Diffusion-controlled regime

Providing that the potential is sufficiently negative, the kinetics of the reduction reaction in equation (2.125) can usually be rendered fast enough to tip the system into the diffusion-controlled regime, as was shown in the discussion of the Butler-Volmer equation in chapter 1. 

The results presented by Bagley et al. [45] imply that the oxide diffusion coefficient is much smaller in the steady-state regime than in the diffusion-controlled regime where physical bombardment is absent. It may be possible to account for this effect in terms of the diffusive transport model presented earlier by using a smaller oxide diffusion coefficient in the steady-state regime. To explore this possibility, one may set dX/dt= 0 in Eq. 7 to obtain... 

Kinetic information for Eqr reactions is not available from techniques that work in the diffusion-controlled regime. However, again, CV allows determination of kg from the dependence of AEp on v [50, 52, 53]. The transfer coefficient is also accessible from cyclic voltammograms [53]. Often a... 

Comparing these results with the half-equilibration time of the aqueous phase, tm (see table above) we conclude that the aqueous concentration reaches its saturation value well before the exchange process switches from the boundary-layer-controlled to the NAPL-diffusion-controlled regime. Thus, diffusive transport of the diesel components from the interior of the NAPL to the boundary never controls the transfer process. Consequently, the simplex box model described in answer (a) is adequate. 

The existence of the (quasi) steady-state in the model of particle accumulation (particle creation corresponds to the reaction reversibility) makes its analogy with dense gases or liquids quite convincing. However, it is also useful to treat the possibility of the pattern formation in the A + B —> 0 reaction without particle source. Indeed, the formation of the domain structure here in the diffusion-controlled regime was also clearly demonstrated [17]. Similar patterns of the spatial distributions were observed for the irreversible reactions between immobile particles - Fig. 1.20 [25] and Fig. 1.21 [26] when the long range (tunnelling) recombination takes place (recombination rate a(r) exponentially depends on the relative distance r and could... 

Kinetics of the tunnelling recombination depends greatly upon the defect mobility (whether a static tunnelling luminescence regime at low temperatures or the diffusion-controlled regime arising at higher temperatures when defects become mobile) and their spatial distribution. 

In using CVD for microelectronics applications, the deposit thickness must be as uniform as possible. This can best be achieved by conducting the deposition in a surface-controlled, not a diffusion-controlled, regime. 

D Apparent order of chemical reaction in diffusion controlled regime ... 

In the diffusion-controlled regime different equations should be derived, taking into account that the interaction eneigy is now modulated by fluctuations in r between d and infinity. In this case the kind of integration to be performed depends on the model assumed for the diffusional behavior of the system. According to one of the most commonly used models for diffusion [11,12], the following equations have been derived when to is the dominant correlation time ... 

Influence of Sample Thickness and 02 Diffusion. As shown above, the overall conversion of thermal degradation can depend of the sample thickness in the diffusion-controlled regime. Thus, stability comparisons are only valid for samples of comparable thickness. Let us now compare two polymers of glass transition temperatures Tgl and Tg2, oxidized at a temperature T, such that Tgl < T < Tg2. Even if the intrinsic oxidation rates are equal, polymer 1 will appear more unstable than polymer 2 because oxygen diffusion is faster above than below Tg. The thickness of the oxidized layer will be higher for polymer 1 than for polymer 2. 

Analytical detection of constituents in a gas mixture is also feasible by the alternating catalyst temperatures in the temperature region of the diffusion-controlled regime. Even under conditions where the total rate of catalytic... 

At the other extreme, we have higher pressures (smaller diffusion coefficients) and high surface temperatures. Now, any molecule that can make it to the surface will react rapidly, so that the deposition rate will be more limited by diffusion through the gas adjacent to the surface. Since diffusion is weakly dependent on temperature, this type of "diffusion" controlled regime tends to be relatively insensitive to surface temperature. 

The typical epi silicon reactor operates in the diffusion-controlled regime at high rates of deposition. The behavior of such a reactor is governed by the fluid dynamics of multicomponent gases. The gas phase reactions discussed in Chapter 1 are generally neglected. 

In principle, epi reactors that operate in the diffusion-controlled regime could be designed by solving the partial differential equations governing the fluid dynamics16 17 so that deposition rates could be predicted. In fact, such a procedure is generally not followed, since experimental evaluation of the flow behavior seems to be preferred.18... 

During growth of the ApBq layer in the diffusion controlled regime, the condition k0Bi k Bfx is satisfied in equations (1.6) to (1.8). In this case, the rate of growth of the layer is inversely proportional to its total thickness, x, existing at a time, t ... 

During its growth in the diffusion controlled regime with regard to component, ... 

---