Friday, 24 April, 2026
Redox Speciation
Redox speciation describes the distribution of an element among its different oxidation states in solution or within a solid matrix. For redox-active elements (Cr, Fe, Se, As, Sb, Mo, Mn, U), this distribution controls mobility, toxicity, adsorption, and isotopic fractionation. IsoFind resolves speciation based on physico-chemical conditions (Eh, pH, dissolved O₂) via a coupled model bridging thermodynamic estimation (Pourbaix diagrams) and Machine Learning prediction through the Nexus bridge. This page details the internal model, hard-coded thresholds, and supported systems.
The Two Approaches Resolved by IsoFind
The engine combines two levels of prediction. Machine Learning prediction, when available via the Nexus bridge, utilizes models trained on extensive thermodynamic speciation databases. The thermodynamic fallback remains active when Nexus is unavailable or provided conditions are insufficient.
| Approach | Engine | Inputs | Return Source |
|---|---|---|---|
| ML Nexus | Bridge /api/nexus/predict_speciation | Element, concentration, pH, Eh, DO, matrix | source = 'ml_speciation' |
| Thermodynamic | Function _estimate_cr_speciation_from_eh | pH, Eh only | source = 'thermodynamic' |
| Rayleigh Fallback | Function fraction_reduite_depuis_redox | Eh, DO, depth (automated estimations) | Reduced fraction and epsilon based on regime |
Thermodynamic Model for Cr(VI) / Cr(III)
Chromium is the most strictly codified case in IsoFind. Cr(VI), oxidized and mobile (chromate CrO₄²⁻), is the primary contaminant of interest, whereas reduced Cr(III) is significantly less mobile and toxic. The Cr(VI) → Cr(III) conversion is therefore a key objective for natural or active remediation. IsoFind's thermodynamic model is based on a simplified pe-pH diagram for Chromium.
pe = Eh / 59.16 (mV → pe conversion at 25 °C)
pe_boundary = 23.0 − 1.33 × pH
f_Cr(VI) = 1 / (1 + exp(−0.8 × (pe − pe_boundary)))
pe_boundary = 23.0 − 1.33 × pH
f_Cr(VI) = 1 / (1 + exp(−0.8 × (pe − pe_boundary)))
This formulation produces a sigmoid curve of the Cr(VI) fraction centered on the Cr(VI)/Cr(III) thermodynamic boundary. The 0.8 slope in the sigmoid represents the intrinsic uncertainty around the boundary: a sharp transition is unrealistic in natural systems where multiple mineral phases and complexing species coexist.
Numerical values (pe° = 23.0; pH slope -1.33; sigmoid factor 0.8) are hard-coded in the _estimate_cr_speciation_from_eh function within prediction_routes.py. They approximate the Cr Pourbaix diagram under moderate dilution at 25 °C, without ionic strength adjustment. For critical work, Nexus ML prediction is preferred as it integrates more variables.
Coded Reduction Thresholds
Independently of the pure thermodynamic model, IsoFind uses a cascade of Eh and O₂ thresholds to estimate the reduced fraction and select the appropriate isotopic epsilon. These thresholds are coded as constants and guide the Rayleigh model.
| Constant | Value | Meaning |
|---|---|---|
| EH_SEUIL_OXIQUE | +350 mV | Above: Oxic conditions, no significant reduction |
| EH_SEUIL_REDUCTION_PARTIEL | +200 mV | Below: Partial reduction possible |
| EH_SEUIL_REDUCTION_FORT | −50 mV | Below: Complete reduction likely |
| DO_SEUIL_ANOXIQUE | 0.5 mg/L | Below: Strict anoxic conditions |
The Three Reduction Regimes
The fraction_reduite_depuis_redox function classifies each sample into one of three regimes based on Eh and DO, then applies the relevant epsilon. The choice of epsilon reflects that biological pathways (sulfate-reducing bacteria) and abiotic pathways (aqueous Fe(II), mineral surfaces) fractionate chromium differently.
