A New Method for Corrosion Current Measurement: the Dual-Electrochemical Cell (DEC)

In order to compare the ${i}_{{\rm{corr}}}$ obtained using the DEC method to that obtained using other polarization methods, experiments using carbon steel (CS) in aerated solutions at pH 6.0 were performed. This pH was chosen for the comparison study because it is close to the pH of unbuffered water in the presence of normal air, and hence a common pH to which CS is exposed. In addition, at this pH the solubility of Fe²⁺ is still high but has a finite value. As shown later, at this pH the overall amount of dissolved metal cation increases linearly with time for a certain period of time, but starts deviating from linear time-dependence within the test duration of 40 to 72 h. This allows a comparison of the ${i}_{{\rm{corr}}}$ obtained by different methods to be made not only over the linear-kinetic period (during which there is no ambiguity in the nature of metal redox half-reaction involved in corrosion) but also the ${i}_{{\rm{corr}}}$ at longer times when the overall metal oxidation rate no longer follows linear kinetics (see further discussion in the section describing electrode reaction dynamics underlying the DEC method). Note that linear-kinetics or linear dynamics refer to the dynamics of a chemical process, when the rate of the overall process, consisting of a series of rate-determining steps (RDS), can be expressed using the 1^st-order rate equations of the individual RDS with the assumption that the kinetics of individual RDS do not influence each other.^11,12 The concept of linear dynamics, applied to an electrochemical reaction, is that Butler-Volmer kinetics, i.e., the exponential dependence of current on overpotential, is not affected by the rate of mass transport flux, or vice versa. This is the basic concept underlying the Koutecky-Levich equation.⁷ It is also the basic concept underlying electric equivalent circuit analysis, which expresses the inverse of the 1^st-order rate coefficient as a resistance. In electric equivalent circuit analysis, the values of resistances (more precisely RC components) of individual RDS are constant, independent of the current flowing through them or the overall electric power voltage applied to the circuit.¹³

The potentiodynamic (PD) scan and linear polarization (LPR) experiments were conducted using conventional three-electrode electrochemical cell set-up as in cell#1 of the DEC method. In all experiments, the working electrode (WE) was SA36 (0.15 wt% C) carbon steel with a surface area of 0.46 cm.² The reference electrode was a saturated calomel electrode (SCE) and the counter electrode was made of Pt mesh (Alfa Aesar, 99.9% purity). The electrolyte (with volume of 0.5 l) was prepared from 0.01 M Na₂B₄O₇ (analytical grade, EMD Inc.), and the pH was adjusted to 6.0 by adding H₃BO₃ (analytical grade, Caledon Laboratories Ltd). During the experiments, the electrolytes in cell#1 and cell#2 were continuously purged with compressed air and Ar, respectively. The dissolved O₂ content in the aerated solution is expected to be in equilibrium with the O₂ in the purging air (0.21 atm partial pressure).

The electrochemical tests were conducted using a BioLogic VMP-300 multichannel potentiostat (controlled by EC-Lab software, version 10.44). For the PD scan analyses, each test was conducted using a separate CS electrode. Prior to the ${E}_{{\rm{corr}}}$ measurements, each electrode was subjected to 5-min cathodic cleaning at −1.1 V_SCE. After monitoring ${E}_{{\rm{corr}}}$ for a specified duration, the potential scan was performed over the range (${E}_{{\rm{corr}}}$ − 0.3) V_SCE to −0.3 V_SCE at a scan rate of 1 mV s⁻¹. For the LPR analysis, ${E}_{{\rm{corr}}}$ was monitored following 5-min cathodic cleaning at −1.1 V_SCE. The ${E}_{{\rm{corr}}}$ measurement was interrupted every 2 h to perform an LPR measurement. The ${E}_{{\rm{elec}}}$ scan range in each measurement was from ${E}_{{\rm{corr}}}$ to ${E}_{{\rm{corr}}}-10\,{\rm{mV}},$ to ${E}_{{\rm{corr}}}+10\,{\rm{mV}}$ and then back to ${E}_{{\rm{corr}}}$ at a scan rate of 0.167 mV s⁻¹. Each LPR measurement took ∼ 4 min.

After the CS electrodes had corroded for different durations, they were dried with Ar. The morphologies of the surfaces and cross-sections were then examined by optical microscope (Leica DVM6) and scanning electron microscopy (LEO (Zeiss) 1540XB SEM).

The dissolved iron concentration in the solution after each test was analyzed using a Perkin Elmer Avio 200 inductively coupled plasma optical emission spectrometer (ICP-OES). Prior to the solution analysis the samples were digested using nitric acid (Trace analytical grade, Fisher Scientific) to dissolve any colloidal particles present. Therefore, the measured dissolved iron concentration may include any colloid particles if present in the solution. The measured concentration was multiplied by the solution volume in the cell (0.5 l) and then normalized to the electrode surface area.

The ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ monitored in real time using the DEC method are presented in Fig. 2. The results from four separate tests over different durations are presented together to illustrate their reproducibility. The data are plotted on two different time scales. The variation in the time-dependent behaviour of ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ between tests conducted using the DEC method was small. In all tests, ${E}_{{\rm{corr}}}$ approached a near steady-state value very quickly and remained close to this value over the test duration (0.5 h to 72 h). The main variation was in the steady-state ${E}_{{\rm{corr}}}$ value, which was either −0.630 ± 0.005 V_SCE or −0.615 ± 0.005 V_SCE. The ${E}_{{\rm{corr}}}$ value is a function of the ${E}_{{\rm{eq}}}$ values of the oxidant reduction and metal oxidation half-reactions. For CS corrosion at pH 6.0 in aerated solutions, there is more than one metal oxidation path available. The difference between the two ${E}_{{\rm{corr}}}$ values observed is 15 mV, which is half the difference between the ${E}_{{\rm{eq}}}$ values of Fe⁰ + 2 H₂O ⇄ Fe(OH)₂ + 2 H⁺ + 2 e⁻; and 3 Fe(OH)₂ ⇄ Fe₃O₄ + 2 H₂O + 2 H⁺ + 2 e⁻. The two different values obtained are thus not due to variations in surface preparation or instrumental uncertainties.

