A mechanistic study of iron passivation and transpassive behavior in sulfate solutions using thermo-kinetic diagrams

Abstract

Understanding the dissolution and passivation of iron in aqueous environments is essential for enhancing its corrosion resistance and expanding its applications. We present Thermo-Kinetic (TK) diagrams for iron in deaerated solutions with no added sodium sulfate (Na₂SO₄) and with 0.1 M Na₂SO₄ over the pH range 1–14, constructed by integrating current density contours from potentiodynamic polarization with thermodynamic E-pH diagrams. TK diagrams indicate that in solutions with no added Na₂SO₄, iron passivates above pH 7, with a minimum passive current density (i_p) of 5 ×10⁻⁶ mA·cm⁻² at pH 8. The addition of 0.1 M Na₂SO₄ delayed passivation until pH 12 and increased i_p nearly tenfold. Galvanostatic (GS) polarization and EIS validated the TK diagram results. XPS after GS polarization revealed an FeOOH/Fe₂O₃ film at pH 10, while Fe₃O₄/Fe₂O₃ dominated at pH 12 and 14. These results clarify how sulfate compromises iron passivity and highlight TK diagrams as a powerful tool for mapping corrosion behavior.

Introduction

Iron is the most abundant metal on Earth and is widely used in various industries, primarily as steel, due to its low cost, favorable mechanical properties, low toxicity, and high recyclability^1–3. Its electrochemical characteristics also make it valuable for emerging applications, including (i) anode materials in iron-air batteries^4,5, (ii) electrodes for hydrogen and oxygen evolution in water-splitting^6,7, (iii) electrocoagulation processes for wastewater treatment^8,9, (iv) storing radioactive waste^10–12, and (v) biomedical engineering due to its biocompatibility^13,14. However, iron is highly susceptible to corrosion in aqueous environments, necessitating a thorough understanding of its active dissolution, passivation, and transpassive corrosion to improve its durability and performance^15,16.

The mechanism and kinetics of iron’s anodic dissolution have been studied for over a century and continue to be a topic of debate^17–20. Nevertheless, there is still a significant gap in the systematic evaluation of iron’s active dissolution, passivation, and transpassive corrosion. Both applied potential and pH are fundamental factors that govern iron’s anodic behavior^21–23, yet their combined effects have not been thoroughly explored.

The presence of aggressive anions further complicates the prediction of iron’s anodic behavior by influencing passive film formation and stability. Sulfate (SO₄²⁻) and chloride (Cl⁻) are among the most studied anions in this context. While chloride is well known for its role in pitting corrosion^22,24, the impact of sulfate on iron’s passive film integrity and depassivation remains inconclusive. Some studies suggest that sulfate promotes the active corrosion of iron and inhibits passivation in alkaline conditions^25–27. However, conflicting reports indicate that even at concentrations as high as 0.2 M, sulfate ions do not show significant aggressiveness toward the passive film in highly alkaline environments and may even facilitate the formation of a stable passive layer^28,29. Moreover, sulfate’s impact on corrosion has been shown to be highly dependent on environmental variables such as pH, temperature, and redox conditions³⁰.

Thermo-Kinetic (TK) diagrams have emerged as advanced tools for assessing alloy corrosion behavior by integrating both thermodynamic and kinetic information. Traditionally, Pourbaix diagrams (E–pH diagrams) map the equilibrium stability regions of metals, oxides, and ionic species as a function of pH and potential. However, these classical diagrams are limited to purely thermodynamic predictions; they do not account for reaction kinetics and are typically restricted to pure metal systems³¹. TK diagrams overcome these limitations by superimposing experimental data—typically obtained from potentiodynamic polarization experiments conducted across a range of pH values—onto the classical E–pH framework. The integration of experimental data into E–pH diagrams was pioneered in the 1970s and 1980s by Ellis Verink and colleagues at the University of Florida, in collaboration with Marcel Pourbaix^31–33. They developed “experimental Pourbaix diagrams” by incorporating key electrochemical parameters—such as corrosion potential, passivation potential, breakdown (pitting) potential, and protection potential—from cyclic polarization studies. This methodology was applied to a range of alloys, including Fe–Cr and Cu–Ni alloys, in corrosive environments such as sodium chloride solutions. These diagrams provided an early experimental complement to purely thermodynamic models. Subsequent studies extended this approach to a broader variety of alloy–electrolyte systems^34–38.

More recently, Deen and Asselin advanced the concept by directly plotting measured current densities as contour maps, and overlaying them onto classical E–pH diagrams to reflect the rate of anodic processes^39,40. Building on this, Khollari and Asselin demonstrated the application of TK diagrams for predicting localized corrosion phenomena—such as dealloying in Alloy 400 and pitting in Alloy 800—by comparing TK diagrams for both the alloy and its constituent elements^41–43. Collectively, these developments have transformed TK diagrams into robust, experimentally grounded tools that provide practical and realistic insights into corrosion behavior under non-equilibrium conditions.

Here, we first develop TK diagrams for pure iron in deaerated solutions with no added sodium sulfate (Na₂SO₄) and with 0.1 M Na₂SO₄ across a pH range of 1–14 to comprehensively assess its corrosion behavior. To further evaluate active dissolution, passivation, and transpassive corrosion, galvanostatic (GS) polarization was conducted at different anodic currents in 0.1 M Na₂SO₄ solutions. Additionally, electrochemical techniques, including Electrochemical Impedance Spectroscopy (EIS) and linear polarization, and surface analysis through X-ray Photoelectron Spectroscopy (XPS), were employed to characterize the surface films. Our findings provide deeper insight into surface processes on iron, especially in the presence of aggressive anions, across a wide range of pH and potential, which is essential for effective corrosion control. Moreover, understanding the electrochemical performance of iron could pave the way for its broader use in energy storage and environmental sustainability applications.

Results and discussion

TK diagrams

The PDP curves for the iron RDE in deaerated solutions with no added Na₂SO₄ and with 0.1 M Na₂SO₄ across a pH range of 1–14 at 25 °C are shown in Supplementary Fig. S2. The TK diagrams for iron were constructed using these curves (Fig. 1a, b) with the corresponding OCP values at each pH represented by black dots. As shown in Fig. 1a, in no added Na₂SO₄ solutions, iron behaves as an active metal under acidic conditions (pH <7), as its immunity region lies below the equilibrium line for the H⁺/H₂ redox reaction (line a). In this pH range, the anodic current increases rapidly with rising anodic potential as the metal surface undergoes progressive oxidation^44–46, followed by a steady increase leading to the appearance of a limiting current. The emergence of the limiting current is most likely due to diffusion-controlled processes, resulting from the precipitation of reaction products on the alloy surface in the form of a salt film⁴⁷. Several researchers have reported the formation of such salt films during the anodic polarization of iron in sulfuric acid^48–55. This phenomenon is distinct from passivation, which involves the formation of a thin, protective oxide film that severely limits both charge transfer and species transport, resulting in a sharp drop in anodic current⁵⁶.

