Resistance cathode-solution interface

Another governing relationship, however, is Ohm s law, which leads to a dependency of the corrosion current on both the polarization characteristics of the anodic and cathodic reactions and on the total electrical resistance of the system, Rtotal. Rtotal includes the resistance in the metal between anodic and cathodic areas, RM a metal junction resistance if different metals are associated with the two areas, Rac any anode- or cathode-solution interface resistance, Rai and Rci and the solution resistance, Rs. The latter depends on the specific resistivity or conductivity of the solution and the geometry of the anode-solution-cathode system. 

Fig. 1.69 Effect of resistivity of solution on the distribution of corrosion on the more negative metal of a bimetallic couple, (a) Solution of very low resistivity and (b) solution of very high resistivity. Note that when the resisitivity is high the effective areas of the cathodic and anodic metals are confined to the interface between the two metals...

Figure 29.4 shows an example, the energy diagram of a cell where n-type cadmium sulfide CdS is used as a photoanode, a metal that is corrosion resistant and catalytically active is used as the (dark) cathode, and an alkaline solution with S and S2 ions between which the redox equilibrium S + 2e 2S exists is used as the electrolyte. In this system, equilibrium is practically established, not only at the metal-solution interface but also at the semiconductor-solution interface. Hence, in the dark, the electrochemical potentials of the electrons in all three phases are identical. 

An overpotential contribution is required for both the anodic and the cathodic reaction and, in this case, it is mainly to oxidize water at the Pt anode. As copper is deposited and the concentration of Cu ions falls, both the ohmic potential drop IR across the electrolyte and the overpotential decrease. If we assume that the solution resistance R remains fairly constant, the ohmic potential drop is directly proportional to the net cell current. The overpotential increases exponentially with the rate of the electrode reaction. Once the Cu ions cannot reach the electrode fast enough, we say that concentration polarization has set in. An ideally polarized electrode is one at which no faradaic reactions ensue that is, there is no flow of electrons in either direction across the electrode-solution interface. When the potential of the cathode falls sufficiently to reduce the next available species in the solution (H" ions, or nitrate depolarizer), the copper deposition reaction is no longer 100% efficient. 

In an anodic process, the electron appears between the produced species and can be always supplied to the metal surface by means of an external electric current, such as in the case of cathodic protection. On the other hand, if the process involves also metal dissolution, the metal ions must leave the metal/solution interface, and they will cause an increase in concentration of the metal ion at the surface. In this case, the diffusion, although it cannot be a significant resistance to the anodic process, is, in general, not able per se to limit the corrosion rate to values acceptable from a corrosion point of view. 

If the cathodic reaction (oxygen reduction) takes place at the limiting current, then the resistance at the electrode-solution interface of the cathode, / pjj (Figure 7.4), behaves as a non-linear electrical element that limits the current (current limiter). Indeed, at the limiting current plateau one has = (dE/dT)n = oo. The anode corrosion rate Vj depends, in this case, only on the value of limiting current density at the cathode, t lji that is determined by prevailing mass transport conditions. Neglecting the currents 1 i and 4 n, we find ... 

Finally, it is important to point out that although in localised corrosion the anodic and cathodic areas are physically distinguishable, it does not follow that the total geometrical areas available are actually involved in the charge transfer process. Thus in the corrosion of two dissimilar metals in contact (bimetallic corrosion) the metal of more positive potential (the predominantly cathodic area of the bimetallic couple) may have a very much larger area than that of the predominantly anodic metal, but only the area adjacent to the anode may be effective as a cathode. In fact in a solution of high resistivity the effective areas of both metals will not extend appreciably from the interface of contact. Thus the effective areas of the anodic and cathodic sites may be much smaller than their geometrical areas. 

This sharp decline in cell output at subzero temperatures is the combined consequence of the decreased capacity utilization and depressed cell potential at a given drain rate, and the possible causes have been attributed so far, under various conditions, to the retarded ion transport in bulk electrolyte solutions, ° ° - ° ° the increased resistance of the surface films at either the cathode/electrolyte inter-face506,507 Qj. anode/electrolyte interface, the resistance associated with charge-transfer processes at both cathode and anode interfaces, and the retarded diffusion coefficients of lithium ion in lithiated graphite anodes. - The efforts by different research teams have targeted those individual electrolyte-related properties to widen the temperature range of service for lithium ion cells. 

From this physical model, an electrical model of the interface can be given. Free corrosion is the association of an anodic process (iron dissolution) and a cathodic process (electrolyte reduction). Ther ore, as discussed in Section 9.2.1, the total impedance of the system near the corrosion potential is equivalent to an anodic impedance Za in parallel with a cathodic impedance Zc with a solution resistance Re added in series as shoxvn in Figure 13.13(a). The anodic impedance Za is simply depicted by a double-layer capacitance in parallel with a charge-transfer resistance (Figure 13.13(b)). The cathodic branch is described, following the method of de Levie, by a distributed impedance in space as a transmission line in the conducting macropore (Figure 13.12). The interfacial impedance of the microporous... 

Dissolution of PS. The dissolution of PS during PS formation may be due to two proeesses a proeess in the dark and a proeess under illumination. Both are essentially eorrosion proeesses by which the silicon in the PS is oxidized and dissolved with simultaneous reduction of the oxidizing species in the solution. The corrosion process is responsible for the formation of micro PS of certain thickness (stain film) as well as the dissolution of the existing PS. The material in the PS which is at a certain distance from the pore tips is little affected by the extanal bias due to the high resistivity of PS and is essentially at an open-circuit condition (OCP). This dissolution process, which is often referred to as chemical dissolution, is an electrochemical process because it involves charge transfer across the interface. The anodic and cathodic reactions in the microscopic corrosion cells depend on factors such as surface potential and carrier concentration on the surface which can be affected by illumination and the presence of oxidants in the solution. 

Figures 4.3(a) and (b) are sections in the zx-plane showing the distribution of potential (( )) in the solution as cross sections of imaginary surfaces in the solution of equal potential (isopotentials) and the distribution of current as current channels with cross sections defined by traces of the surfaces. ..(n - l),n, (n + 1)... perpendicular to the isopotentials. These traces are located such that each current channel carries the same total current. Figure 4.3(a) applies to an environment of higher resistivity (e.g., water with specific resistivity of 1000 ohm-cm) and Fig. 4.3(b) to an environment of lower resistivity (e.g., salt brine, 50ohm-cm). The figures are representative of anodic and cathodic reactions, which, if uncoupled, would have equilibrium half-cell potentials of E M = -1000 mV and E x = 0 mV and would, therefore, produce a thermodynamic driving force of Ecell = E x - E M = +1000 mV. This positive Ecell indicates that corrosion will occur when the reactions are coupled. For the example of Fig. 4.3(a), the high solution resistivity allows the potential E"m at the anode to approach its equilibrium value (E M = -1000 mV) and, therefore, allows the potential in the solution at the anode interface, < )s a, to approach +1000 mV (recall that (j)s = -E"M). The first isopotential above the anode, 900 mV, approaches this value. The solution isopotentials are observed to decrease progressively and approach 0 mV at the cathode reaction site.

The distribution of potential in the solution along the solution/metal interface is shown in Fig. 4.6. If the anode and cathode areas are not connected, they will exhibit their thermodynamic or open circuit potentials, with the potentials in the solution at the anode and cathode being equal to +1000 mV and 0 mV, respectively. When the anode and cathode areas are in contact, current will pass causing polarization of the interface reactions. With a solution-specific resistivity of 1000 ohm-cm, the solution potential at the center of the anode is decreased... 

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