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The ${i}_{{\rm{corr}}}$ measured by the DEC method initially increased to a maximum value of ∼80 μA cm⁻² within 10 min. This was followed by a slow decrease for about 20 h to a minimum value of 50–60 μA cm⁻² and a slow increase for another 20 h before approaching a steady-state value of about 70 μA cm⁻².

The results from the PD scan and LPR methods are presented in Fig. 3. As described above, each PD scan was conducted on a different CS electrode that had been corroded for a different duration. The ${E}_{{\rm{corr}}}$ values recorded over time, prior to the PD scans after 20-h and 72-h corrosion are shown. Those from the 0.5-h and 2-h tests were the same as those obtained for the longer duration. The variation in ${E}_{{\rm{corr}}}$ between tests was similar to that observed in the DEC analysis with the main variation being the steady-state ${E}_{{\rm{corr}}}$ value, which was either −0.630 ± 0.005 V_SCE or −0.615 ± 0.005 V_SCE.

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The PD scans obtained after different corrosion times all show a wide cathodic potential range exhibiting a linear dependence of $\mathrm{log}\left|{i}_{{\rm{meas}}}\right|$ on ${E}_{{\rm{elec}}}.$ Interestingly, the cathodic Tafel region starts about 100 mV below ${E}_{{\rm{corr}}}$ for the 0.5-h corroded CS. However, this starting potential value gradually increases with corrosion time, and after 72-h corrosion it starts at about 30 mV below the ${E}_{{\rm{corr}}}$ value. The Tafel slope also changes with corrosion time, decreasing from −620 mV/dec at 0.5 h to −216 mV/dec at 72 h. The PD scans show no clear anodic potential range with a linear dependence of $\mathrm{log}\left|{i}_{{\rm{meas}}}\right|$ on ${E}_{{\rm{elec}}}.$ Hence, the ${i}_{{\rm{corr}}}$ value was obtained via extrapolation from the cathodic Tafel region. The anodic Tafel slope value was then determined by least square fitting: the ${b}_{{\rm{a}}}$ value that gave the best fitting result for the polarization curve in the potential region from ${E}_{{\rm{corr}}}$ to ${E}_{{\rm{corr}}}+\mathrm{60}\,\mathrm{mV}$ was chosen. The anodic and cathodic Tafel lines are indicated with red lines in Fig. 3a. Also shown in the figure is the fitted polarization curve using the two Tafel slopes (green lines). The ${b}_{{\rm{a}}}$ value thus obtained fluctuated from 107 to 165 mV/dec with no clear time dependence. Because only the cathodic branches of the PD scans exhibited a clear Tafel relationship, the ${i}_{{\rm{corr}}}$ values were obtained by extrapolating the cathodic Tafel slopes to ${E}_{{\rm{elec}}}={E}_{{\rm{corr}}},$ and these values are presented along with the ${E}_{{\rm{corr}}}$ data in Fig. 3a.

The LPR measurements were conducted every 2 h. Only a few examples of the linear polarization curves are shown in Fig. 3b. Presented below the polarization curves are the inverse of ${R}_{{\rm{P}}}$ values determined from the polarization curves conducted every 2 h. The polarization curves over the small potential range (${E}_{{\rm{corr}}}$±10 mV) show a small degree of hysteresis. Because the polarization curves obtained from the PD scan tests were also asymmetric (Fig. 3a), we applied the Stern-Geary equation to convert the LPR resistances (${R}_{{\rm{P}}}$) to the ${i}_{{\rm{corr}}}$ values:

$$\begin{eqnarray}&&{i}_{{\rm{corr}}}=\displaystyle \frac{B}{{R}_{{\rm{p}}}}\,where\,B=\displaystyle \frac{{b}_{{\rm{a}}}\left|{b}_{{\rm{c}}}\right|}{2.303\left({b}_{{\rm{a}}}+\left|{b}_{{\rm{c}}}\right|\right)}\end{eqnarray} \tag{ 4 }$$

The ${b}_{{\rm{a}}}$ and ${b}_{{\rm{c}}}$ values were determined from the PD scans presented in Fig. 3a. As discussed above, the ${b}_{{\rm{a}}}$ and ${b}_{{\rm{c}}}$ values ranged from 107 to 165 mV/dec and from −620 to −216 mV/dec, respectively. Because of the wide ranges and uncertainties in the Tafel slopes, the proportionality constant, B, in the Stern–Geary equation that is required to convert ${R}_{{\rm{p}}}$ to ${i}_{{\rm{corr}}},$ ranged from 31 to 56 mV. The ${i}_{{\rm{corr}}}$ values converted from the ${R}_{{\rm{P}}}$ using the minimum and maximum constants are presented along with the ${E}_{{\rm{corr}}}$ data in Fig. 3b.

The ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ values obtained from the different polarization methods are compared with those from the DEC method in Fig. 4. In this figure, only one set of data from each method is shown. The variations in the time-dependent behaviours of ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ between tests conducted with each method can be seen in Fig. 2 and Fig. 3. As observed in individual analyses, the variation in ${E}_{{\rm{corr}}}$ between tests conducted using different methods was small. In all tests, ${E}_{{\rm{corr}}}$ approached a near steady-state value very quickly and remained near this value over the test duration (72 h). At the studied pH 6.0, the ${i}_{{\rm{corr}}}$ values determined by different methods are also all within a factor of 2 of each other, with the ${i}_{{\rm{corr}}}$ monitored by the DEC method being the highest.

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In order to assess the accuracy of the different electrochemical methods in determining the metal oxidation (or corrosion) rate in the studied system (CS corrosion in aerated solution at pH 6.0), the results were analyzed in relation to the post-test solution and surface analyses. The amounts of dissolved metal in solution (detected by ICP-OES) are presented in Fig. 5. Also presented in Fig. 5 are the amounts of oxidized metal calculated from the ${i}_{{\rm{corr}}}$ obtained using different methods. For the amount of oxidized metal, the total accumulated charge ($Q={\int }^{}{i}_{{\rm{corr}}}{\rm{d}}t$) was obtained from ${i}_{{\rm{corr}}}$ and then converted to the oxidized mass using Faraday's law, assuming all metal oxidation resulted in Fe²⁺. With the DEC method, ${i}_{{\rm{corr}}}$ was monitored continuously so the $Q$ value could be readily obtained. With the LPR and PD techniques, the ${i}_{{\rm{corr}}}$ values were determined periodically and hence interpolation (piecewise cubic) of the ${i}_{{\rm{corr}}}$ values was first performed to obtain continuous time functions of ${i}_{{\rm{corr}}}$ which were then used to obtain the $Q$ values.The surface morphologies of the CS surfaces observed by SEM and optical microscopy are presented in Fig. 6.

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The amounts of oxidized metal calculated from the ${i}_{{\rm{corr}}}$ values obtained by different electrochemical methods are all within a factor of 2 of the measured amounts dissolved in solution. The DEC method gave an oxidized amount close to the dissolved amount at corrosion times less than 20 h, but higher than the dissolved amount at longer times. All the other methods gave oxidized amounts equal to or less than the dissolved amounts, for all time points.

The metal oxidation products include metal hydroxide/oxide precipitates as well as metal cations and their hydrolysis products that are dissolved or dispersed in solution. Hence, the oxidized amount should be always greater than or equal to the amount detected in solution. The oxidized amount obtained from the DEC method is greater than or equal to the dissolved/ dispersed amount at all measured times, but those determined using the other electrochemical methods are lower. The DEC method also shows an increase over time in the difference between the oxidized and the dissolved/dispersed amounts, suggesting that the fraction of oxidized metal resulting in oxide formation increases with time. The SEM and optical images shown in Fig. 6 support this hypothesis.

Because metal dissolution occurs from the surface of α-Fe, over the short duration (≤ 2 h) in which dissolution is the main corrosion reaction, the lamellar structure of the pearlite phase consisting of alternating layers of cementite (Fe₃C) and α-Fe becomes more clearly defined in the SEM image with time. The bluish and black areas in the optical images correspond to the surfaces of the pure α-Fe phase and the pearlite phase, respectively. After 20 h corrosion, the amount of oxidized metal determined using the DEC method starts deviating from the amount of dissolved metal detected by ICP-OES. At this time, the SEM image clearly shows the cementite layers in the pearlite phase (due to dissolution of the intervening α-Fe layer), indicating more extensive Fe dissolution over longer periods of corrosion. The optical image shows that the surface of the α-Fe phase is covered by a thin uniform layer of brownish-yellow hydroxide, with the SEM image indicating that no significant quantities of granular oxide are present. At 20 h the gaps between the cementite layers are partially filled with granular oxides. After 72 h corrosion, the gaps between the cementite layers are filled with granular oxides and the α-Fe phase is covered by a yellow/orange oxide layer. Raman, SEM and XPS analyses were performed to determine the type and morphology of iron hydroxides and oxides that grow on corroding CS (results not shown). A discussion of these results is beyond the scope of this paper and will be reported elsewhere.

The DEC method yields corrosion currents that are more consistent with the sum of metal dissolved in solution and precipitated as metal hydroxides/oxides. Thus, it can be concluded that the ${i}_{{\rm{corr}}}$ measured by the DEC method is a more accurate representation of the actual corrosion rate. The ${i}_{{\rm{corr}}}$ values determined by the conventional polarization methods have larger uncertainties, and in general, underestimate the corrosion rate.

The electrochemical reaction dynamics underlying the DEC method are essentially the same as those underlying other electrochemical methods used for corrosion rate analysis. All electrochemical methods measure the current—potential relationship arising from electrochemical redox half-reactions that occur on the surface of a corroding electrode. In corrosion, these reactions are reduction half-reaction(s) involving dissolved oxidant and oxidation half-reaction(s) involving metal:

$$\begin{eqnarray}&&reduction\,half-reaction:O+n{e}^{-}\rightleftarrows R\end{eqnarray} \tag{ 5a }$$

$$\begin{eqnarray}&&oxidationhalf-reaction:{M}^{0}\rightleftarrows {M}^{n+}+n{e}^{-}\end{eqnarray} \tag{ 5b }$$

$$\begin{eqnarray}&&{\rm{full}}\,{\rm{redox}}\,{\rm{reaction}}:O+{M}^{0}\rightleftarrows R+{M}^{n+}\end{eqnarray} \tag{ 5c }$$

The overall process of each half-reaction occurs through multiple elementary steps that can contribute to the overall reaction rate. The number of RDS to consider varies with reaction conditions and duration as well as the accuracy of the overall rate required for a given application. The RDS for each half-reaction that are typically considered in corrosion rate analysis include (1) the net electron transfer between the redox pair (O and R, or M⁰ and Mⁿ⁺) in the interfacial region; and (2) the overall transport of the redox pair to and from the interfacial region and the bulk solution. For each half-reaction, the overall rate is then obtained by coupling the kinetics of elementary steps, and it is related to the current arising from the half-reaction by Faraday's law.

