited regime. The slope of this line is determined by the adsorption heats of the reactants and the activation energy of the rate-determining surface reaction step. 

All this is valid only in the catalytic or reaction-limited regime (see Chapter 6). There is another effect of the fractal dimension of the surface on the growth rate and on the morphology of the resulting product. This is the ease of transport of the reactants to the surface before they adsorb and react. In the dialytic regime, e.g., in the case of an Eley-Rideal mechanism with slow diffusion, the reaction occurs mainly on the top of a fractal surface and less on the less accessible parts. The Eley-Rideal expression of the rate is then raised to a power dependent on the dimension of the surface.Higher surface dimensions mean relatively higher reaction rates because the reactants have better accessibility to the surface. 

When a reaction-limited regime occurs the substrate concentration does not change significantly. The effect is even augmented for a higher saturation factor (low enzyme saturation, 0 1), where the reaction rate approaches the first order. 

Lattuada M, Sandkuhler P, Wu H, Sefcik J, Morbidelli M (2003) Aggregation kinetics of polymer colloids in reaction limited regime experiments and simulations. Adv Colloid Interface Sci 103 33-56... 

The remaining four sections will be concerned with problems of uniqueness, stability, and asymptotic behavior of the steady states. The results are in close analogy with those obtained in Section 1.9, especially in regard to the behavior of the system in the transport and reaction limited regimes. 

Reaction limited regime 35 Reaction mechanism 4 Reaction rate 2 Rotation of a vector field 97... 

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