Cell 0 Vj 0 A/cm²T 0 °CEfficiency 0 %H₂ 0 g/hClock manualFPS 0

Cyan = hydrogen side (cathode, −), red = oxygen side (anode, +), green + = protons crossing the membrane. Each visible molecule stands for a huge number of real ones. Drag to orbit, wheel or pinch to zoom.

PEM Water Electrolyzer

Why does 1.229 V not split water in practice? Change temperature, membrane, pressure and catalyst and watch the voltage budget.

Cell

Current or renewable supply

Live readouts

Voltage budget vs current density

Efficiency vs current density

One day of wind + sun

Goals

Independent numerical checks

Controls

Drag or one finger: orbit; wheel or pinch: zoom. Presets set the cell; every slider can be changed afterwards.
Manual current: you choose j. Renewable supply: the stack takes whatever power the wind and sun give (up to its limit), j follows from V(j)·I = P; the clock runs 24 h in about 24 s at 1 h/s.
Quality Low = fewer bubbles and no shadows (also ?q=low).

The science

Reversible voltage. E_rev = 1.229 − 8.46·10⁻⁴ (T − 25 °C) + (RT/2F) ln(p_H₂ p_O₂^½); the thermoneutral voltage E_tn = ΔH/2F = 1.481 V (HHV). Above E_tn the cell makes waste heat, below it the cell would cool.

Activation. Butler-Volmer with α = ½: η = (RT/αF) asinh(j / 2j₀) for the oxygen (anode) and hydrogen (cathode) reaction; j₀ follows an Arrhenius law. The exchange current densities (2·10⁻⁴ and 0.2 A/cm² at 25 °C) are lumped, roughness-inclusive model values [перевірити за джерелом]; the anode is the slow side.

Ohmic. η = j (δ/σ + R_c) with the Nafion-type conductivity σ = (0.005139 λ − 0.00326) exp(1268 (1/303 − 1/T)) S/cm, λ = 14 [перевірити за джерелом], R_c = 0.05 Ω·cm² (model value).

Bubbles and mass transport. Gas covers part of the electrode, θ = 0.5 j/(j + 1.5), so the limiting current falls to 5 A/cm²·(1−θ) and η = (RT/2F) ln(1/(1 − j/j_lim)) grows steeply near the limit (illustrative closure, not a fitted law).

Faraday yield. ṅ_H₂ = η_F N I / 2F with crossover loss j_x = 10⁻⁴ A/cm² · p/bar · (125 µm/δ) (model value); η_F = 1 − j_x/j. Specific energy = 26.59 kWh/kg per volt ÷ η_F. Efficiency shown is HHV: η = (E_tn/V)·η_F.

Simplifications. Uniform current density, steady state, no degradation, no full two-phase flow, no 2-D current distribution, ideal pressure-independent kinetics. The picture is a schematic exploded cell (an electrolyte gap on each side of the membrane); a real PEM cell is zero-gap with a catalyst layer on the membrane. Wind speed is a seeded AR(1) process through a cubic power curve; solar is a half-sine^1.5 day. The cell is virtual; this page is not an operating guide and is not affiliated with any manufacturer.

Blender-modelled cell, Three.js r160. Numbers are educational model values.