A lithium-ion battery stores energy through the reversible intercalation of lithium ions between graphite anode layers and metal oxide cathode layers (typically LiCoO₂, LiNiMnCoO₂, or LiFePO₄). During discharge, Li⁺ ions deintercalate from graphite, travel through the electrolyte, and insert into the cathode; electrons flow through the external circuit to power the load. The open-circuit voltage (OCV) reflects the chemical potential difference between anode and cathode and varies with state of charge (SoC) according to a characteristic polynomial curve. The Butler–Volmer equation governs how rapidly electrode reactions proceed at a given overpotential — the deviation from equilibrium voltage.
This simulator lets you explore four interconnected views: the charge and discharge curves at variable C-rates and temperatures; the C-rate comparison showing how faster discharge reduces usable capacity via Ohmic IR losses; the capacity fade model that tracks SEI layer growth, lithium plating, and structural degradation over hundreds of cycles; and the Butler–Volmer kinetics curve with its associated Nyquist impedance semicircle. Preset scenarios model a phone cell, an EV pack, an aged cell, and a cold-start condition.
What is the C-rate and how does it affect battery performance?
The C-rate is the current relative to nominal capacity: 1C means the battery is fully discharged in one hour, 2C in 30 minutes, C/5 in 5 hours. Higher C-rates increase the Ohmic voltage drop (V_terminal = OCV − I×R_int), effectively reducing the usable voltage window before the cutoff voltage of ~3.0 V is reached. A typical 2.5 Ah NMC cell at 1C might deliver 2.45 Ah, but at 5C may only deliver 1.9 Ah due to increased polarisation — a significant capacity penalty relevant to fast-charging EVs.
What is the Solid Electrolyte Interphase (SEI) and how does it cause capacity fade?
The SEI is a passivation layer that forms on the graphite anode during the first few charge cycles as electrolyte solvent (typically ethylene carbonate) is reduced electrochemically. It is chemically complex — containing lithium carbonate, lithium oxide, and organic lithium compounds — and is essential for battery operation, but its continued growth consumes lithium inventory and increases internal resistance over time. SEI thickness grows approximately as √n (square root of cycle number), consistent with diffusion-limited growth, producing a characteristic parabolic capacity-fade curve.
What is the Butler–Volmer equation and what does it describe?
The Butler–Volmer equation, i = i₀[exp(αFη/RT) − exp(−(1−α)Fη/RT)], describes how the electrochemical reaction rate (current density i) depends on overpotential η — the departure from the equilibrium electrode potential. The exchange current density i₀ quantifies the rate of both forward and reverse reactions at equilibrium; a large i₀ means the electrode reaction is fast and low overpotential is needed to drive significant current. The transfer coefficient α (typically ~0.5) describes the asymmetry between the anodic and cathodic branches of the activation barrier.
Lithium plating occurs when lithium ions arrive at the graphite anode faster than they can intercalate — typically at high C-rates, low temperatures, or when the anode is already nearly full (high SoC). Instead of inserting into graphite layers, Li⁺ is reduced to metallic lithium dendrites on the anode surface. Dendrites can grow through the separator and short-circuit the cell, causing thermal runaway — a self-accelerating exothermic reaction that can lead to fire or explosion. Plating onset is accelerated in aged cells with high internal resistance and limited graphite capacity, as modelled in the Capacity Fade tab's "lithium plating onset" slider.
Temperature affects both capacity and internal resistance through Arrhenius-type dependence. At 0°C, capacity can drop 20–30% because lithium-ion diffusion in the electrolyte and in graphite slows substantially. Below −10°C, lithium plating during charging becomes a serious risk. High temperatures (above ~45°C) accelerate SEI growth and electrolyte decomposition, reducing cycle life. The optimal operating temperature for most Li-ion cells is 20–35°C; the temperature slider in the simulator implements a simplified capacity retention factor exp[−0.008(T−25)²/(298)] to capture this behaviour.
A Ragone plot charts specific energy (Wh/kg) on the x-axis against specific power (W/kg) on the y-axis for a battery cell. As C-rate increases, the operating voltage falls due to Ohmic and kinetic overpotentials, reducing total energy but increasing instantaneous power — so higher C-rates shift a cell's Ragone point towards the lower-right (less energy, more power). Li-ion batteries occupy the middle of the Ragone space (100–300 Wh/kg, 200–2000 W/kg); supercapacitors deliver much higher power but far less energy, whilst fuel cells deliver high energy but lower power density.
Industry convention defines battery end-of-life (EOL) at 80% of initial capacity retention — a choice based on early EV market research showing significant user dissatisfaction below this threshold. A typical consumer cell reaches 80% capacity retention after 300–500 full cycles at 1C; an EV-optimised cell with low cobalt NMC or LFP chemistry may reach 1,000–2,000 cycles. After EOL for traction use, cells often find second-life applications in stationary storage where energy density requirements are less stringent.
A Nyquist (or impedance) plot shows the complex impedance Z(ω) = Re(Z) − j·Im(Z) of a battery cell as frequency ω is swept from high to low. At very high frequency, the response is dominated by electrolyte resistance (R_ohm) — a real-axis intercept. A semicircle in the mid-frequency range represents the parallel combination of charge-transfer resistance R_ct and double-layer capacitance C_dl at the electrode interface. At low frequencies, a Warburg diffusion element produces a 45° line. Electrochemical impedance spectroscopy (EIS) is the standard technique for non-destructively diagnosing battery state of health.
