Adsorption Isotherm — Langmuir, BET & Freundlich

Explore how gas or dissolved molecules adsorb onto solid surfaces. Compare Langmuir monolayer, BET multilayer, and empirical Freundlich models with interactive molecular animation.

Model:

Surface Animation

Adsorption Isotherm

0.00

Surface coverage θ

0.00

Adsorbed amount q

0.30

Pressure P/P₀

1.0

Avg. layers

Langmuir

Active model

Relative Pressure P/P₀ 0.30

Affinity constant K 10

BET constant C 50

Freundlich 1/n exponent 0.50

Langmuir Isotherm: θ = KP / (1 + KP) — assumes identical, non-interacting sites; monolayer adsorption only. K is the equilibrium constant (affinity). At high P, θ → 1 (full monolayer coverage).

About Adsorption Isotherms

Adsorption is the accumulation of molecules from a gas or liquid phase onto a solid surface. Unlike absorption (penetration into bulk), it involves surface binding.

Langmuir (1916): θ = KP/(1+KP). Valid for monolayer, identical sites, no lateral interactions. K = k_ads/k_des. Used for chemisorption.

BET (Brunauer, Emmett, Teller, 1938): Extends Langmuir to multilayer physisorption. q/q_m = Cx/[(1−x)(1−x+Cx)] where x=P/P₀, C ≈ exp(E₁−E_L)/RT. Widely used to measure surface area (BET surface area, m²/g).

Freundlich (1906): q = K·C^(1/n) — empirical isotherm for heterogeneous surfaces. 1/n < 1 gives "favourable" shapes, 1/n > 1 "unfavourable".

Applications: Catalysis (catalyst surface area), water treatment (activated carbon), chromatography, drug delivery, gas storage (MOFs).