Mode restSOC 100 %Voltage 4.1 VCurrent 0 ACell 25 °CTime 0Anode 0 VFPS 0

Drag to orbit, wheel or pinch to zoom. Cyan = lithium in the graphite anode (left), orange = lithium in the oxide cathode (right); balls crossing the separator are Li⁺ in the electrolyte. Dots on the wire are electrons.

Lithium-Ion Cell: Intercalation, Nernst Voltage and Butler-Volmer Losses

Cut a cell open. Lithium moves between graphite and an oxide while the terminal voltage is the open-circuit potential minus every loss.

Drive

Cell

Time

Live readouts

Voltage against charge removed

Potentials over time

Experiments

Headless runs of the same model at the current temperature, particle size and resistance.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. Camera buttons jump to the whole cell, the anode, the cathode or the external circuit.
Pick Discharge, Charge or Rest. Charging is constant current to 4.2 V, then constant voltage until the current tapers below C/20. Discharge stops at 3.0 V.
Presets set rate, temperature, particle size and starting charge together. The SOC slider sets the cell instantly. Time scale = simulated seconds per real second (1C takes 3600 s).
Grey curves are earlier finished runs for comparison.

The science

Electrodes and lithium. Discharging pulls Li out of graphite (Li_xC₆, stoichiometry x falls) and pushes it into a layered oxide (Li_yMO₂, y rises); ions cross the electrolyte, electrons cross the external circuit. Total lithium x q_a + y q_c (in Ah) never changes. The cell is a single-particle model: one representative sphere per electrode (anode 10 µm, cathode 5 µm) with the active surface S = 3 q·3600 / (F c_max R).

Nernst open-circuit potential. Each electrode potential carries the lattice-gas Nernst term (RT/F) ln((1 − s)/s), RT/F = 25.69 mV at 25 °C, plus smooth empirical shape terms (graphite staging steps, oxide slope and the steep end near y ≈ 0.97). The shape terms are illustrative fits, not measured data. The cell OCV is U_c(y) − U_a(x), near 4.17 V full and near 3.2 V empty.

Butler-Volmer kinetics. Per electrode, with symmetric transfer (α = 0.5): i = i₀[e^αFη/RT − e^−αFη/RT], inverted exactly as η = (2RT/F) asinh(i / 2i₀). The exchange current density is i₀ = F k √c_e √(c_s(c_max − c_s)), so it collapses when a particle surface is nearly full or empty. Rate constants k and the other numbers are typical values, not a specific cell.

Solid diffusion. Each particle surface differs from its mean by the parabolic two-state approximation: dq/dt = −30 D q / R² − 45 j / (2R²), c_s = c̄ + 8Rq/35 − Rj/(35D), with steady limit c_s − c̄ = −jR/(5D). Large particles and cold temperatures (Arrhenius D, k and resistance) make this lag the main capacity loss at high rate.

Terminal voltage. V = U_c(y_s) − U_a(x_s) − η_c − η_a − I R₀, I positive on discharge, R₀ = 30 mΩ at 25 °C. While charging, the anode potential against Li/Li⁺ is estimated as U_a − |η_a| − 25 % of IR₀; below 0 V metallic lithium can plate, the classic cold fast-charge damage.

Simplifications. Isothermal (no self-heating), no electrolyte concentration gradient, no SEI growth or ageing, no hysteresis, one particle per electrode, empirical OCV shapes, no cell-to-cell variation. Treat the plating threshold as a qualitative guide. Not affiliated with any vehicle or battery maker; the car and charger are generic. Assets built with Blender; scene by Three.js.