Fig. 1. Effect of Na₂SO₄ on iron TK diagrams.

TK diagrams for iron rotating disk electrode in deaerated solutions with (a) no added Na₂SO₄ and (b) 0.1 M Na₂SO₄ across a pH range of 1–14 a t 25 °C. The black dots represent the measured OCP values at each pH. In constructing the thermodynamic E-pH diagrams, a total concentration of 10⁻⁶ m was assumed for the iron species and 0.1 M for sulfate species. Dashed lines a and b correspond to hydrogen evolution and oxygen reduction reactions, respectively.

Furthermore, as pH decreases, the higher proton concentration boosts the cathodic reaction rate, which in turn increases the anodic current and corrosion rates in a closed system^57,58. While iron dissolution in acidic conditions is primarily driven by protons (H⁺), the addition of Na₂SO₄ can also influence the process through secondary effects, such as complex formation, which will be discussed in the following section.

The measured OCP values under acidic conditions lie between line a and the Fe²⁺/Fe redox line, attributed to the nature of the OCP as a mixed potential, which falls between the equilibrium potentials of the cathodic and anodic reactions (i.e., hydrogen evolution and iron dissolution, respectively)^41,59.

At pH ≥7, a large positive shift in OCP is observed, corresponding to the formation of a passive layer because the measured OCP falls within the Fe₂O₃ stability region. This shift is linked to the increased concentration of hydroxide ions, which play a key role in the development of the (hydr)oxide layer^60,61. The formation of the passive layer results in a decrease in the measured current density, with a minimum passive current density (i_p) recorded at pH 8 (i_p = 5 ×10⁻⁶ A·cm⁻²). A slight increase in current density is observed as pH is increased above 8. This may be attributed to the anionic dissolution of iron at highly alkaline pH values, possibly in the form of Fe(OH)₄²⁻, as predicted by thermodynamic calculations.

Within the pH 12–14 range, under highly oxidizing conditions, a rapid increase in anodic current is evident, indicating the onset of transpassive dissolution alongside the oxygen evolution reaction (OER)^62,63. Independent studies by Beck et al.⁶⁴ and Serebrennikova et al.⁶⁵ proposed that in highly alkaline solutions, transpassive dissolution of iron occurs alongside the OER, resulting in the release of ferrate(VI) ions (FeO₄²⁻) into solution. Figure 1a shows that this onset shifts to lower potentials with increasing pH, consistent with the Nernst equation, which predicts a decrease in the potentials for both the OER (line b in Fig. 1a) and the transpassive corrosion of iron as pH increases^66,67.

As shown in Fig. 1b, the presence of 0.1 M Na₂SO₄ accelerates iron dissolution under acidic conditions (pH < 7) compared to no added Na₂SO₄ solutions. This is evident from the higher anodic current densities, suggesting that adding Na₂SO₄ promotes iron dissolution by forming soluble sulfate complexes^68,69. A rapid increase of the anodic current with anodic potential is observed, followed by a steady increase due to the salt film formation.

Although iron (hydr)oxides are typically soluble in strongly acidic media⁷⁰, passive films may still form under highly oxidizing potentials. This is demonstrated in Supplementary Fig. S3a, which compares the PDP curves for the iron RDE in deaerated 0.1 M sodium sulfate solutions at pH = 1, recorded at different scan rates. A limiting current associated with the salt film formation is observed, followed by a sharp decline in anodic current indicative of passivation. Decreasing the scan rate leads to reductions in both the limiting current and the potential at which passivation initiates. The increase in current at higher scan rates arises from a combination of faradaic (charge-transfer) and non-faradaic (double-layer charging) contributions, whereas at the lowest scan rate, the contribution from double-layer charging is negligible⁷¹.

Furthermore, Supplementary Fig. S3b shows that RDE rotation speed also influences the passivation potential. Therefore, the TK diagrams in this work should be viewed as quasi-steady-state representations of iron anodic behavior derived from potentiodynamic scans and intended to provide comparative maps of iron corrosion in both no added Na₂SO₄ and 0.1 M Na₂SO₄ solutions.

The formation of a passive film at highly oxidizing potentials can be explained according to the Point Defect Model (PDM)⁷², which describes the oxide layer as a defective semiconductor containing mobile anion and cation vacancies. These defects migrate under the influence of an electric field, facilitating film growth. As the oxide thickens, the internal field strength diminishes, slowing further growth. Nonetheless, if the rate of oxide formation exceeds that of chemical dissolution, a kinetically stable passive film can still develop under these conditions^72,73.

In the pH range of 7–11.5, sulfate species inhibit passivation, resulting in current densities approximately three orders of magnitude higher than in no added Na₂SO₄ solutions. Chen et al.⁷⁴ observed a transition from passivation to active corrosion for iron in deaerated 0.05 M NaHCO₃ (pH 8.4) upon the addition of 1 M sulfate ions. A similar phenomenon was reported by Gui and Devine⁷⁵ for iron in 0.3 M sodium sulfate at pH 10. This effect is likely due to preferential sulfate adsorption and complexation with iron, which prevents passive film formation. Using Density Functional Theory, Liu et al.⁷⁶ demonstrated that sulfate has a highly negative adsorption energy on the (100) lattice plane, indicating a strong interaction with iron. This high affinity suggests that sulfate can achieve extensive surface coverage, limiting the adsorption of other ions, such as OH⁻, and ultimately hindering passivation. Similar preferential adsorption of sulfate ions has been reported on other metal surfaces. Ma et al.⁷⁷ showed that in 1 M sodium hydroxide with 0.5 M chloride ions, the addition of 0.05 M sulfate anions led to their preferential adsorption onto a nickel anode surface, forming a negatively charged layer. This layer repelled chloride and OH⁻ ions away from the anode surface through electrostatic repulsion. Likewise, Lesnykh et al.⁷⁸ reported competitive adsorption of sulfate and hydroxide ions on silver surfaces. Their study demonstrated that in alkaline solutions containing sulfates, the rate of silver dissolution increases due to the formation of sulfate–hydroxide complexes.