Common Li-ion cathode materials include LCO (LiCoO₂, ~150 mAh/g, ~3.7 V, used in phones), NMC (LiNiMnCoO₂, ~200 mAh/g, 3.7 V, EV mainstream), NCA (LiNiCoAlO₂, ~200 mAh/g, used by Tesla), and LFP (LiFePO₄, ~160 mAh/g, 3.2 V, thermally very stable, preferred for budget EVs and stationary storage). LFP has a notably flat OCV vs SoC plateau near 3.2–3.3 V — making SoC estimation from voltage alone very difficult — while NMC shows the sloping polynomial curve modelled in this simulator.
Solid-state batteries replace the liquid electrolyte with a solid ionic conductor (typically a ceramic oxide, sulfide, or polymer). Benefits include higher energy density (metallic lithium anode, ~3,860 mAh/g vs graphite's 372 mAh/g), elimination of flammable electrolyte, wider operating temperature range, and suppression of lithium dendrite growth. The main challenges are high solid–solid interfacial resistance, mechanical stress during cycling, and manufacturing costs. Most analysts expect commercialisation in automotive applications in the late 2020s, with Toyota and several start-ups leading development.
Charging speed is limited by three factors: (1) lithium-ion transport through the electrolyte and SEI — a diffusion bottleneck modelled by the Warburg impedance; (2) the risk of lithium plating at the anode if charging current exceeds the intercalation rate, especially at low temperatures; and (3) heat generation from Ohmic losses (I²R) that must be managed by the thermal management system to prevent degradation. Modern fast chargers use sophisticated multi-stage protocols — constant current (CC) to ~80% SoC, then constant voltage (CV) — and may apply pulse charging or temperature pre-conditioning to safely maximise charge rate.
This simulation models the electrochemistry of a lithium-ion cell as it charges, discharges and ages. Terminal voltage is built from an open-circuit voltage (OCV) curve that depends on state of charge, minus an Ohmic voltage drop set by current and internal resistance, whilst electrode kinetics follow the Butler–Volmer equation linking reaction rate to overpotential. A separate capacity-fade model tracks how SEI-layer growth and lithium plating shrink usable capacity over hundreds of cycles. Four tabs let you compare charge/discharge behaviour, C-rate effects, long-term ageing and reaction kinetics side by side.
The Charge/Discharge tab plots terminal voltage against capacity in both directions, with the resting OCV curve shown as a dashed reference and the state-of-charge bar tracking the midpoint. The C-Rate tab overlays discharge curves from C/5 to 5C alongside a Ragone plot of energy versus power. The Capacity Fade tab traces retained capacity across up to 1,000 cycles down to the 80% end-of-life threshold, and the Butler–Volmer tab draws the current–overpotential curve that sets how fast the electrode reaction runs.
Switch modes with the four tab buttons, then adjust the sliders for that view: nominal capacity, C-rate, internal resistance and temperature on Charge/Discharge; capacity and resistance on C-Rate; fade rate, SEI growth exponent and lithium-plating onset on Capacity Fade; and exchange current, transfer coefficient and temperature on Butler–Volmer. The four preset buttons — Phone cell, EV pack, Aged cell and Cold start — load realistic parameter sets in one click, and the live readouts update instantly as you drag.
Industry convention treats 80% of original capacity as a battery's end of life — not because the cell stops working, but because early electric-vehicle trials found driver satisfaction dropped sharply below that threshold, even though many packs still perform well past it in second-life storage roles.
1C means a battery can be fully discharged in one hour at its rated current; 2C halves that to 30 minutes, and C/5 stretches it to five hours. Raising the C-rate increases the Ohmic voltage drop (current × internal resistance), so the terminal voltage reaches the cutoff sooner and less usable capacity is delivered — the effect the C-Rate tab visualises directly.
It calculates the net current density produced by an electrode reaction at a given overpotential, the voltage departure from equilibrium. The exchange current i₀ sets how fast the reaction runs at zero overpotential, and the transfer coefficient α controls how asymmetric the forward and reverse branches are — both adjustable with the Butler–Volmer tab's sliders.
Two competing mechanisms are modelled: growth of the solid electrolyte interphase (SEI), a passivation layer that consumes lithium roughly in proportion to the square root of cycle count, and lithium plating, which sets in once cycling passes the onset threshold you choose and removes capacity at a steeper, near-linear rate. Together they produce the curve traced on the Capacity Fade tab, with the dashed line marking the conventional 80% end-of-life point.
Low temperature slows lithium-ion diffusion in both the electrolyte and the electrode particles, which the Temperature slider represents through a Gaussian retention factor centred on 25°C. Below roughly −10°C the reaction can no longer keep pace with the charging current, and lithium is deposited as metal instead of intercalating — this is why the Cold start preset shows reduced usable voltage.
Open-circuit voltage (OCV) is the resting voltage at a given state of charge, read from a fitted polynomial curve typical of an NMC cathode. Terminal voltage is what the cell actually delivers under load: OCV minus the Ohmic drop during discharge, or OCV plus that drop during charge. The gap between the two readouts widens with C-rate and internal resistance, and shrinks to zero once the current drops to zero.