Same two-electrode open-circuit model as the 3D cell, but here plotted directly instead of animated as moving ions — the representation battery scientists actually read:
V_cathode(x) = 3.00 + 0.90(x-0.5) - 0.05 ln[(x+0.02)/(1.02-x)]
V_anode(x) = 0.08 + 0.50 e^(-6x) + 0.03 ln[(1.03-x)/(x+0.03)]
V_cell = V_cathode(x) - V_anode(x) - I_eff * R_int
Top chart: terminal voltage vs state of charge (SoC), open-circuit and under-load, with a live marker tracing the operating point. Middle chart: the two electrode potentials plotted separately vs SoC — this is where the hard-carbon anode's near-zero-volt plateau near full sodiation is visible directly as a flat segment. Bottom chart: the numerical derivative dVanode/dSoC of the anode curve alone — it falls smoothly through the sloping region, then crashes to exactly zero the instant the anode hits its physical floor near SoC ≈ 0.96, marking the plateau's cliff-edge onset (the cell voltage's own derivative, by contrast, stays smooth here and does not show this feature — it is the anode term specifically that carries the signature).
- Charge / Discharge — sets current direction; the marker sweeps right (charge) or left (discharge) along all three curves in lockstep.
- C-rate — sweep speed, and the vertical gap between the OCV and loaded voltage curves (I·R_int overpotential).
- Cycles aged — capacity retention follows SOH = 100 e^(-cycles/1400); the accessible SoC window (shown as a shaded band) shrinks as SOH drops.
Simplified, illustrative two-electrode intercalation model, not a fit to a specific manufacturer's cell.