Surface Reaction-Controlled Growth

The second case we consider is that of surface reaction-controlled growth, namely, when the rate of particle growth is controlled by the rate at which adsorbed A on the particle surface is converted to another species B. Thus we take, as the simplest representation of such a situation, the sequence. 

If the concentration of adsorbed A on the surface is Q, and the rate of conversion to B is first order, with rate constant ks, the rate of gain of particle mass due to the surface reaction is 4tt RpM ksCs- At steady state this rate must equal the rate of diffusion of molecules of A to the surface, which is given by (12.9) or the equivalent (12.114). Thus 

Let us assume that adsorption equilibrium can be expressed as a relation of the form 

The two terms in the denominator of (12.125) correspond to the rates of surface reaction and mass transfer from the gas phase. When the surface reaction is the rate-determining step, its rate is slower than the mass transfer rate. Mathematically this means that the second term in the denominator of (12.125) dominates the first term and (12.125) reduces to 

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Surface reaction controlled growth Diffusion-controlled growth... 

Analogously, if cs c c the growth rate is surface reaction controlled. See Figure 1. 

The remarkable goodness of fits (x2 = 0.95 and R2 = 0.989) over the entire range of experimental data by the mixed diffusion-reaction control model is shown by a thick solid curve in Figure 9b. Thus, the growth of the PVP-capped ZnO nanorods deviates sufficiently from the diffusion-limited Ostwald ripening model and follows a mechanism involving both diffusion-control and surface reaction control. 

Analogous to surface reaction-controlled crack growth in gaseous environments, electrochemical reaction-controlled crack growth is given by ... 

The main objective of this section is to theoretically compare aerosol size spectra evolving by the mechanisms of diffusion-, surface reaction-, and volume reaction-controlled growth. The results will provide a basis for the interpretation of atmospheric and laboratory aerosol size spectra with respect to the original growth mechanisms. 

If a crystallization process were entirely diffusion-controlled or surface reaction controlled, it should be possible to predict the growth rate by fundamental reasoning. In the case of diffusion-controlled growth, for example, the molecular flux, F (mols cm ) is related to the concentration gradient, dc/dx, by... 

The growth kinetics of this process are reported to be second order and surface reaction controlled. The precipitation of silver iodide in ethanol by the reaction... 

Reactions of the general type A + B -> AB may proceed by a nucleation and diffusion-controlled growth process. Welch [111] discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. 

In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process and the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased. 

Massive barite crystals (type C) are also composed of very fine grain-sized (several xm) microcrystals and have rough surfaces. Very fine barite particles are found on outer rims of the Hanaoka Kuroko chimney, while polyhedral well-formed barite is in the inner side of the chimney (type D). Type D barite is rarely observed in black ore. These scanning electron microscopic observations suggest that barite precipitation was controlled by a surface reaction mechanism (probably surface nucleation, but not spiral growth mechanism) rather than by a bulk diffusion mechanism. 

Nielsen, A.E. (1959b) The kinetics of crystal growth in barium sulphate precipitation. 111. Mixed surface reaction and diffusion-controlled rate of growth. Acta Chem. Scand., 13, 1680-1686. 

The kinetics of CO oxidation from HClOi, solutions on the (100), (111) and (311) single crystal planes of platinum has been investigated. Electrochemical oxidation of CO involves a surface reaction between adsorbed CO molecules and a surface oxide of Pt. To determine the rate of this reaction the electrode was first covered by a monolayer of CO and subsequently exposed to anodic potentials at which Pt oxide is formed. Under these conditions the rate of CO oxidation is controlled by the rate of nucleation and growth of the oxide islands in the CO monolayer. By combination of the single and double potential step techniques the rates of the nucleation and the island growth have been determined independently. The results show that the rate of the two processes significantly depend on the crystallography of the Pt surfaces. 

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