Activation controlled processes

For purely activation controlled processes, each reaction can be described by a straight line on an E versus Log i plot, with positive Tafel slopes for anodic processes and negative Tafel slopes for cathodic processes. 

The following example illustrates the polarization behavior of carbon steel in a deaerated solution maintained at 25°C with a pH of zero. The solid line in Fig. 5.14 is the polarization plot itself and the dotted lines in this figure represent the anodic reaction in Eq. (5.19) and the cathodic reaction in Eq. (5.20) that describe the corrosion behavior of steel in these conditions. These lines are extrapolated from the linear sections of the plot on either the anodic or cathodic sides of the curve. 

While it is relatively easy to estimate the corrosion potential from the sharp peak observed at -0.221 V vs. standard 

The second example shows the carbon steel polarization behavior when exposed to a deaerated solution maintained at 25°C and pH of five. The mixed potential diagram of this system is shown in Fig. 5.15. The shift of the E to a more negative value of -0.368 V vs SHE should be noted. The modeled projected lines provide an estimate of the corrosion current density of 4 pA cm in this case and this current translates into a penetration rate of 0.05 mm 

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Active-passive transition It has been shown that /p, the current required to maintain a passive film, increases with temperature at a much greater rate than the critical current for passivation as a result of an activation-controlled process. At some temperature /p will exceed /pri,. and no active-passive transition will be observed, and more important no protection by a passive film is possible because of the high rate of dissolution. At this stage the slow process becomes the diffusion of reactants and control of the rate is... 

Accountability, management practices, 69-70 Active controls, process controls, 98 Active monitoring, management practices, 114... 

In the case of an activation-controlled process, the supporting electrolyte modifies the activation coefficients of the reactants and it is out of the scope of this work to enter in the mathematical treatment. A detailed approach of this case can be found in Simonin and Hen-drawan (2001). 

So far we have concentrated our attention on activation-controlled processes. Since the rate of such processes increases exponentially with potential, it is usually possible to drive them fast enough, to ensure that mass transport becomes the limiting factor. For a measurement to be truly activation controlled, the current must be small compared to the mass-transport-controlled limiting current. The latter is given, as we have seen by... 

Fig. IG Equivalent circuit for an activation controlled process, showing the three basic circuit elements the double-layer capacitance,...

A "small" perturbation in this context is one for which nrjF/vRT 1 or i/i 1. The linearity of the response allows easier and more rigorous mathematical treatment and is, therefore, often preferred. It is interesting to note that a linear response is also obtained when a small perturbation is applied to a system far away from equilibrium. To show this, we write the usual rate equation for an activation controlled process in the linear Tafel region (cf. Eq. 7F) namely ... 

Fig. 4K is discussed later. Suffice it to note here that the relaxation time for the activation-controlled process is inversely proportional to the exchange current density while x, the diffusional relaxation time, is independent of i. Thus, a large value of x /x indicates that the electrode reaction is slow, and vice versa. 

So far we have discussed the properties of the limiting current density at the RDE. What about activation or mixed control For a purely activation-controlled process, the current should be independent of rotation rate, or should at least become independent of it beyond a certain value. If one has mixed control, the activation and mass-Iransport-controlled current densities combine to yield the total current density as the sum of reciprocals, namely... 

Here, for obvious reasons, we confine the discussion to activation-controlled processes thus avoiding complications due to concentration and nucleation overpotentials which are not relevant to the present discussion. 

Basic investigations [58] have shown that the cathodic reduction of CIOJ in alkaline media is an activation-controlled process proceeding at very low rates. Mass balance studies have shown that the CIO3 ion can indeed be reduced to chloride, the reaction being favored only on Fe surfaces, and not on metals such as Co, Ni, Mo, Ti, Hg, and carbon, in smooth form (Fig.,4.2.151. The exact mechanism leading to this specificity is not clear and more fundamental studies are required to decipher the pathways controlling the chlorate reduction process. 

Simple linear regressions between each of the independent variables can be used to produce a correlation matrix. The values of R in this matrix can be used to identify possible covariance problems. Once statistical significance of various factors is established, the corrosion researcher should consider the corrosion processes and first principles in reaction kinetics to evtiluate the consistency of the statistical model with a physical model. Best fits of data to physical models can yield valuable information such as activation energies that can point toward diffusion controlled or activation controlled processes. 

Other recent, interesting studies include that of Nyrkova and Semenov [84,91] on block copolymers. They showed that the activation barrier to micelle formation may be so large that it is kinetically unfeasible at the conventional cmc, as the timescale would be too great. Instead, micelles form at an increased apparent cmc, emphasizing the fact that micellization is indeed an activation-controlled process, and that thermodynamics as well as kinetics must be considered for a complete understanding. 

Z Frequency factor for an activation controlled process Dimensionless Groups ms 3... 

Consider three conditions which can arise when a cathodic process is superimposed on the curve. The three cases are discussed below to illustrate the polarization behavior of activation metals. The three curves representing different activation controlled process with different exchange current densities are shown in Fig. 3.27. The three reactions represent different rates of hydrogen reduction on the metal surface. The three exchange current densities associated with these reduction reactions are shown in Fig. 3.27 by io(H)i> o(H)2 and io(h)3-... 

Figure 3.27 Three curves representing different activation controlled process with different exchange current...

When the fluid velocity increases, diffusion in the boundary layer increases, it no longer controls the corrosion rate which becomes controlled by the interface reaction rate between the solid material and the liquid metal. It is the activation-controlled process. The corrosion rate no longer depends on the fluid velocity. 

Figure 8.1 Equivalent circuit for an activation-controlled process, showing the three basic circuit elements the double-layer capacitance, Qi, the Faradaic resistance, and the residual solution resistance, (a) general (b) ideally polarizable (c) Ideally non-polarizable,...

It is interesting to note that a linear response is also obtained when a small perturbation is applied to a system far away from equilibrium. To prove this, we write the usual rate equation for an activation controlled process in the linear Tafel region... 

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