The electron transfer step of each half-reaction is a reversible process. Typically, the Butler–Volmer equation (or the approximate equations described in the introduction section) is applied to the net electron transfer step. For the mass transport step, the Nernst–Planck or other simplified mass flux equation is used.² Other chemical processes such as chemisorption and homogeneous solution reactions in the diffusion layer, and metal oxide deposition and growth do not generate current directly. However, these chemical processes can influence the kinetics of the net electron transfer and the overall mass transport steps. The effects of these chemical processes are typically incorporated into the pseudo-1^st order rate coefficients describing the kinetics of the two steps. The more sophisticated analyses include the chemical processes as additional elementary steps. In coupling the kinetics of the two steps to obtain the overall kinetics it is also assumed that the kinetics of each step do not influence the other. That is, the dependence of the net electron transfer rate on ${E}_{{\rm{elec}}}$ does not change when the mass transport conditions change, or vice versa. This allows the use of a Koutecky-Levich-type equation to separate the dependence of the overall rate of the half-reaction on ${E}_{{\rm{elec}}}$ from the mass transport parameters.

The approach described above to obtain the overall kinetics of an electrochemical redox half-reaction works very well for redox reactions between two soluble species, such as an oxidant reduction half-reaction (5a).^14–16 However, the above approach may not work very well for metal oxidation half-reactions (5b).^17–21 As discussed in more detail below, for metal oxidation during corrosion, the net electron transfer step may not follow Butler–Volmer kinetics, and the kinetics of the electron transfer and the transport steps may not be independent of each other. As a result, the net metal oxidation current ${i}_{{\rm{ox}}}$ may not depend exponentially on ${E}_{{\rm{elec}}},$ and it may not be negligible even at ${E}_{{\rm{elec}}}\lt {E}_{{\rm{corr}}}.$ An inaccurate understanding of the dependence of ${i}_{{\rm{ox}}}$ on ${E}_{{\rm{elec}}}$ in the cathodic Tafel region can lead to an incorrect determination of the dependence of ${i}_{{\rm{red}}}$ on ${E}_{{\rm{elec}}}.$

The electron transfer step is reversible; the forward rate (${\upsilon }_{{\rm{f}}}$) and the reverse rate (${\upsilon }_{{\rm{r}}}$) are much faster than the net rate (${\upsilon }_{{\rm{net}}}={\upsilon }_{{\rm{f}}}-{\upsilon }_{{\rm{r}}}$). The rate of each direction is proportional to the chemical activity (≈ concentration) of the reactant in the interfacial region (${\left[{\rm{O}}\right]}_{{\rm{int}}}$ or ${\left[{\rm{R}}\right]}_{{\rm{int}}}$)²:

$$\begin{eqnarray}&&{\upsilon }_{{\rm{net}}}={\upsilon }_{{\rm{f}}}-{\upsilon }_{{\rm{r}}}={k}_{{\rm{f}}}\cdot {\left[{\rm{O}}\right]}_{{\rm{int}}}-{k}_{{\rm{r}}}\cdot {\left[{\rm{R}}\right]}_{{\rm{int}}}\end{eqnarray} \tag{ 6 }$$

where ${\upsilon }_{{\rm{net}}},$ ${\upsilon }_{{\rm{f}}}$ and ${\upsilon }_{{\rm{r}}}$ are the rates per electrode surface area, ${k}_{{\rm{f}}}$ and ${k}_{{\rm{r}}}$ are the electron transfer rate coefficients from O to R, and from R to O, via the electrode. The rate coefficients depend on the electrochemical potential for the reaction of O to R in the interfacial region, which is related to the electrode potential by $nF\cdot {E}_{{\rm{elec}}}.$² Tafel was the first one to recognize that the rates (currents) of most of electrochemical reactions increase exponentially with increasing or decreasing ${E}_{{\rm{elec}}}$ and formulated this empirical observation into what is now referred to as the Tafel equation.²² Later, Marcus provided theoretical support for this exponential dependence of electrochemical reaction rate on ${E}_{{\rm{elec}}}.$^23,24 The Tafel equation and Marcus theory are to electrochemical reaction kinetics what the Arrhenius equation and Eyring's transition state theory are to homogeneous chemical reaction kinetics.

$$\begin{eqnarray}&&{k}_{{\rm{f}}}={k}_{{\rm{f}}}^{0}\cdot \exp \left(\displaystyle \frac{\alpha nF}{RT}\cdot {E}_{{\rm{elec}}}\right)\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{k}_{{\rm{r}}}={k}_{r}^{0}\cdot \exp \left(-\displaystyle \frac{\left(1-\alpha \right)nF}{RT}\cdot {E}_{{\rm{elec}}}\right)\end{eqnarray} \tag{ 8 }$$

where ${{k}_{{\rm{f}}}}^{0}$ and ${{k}_{{\rm{r}}}}^{0}$ represent the rate coefficients (in units of cm^·s⁻¹) when ${E}_{{\rm{elec}}}=0,$ and $\alpha$ is the symmetry coefficient for electron transfer from the transition state to O vs R, and is typically 0.5.

