The BET model (Brunauer, Emmett, Teller, 1938) extends Langmuir's single-layer picture to physisorption, where gas can stack in multiple layers on a solid. Each surface site is simulated as an independent stochastic column that gains or loses molecules according to real transition rates, not a pre-drawn curve:
Site empty → 1st layer: rate = C·x (strong solid-gas bond)
1st layer → empty: rate = 1 (b₁, reference rate)
layer n → n+1 (n≥1): rate = x (a·P, same as bulk condensation)
layer n → n−1 (n≥2): rate = 1 (b, same as bulk evaporation)
where x = P/P₀ is the relative pressure and C reflects the heat of adsorption of the first layer relative to the heat of liquefaction of the adsorbate. At steady state this microscopic birth–death process reproduces the classic BET isotherm:
V/Vₘ = C·x / [ (1−x)·(1−x+C·x) ]
V/Vₘ is the average number of molecular layers per site — exactly what "Measured n̄" tracks live from the 3D grid, converging to the "BET theory" value. A large C means the first layer binds far more strongly than the gas condenses on itself, so a sharp monolayer knee appears before multilayer buildup — the basis of the real BET surface-area method used in catalysis and porous-materials labs. x is capped below 1 because the isotherm diverges at P/P₀ = 1 (bulk condensation).
- P/P₀ — how close the gas is to its saturation vapor pressure; higher values pack on more layers.
- C — surface affinity; low C (~1) gives gradual, Langmuir-like uptake, high C (~100+) gives a sharp monolayer step.
- Grid size — number of independent sites sampled; more sites average out noise around the theoretical curve.