At pH ≥12, the formation of a passive film is observed, indicating a shift from sulfate to hydroxide adsorption. Hackerman and Stephens⁷⁹ demonstrated that sulfate adsorption on iron surfaces is pH-dependent; up to pH 11, the amount of actively adsorbed sulfate remained relatively constant, but above this pH, it decreased significantly. The competitive adsorption model by Taylor et al.⁸⁰ predicts that as pH increases, the coverage of corrosive anions on the surface decreases due to the increased adsorption of OH⁻ ions. The OH⁻ adsorption plays a key role in the early stages of passivation as a stable Fe(OH)₂ layer allows oxygen to diffuse into the iron substrate without substantial iron dissolution. As a result, iron oxidation occurs in the underlying layers⁸¹.

Based on Fig. 1b, the lowest i_p (~1 ×10⁻⁴ A·cm⁻²) is recorded at pH 12 and a slight decrease in the passive layer protection is observed at pHs 13 and 14, likely due to the increased solubility of iron oxides and hydroxides at highly alkaline pHs⁷⁰. A similar trend was observed in no added Na₂SO₄ solutions (Fig. 1a). The results are in agreement with the findings of Amaral and Muller²⁷, reporting that for an iron RDE in 0.05 M Na₂SO₄ solutions within a pH range of 10–13, i_p is lowest at pH 12.

As highly alkaline solutions (pH 13 and 14) in this study were prepared using a mixture of sodium and potassium hydroxides, the observed increase in passive current density at pH >12 might be attributed to variations in cation composition. To evaluate this possibility, PDP were conducted at pH 12 in 0.1 M Na₂SO₄ solutions, with the pH adjusted using either sodium hydroxide or potassium hydroxide (Supplementary Fig. S4). The results revealed that the passive current density in the potassium hydroxide-based solution was only slightly lower than that in the sodium hydroxide-based counterpart, indicating that potassium ions do not detrimentally affect iron passivity under these conditions. Therefore, the increase in passive current densities observed at pH 13 and 14 reflects the intrinsic influence of higher pH on the passive film characteristics.

At pH ≥12, in the presence of Na₂SO₄, the passive layer shows higher i_p (1 ×10⁻⁴ to 3 ×10⁻⁴ A·cm⁻²) compared to the no added Na₂SO₄ solution (1 ×10⁻⁵ to 8 ×10⁻⁵ A·cm⁻²), suggesting reduced protection. Cekerevac et al.²⁶ reported that the addition of 0.05 M sulfate ions to a 10 M KOH solution (pH 14.2) increases i_p from 7 ×10⁻⁵ A·cm⁻² to 5 ×10⁻⁴ A·cm⁻². They attributed this increase to the formation of soluble sulfate-hydroxide complexes. Additionally, there is a possibility that sulfate incorporation into the passive layer may weaken its structural integrity and accelerate its dissolution rate⁸².

Compared to no added Na₂SO₄ conditions, the presence of 0.1 M Na₂SO₄ leads to an increase in current density under highly alkaline and oxidizing conditions (top-right corner of the TK diagram). This increase may result from sulfate-induced weakening of the passive film, thereby accelerating the transpassive dissolution of iron^26,76. It could also arise from enhanced OER activity, as sulfate is known to enhance OER activity through multiple mechanisms: (i) facilitating local charge redistribution at active metal sites, thereby optimizing the adsorption energy of OER intermediates (e.g., OOH*)^83,84; (ii) promoting the formation of oxygen vacancies, which enhances charge transfer⁸⁵; (iii) introducing coordination-unsaturated metal centers, increasing the density and reactivity of active sites⁸⁵; and (iv) assisting in the electrochemical reconstruction of pre-catalysts into catalytically active oxyhydroxide phases, while preventing their transformation into less active oxides^86,87.

It is also worth noting that the addition of 0.1 M Na₂SO₄ significantly increases the solution conductivity (Fig. 2), which can influence the dissolution behavior of iron. However, surface phenomena such as passivation play a more dominant role in governing the electrochemical response. This is clearly demonstrated by comparing the behavior of iron in 0.1 M Na₂SO₄ solutions at pH 11 and 12 (Fig. 1b). Although the conductivity at pH 12 is higher, a much lower current was recorded during PDP due to passivation, whereas at pH 11, active corrosion with high current density was observed. This highlights the dominant role of the passive film’s barrier properties over bulk solution characteristics, such as conductivity.

Fig. 2. Comparing conductivity of no added Na₂SO₄ and 0.1 M Na₂SO₄ solutions.

Measured conductivity of no added Na₂SO₄ (black dots) and 0.1 M Na₂SO₄ (red dots) solutions across various pH levels, adjusted using sulfuric acid or sodium hydroxide. Note: Conductivity at pH 14 exceeded the instrument’s measurement range.

GS polarization results

To further investigate the stability, growth, and breakdown of the passive film on iron, GS experiments were conducted in deaerated 0.1 M Na₂SO₄ solutions across the pH range of 1–14. As the minimum i_p in the presence of Na₂SO₄ was recorded at pH 12, equal to 1 ×10⁻⁴ A·cm⁻², three constant anodic currents were selected for GS experiments: I₁ = 0.01 mA (i₁ = 5 ×10⁻⁵ A·cm⁻²), I₂ = 0.1 mA (i₂ = 5 ×10⁻⁴ A·cm⁻²), and I₃ = 1 mA (i₃ = 5 ×10⁻³ A·cm⁻²). With i₁ < i_p, the goal was to assess conditions favoring passive film growth, while i₂ and i₃ > i_p were used to promote depassivation and to evaluate film breakdown (Fig. 3).

Fig. 3. Rationale for Selecting Galvanostatic Currents.

Potentiodynamic polarization curve of an iron rotating disk electrode in deaerated 0.1 M Na₂SO₄ solution at pH 12. The marked i₁ and i₂ correspond to constant currents of 0.01 mA (5 × 10⁻⁵ A·cm⁻²) and 0.1 mA (5 × 10⁻⁴ A·cm⁻²), respectively, used in galvanostatic polarization experiments.