| Regime | Conditions | ε ⁵³Cr (‰) | Literature Reference |
|---|---|---|---|
| Biological | DO < 0.5 mg/L and Eh < +200 mV | −1.5 | Bain & Bullen 2005, Zink et al. 2010 |
| Abiotic | Eh < +200 mV but DO not anoxic | −3.5 | Zink et al. 2010 (reduction by Fe(II), mineral surfaces) |
| Mixed / Oxic | Eh > +200 mV or transition | −2.5 (default) | Consensus value if data is insufficient |
Dissolved Oxygen Inhibition
Dissolved O₂ inhibits Cr(VI) reduction even when the Eh potential is moderately favorable. The inhibition factor is coded as follows in the fraction_reduite_depuis_redox function.
do_factor = max(0 ; 1 − DO / 3)
Practical interpretation: DO = 0 mg/L yields a factor of 1 (no inhibition); DO = 1 mg/L yields 0.67; DO = 2 mg/L yields 0.33; DO = 3 mg/L yields 0 (total inhibition). This empirical correction compensates for the fact that probe-measured Eh does not always correctly capture residual O₂, and that Cr(VI) reduction is kinetically slowed in the presence of oxygen even if thermodynamics would allow it.
Isotopic Fractionation of the Residual
When a fraction of Cr(VI) is reduced to Cr(III), the remaining Cr(VI) fraction is enriched in ⁵³Cr according to the Rayleigh equation. This is the foundation for using δ⁵³Cr as evidence of active reductive degradation.
δ⁵³Cr(t) = δ₀ + ε × ln(f)
where f = fraction of Cr(VI) not yet reduced
where f = fraction of Cr(VI) not yet reduced
For a biotic epsilon of -1.5 ‰, a 50% reduction of Cr(VI) enriches the residual by +1 ‰; a 90% reduction enriches it by +3.5 ‰. These magnitudes are routinely detectable via MC-ICP-MS. The engine also calculates the δ⁵³Cr of the cumulative Cr(III) which integrates the total reduced product: δ_product_cumul = δ₀ − ε × (1−f) / f × ln(f).
Other Key Redox Systems
Beyond Chromium, several redox systems deserve specific attention. Principles are analogous, but thermodynamic thresholds, epsilons, and usage contexts vary.
Fe(II) / Fe(III)
Iron is the most abundant redox-active element in aquifers. Its speciation controls the local redox cycle and secondary couples (Cr, As, Mn). Fe(II) is soluble, while Fe(III) precipitates as poorly mobile oxyhydroxides at neutral pH.
| Parameter | Value |
|---|---|
| Abiotic ε ⁵⁶Fe (reduction) | −1.5 ‰ |
| Biological ε ⁵⁶Fe (dissimilatory reduction) | −2.0 to −3.0 ‰ |
| Pourbaix Boundary at pH 7 | Eh ≈ +220 mV (Fe(OH)₃ precipitation) |
| Fe(II) anomaly in oxic water | Indicates anthropogenic input or disconnected reducing layer |
As(III) / As(V)
Arsenic exists in two primary forms with different toxicities. Arsenite As(III) is more mobile and toxic than arsenate As(V). The redox boundary is close to that of Cr, around Eh ≈ +100 to +200 mV at pH 7.
| Parameter | Value |
|---|---|
| Abiotic ε ⁷⁵As | −2.0 ‰ |
| Biological ε ⁷⁵As | −3.0 ‰ |
| Diagnosis via δ⁷⁵As | As(V) → As(III) reduction in anoxic zones |
| Methylation (As(III) → MMA, DMA) | Sulfate-reducing bacteria, additional fractionation |
Se(VI), Se(IV), Se(0), Se(−II)
Selenium has four stable oxidation states, making it one of the richest systems for redox forensics. Se(VI) and Se(IV) are soluble; native Se(0) precipitates; Se(−II) forms metal selenides.
