Voltage 0 VCurrent 0 ASOC 0 %Cell 0 °CTime 0FPS 0

The 18650-style cell is opened at the top: layers of the jelly roll (copper, graphite, separator, NMC, aluminium) spiral inwards. Cyan dots are lithium ions hopping between electrodes; yellow dots are electrons in the wire. The two cut spheres show lithium concentration inside one graphite particle (left) and one NMC particle (right): blue = empty, red = full. Sizes are exaggerated.

Lithium-Ion Cell Under Load

Open up a graphite / NMC cell and watch why voltage sags: lithium has to diffuse through solid particles, cross an interface and push through resistance. Discharge it, charge it, heat it or freeze it.

Operating mode

Live readouts

Terminal voltage and equilibrium voltage (V) against charge delivered

Voltage losses (mV)

Graphite surface potential vs lithium (mV)

Experiments

Each runs whole cycles headless with the current temperature and prints the result.

Independent numerical checks

Controls and missions

Drag / one finger: orbit; wheel / pinch: zoom. Changing the current or temperature acts immediately on the running cell.
Mission 1: find the C-rate at which the cell delivers less than 80 % of its slow-discharge capacity at 25 °C.
Mission 2: at 0 °C, how much capacity do you lose at 1C compared with 25 °C, and which loss grows most?
Mission 3: charge at 2C at -10 °C and watch the graphite potential; what happens below zero?
Mission 4: which loss dominates near the end of a 3C discharge?

The science

Single-particle model. Each electrode is represented by one spherical particle in which lithium diffuses: ∂c/∂t = D r^-2 ∂/∂r (r² ∂c/∂r), with flux −D ∂c/∂r = j/F at the surface set by the cell current (backward-Euler finite volume, 16 shells). Diffusivity follows an Arrhenius law with temperature.

Open-circuit voltage. The equilibrium cell voltage is the difference of the electrode potentials at the surface stoichiometries, U = U_p(y_s) − U_n(x_s), using empirical fits of the published form for graphite and NMC811 (rounded parameters recalled from the literature; the cell is scaled to 3 Ah).

Kinetics. Butler-Volmer at each electrode with symmetric transfer coefficients: j = j₀[exp(αFη/RT) − exp(−(1−α)Fη/RT)], so η = (2RT/F) asinh(j/2j₀), and j₀ = k √(c_e c_s(c_max − c_s)). A single lumped ohmic resistance R₀ (30 mΩ at 25 °C, rising in the cold) stands for contacts, foils and electrolyte.

Terminal voltage and heat. V = U − η_p − η_n − I R₀ in discharge; heat generation is I (U − V) and the lumped cell obeys m c_p dT/dt = I (U − V) − hA (T − T_amb) (41 J/K, 0.16 W/K).

Plating indicator. The potential of the graphite surface versus lithium metal is φ_n = U_n(x_s) + η_n (η_n is negative while charging). When it falls below 0 V, lithium metal can deposit on the graphite instead of intercalating. Real onset also depends on the electrolyte potential drop and the local current distribution, which this single-particle model does not resolve, so treat it as a qualitative warning.

Simplifications and honesty. No electrolyte transport, no particle-size distribution, no hysteresis, no ageing, no entropic heat, constant electrolyte concentration; parameters are rounded typical values for an NMC811 / graphite cell, not data for any real product. The charge protocol is a textbook CC-CV (4.2 V, cut-off C/20). The jelly roll is drawn with thick layers for visibility, and no brand or product is represented. Assets were modelled in Blender; the ions, electrons, particle colours and lamp are driven by the simulation numbers.