Supplementary Fig. S5 presents the chronopotentiometric curves. Based on Figs. S5a and b, at pH <10, only a small anodic overpotential is needed to sustain an anodic current of 0.01 mA, indicating that iron remains in an active dissolution state^88,89. In the pH range of 10–11, the potential initially increases, then decreases and stabilizes, suggesting the formation of a transient surface film that eventually dissolves^90,91. At pH 12–14, a gradual increase in potential over time indicates the growth of a passive film^89,90. When the current increases to 0.1 mA (Supplementary Fig. S5c, d), at pH 1–11, the potential initially rises, reaching a peak before gradually declining to a stable value. This behavior reflects the formation of a transient anodic film that eventually breaks down^90,91. In contrast, at pH 12–14, the potential rises rapidly and remains stable throughout the test due to transpassive dissolution^92–95.

Galvanostatic measurements were also conducted at an anodic current of 1 mA (5 mA·cm⁻²) to exceed the expected critical current density for passivation, thereby evaluating whether higher applied anodic currents could induce passivation at pH values below 12. The resulting chronopotentiometric curves (Supplementary Fig. S5e, f) indicate that, across the entire pH range below 12, a transient anodic film may initially form but ultimately breaks down over time. These results confirm that the absence of passivation under these conditions is not due to insufficient anodic current, but rather reflects an inherent instability of the passive film.

Results of GS polarization at 0.1 mA are summarized in Fig. 4. This anodic current corresponds to a total dissolved iron concentration of 10⁻⁵ M during active corrosion. Accordingly, Fig. 4 shows the potential required to dissolve this amount of iron in deaerated 0.1 M Na₂SO₄ solutions at pH <12. The figure highlights distinct regions of active corrosion, passivation, and transpassive corrosion. It is evident that in the presence of Na₂SO₄, iron does not undergo passivation until pH ≥12. At this point, a passive film forms; however, beyond a certain anodic potential, passivity breaks down, accompanied by the OER. The potentials corresponding to 0.1 mA (5 × 10⁻⁴ A·cm⁻²) at each pH level, as predicted by the TK diagram in Fig. 1b, are also shown in Fig. 4. The strong agreement between the measured potentials from the two methods confirms the accuracy of the TK diagram in evaluating iron’s dissolution behavior.

Fig. 4. Comparing galvanostatic polarization results and TK diagram results.

Summary of galvanostatic polarization results (black triangles) for an iron rotating disk electrode subjected to an anodic current of 0.1 mA for 1800 s in deaerated 0.1 M Na₂SO₄ solutions across a pH range of 1–14. For comparison, the corresponding potentials at the same current (0.1 mA) from the TK diagram in Fig. 1b are also included (blue stars).

OER contribution

As discussed, transpassive dissolution occurs concurrently with the oxygen evolution reaction (OER). To quantify their respective contributions, the amount of dissolved iron after GS polarization at 0.1 mA (5 × 10⁻⁴ A · cm⁻²) at pH 12 and 14 was measured by ICP and converted into current (Fig. 5). The calculation methodology is detailed in Supplementary Material, Section 3. The results show that under the applied anodic current of 0.1 mA, only a negligible fraction of the faradaic current (<3%) is due to iron dissolution at pH 12, whereas at pH 14, iron dissolution accounts for a more significant portion, ~12.4% of the total faradaic current.

Fig. 5. Oxygen Evolution vs. Iron Dissolution Contributions at 0.1 mA.

Contribution of oxygen evolution (red rectangles) and iron dissolution (blue rectangles) to the total current measured during galvanostatic polarization at 0.1 mA in deaerated 0.1 M Na₂SO₄ solution at pH 12 and 14.

EIS results

So far, we have observed that in the presence of 0.1 M Na₂SO₄, applying a constant anodic current of 0.1 mA causes active dissolution at pH values below 12, and passive film breakdown accompanied by the OER at pH values above 12. To further investigate the effect of transpassive corrosion on passive film properties, EIS experiments were performed both (i) before and (ii) immediately after GS polarization at 0.1 mA in 0.1 M Na₂SO₄ solutions. The potential cycle is shown in Supplementary Fig. S1. This approach, rather than performing EIS at a high anodic potential, helps avoid interference from the OER. Comparing the EIS results under these two conditions provides insights into changes in passive film properties after transpassive corrosion. The Nyquist, Bode phase, and Bode impedance plots are presented in Fig. 6. To verify the physical validity of the EIS data, Kramers–Kronig analysis was performed, confirming that the system met the criteria of linearity, stability, and causality, thereby validating the impedance spectra.

Fig. 6. Electrochemical Impedance Spectroscopy (EIS) results.

a, b Nyquist, c, d Bode phase, and e, f Bode magnitude plots of an iron rotating disk electrode in deaerated 0.1 M Na₂SO₄ solutions of various pHs (a, c, e) at OCP and (b, d, f) after galvanostatic polarization at an anodic current of 0.1 mA for 1800 s.

At OCP, Nyquist plots in pH 4 and 8 solutions show a capacitive semicircle in the high to intermediate-frequency range and an inductive loop in the low-frequency range (Fig. 6a). The diameter of the capacitive semicircle corresponds to the charge transfer resistance^96,97. The inductive loop likely results from the adsorption of intermediate corrosion products like [FeOH]_ads, sulfate complexes, or [H⁺]_ads on the electrode surface^68,69,98,99. At pH 10, the Nyquist plot shows a capacitive semicircle over the entire frequency range, whereas the spectra for pH 12 and 14 also display a linear region at lower frequencies related to diffusion-limited processes^100,101. After GS polarization, the overall shape of the Nyquist plots does not change (Fig. 6b); however, the inductive loop observed at pH 4 and 8 disappears.

The Bode phase plots at OCP (Fig. 6c) show a symmetric peak at intermediate frequencies for pH 4, 8, and 10, indicating a single time constant associated with the charge transfer process¹⁰². In contrast, at pH 12 and 14, the phase angle shows asymmetric behavior, suggesting the presence of two overlapping time constants¹⁰³. The second time constant is likely associated with the formation of a passive film in high pH solutions. After GS polarization (Fig. 6d), the Bode phase plots for pH 4–10 show a symmetric peak around 1 Hz, whereas two time-constants are detected in solutions with pH 12 and 14.

The Bode impedance plots at OCP and after GS polarization are shown in Fig. 6e and f, respectively. In these plots, low-frequency impedance reflects charge transfer resistance and increases with pH up to 12, and then slightly decreases at pH 14.

