Potential vs RHE (V)
Active Material Proton Concentration
Electrolyte Concentration Profile
Active Particle SOC Profile (DFN)
Potential vs Hydrogen Concentration
Model Equations & Physical Framework
This simulator implements a rigorous 1D/2D Doyle-Fuller-Newman (DFN) Pseudo-2D (P2D) model of an aqueous alkaline symmetric cell. The equations conserve species and charge in both the solid and liquid phases.
Electrolyte Mass Conservation
Tracks KOH salt concentration in the liquid phase. Mass transport occurs via diffusion and migration, driven by the reaction flux j_n.
Electrolyte Charge Conservation
Governs the electrolyte potential φ_e. Conductive current is driven by electric field and ionic concentration gradients (diffusional conductivity).
Solid-Phase Charge Conservation
Governs the solid active material potential φ_s. Current is carried by electron conduction in the electrode matrix and consumed by reaction j_n.
Solid Species Diffusion (1D Spherical)
Tracks proton intercalation inside active particles. Solved radially at each electrode node x. Boundary condition at surface: -D_s · ∂c_s/∂r = j_n.
Equilibrium Potential (OCV) Curves
Thermodynamic equilibrium potential (Open Circuit Voltage) vs. hydrogen concentration (absorption capacity) for both active materials at 298.15 K, converted to the Reversible Hydrogen Electrode (RHE) scale.
Material Equilibrium OCV vs Hydrogen Concentration
Metal Hydride (MH) Electrode
Model features a flat equilibrium plateau in the two-phase coexistence region (0.1 ≤ θ ≤ 0.9) at approximately +0.02 V vs. RHE.
Literature Sources:- P. De Vidts, R. E. White, J. Electrochem. Soc., 142 (1995) 1502.
- H. Gu, C. Y. Wang, Electrochimica Acta, 45 (1999) 733.
- M. Viitanen, J. Appl. Electrochem., 23 (1993) 14.
Indigo (Organic) Electrode
Model implements a modified Nernst equation with a solid-solution interaction parameter (ω = -2500 J/mol) to capture non-ideal intermolecular lattice forces. Standard potential is +0.27 V vs. RHE.
Literature Sources:- M. Yao et al., Chemistry Letters, 39 (2010) 950.
- M. Kato, M. Yao et al., ACS Omega, 5 (2020) 19309.
- Frumkin/Regular solution thermodynamics for organic intercalation.
Detailed Material Parameters
| Parameter | Symbol | Metal Hydride (MH) | Indigo (Organic) | Unit |
|---|---|---|---|---|
| Max Solid Concentration | c_s,max | 30,000 | 15,000 | mol/m³ |
| Standard Charge-Transfer Rate | k_0 | 1.0 × 10⁻⁵ | 5.0 × 10⁻⁶ | mol/(m²·s) / (mol/m³)^1.5 |
| Solid-State Diffusion Coeff. | D_s0 | 1.0 × 10⁻¹² * | 5.0 × 10⁻¹⁴ | m²/s |
| Particle Radius | R_p | 10.0 | 5.0 | μm |
| Solid Electronic Conductivity | σ_s | 100 | 10 | S/m |
| Active Volume Fraction | ε_s | 0.50 | 0.40 | - |
| Specific Surface Area | a_s | 150,000 | 240,000 | m⁻¹ |
| Bruggeman Exponent | α_brugg | 1.5 | 1.5 | - |
| Standard Potential | U_0 | +0.03 (Plateau: +0.02) | +0.27 | V vs. RHE |
* Metal Hydride solid-state diffusion includes a phase-coexistence peak model that increases diffusivity up to 50-fold in the two-phase region.
Electrolyte & Thermodynamics (6M KOH Aq.)
The electrolyte is modeled as concentrated aqueous Potassium Hydroxide (KOH). The physical properties are calculated as functions of temperature and KOH concentration:
- Electrolyte Diffusivity (D_e): Computed based on temperature-dependent concentrated solution theory (nominally 2.0 × 10⁻⁹ m²/s at 6M).
- Ionic Conductivity (κ): Concentrated KOH conductivity with peak near 6M (nominally 60 S/m).
- Proton Transference Number (t_+^0): Set to 0.78 for alkaline system.
- Thermodynamic Activity Correction: Calculated from the activity coefficient derivative d(ln f_±)/d(ln c_e) to scale the diffusional conductivity term κ_D.