1.2 Corrosion Basics
1.2.2 Kinetics of Aqueous Corrosion
While thermodynamics describes the possibility and spontaneity for a reaction to proceed it does not provide information on the rate of a reaction. The rate of a reaction is described by kinetics [31], with the current measured at the prevailing potential representative of the kinetics of the electron transfer reaction. If there are no restriction exerted by either mass transport or passivity, the reaction is said to be under activation control. The rate-determining step under activation control is the electron transfer reaction at the metal/solution interface [29]. Commonly, current (I) is converted to current density (i) if the surface area over which the current occurs is known.
At the equilibrium potential, the potential of a half-reaction is given by the Nernst equation, Eq. (1.5), and the forward/reduction and backward/oxidation reactions are occurring at the same rate, resulting in a net zero current or current density, reaction (1.9) in any external measurement circuit. This current density of either the forward or backward reaction is defined as the exchange current density (i0), reflecting the intrinsic rate of a reversible redox reaction. This exchange current density of the forward/reduction reaction is equal but opposite in sign with that of the backward/oxidation reaction, as expressed in Eq. (1.10).
ππ₯ + π
β(πβ
π) (ππ)π ππ
(1.9)π
πππ‘= π
π0+ β β π
π0β = 0
(1.10) When a metal is freely corroding in an electrolyte, the corrosion process will polarize both half-reactions away from their equilibrium potentials, resulting in a current response. Polarization is the potential change from the equilibrium potential to the corrosion potential (Ecorr). The amount of polarization is represented as an over-potential (Ξ·= EβEeq) [34]. A positive current will be generated for the anodic half-reaction, and a negative current for the cathodic half-reaction. These currents are equal and opposite insign [30], and the corrosion current (Icorr) is given by Eq. (1.11). This current can be converted into an equivalent mass loss using Faradayβs Law, Eq. (1.12), in which m is the mass of the metal in gram, and M is the molar mass of the metal in gram/mole.
πΌ
ππππ= πΌ
π= β β πΌ
πβ
(1.11)πΌ =
ππΉπππ‘ (1.12)
The current density of the forward/reduction reaction (1.9) can be expressed by Eq. (1.13), in which kc is the rate constant of the forward reaction, and Cox is the surface concentration of the oxidant at time t.
π
π= ππΉπ
ππΆ
ππ₯ (1.13)Since an electron transfer process requires an activation energy and the rate of this process is exponentially related to ΞG [30], the rate constant of the forward/reduction reaction can be then expressed by the Arrhenius form, Eq. (1.14). A similar expression can be derived for the backward/oxidation reaction from reaction (1.9), given by Eq. (1.15), where Ξ±a and Ξ±c are the transfer coefficients of the backward and forward reactions, a measure of the reaction symmetry (taken to be 0.5 for simple electron transfers [30], with Ξ±a+ Ξ±c=1).
π
π= π
0ππ₯π (
βπΌππΉπ π
(π))
(1.14)π
π= π
0ππ₯π (
(πΌπ)πΉπ π
(π))
(1.15)Combining Eq. (1.13), (1.14), and (1.15), yields the current-potential relationship termed the Butler-Volmer equation, Eq. (1.16) [29]. This relationship only applies when the reaction is activation controlled and not influenced by transport processes. Under these conditions, the concentrations of the redox-active species are equal to the concentrations in the bulk solution [31].
π = π
0[ππ₯π
(1βπΌ)ππΉππ π
β ππ₯π
βπΌππΉπ
π π
]
(1.16)In a corrosion reaction, when both half-reactions are polarized away from their equilibrium potentials to the corrosion potential (Ecorr), charge balance is achieved between the anodic and cathodic half reactions. The kinetics of a freely corroding system is described by mixed potential theory, in which at least one anodic and one cathodic reaction
are coupled, with the current-potential relationship described by the Wagner-Traud equation [35].
π = π
ππππ[ππ₯π
πΌπ΄ππΉ(πΈβπΈππππ) π πβ ππ₯π
βπΌπΆππΉ(πΈβπΈππππ) π π]
(1.17) In Eq. (1.17), Ξ±A and Ξ±C are the transfer coefficients of the anodic and cathodic half- reactions, respectively. The value of 0.5 is commonly adopted for the transfer coefficient, since the symmetry of the barrier is generally unknown [29]. The term EβEcorr is the difference between an externally applied potential and Ecorr. When the applied potential is equal to zero, the corrosion reaction will occur at Ecorr.Current density Anodic Cathodic Potential Ecorr ia ic neβ Mn+ M + Red Ox ne+ β (Ee) Red /Ox (Ee) Mn+/M (i0) Mn+
/M (Large) (i0) Red /Ox(small)
ia+ ic= 0
At Ecorr:
ia= ββicβ
Figure 1.12: A schematic showing the individual current-potential relationships for the reversible half reactions and their sum yielding the current-potential relationship for the coupled corrosion process represented by the Wagner-Traud equation. As shown, the anodic reaction has a large i0 compared to the cathodic reaction and, hence, determines the position of Ecorr. The anodic half of the metal dissolution/deposition reaction is denoted by the green curve, the cathodic half of the other redox reaction (reduction reaction) is denoted by the orange curve, and the Ecorr is the intersections between a horizontal line for zero current density and Wagner- Traud current-potential curve, denoted by a purple arrow.
Figure 1.12 shows the two current-potential relationships, defined by the Butler- Volmer equation, for a reversible metal dissolution/deposition reaction (π β ππ++ ππβ)
and a redox reaction for a potential oxidant (ππ₯ + ππβ β π ππ). In this figure, (Ee) Mn+/M and (Ee) Red/Ox are the respective equilibrium potentials, as defined by equation 1.5, and (i0) Mn+/M and (i0) Ox/Red are the respective exchange current densities. These two reactions couple at the Ecorr to yield an overall corrosion reaction (π + ππ₯ β ππ++ π ππ) providing the condition in (Eq. (1.18)) is met.