Based on the features of EIS data, the electrochemical equivalent circuit shown in Fig. 7a was chosen to fit the EIS spectra at pH 4 under OCP conditions before GS polarization. In this model, R_s represents the solution resistance, CPE_dl is a constant phase element (CPE) representing the double layer capacitance, R_ct is charge-transfer resistance, R_L is the inductive resistance, and L is the inductance¹⁰⁴. The inductive elements (R_L and L) were incorporated to account for the inductive loops observed in the impedance plots. Owing to the presence of depressed semicircles in the Nyquist plots, the CPE was used instead of an ideal capacitor¹⁰⁵. The impedance of a CPE is given in Eq. (1):

$${\mathrm{Z}}_{\mathrm{CPE}}={{\mathrm{Y}}_0}^{-1}{\left(\mathrm{j}\mathrm{\omega }\right)}^{-\mathrm{n}}$$ 1

where Y₀ is the admittance, j² = −1, ω is the angular frequency, and n is the dispersion coefficient¹⁰⁵. To fit the EIS data recorded at OCP for pH 8 and 10, as well as after GS polarization at pH 4–10, the same equivalent circuit was used, excluding the inductive elements (R_L and L), since no inductive behavior was observed under these conditions.

Fig. 7. Electrochemical equivalent circuit used to simulate the EIS data of an iron rotating disk electrode in deaerated 0.1 M Na₂SO₄ solutions at OCP and after galvanostatic polarization at an anodic current of 0.1 mA for 1800 s.

a For pH 4, 8, and 10, and b for pH 12 and 14.

Figure 7b shows the equivalent circuit used to fit the impedance curves obtained at pH 12 and 14. This model consists of R_s in series with a high-frequency time constant representing the resistance of the defective and porous passive film (R_f) and its corresponding capacitance (CPE_f), and a low-frequency time constant which accounts for the charge transfer resistance (R_ct) and the double layer capacitance (CPE_dl). Also, R_ct is in series with an infinite Warburg element (W), indicating that corrosion reaction is limited by mass transfer^106,107.

The fitted EIS results before and after GS polarization are summarized in Table 1. Good fitting quality was confirmed by chi-squared (χ²) values less than 5 × 10^−4 108. To assess the statistical independence of these fitting parameters and ensure the equivalent circuit model was not over-specified, a Pearson correlation matrix was constructed using EIS data collected across all pH values and conditions (before and after GS polarization). The resulting heatmap, shown in Supplementary Fig. S6, visualizes the correlation coefficients. Most correlations were consistent with expected electrochemical trends, and each circuit element contributed meaningfully to capturing distinct electrochemical processes. Full details of the correlation analysis and its interpretation are provided in the Supplementary Material, Section 3.

Table 1.

EIS fitting results for an iron rotating disk electrode in deaerated 0.1 M Na₂SO₄ solutions at various pH levels at OCP and after galvanostatic polarization at anodic current of 0.1 mA for 1800 s

pH	RS (Ω.cm2)	CPEdl		Rct (Ω.cm2)	RL (Ω.cm2)	L (H.cm2)	CPEf		Rf (Ω.cm2)	σ (Ω.cm2.s−0.5)
		Y0,dl (Ω−1.cm−2.sn)	ndl				Y0,f (Ω−1.cm−2.sn)	nf
Before GS
pH = 4	11.8	1.8 ×10−3	0.81	129.1	290.9	5963.8	–	–	–	–
pH = 8	11.1	4.9 ×10−3	0.67	166.2	–	–	–	–	–	–
pH = 10	11.3	5.5 ×10−3	0.78	237.1	–	–	–	–	–	–
pH = 12	8.7	5.3 ×10−4	0.47	900.6	–	–	3.4 ×10−5	0.93	127.2	1498.1
pH = 14	4.5	1.2 ×10−3	0.39	1481	–	–	5.2 ×10−5	0.94	30.8	613.9
After GS
pH = 4	12.9	5.4 ×10−3	0.70	134.0	–	–	–	–	–	–
pH = 8	10.2	3.5 ×10−3	0.62	208.5	–	–	–	–	–	–
pH = 10	11.4	3.7 ×10−3	0.58	403.5	–	–	–	–	–	–
pH = 12	7.6	3.6 ×10−4	0.36	4647.9	–	–	2.9 ×10−5	0.93	70.6	1534.2
pH = 14	1.9	1.1 ×10−3	0.37	2111.5	–	–	4.9 ×10−5	0.92	20.4	406.5

Based on Table 1, before GS polarization, at pH 4–10, R_ct is low, while Y_0,dl is high, indicating an active charge transfer process at the electrode/electrolyte interface¹⁰⁹. Under these conditions, the n_dl value ranges from 0.5 to 1, suggesting a rough and heterogeneous surface typical of active corrosion¹¹⁰. At pH 12, the increase in R_ct and the decrease in Y_0,dl are significant, and a Warburg coefficient (σ) appears, consistent with surface passivation that inhibits electrochemical reactions¹⁰⁴. At pH 14, despite a higher R_ct, a lower R_f, along with a higher Y_0,dl and Y_0,f, and a notable lower Warburg coefficient compared to pH 12 suggest a less protective passive film. The findings support the TK diagram results (Fig. 1b), confirming active corrosion at pH 4–10 and spontaneous passivation at pH ≥12. The passive layer at pH 12 has the highest corrosion resistance.

After GS polarization, both R_ct and Y_0,dl increase at pH 4, showing active corrosion. At pH 8 and 10, a slight increase in R_ct couples with a minor decrease in Y_0,dl, suggest the formation of corrosion products that partially block active sites and reduce the exposed surface area¹⁰⁷. At pH 12, despite a decrease in R_f, R_ct increases with a slight increase in σ, implying that transpassive dissolution at 0.1 mA caused negligible damage to the passive film. In contrast, at pH 14, passive film degradation is more pronounced, as evidenced by a smaller increase in R_ct, decrease in R_f, and a reduction in σ. Since σ is inversely related to defect concentration¹¹¹, it can be inferred that after GS polarization, the passive film has a higher defect density at pH 14 compared to pH 12. These findings confirm that transpassive dissolution remains limited at pH 12 but becomes more significant at pH 14.

