Nonlinear response of chemical reaction dynamics

AC corrosion protection

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When one does a specific action and observes a specific result; then, the opposite action should cause the opposite result. This is an example of a linear response system. According to Newton's second law, a pulling force on the right side of an object will accelerate it toward the right. A pulling force on the left side, will accelerate that object toward the left. If the magnitudes of the forces are doubled, the acceleration will be doubled. What are the limitations of such linear responses? What happens when this fails? Let us choose an important chemical system to take a closer look: rusting steel structures–the corrosion of iron.

Rusting occurs when iron or steel are in an oxidizing environment such as atmospheric oxygen and water. The metal turns into ferric rust, a soft red-brown compound. The degradation of metals by corrosion is a very common reaction for metals, because the oxide of the metal has a much lower energy state than the metal itself. Therefore, metals have a strong tendency to oxidize. The National Association of Corrosion Engineers estimates that the cost of corrosion of steel bridges, pipelines, steel embedded in concrete, and vehicles will exceed one trillion dollars in the United States in 2013 [1]. The most common corrosion protection methods are plating, painting, and application of enamel. However, the metal is unprotected when the coating is damaged by abrasion or when differences in the physical properties between the metal and the coating create cracks and detachments. Cathodic protection is a method to suppress corrosion if other methods fail. It suppresses corrosion by shifting the electric potential difference between the steel and the surrounding medium such that the metal is immune to oxidation.

The first step of the corrosion process of steel in a wet environment is the oxidation of metalic iron to ferric ions,

display math(1)

where the ferric ion is dissolved in water and the electrons remain in the metal. Ferric ions react with oxygen and water and can eventually turn into rust. However, if there are already many electrons on the metal surface this reaction is reversed and the metal is immune to corrosion. Figure 1(a) shows that for moderate pH values, iron is immune to corrosion if the electric potential of the metal is 0.85 V lower than the potential of the surrounding liquid.

Figure 1.

Iron equilibrium diagram: Iron at 25°C in water (a). The diagram shows the stable forms of the element as a function of the pH of the water and applied electric voltage difference E in volt between the metal and the surrounding water [2]. Here, an impressed current switches the voltage periodically between state A and state B (b). In both states there is little or no corrosion (AC corrosion protection).

If the voltage is reversed, linear response theory would predict that the reaction [see Eq. (1)] is also reversed and the corrosion rate is increased. Therefore, an impressed alternating current (AC) as illustrated in Figure 1(b) would have no net effect in protecting the metal. When the voltage difference is negative, the corrosion would be stopped; but when the voltage difference is positive the corrosion is accelerated.

But Fig. 1a shows that this does not happen. When the voltage is switched from negative to positive for the first time, initially more ferric ions are created. But, at large positive potentials they form a thin adherent film of Fe2O3 [2]. This passivation layer blocks surface reactions and increases the electrical resistance of the metal-liquid interface by several orders of magnitude [3]. Therefore, corrosion rates are greatly reduced in the passivation region of the equilibrium diagram [see Figure 1(a)]. If the applied voltage is switched between −1 V (state B, immunity) and 1 V (state A, passivation), as shown in Figure 1(b), the corrosion rate is expected to be much lower than without an impressed AC current. Direct current (DC)-currents which keep the metal in the immunity region would reduce the corrosion rate even further. However, AC currents can reach and protect metal surfaces which DC currents cannot reach: such as, the metal-liquid interface of a water droplet on a steel structure in moist air. A DC current charges the air-water interface but does not charge the water-metal interface. In such cases AC currents can provide at least some level of corrosion protection. This would be very useful in low-cost life extension of the structures that are not currently under protection. This method would also work and be extremely useful in a more alkaline (higher pH) environment, where the structure would go through the Fe3O4 region instead of the corrosion region, as shown in Figure 1(a).

In summary, linear response theory suggests that the opposite actions create the opposite responses. For the dynamics of chemical reactions, it would suggest that a positive voltage might undo the response of a negative voltage. Therefore, one might think that corrosion protection with impressed AC currents would not work, because the beneficial effects of a large negative voltage are undone by the harmful effects of a large positive voltage. However, the equilibrium diagram of iron (see Figure 1) shows that different chemical reactions dominate at positive and negative voltages. Therefore, both negative and positive voltages can be beneficial for corrosion protection. The net effect of AC current on corrosions appears to be favorable.

The impact of AC current on corrosion protection could be increased by optimizing the wave form and the frequency of the impressed AC current. Different chemical reactions have different reaction rates; the pH near the interface can change gradually and the thickness of the passivation layer dominates the resistance of the interface. The waveform and frequency of the impressed AC current could match these time scales to maximize the level of protection. Nonlinear optimal control methods [4-7] could be used to optimize the time dependence of impressed currents systematically.

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