Oxidation-enhanced diffusion equation

Equation 36 is divided into the contributions to the diffusion of substitutional impurity under nonoxidizing conditions, DSI, and the enhanced contribution due to oxidation, AD0. Figure 16 shows the data of Taniguchi et al. (44) for oxidation-enhanced diffusion of P and B versus the total number of dopant impurities per square centimeter, QT. The calculated values of DSI and AD0 are shown in comparison with the experimental data. Reasonable agreement is obtained. Thus, Taniguchi s model of self-interstitial recombination with vacancies is consistent with the models of high-concentration diffusion of B and P used by Fair in his calculations. 

In the presence of oxygen, the chemiluminescence intensity (/CL) is significantly enhanced with respect to the emission produced under nitrogen. As the samples are highly oxidized in a diffusion-controlled reaction simultaneous to the emission, reaction (b) in Scheme 3.1 is very fast and the relative concentration of [POO ] will be larger in proportion to that of [P ]. The rate of oxidation (R,) in Equation 3.2 increases under these conditions, the bimolecular termination of peroxy radical, reactions (f) and (g) in Scheme 3.1, is, therefore, predominant. All these parameters can be used to evaluate the degradation in different materials and the effectiveness of antioxidants in the polymer stability. 

As described in the introduction, submicrometer disk electrodes are extremely useful to probe local chemical events at the surface of a variety of substrates. However, when an electrode is placed close to a surface, the diffusion layer may extend from the microelectrode to the surface. Under these conditions, the equations developed for semi-infinite linear diffusion are no longer appropriate because the boundary conditions are no longer correct [97]. If the substrate is an insulator, the measured current will be lower than under conditions of semi-infinite linear diffusion, because the microelectrode and substrate both block free diffusion to the electrode. This phenomena is referred to as shielding. On the other hand, if the substrate is a conductor, the current will be enhanced if the couple examined is chemically stable. For example, a species that is reduced at the microelectrode can be oxidized at the conductor and then return to the microelectrode, a process referred to as feedback. This will occur even if the conductor is not electrically connected to a potentiostat, because the potential of the conductor will be the same as that of the solution. Both shielding and feedback are sensitive to the diameter of the insulating material surrounding the microelectrode surface, because this will affect the size and shape of the diffusion layer. When these concepts are taken into account, the use of scanning electrochemical microscopy can provide quantitative results. For example, with the use of a 30-nm conical electrode, diffusion coefficients have been measured inside a polymer film that is itself only 200 nm thick [98]. 

Regime 1 has been described as erosion-enhanced oxidation, because the scale is thinner than it would have been in the absence of erosion, thus the scaling rate is enhanced. The scale grows under diffusion control but its outer surface is eroded at a constant rate by the erosive flux. This situation can be represented by the relationship given in Equation (9.1) ... 

Although the microscopic mechanism of pit initiation and oxide breakdown is still not fully understood (40, 41), the macroscopic behavior of enhanced local dissolution and diffusion of dissolved metal ions can be described using current-potential (i-E) curves (Figure 3). The solution conditions in a pit create two distinct electrochemical cells. At the bottom of the pit, the oxidation half-reaction is acidic dissolution of Fe (equation 1), which is balanced primarily by reduction of water to hydrogen gas (equation 3). The second cell is at the mouth of the pit, where the halfreactions are dissolution at a passivated iron metal surface (alkaline conditions) and reduction of water or stronger oxidants such as O2 or RX. 

The densifieation of a metal oxide MO is controlled by the diffusion of oxygen vaeancies. The oxide has a native defect structure of oxygen vaeaneies. Develop equations for the defect equilibria and discuss how the densifieation rate can be enhanced. 

Recall that there are a number of reactions where homogeneous catalysis involves two phases, liquid and gas, for example, hydrogenation, oxidation, carbonylation, and hydroformylation. The role of diffusion becomes important in such cases. In Chapter 6, we considered the role of diffusion in solid catalyzed fluid-phase reactions and gas-liquid reactions. The treatment of gas-liquid reactions makes use of an enhancement factor to express the enhancement in the rate of absorption due to reaction. A catalyst may or may not be present. If there is no catalyst, we have a simple noncatalytic gas-liquid heterogeneous reaction in which the reaction rate is expressed by simple power law kinetics. On the other hand, when a dissolved catalyst is present, as in the case of homogeneous catalysis, the rate equations acquire a hyperbolic form (similar to LHHW models discussed in Chapters 5 and 6). Therefore, the mathematical analysis of such reactions becomes more complex. 

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