Surface reaction controlled regime

Question Calculate the crossover temperature between the surface-reaction-controlled regime and the diffusion-controlled regime for the active gas corrosion of Ti(s) by HCl(g). In other words, calculate the temperature at which the rates of these two processes are equal. Use the same values provided in Examples 5.2 and 5.3 and assume that Z>hci is independent of temperature. 

Accoring to the processing conditions of a CVD process, supersaturation can be divided into two categories, bulk supersaturation and local supersaturation [13], If a CVD process occurs in the chemical reaction control regime discussed in Section 4.3.4, it is reasonable to assume that the compositions of a gas on the substrate surface equal that in the bulk gas. Accordingly, the expression of supersaturation in Equation (6.2) is used for calculation. However, if a CVD process occurs in the... 

The experimental data are shown In Figure 11a, together with a dotted line, extrapolating the reaction controlled regime to zero time. On the other hand some model calculations have been performed under the assumption that, at the beginning of the experiment, the reaction rate is in the diffusion controlled regime. Then only a restricted spherical shell close to the bead surface Is participating In the substrate conversion. If superimposed on the reaction a time dependent catalyst deactivation occurs, the reactive shell should move to the center of the catalyst particle where active cells are available to substitute for the deactivated cells closer to the surface. 

FIGURE 5.5 Summary of the key kinetic concepts associated with active gas corrosion under the surface reaction, diffusion, and mixed-control regimes, (a) Schematic iUusIration and corrosion rate equation for active gas corrosion under surface reaction control, (b) Schematic illustration and corrosion rate equation for active gas corrosion under reactant diffusion control. (c) Schematic illustration and corrosion rate equation for active gas corrosion under mixed control, (d) Illustration of the crossover from surface-reaction-conlrolled behavior to diffusion-controlled behavior with increasing temperature. The surface reaction rate constant (k ) is exponentially temperature activated, and hence the surface reaction rate tends to increase rapidly with temperature. On the other hand, the diffusion rate inereases only weakly with temperature. The slowest process determines the overall rate. 

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. 

Heat transfer is an extremely important factor in CVD reactor operation, particularly for LPCVD reactors. These reactors are operated in a regime in which the deposition is primarily controlled by surface reaction processes. Because of the exponential dependence of reaction rates on temperature, even a few degrees of variation in surface temperature can produce unacceptable variations in deposition rates. On the other hand, with atmospheric CVD processes, which are often limited by mass transfer, small susceptor temperature variations have little effect on the growth rate because of the slow variation of the diffusion with temperature. Heat transfer is also a factor in controlling the gas-phase temperature to avoid homogeneous nucleation through premature reactions. At the high temperatures (700-1400 K) of most... 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

Initially, when the ApBq layer is very thin, the reactivity of the A surface is realised to the full extent because the supply of the B atoms is almost instantaneous due to the negligibly short diffusion path. In such a case, the condition kom kW]/x is satisfied. Therefore, if the surface area of contact of reacting phases A and ApBq remains constant, chemical reaction (1.1) takes place at an almost constant rate. In practice, this regime of layer growth is usually referred to as reaction controlled. The terms interface controlled regime and kinetic regime are also used, though less suited. 

Variation of catalyst area. The catalytic rate is proportional to the total surface area, A, external and internal, for reactions controlled by surface kinetics. In the case of internal or pore diffusion control, the rate is proportional to A1,2 and is also a function of the catalyst shape and size [49, 53]. Under an external diffusion regime, the catalytic rate is proportional to the external surface area of the catalyst, Aex. 

The kinetics of coating growth is basically dependent on temperatures. A CVD reaction is divided into either surface kinetic or mass transport control. Figure 11 shows a model as how the growth process depends on the surface kinetics and mass control regimes. is the concentration of the bulk gas and is the concentration at the substrate interface. The concentration of the reactants drops from the bulk to the substrate surface and the corresponding mass flux is given by,... 

As is seen in Section B.4, if the reaction rate at the surface and the gas pressure are high enough, then the burning rate is controlled by the rate of diffusion in the gas. The occurrence of this diffusion-controlled regime is well established for carbon combustion [31], [37]-[39]. The following analysis will be restricted to this limit, which ceases to apply if the dimensions of the carbon materials become too small [39], [40], [41]. 

FIGURE 18 Rate-controlling regimes in gas-solid reactions for an impervious solid m is the rate controlled by mass transfer of the oxidizer to the solid s is the rate controlled by surface reaction, (S) solid (B) boundary layer (b) bulk concentration of oxidizer (z) zero concentration of oxidizer (from Mulcahy and Smith [30]). 

From the characteristics of our reactivity curves (presented later), we selected the random pore model developed by Bhatia and Perlmutter as the model can represent the behaviour of a system that shows a maximum in the reactivity curve as well as that of a system that shows no maximum. The maximum arises from two opposing effects the growth of the reaction surface associated with the growing pores and the loss of surface as pores progressively collapse at their intersections (coalescence). In the kinetically controlled regime, the model equations derived for the reaction surface variation (S/S ) with conversion and conversion-time behaviour are given by ... 

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