Equations 6 to 8 show that the net half-reaction does not follow 1^st-order kinetics on ${\left[{\rm{O}}\right]}_{{\rm{int}}},$ but that it also depends on ${\left[{\rm{R}}\right]}_{{\rm{int}}}.$ However, the net rate equation can be modified to the Butler–Volmer equation using the rate parameters at equilibrium; at ${E}_{{\rm{elec}}}={E}_{{\rm{eq}}},$ ${\left.{\upsilon }_{{\rm{net}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{eq}}}}=0,$ ${\left[{\rm{O}}\right]}_{{\rm{int}}}={\left[{\rm{O}}\right]}_{{\rm{eq}}}$ and ${\left[{\rm{R}}\right]}_{{\rm{int}}}={\left[{\rm{R}}\right]}_{{\rm{eq}}}:$

$$\begin{eqnarray}&&{i}_{{\rm{net}}}=nF\cdot {\upsilon }_{{\rm{net}}}\end{eqnarray} \tag{ 9a }$$

$$\begin{eqnarray}&&{i}_{{\rm{net}}}={i}_{0}\cdot \left\{\exp \left(\displaystyle \frac{\alpha nF}{RT}\cdot \eta \right)-\exp \left(-\displaystyle \frac{\left(1-\alpha \right)nF}{RT}\cdot \eta \right)\right\}\end{eqnarray} \tag{ 9b }$$

$$\begin{eqnarray}&&\eta ={E}_{{\rm{elec}}}-{E}_{{\rm{eq}}}\end{eqnarray} \tag{ 9c }$$

where ${i}_{0}$ is the exchange current density and ${i}_{0}=-nF\,\cdot {\left.{\upsilon }_{{\rm{f}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{eq}}}}{\left.=nF\cdot {\upsilon }_{r}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{eq}}}}.$

The Butler-Volmer equation does not explicitly use ${\left[{\rm{O}}\right]}_{{\rm{int}}},$ ${\left[{\rm{R}}\right]}_{{\rm{int}}},$ ${{k}_{{\rm{f}}}}^{0}$ and ${{k}_{{\rm{r}}}}^{0}.$ Instead, these parameters are incorporated into ${i}_{{\rm{ex}}}$ and ${E}_{{\rm{eq}}}.$ However, the implicit assumption underlying the use of overpotential in the equation is that O and R in the interfacial region are in (quasi-) chemical equilibrium throughout the redox half-reaction. The individual concentrations, ${\left[{\rm{O}}\right]}_{{\rm{int}}}$ and ${\left[{\rm{R}}\right]}_{{\rm{int}}},$ may change with time and reaction conditions, and the net rate of the electron transfer deviates from Butler-Volmer kinetics.

For a transition metal, the most important parameter that affects the net electron transfer rate from M⁰ to Mⁿ⁺ is the solubility of Mⁿ⁺ in the interfacial region. One monolayer of metal dissolution into the volume of water within 10 nm of the surface would produce an average Mⁿ⁺ concentration in that water volume higher than 1 M. That is to say, the concentration of Mⁿ⁺ in the interfacial region quickly reaches its saturation limit, and the saturated volume quickly expands beyond the interfacial region. The net electron transfer from M⁰ to Mⁿ⁺ in the interfacial region can occur only at the rate of expansion of the Mⁿ⁺ saturation front. That is, at ${E}_{{\rm{elec}}}$ above a specific potential of ${E}_{{\rm{\min }}},$ the net electron transfer rate for metal oxidation becomes independent of ${E}_{{\rm{elec}}},$ which is said to be in the "complete concentration polarization" potential range (or above the "mass transfer overpotential").² At these potentials the overall metal oxidation rate is determined by the displacement of the Mⁿ⁺ saturation front, ${\upsilon }_{{\rm{mt}}-{{\rm{M}}}^{{\rm{n}}+}}:$

$$\begin{eqnarray}&&{i}_{{\rm{ox}}}\approx nF\cdot {\upsilon }_{{\rm{mt}}-{{\rm{M}}}^{{\rm{n}}+}}\,{\rm{when}}\,{E}_{{\rm{elec}}}\gt {E}_{{\rm{\min }}}\end{eqnarray} \tag{ 10 }$$

The movement of the Mⁿ⁺ saturation front is not a step-function of distance away from the metal surface, because of the convective and diffusional components in the overall transport flux equation.

The solubility of transition metals strongly depends on pH. Hence, during corrosion of a transition metal at a pH higher than mildly acidic or neutral, the complete concentration polarization potential typically lies below ${E}_{{\rm{corr}}}.$ Complete concentration polarization potential, or mass transfer overpotential, refers to the overpotential beyond which net interfacial electron transfer rate no longer increases with increasing overpotential.² This happens because the chemical activities of the redox pair (M⁰ and Mⁿ⁺) in the interfacial region can no longer change. This situation is commonly encountered in electrochemical deposition of metals²⁵ because the chemical activity of a pure solid metal is 1.0 and the metal cation bulk concentration is kept constant. In corrosion, complete concentration polarization for a metal oxidation half-reaction occurs when the redox pair are a metal (with chemical activity of 1.0) and a metal cation with chemical activity at its saturation level. As discussed earlier, a single monolayer dissolution of metal can quickly saturate the solution in the interfacial region (where electron exchanges between the redox pair and the electrode can occur) except for at very low pHs and/or for highly soluble metal cations. That is, the ${i}_{{\rm{ox}}}$ does not decrease exponentially with ${E}_{{\rm{elec}}}$ in the ${E}_{{\rm{elec}}}$ range below ${E}_{{\rm{corr}}},$ and its contribution to ${i}_{{\rm{meas}}}$ may not be negligible even at ${E}_{{\rm{elec}}}$ < $\left({E}_{{\rm{corr}}}-\mathrm{30}\,\mathrm{mV}\right),$ which is normally considered to be the cathodic Tafel region.