| State | Name | Mobility | Indicator |
|---|---|---|---|
| Se(VI) | Selenate SeO₄²⁻ | Very mobile | Oxic waters, irrigation |
| Se(IV) | Selenite SeO₃²⁻ | Mobile with adsorption | Neutral to acidic soils |
| Se(0) | Native Selenium | Low mobility (precipitate) | Reducing zone, bacterial product |
| Se(−II) | Selenide | Immobile (metal selenide) | Highly reducing sulfidic conditions |
The biological epsilon for Se (-5 ‰) is the largest in the _EPSILON_TABLE for redox elements, making δ⁸²Se a particularly sensitive marker for microbial reduction.
Elements Without Aqueous Redox
Reminder: Eleven elements in the IsoFind catalog remain in a single form in aqueous solution and do not support dynamic speciation: Pb, Zn, Cu, Cd, Ni, Co, Sr, Ca, Na, K, Mg. For these elements, the Geochemistry view reports total concentration only. Adsorption and transport are still modeled, but without a speciation branch.
Integration with Adsorption and Fractionation
The redox speciation of an element is the entry point for several environmental behaviors. The IsoFind engine propagates the reduced fraction to these secondary modules.
| Coupling | Mechanism |
|---|---|
| Differential Adsorption | Cr(III) preferentially adsorbed on Fe(III) oxides, Cr(VI) remains mobile |
| Epsilon correction by Adsorption | Correction = favorability × f_reduced × ε_adsorption |
| Precipitation | Fe(III) precipitates as Fe(OH)₃, Se(VI)→Se(IV)→Se(0) with terminal precipitation |
| Inter-element Coupling | Fe(II) reduces As(V) and Cr(VI), secondary redox cascade |
Visualization in IsoFind
Speciation results are integrated into several IsoFind visualizations. Users can find speciation data relevant to their specific view.
| View | Speciation Display |
|---|---|
| Sample Geochemistry Tab | Cr(VI) / Cr(III) badge with percentages if pH and Eh are provided |
| 3D Simulation | "Simulation" rendering mode colors by reduced fraction |
| Nexus Quick Match Process | f_reduced estimation based on entered conditions |
| Speciation Report Block | Table of percentages per element and per sample |
API Access
| Endpoint | Usage |
|---|---|
| POST /api/predict/speciation | Redox speciation of an element from pH, Eh, DO |
| POST /api/predict/infer | Full inference: Speciation + Fractionation + Adsorption |
| POST /api/nexus/predict_speciation | Direct call to the Nexus ML bridge (if available) |
Limitations and Best Practices
- Predicted speciation is a thermodynamic or ML estimation. It does not replace direct speciation measurements by HPLC-ICP-MS, which remains the reference method for legal or regulatory cases.
- Eh values measured in wells are often unreliable (O₂ contamination, slow electrode kinetics). Prioritize chemical indicators (measured Fe²⁺, sulfide, depleted NO₃⁻) when available.
- Coded thresholds (+350 oxic, +200 partial, -50 strong) are suitable benchmarks for neutral aquifers. For highly acidic (sulfate soils) or highly alkaline (carbonate aquifers) environments, local calibration improves prediction.
- Kinetics are not accounted for in the thermodynamic model: water may remain transiently in a non-equilibrium state (e.g., residual Cr(VI) in a reducing zone for months). The Nexus ML bridge partially integrates this via its training data.
- For litigation cases, maintain a record of the physico-chemical conditions used for prediction. The IsoFind Speciation report block automatically includes the pH, Eh, and DO values used.
Learn More
- Majors and Traces: The total concentrations feeding the speciation model.
- Diagnostic Ratios: Complementary diagnostics via elemental combinations.
- Speciation and Propagation: Usage of speciation within the 3D simulation engine.
- Cr(VI) Plume Case Study: A full simulation example with active redox speciation.