The effective capacitance (C_eff) of the passive film can be extracted from the CPE_f element using Eq. (2)^106,112,113:

$${\mathrm{C}}_{\mathrm{eff},\mathrm{f}}={{\mathrm{Y}}_{0,\mathrm{f}}}^{\frac{1}{{\mathrm{n}}_{\mathrm{f}}}}{{.\mathrm{R}}_{\mathrm{f}}}^{\frac{1-{\mathrm{n}}_{\mathrm{f}}}{{\mathrm{n}}_{\mathrm{f}}}}$$ 2

The film thickness (L) can be roughly calculated using the following Equations:

$$\mathrm{L}=\frac{{{(\mathrm{\epsilon \; \epsilon }}_0)}^{n_f}}{g.{\mathrm{C}}_{\mathrm{eff}}{.{\rho }_{\delta }}^{1-n_f}}$$ 3

$$g=1+2.88{\left(1-n_f\right)}^{2.375}$$ 4

Where ε is the dielectric constant of the passive film (12 for iron oxide), ε₀ is the vacuum permittivity (8.8542 × 10⁻¹⁴ F/cm), and ρ_δ is the oxide resistivity (450 Ω.cm)^112,114,115. The passive film thickness after GS polarization was calculated to be 2.6 nm at pH 12 and 2.2 nm at pH 14 (Fig. 8a). The thinner film at pH 14 could be due to higher transpassive dissolution.

Fig. 8. Passive film thickness and comparison of EIS and LPR results.

a Calculated passive film thickness based on XPS (red) and EIS (blue) results after galvanostatic polarization of an iron rotating disk electrode at 0.1 mA for 1800 s in deaerated 0.1 M Na₂SO₄ solutions at pH 12 and 14. b Comparison of the R_p values obtained from linear polarization (LPR) (red dots) and EIS fitting (blue dots) after galvanostatic polarization.

LPR was also performed after GS polarization and the calculated R_p values¹¹⁶ were compared with those extracted from EIS fitting (Fig. 8b), assuming that R_ct from the EIS result corresponds to R_p. The highest R_p value was obtained at pH 12, and a strong agreement between the results is observed.

Surface film composition

XPS analysis was conducted after GS polarization at 0.1 mA in deaerated 0.1 M Na₂SO₄ solutions at pH 10, 12, and 14 to assess the composition of surface films. The survey scans (Fig. 9a, d, g) show peaks corresponding to carbon (surface contamination), iron and oxygen (from surface film or substrate), and silicon. At pH 14, sodium and potassium signals were also detected, likely originating from the solution. Sulfur peaks were observed at pH 10 and 14, indicating the presence of adsorbed sulfate species. These findings suggest preferential sulfate adsorption at pH <12, while sulfur detected at pH 14 is likely associated with sulfate adsorption during transpassive corrosion.

Fig. 9. X-rays photoelectron spectroscopy analysis.

XPS survey, Fe 2p, and O 1s spectra of an iron rotating disk electrode after galvanostatic polarization in deaerated 0.1 M Na₂SO₄ solutions at an anodic current of 0.1 mA for 1800 s with a–c pH 10, d−f pH 12, and g–i pH 14.

To evaluate the oxidation state of iron, Fe 2p spectra were deconvoluted. At pH 10 (Fig. 9b), the Fe 2p_3/2 peak was deconvoluted into the subpeaks of Fe₃O₄, Fe₂O₃, and FeOOH^117–119. The ratio of Fe(II) (mainly from Fe₃O₄) to Fe(III) species (from Fe₂O₃ and FeOOH) is low. Since magnetite (Fe₃O₄) is considered the more corrosion-resistant component of the passive film^103,120, its reduced presence suggests that the surface film formed at pH 10 is not protective. This interpretation is consistent with the EIS results, indicating that, although iron oxides and hydroxides are present, the film at pH 10 likely consists of loosely adherent corrosion products rather than a compact, protective passive layer.

The Fe(II)/Fe(III) ratios presented in this work are derived using envelope fitting of the Fe 2p region, following the methodology of Biesinger et al.¹²¹, and are intended as semi-quantitative estimates. Given the spectral complexity and potential peak overlap in mixed oxide systems, these values are used primarily to support comparative trend analysis rather than precise stoichiometric determination^121–123.

At pH 12 and 14 (Fig. 9e, h), the Fe 2p_3/2 peak undergoes deconvolution into Fe₃O₄ and Fe₂O₃ subpeaks, with an additional subpeak at 706.5 eV attributed to metallic iron (Fe⁰)¹²⁴. It has been reported that in alkaline environments, increasing the applied potential gradually oxidizes the iron passive film from magnetite (Fe₃O₄) to hematite (Fe₂O₃), corresponding to a progressive decrease in Fe(II) content^125,126. In particular, in 0.1 M sodium hydroxide, the passive film becomes predominantly composed of Fe(III) species at potentials above ~0.1–0.2 V_SHE¹²⁷. Since this oxidation process is reversible¹²⁷, the presence of Fe₃O₄ at pH 12 and 14 may arise from partial reduction of Fe(III) species upon returning to OCP after GS polarization. Furthermore, the simultaneous detection of Fe₃O₄ and Fe₂O₃ aligns with the well-established bilayer structure of the passive film in alkaline solutions, comprising an inner Fe₃O₄ layer and an outer layer of FeOOH or its dehydrated form Fe₂O₃^128,129.

Equations (5) and (6) were used to calculate the thickness of the Fe₃O₄ and Fe₂O₃ layers, respectively, based on the ratios between the deconvoluted peak areas of oxide and metal components obtained from the fitted XPS spectra^42,130–133:

$$d_{{\mathit{Fe}}_3{O}_4}={\lambda }_{\mathit{Fe}}^{{\mathit{Fe}}_3{O}_4}.\mathit{Sin}\theta .ln\left[1+\frac{N_{\mathit{Fe}}^{\mathit{metal}}\times {\lambda }_{\mathit{Fe}}^{\mathit{metal}}\times I_{\mathit{Fe}}^{{\mathit{Fe}}_3{O}_4}}{N_{\mathit{Fe}}^{{\mathit{Fe}}_3{O}_4}\times {\lambda }_{\mathit{Fe}}^{{\mathit{Fe}}_3{O}_4}\times I_{\mathit{Fe}}^{\mathit{metal}}}\right]$$ 5

$$d_{{\mathit{Fe}}_2{O}_3}={\lambda }_M^{{\mathit{Fe}}_2{O}_3}.\mathit{Sin}\theta .ln\left[1+\frac{N_M^{\mathit{metal}}\times {\lambda }_M^{\mathit{metal}}\times I_M^{{\mathit{Fe}}_2{O}_3}}{N_M^{{\mathit{Fe}}_2{O}_3}\times {\lambda }_M^{{\mathit{Fe}}_2{O}_3}\times I_M^{\mathit{metal}}}.\exp \left(\frac{-d_{{\mathit{Fe}}_3{O}_4}}{{\lambda }_M^{{\mathit{Fe}}_3{O}_4}.\mathit{Sin}\theta }\right)\right]$$ 6