Thus, even when no chemisorption of metal cation nor deposition of metal hydroxide/oxide on the surface occurs, and oxidant reduction and metal oxidation both involve only one electron transfer step, it is difficult to determine the potential range where the observed dependence of ${i}_{{\rm{meas}}}$ on ${E}_{{\rm{elec}}}$ can be primarily attributed to that of ${i}_{{\rm{ox}}}$ or ${i}_{{\rm{red}}},$ i.e., the anodic or cathodic Tafel region. Deconvoluting the dependence of ${i}_{{\rm{ox}}}$ on ${E}_{{\rm{elec}}}$ from that of ${i}_{{\rm{red}}}$ becomes even more complicated when the overall oxidant reduction or the overall metal oxidation occurs in multiple electron-transfer steps. For example, the reduction of O₂ to OH⁻ is known to occur in two 2-e transfer steps: O₂ + 2 e⁻ + 2 H⁺ ⇄ H₂O₂ followed by H₂O₂ + 2 e⁻ ⇄ 2 OH⁻.²⁶ Depending on ${E}_{{\rm{elec}}},$ the ${i}_{{\rm{red}}}$ follows the Tafel relationship of the 1^st electron transfer step, O₂ transport limit, or the Tafel relationship of the 2^nd electron transfer step.²⁶ Multiple electron transfer steps are more common for metal redox half-reactions because transition metal cations have more than one stable oxidation state in solution.^27–33 Thus, depending on ${E}_{{\rm{corr}}}$ and mass transport conditions, polarizing ${E}_{{\rm{elec}}}$ away from ${E}_{{\rm{corr}}}$ can change the rate determining step, resulting in a current-potential relationship very different from that at ${E}_{{\rm{corr}}}.$

The perturbation of ${E}_{{\rm{elec}}}$ away from ${E}_{{\rm{corr}}}$ and the uncertainties in the analysis of the observed dependence of ${i}_{{\rm{meas}}}$ on ${E}_{{\rm{elec}}}$ can result in incorrect determination of ${i}_{{\rm{ox}}}$ at ${E}_{{\rm{corr}}}$ (i.e., ${i}_{{\rm{corr}}}$), consequently leading to the development of an inaccurate corrosion model. The DEC method recognizes that ${i}_{{\rm{ox}}}$ and ${i}_{{\rm{red}}}$ depend on ${E}_{{\rm{elec}}}.$ However, unlike conventional polarization methods, the DEC method does not rely on establishing the exact dependences of ${i}_{{\rm{ox}}}$ and ${i}_{{\rm{red}}}$ on ${E}_{{\rm{elec}}}.$ Instead, ${E}_{{\rm{elec}}}$ is maintained at ${E}_{{\rm{corr}}}$ throughout the corrosion duration. Relying on the simple charge conservation law, i.e., ${\left.{i}_{{\rm{meas}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{corr}}}}={\left.{i}_{{\rm{ox}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{corr}}}}-\left|{\left.{i}_{{\rm{red}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{corr}}}}\right|$ under given transport conditions, the DEC method just eliminates the contribution of oxidant reduction current to the measured current at ${E}_{{\rm{corr}}}:$ ${\left.{i}_{{\rm{meas}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{corr}}}}={\left.{i}_{{\rm{ox}}}\right|}_{{E}_{{\rm{elec}}}={E}_{{\rm{corr}}}}={i}_{{\rm{corr}}}.$

As described earlier, other chemical processes such as chemisorption, homogeneous solution reactions in the diffusion layer, and metal oxide deposition and growth can influence the overall rate of each half-reaction by influencing the kinetics of the electron transfer and mass transport steps.² Hence, the next key question is whether the effects of these processes on ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ can be simulated and/or accounted for in the analysis of the DEC and other electrochemical techniques.

Chemical reactions of the redox pair (O and R, or M⁰ and Mⁿ⁺) during an electrochemical redox half-reaction do not generate current directly, but they can affect the overall rate of the half-reaction. If the redox-active species are chemisorbed on the electrode surface, the chemisorbed layer can become a potential barrier for electron transfer between the redox pairs, which occurs via the electrode. As a result, the effective overpotential (η) for a metal oxidation half reaction changes^18,32,34:

$$\begin{eqnarray}&&\left|\eta \right|=\left|{E}_{{\rm{elec}}}-{E}_{{\rm{eq}}}\right|-{\rm{\Delta }}{E}_{{\rm{e}}-{\rm{trans}}}\end{eqnarray} \tag{ 11 }$$

where ${\rm{\Delta }}{E}_{{\rm{e}}-{\rm{trans}}}$ represents the potential drop due to the chemisorbed layer. Thus, a chemisorbed layer will influence the overall rate of a half-reaction by affecting the effective overpotential. (This is equivalent to moving the Tafel slope in the Evans diagram up (for the cathodic slope) or down (for the anodic slope) on the potential scale without affecting the slope). The chemisorbed layer will not affect the overall mass transport step to and from the surface and the bulk solution.

On the other hand, chemical reactions of redox-active species in the mass transport (diffusion) layer can affect the overall transport step. Depending on the contribution of the overall mass transport step to determination of the overall half-reaction rate, ${i}_{{\rm{ox}}}$ and ${i}_{{\rm{red}}}$ at any given time can be affected by the kinetics of the chemical reactions occurring. If the chemical reactions induce precipitation of solid particles and/or gelatinous layers, they can act as a transport barrier for the solution and/or redox-active species from the surface to the bulk solution and vice versa. The effect of chemical reactions in the mass transport layer will thus affect the currents, ${i}_{{\rm{ox}}}$ and ${i}_{{\rm{red}}}.$

Chemisorption and chemical reactions of dissolved oxidants and their reduction products are typically negligible. Their concentrations in the bulk solution are already below their saturation limits and hence their concentrations in the interfacial region and diffusion layer are also always below their saturation limits. Hence, chemisorption or the homogeneous solution reactions of dissolved oxidants are typically negligible compared to electrochemical reduction of the oxidant. Their reduction products are less likely to be chemisorbed on the metal surface during natural corrosion. That is, chemisorption or chemical reactions in the diffusion layer of dissolved oxidants and their reduction products will not be significant during natural electrochemical corrosion.

During corrosion, the chemical reactions of concern are mostly those of the metal oxidation product, the metal cation. Chemisorption of M⁰ and Mⁿ⁺ on the metal surface is somewhat of a moot point, because metal oxidation occurs at the surface. However, as described earlier, the interfacial region may be quickly saturated by the metal cation, and the metal oxidation half-reaction reaches steady state when the saturated volume stops expanding. At steady state, the net electron transfer rate becomes the same as the M²⁺ flux rate from the interfacial region to the saturated volume and is also the same as the M²⁺ removal rate from the saturated volume by mass transport and chemical reactions.

Chemical reactions of the metal cation in the saturated volume will affect the overall flux of M²⁺ from the interfacial region to the bulk solution, by competing with the transport process for M²⁺. More importantly, in a saturated volume the hydrolysis of Mⁿ⁺ to produce metal hydroxide can occur at an appreciable rate, producing metal hydroxide that aggregates as a hydrogel network, which can hinder solution diffusion between the surface and the bulk solution. Because of the strong interdependence between the kinetics of electron transfer and mass transport steps in metal oxidation as discussed above, this can change ${i}_{{\rm{ox}}},$ the net rate of production of Mⁿ⁺, which is the precursor for hydroxide formation. When such systemic feedback occurs, a small change in the kinetics of individual steps can induce a significant change in the overall metal oxidation rate ${i}_{{\rm{ox}}}.$ If systemic feedback between the different RDS steps of the metal oxidation half-reaction develops, a small shift of ${E}_{{\rm{elec}}}$ away from ${E}_{{\rm{corr}}}$ can accelerate or decelerate the overall metal oxidation. This makes it very difficult to extrapolate the observed ${i}_{{\rm{meas}}}$ vs ${E}_{{\rm{meas}}}$ relationship to obtain the ${i}_{{\rm{ox}}}$ at ${E}_{{\rm{corr}}}.$

Polyoxygenated anions such as nitrate/nitrite can act as oxidants,^35,36 but also complex with metal cations to form a metal-hydroxide-anion salt(s). Although these anions may possess a large driving force for metal oxidation, the rearrangement of multiple N—O bonds involves a high activation energy.^37,38 The electrochemical reduction (i.e., electron transfer) rate of such an oxidant is thus slower than that of O₂. Their reactions and complexation with metal cations are slow processes and become important only when the solution becomes saturated with metal cations. That is, the kinetics of metal-OH-anion salt formation depend on overall metal oxidation by O₂ and on the pH.

The salting out process and Ostwald ripening of the salt crystals^39,40 should not have a significant effect on the overall metal oxidation, but could change the surface morphology considerably. The effect of nitrate/nitrite on corrosion of metal in aerated solutions can be accounted for effectively using the DEC method with the same nitrate/nitrite solution but free of O₂. The electrochemical half-reaction involving the nitrate/nitrite pair has also its own potential dependence.⁴¹ This is all the more reason why conventional polarization techniques do not accurately estimate the corrosion rate.

Other anions such as chloride and sulphide are not oxidants, but they are considered to be very corrosive ions. (They do still need an oxidant but it may not require a strong oxidant.) For chloride, complexation with metal cations and OH⁻ to form a metal-hydroxide-chloride salt can have a considerable effect on overall corrosion because this stabilizes the metal hydroxide complex, which in turn affects the mass transport of metal cations to the bulk solution. Again in this case, the effect of chloride on the corrosion of metal in aerated solutions can be accounted for effectively using the DEC method with the same chloride solution but free of O₂. Of course, some anions such as sulphide are chemically very reactive towards certain metals.⁴² For the study of corrosion by chemical oxidation, there is no electrochemical technique that is suitable for determining the electrochemical corrosion rate.

With the DEC method, the electrode potential is not polarized away from ${E}_{{\rm{corr}}}$ but the oxidant reduction current is eliminated. As described above, the chemical reactions of the dissolved oxidant and its reduction product would be negligible. But the chemical reactions of the metal oxidation product, Mⁿ⁺, can induce significant changes in the overall kinetics of metal oxidation and oxidant reduction half-reactions. With the DEC method the chemical reactions of Mⁿ⁺ and their product formation over corrosion duration are effectively simulated by applying ${E}_{{\rm{corr}}}$ in real time, as the ${i}_{{\rm{corr}}}$ (or ${i}_{{\rm{meas}}\#2}$) measures the metal oxidation current in the same chemical reaction and transport environment the corroding metal is exposed to.