where d is the thickness of the layer, λ_M^oxide and λ_M^metal are the inelastic mean free path of photoelectrons for iron in oxide or metal matrix and were estimated using the TPP-2 formula proposed by Tanuma et al.^133–135, θ is the photoelectron take-off angle (90° in this case), N_Fe^oxide and N_Fe^metal are the atomic density of iron in oxide or metal, and I_Fe^oxide and I_Fe^metal are the normalized XPS peak area of oxide or metal. A detailed description of the calculation procedure is provided in the Supplementary Material, Section 4. The relative atomic percentages shown in Fig. 9 were used to calculate the weighted thicknesses of the oxide layer (Fig. 8a). The results show a thinner film at pH 14 compared to pH 12 and a good agreement between the estimated thicknesses based on XPS and EIS results can be seen.

The O 1s spectra (Fig. 9c, f, i) revealed three components: lattice oxide (O²⁻) at ~529.7 eV, hydroxide (OH⁻) or defective oxide species at ~531.1 eV, and organics at ~531.2 eV^136,137. In addition, at pH 12 and pH 14, a contribution at ~533 eV is attributed to oxygen bound to silicon (SiO₂)¹³⁸, likely originating from trace silica contamination. It should be noted that in interpreting O 1s spectra, it is critical to account for the contribution of oxygen-containing functional groups associated with adventitious carbon, which can overlap with hydroxide and defect oxide signals and leads to overestimation of these components¹³⁹. At pH 10, the hydroxide/defective oxide component dominated, corresponding to FeOOH oxyhydroxide, along with lattice oxide mainly from Fe₂O₃. At pH 12 and 14, the lattice oxide peak was most prominent, in agreement with Fe 2p results indicating significant Fe₃O₄ and Fe₂O₃ content.

Taken together, these complementary techniques provide a unified picture of how sulfate alters the dissolution, passivation, and transpassive behavior of iron across a wide pH and potential range. The TK diagrams revealed that passivation occurs above pH 7 in deaerated solutions with no added Na₂SO₄, with optimal stability at pH 8, whereas the presence of 0.1 M Na₂SO₄ delayed passivation until pH 12 and significantly increased passive current densities. This demonstrates that sulfate anions act as aggressive species that destabilize the passive film, suppress its protective qualities, and shift the passivation window to more alkaline conditions. Galvanostatic polarization further showed that active dissolution dominates below pH 12 in 0.1 M Na₂SO₄ solution, with transpassive processes emerging at higher pH values. ICP analyses clarified that under strongly alkaline, oxidizing conditions, oxygen evolution competes with transpassive dissolution, contributing substantially to the overall anodic current. EIS and XPS measurements confirmed pH- and sulfate-dependent differences in passive film properties and compositions, demonstrating a transition from loosely adherent products at pH 10 to more protective but compositionally distinct oxides at pH 12 and 14. Altogether, these results emphasize the critical role of sulfate in compromising iron’s passivity and highlight the interplay between pH, potential, and aggressive anions in governing dissolution and passivation behavior of iron. Beyond mechanistic insights, the findings also offer practical guidance for improving the durability of iron-based materials in sulfate-rich environments.

Methods

Electrode and test solutions

A 99.99% iron rod with 5 mm diameter was used. Samples in disk shape, with a length of 10 mm were cut from the rod and press-fitted into interchangeable holders made of Polytetrafluoroethylene (PTFE) from PINE Research (E4TQ ChangeDisk) to form rotating disk electrodes (RDEs) with an exposed surface area of ~0.2 cm². Prior to each test, the RDEs were wet-ground up to 1200 grit using SiC papers, followed by rinsing in deionized (DI) water and drying in a stream of hot air.

The electrochemical tests were performed in deaerated solutions at 25 °C, covering a pH range from 1 to 14. Two types of electrolytes were used: (i) deionized (DI) water as the base electrolyte, with pH adjusted by adding sulfuric acid (acidic pHs), sodium hydroxide (neutral or alkaline pHs), or a 6 M NaOH/KOH mixture (1:1 w/w) for highly alkaline conditions (pH 13 and 14). These solutions will be referred to as “no added Na₂SO₄” in this paper. (ii) a 0.1 M Na₂SO₄ solution was first prepared in DI water, after which the pH was adjusted using the approach as above. Figure 2 summarizes the measured conductivity of prepared solutions.

It should be mentioned that in the no added Na₂SO₄ solution at pH 1, the addition of sulfuric acid for pH adjustment introduces ~0.026 M sulfate ions. Under near-neutral and mildly acidic conditions, however, this contribution is much smaller (e.g., ~0.005 M at pH 2) because only small amounts of acid are required and the second dissociation of sulfuric acid is limited (K_a2 ≈ 1.1 ×10⁻²)^140,141. The details of the calculations are provided in Supplementary Materials, Section 1.

Electrochemical tests

Electrochemical tests were conducted using a three-electrode setup consisting of the iron RDE as the working electrode, a platinum counter electrode (surface area of 2.1 cm²), and an Ag/AgCl reference electrode (RE) filled with saturated KCl (0.197 V vs SHE at 25 °C), housed within a water-jacketed cell (AKCELL3, PINE Research). Prior to each experiment, nitrogen purging was conducted for 60 min and maintained throughout the experiment.

After recording open circuit potential (OCP) for 60 min, potentiodynamic polarization (PDP) was performed through a potential range from −0.8 to 1 V versus the RE. The tests were conducted in deaerated solutions with no added Na₂SO₄ and with 0.1 M Na₂SO₄ across a pH range of 1–14 at 25 °C, using a scan rate of 0.167 mV/s and a working electrode rotation speed of 500 rpm.

Galvanostatic (GS) polarization was carried out in deaerated solutions of 0.1 M Na₂SO₄ across a pH range of 1–14 under anodic currents of 0.01, 0.1, and 1 mA for 1800 s. Based on Faraday’s law, these currents correspond to dissolved iron concentrations of ~10⁻⁶ M, 10⁻⁵ M, and 10⁻⁴ M under active dissolution conditions (assuming n = 2). During transpassive corrosion (assuming n = 3), the corresponding concentrations are ~6 ×10⁻⁷ M, 6 ×10⁻⁶ M, and 6 ×10⁻⁵ M, respectively. Calculation details are provided in the Supplementary Material, Section 2.