In all electrochemical methods, the experimentally determined ${i}_{{\rm{ox}}}$ at ${E}_{{\rm{corr}}}$ (or ${i}_{{\rm{corr}}}$) may not represent the total metal loss rate when the overall metal oxidation occurs via more than one electron transfer step and produces solid species. This is not due to an incorrect determination of ${i}_{{\rm{corr}}},$ but rather an improper derivation of the corrosion rate from ${i}_{{\rm{corr}}}.$

Conventional polarization methods indirectly determine ${i}_{{\rm{corr}}}$ by monitoring ${i}_{{\rm{meas}}}$ while polarizing ${E}_{{\rm{elec}}}$ away from ${E}_{{\rm{corr}}},$ and then extrapolating the observed ${i}_{{\rm{meas}}}$ vs ${E}_{{\rm{elec}}}$ relationship to determine ${i}_{{\rm{ox}}}$ at ${E}_{{\rm{corr}}}.$ If time-dependent information on corrosion behaviour is required, these polarization tests must be performed periodically, and there is a possibility that these periodic perturbations will affect the corrosion behaviour. In addition, the observed ${i}_{{\rm{meas}}}$ vs ${E}_{{\rm{elec}}}$ relationship is analyzed by applying various combinations of approximated forms of the Butler-Volmer equations for individual redox half-reactions. However, the assumptions used in deriving the approximated equations are not always valid. Furthermore, metal oxidation kinetics may not always follow Butler-Volmer kinetics, which can result in an incorrect identification of the cathodic Tafel region and the dependences of ${i}_{{\rm{red}}}$ and ${i}_{{\rm{ox}}}$ on ${E}_{{\rm{corr}}}.$

The DEC method does not polarize the corroding system away from the ${E}_{{\rm{corr}}}$ of the metal corroding in the oxidizing environment of interest, but instead eliminates the reduction half-reaction of the oxidant occurring on the metal electrode. Determination of ${i}_{{\rm{corr}}}$ by DEC does not rely on prior knowledge or determination of the dependence of ${i}_{{\rm{ox}}}$ or ${i}_{{\rm{red}}}$ on ${E}_{{\rm{elec}}}.$

Because the DEC method measures ${i}_{{\rm{ox}}}$ at ${E}_{{\rm{elec}}}={E}_{{\rm{corr}}}$ directly, it allows for continuous real-time monitoring of ${i}_{{\rm{corr}}}$ as ${E}_{{\rm{corr}}}$ varies with time. In other methods, individual polarization curves take finite amounts of time, and the electrode reaction system must be at a (pseudo) steady state during each measurement, in order to apply a Tafel equation to the observed $\mathrm{log}\left|{i}_{{\rm{meas}}}\right|$ vs ${E}_{{\rm{elec}}}$ relationship. Conventional polarization techniques are, therefore, not suitable when the system is evolving rapidly: i.e. the steady-state requirement is not met.³ A cogent example of the power of real-time measurement of ${i}_{{\rm{corr}}}$ when a corroding system does not remain a stable steady state but evolves rapidly is presented in Fig. 7. Shown in the figure are the time-dependent behaviours of ${E}_{{\rm{corr}}}$ and ${i}_{{\rm{corr}}}$ observed during CS corrosion in aerated solutions at pHs between 7 and 8.²⁹ At a pH in this range, the ${E}_{{\rm{corr}}}$ stays at the initial (pseudo-) steady state only for a certain duration, followed by a rapid change with time before it reaches another steady state. The time-dependent behaviour varies considerably with pH. The DEC method allows continuous monitoring of ${i}_{{\rm{corr}}}$ even when ${E}_{{\rm{corr}}}$ changes rapidly, as shown in Fig. 7. The reasons for the observed effects of pH on the evolution of ${i}_{{\rm{corr}}}$ and ${E}_{{\rm{corr}}}$ and the non-linear corrosion dynamics underlying these observations are beyond the scope of this study and will be presented elsewhere.

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The examples presented in this paper demonstrate that if corrosion is induced primarily by electrochemical oxidation of metal (and hence the corrosion rate can be studied effectively by electrochemical techniques) the DEC method is superior to other electrochemical methods which involve polarization away from the naturally corroding potential.

The DEC method is also the only reasonable method to use to investigate radiolysis-induced corrosion. Radiolysis products are formed in situ during irradiation. Under continuous irradiation the type and concentrations of radiolytically produced oxidants are difficult to quantify and the polarization results are difficult to analyze.^43,44 The DEC method is also a very useful tool for investigating galvanic corrosion of dissimilar metals. In galvanic corrosion, the cathodic current on the more active metal is due to oxidant reduction on the surface as well as the coupling current (${i}_{{\rm{cpl}}}$). As a result, the metal oxidation current increases, and the ${E}_{{\rm{corr}}}$ of the active metal, also known as the coupling potential (${E}_{{\rm{cpl}}}$), increases. The conventional way of analyzing galvanic corrosion rate is to measure the ${E}_{{\rm{cpl}}}$ and ${i}_{{\rm{cpl}}}.$ The coupling current on its own does not indicate the overall metal oxidation rate.⁴⁵ The DEC method allows direct measurements of ${E}_{{\rm{corr}}}$ (= ${E}_{{\rm{cpl}}}$) and ${i}_{{\rm{ox}}}$ after coupling.

Some ionic oxidants, that complex with metal cations and OH⁻ to form a metal-hydroxide-anion salt, can affect ionic strength and pH, and their products can precipitate as salt crystals. Hence, these oxidants should not be removed from electrolyte solutions in any electrochemical analysis techniques, including DEC. If these chemically reactive species are the primary oxidants, and hence metals are being degraded primarily by chemical oxidation, no electrochemical technique (including DEC) is suitable. However, if they are not the primary oxidants, the DEC method still allows for a more accurate measurement of corrosion current than other electrochemical methods.