Electrochemical impedance spectroscopy (EIS) was performed before and after GS polarization at 0.1 mA for 1800 s in deaerated solutions of 0.1 M Na₂SO₄ at pH values of 4, 8, 10, 12, and 14 to evaluate changes in the surface and interfacial properties of the iron RDE due to GS polarization. The sequence was as follows: OCP monitoring for 60 min, EIS measurements over a frequency range of 0.01–100 kHz with a 10 mV AC signal (root mean square), a second 60-min OCP monitoring, GS polarization at 0.1 mA for 1800 s, a second round of EIS measurements across a frequency range of 0.01–100 kHz using a 10 mV AC perturbation (root mean square), a 30-min OCP recording, and finally, a linear polarization resistance (LPR) test. Supplementary Fig. S1 shows a schematic of the potential cycle.

Constructing E-pH diagrams

Details of the procedure for constructing the thermodynamic E-pH diagrams can be found in ref. ¹⁴² and the associated references. In brief, a comprehensive review was first conducted to determine the standard thermodynamic properties for all possible species^143–146. An Excel Visual Basic (VBA) code was then developed to calculate the equilibrium distribution of the species as a function of pH, assuming total concentrations of Fe(II) and Fe(III) equal to 10⁻⁶ M, and 0.1 M for sulfate species. Finally, E-pH diagrams for the Fe-H₂O and Fe-SO₄²⁻-H₂O systems were constructed using Eqs. (7) and (8) for electrochemical and nonelectrochemical reactions, respectively:

$$\mathrm{aA}+\mathrm{bB}+\mathrm{m}{\mathrm{H}}^{+}+\mathrm{n}{\mathrm{e}}^{-}=\mathrm{cC}+\mathrm{dD};\mathrm{E}={\mathrm{E}}^{\circ }+\frac{\mathrm{RT}}{\mathrm{nF}}\ln \left(\frac{{\mathrm{a}}_{\mathrm{A}}^{\mathrm{a}}.{\mathrm{a}}_{\mathrm{B}}^{\mathrm{b}}.{\mathrm{a}}_{{\mathrm{H}}^{+}}^{\mathrm{m}}}{{\mathrm{a}}_{\mathrm{C}}^{\mathrm{c}}.{\mathrm{a}}_{\mathrm{D}}^{\mathrm{d}}}\right)$$ 7

Here E⁰, R, T, n, F, and a_A are the standard potential, gas constant, absolute temperature, number of transferred electrons, Faraday’s constant, and activity of species.

$$\mathrm{wW}+\mathrm{xX}=\mathrm{yY}+\mathrm{zZ}+\mathrm{m}{\mathrm{H}}^{+};\mathrm{l}\mathrm{nK}=\ln \left(\frac{{\mathrm{a}}_{\mathrm{Y}}^{\mathrm{y}}.{\mathrm{a}}_{\mathrm{Z}}^{\mathrm{z}}.{\mathrm{a}}_{{\mathrm{H}}^{+}}^{\mathrm{m}}}{{\mathrm{a}}_{\mathrm{W}}^{\mathrm{w}}.{\mathrm{a}}_{\mathrm{X}}^{\mathrm{x}}}\right)=-\frac{{\mathrm{\Delta }\mathrm{G}}^{\circ }}{\mathrm{RT}}$$ 8

Constructing TK diagrams

The measured current densities during the PDP were plotted as contours on the thermodynamic E-pH diagram of iron, with E and pH representing the electrode potential and the proton activity, respectively^39,40,43. Regions with a negative current density (where the cathodic reaction prevails) and current densities below 1 × 10⁻⁷ A·cm⁻² (equal to a corrosion rate of ~1 µm/y) were labeled as the immunity zone (shown in green). Current densities exceeding 1 × 10⁻⁵ A·cm⁻² (a corrosion rate of ~100 µm/y) were categorized as the corrosion zone (orange to red), while those falling in between considered as passivation zone (displayed in blue and yellow). The OCP values measured at each pH were added to the TK diagram.

Characterization

An Agilent 7700x quadrupole Inductively Coupled Plasma Mass Spectrometer (ICP-MS), operating in helium collision cell mode, was used to measure the concentrations of dissolved iron ions after GS polarization.

The composition of the surface film was analyzed using a Kratos AXIS Supra X-ray photoelectron spectrometer (XPS) equipped with a monochromatic Al Kα source (15 mA, 15 kV). To ensure accuracy, the work function of the instrument was calibrated by setting a binding energy of 83.96 eV for the Au 4f7/2 line representing metallic gold. Also, the spectrometer dispersion was adjusted to achieve a binding energy of 932.62 eV for the Cu 2p_3/2 line corresponding to metallic copper. The analysis area and the pass energy selected were 300 × 700 µm² and 160 eV, respectively. To correct for charge effects, the aliphatic (C-C) adventitious carbon peak was set to 284.8 eV. Signal processing and deconvolution were conducted using CasaXPS software with Shirley background subtraction. The deconvolution of high-resolution Fe 2p spectra was performed using the multiplet-split envelope method, with established fitting parameters and constraints based on standard metallic and oxide samples of Fe and theoretical XPS modeling^121–123. The contribution of oxygen from adventitious carbon (organic oxygen) to the O 1s envelope was quantified following the method of Henderson et al.¹³⁹. The C 1s spectrum was deconvoluted into C–C/C–H, C–O, C=O, and O–C=O components. The atomic percentage of oxygen associated with each oxidized carbon component was calculated using stoichiometric ratios and converted to an equivalent O 1s peak area using the O 1s/C 1s relative sensitivity factor. This calculated organic-oxygen area was then constrained in the O 1s fit at the appropriate binding energy to prevent overestimation of hydroxide/defective oxide contributions.

Author contributions

Mohammad Amin Razmjoo Khollari: Conceptualization, Methodology, Investigation, Software, Formal analysis, Data Curation, Visualization, Writing - Original Draft, Writing - Review & Editing. Kashif Mairaj Deen: Conceptualization, Methodology, Investigation, Data Curation, Visualization, Writing - Review & Editing. Edouard Asselin: Funding acquisition, Conceptualization, Writing - Review & Editing, Supervision.

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41529-025-00667-7.