About Adsorption Isotherm
Adsorption is the process by which gas or dissolved molecules accumulate on a solid surface rather than penetrating into its bulk — a phenomenon crucial in catalysis, water purification, and drug delivery. This simulator lets you explore three fundamental models: the Langmuir isotherm (monolayer, identical sites), the BET model (multilayer physisorption), and the empirical Freundlich isotherm (heterogeneous surfaces). Each produces a characteristic curve relating the amount adsorbed to pressure or concentration, revealing how surface chemistry governs real-world separations and reactions.
Adjust the relative pressure P/P₀, the affinity constant K, the BET constant C, and the Freundlich 1/n exponent to observe how surface coverage changes. The animated surface panel shows individual molecules landing on or leaving adsorption sites in real time, whilst the isotherm plot tracks your current operating point on all three model curves simultaneously.
Frequently Asked Questions
What is the Langmuir isotherm and when does it apply?
The Langmuir isotherm, θ = KP/(1 + KP), assumes that adsorption occurs on a fixed number of identical, independent sites and that only a single molecular layer can form. It was derived by Irving Langmuir in 1916 and earned him the Nobel Prize in Chemistry in 1932. It is most applicable to chemisorption — situations where molecules form chemical bonds with the surface, such as CO on platinum catalysts or enzyme–substrate binding.
How does the BET model differ from Langmuir?
The BET (Brunauer–Emmett–Teller) model extends Langmuir by allowing multiple molecular layers to build up on top of one another, governed by the equation q/q_m = Cx/[(1−x)(1−x+Cx)] where x = P/P₀. The BET constant C is related to the difference in heat of adsorption between the first layer and subsequent condensation layers. At P/P₀ approaching 1, the BET curve rises steeply as multilayer coverage diverges, unlike the Langmuir plateau.
What does the affinity constant K represent physically?
The Langmuir affinity constant K equals the ratio of the rate of adsorption to the rate of desorption (k_ads/k_des). A large K means the surface has a strong preference for the adsorbate — the curve saturates at low pressures. Physically, K is related to the Gibbs free energy of adsorption: K = K₀ exp(−ΔG_ads/RT), so increasing K corresponds to a more exothermic, thermodynamically favourable binding event.
What is BET surface area analysis and why is it important?
BET surface area analysis uses the multilayer isotherm measured with nitrogen gas at 77 K to calculate a material's total surface area in m²/g. The technique is the international standard for characterising porous materials such as activated carbons, zeolites, and metal–organic frameworks (MOFs). A high BET surface area — up to 7,000 m²/g for some MOFs — means more active sites for catalysis, adsorption, or gas storage per gram of material.
What does a Freundlich exponent 1/n below 1 mean?
When 1/n < 1 in the Freundlich equation q = K·C^(1/n), the isotherm is concave downward ("favourable"), meaning that adsorption efficiency is highest at low concentrations — the surface fills up readily before becoming less effective. This shape is desirable for removing trace pollutants from water. When 1/n = 1 the relationship is linear (Henry's law regime); when 1/n > 1 the isotherm is "unfavourable", which is unusual for physical adsorption.
How does temperature affect adsorption?
Physical adsorption (physisorption) is generally exothermic, so higher temperatures reduce the amount adsorbed — consistent with Le Chatelier's principle. The van't Hoff equation d(ln K)/dT = ΔH_ads/RT² quantifies this: a more negative adsorption enthalpy means stronger temperature sensitivity. Chemisorption can exhibit a maximum with temperature because the process requires activation energy; below a threshold temperature it is kinetically slow, above it desorption dominates.
What is the difference between physisorption and chemisorption?
Physisorption involves weak van der Waals forces (binding energies roughly 5–40 kJ/mol) and is fully reversible, forming multiple layers at high pressures. Chemisorption forms chemical bonds (40–400 kJ/mol), is limited to one monolayer, often requires activation energy, and can be irreversible. The Langmuir model was originally derived for chemisorption, while the BET model describes physisorption. In practice, both mechanisms can occur on real heterogeneous surfaces.
How is adsorption used in water treatment?
Activated carbon is the most widely used adsorbent for water purification, removing organic pollutants, pesticides, and pharmaceuticals through physisorption. Its surface area can exceed 1,500 m²/g, and its adsorption behaviour is well described by Freundlich or Langmuir isotherms at relevant concentrations. When the carbon becomes saturated, it can be thermally regenerated at 800–900 °C, restoring most of its capacity — an example of the industrial importance of understanding isotherm shapes.
Why does the BET isotherm diverge near P/P₀ = 1?
As relative pressure approaches 1 (the saturation vapour pressure), condensation of liquid on the surface becomes thermodynamically equivalent to bulk condensation, so in principle an infinite number of molecular layers can accumulate. The BET model captures this mathematically: the denominator (1−x) tends to zero as x → 1. In practice, pore filling in mesoporous materials causes capillary condensation well before P/P₀ = 1, producing a hysteresis loop in the experimental isotherm.
What are metal–organic frameworks and why do they matter for adsorption?
Metal–organic frameworks (MOFs) are crystalline porous materials built from metal nodes connected by organic linker molecules, creating precisely engineered cavities. Their BET surface areas can exceed 7,000 m²/g — far beyond activated carbon — making them candidates for hydrogen storage, CO₂ capture, and drug delivery. By tuning the linker chemistry, researchers can target specific adsorption isotherms, from near-linear Henry isotherms for dilute capture to steep S-shaped isotherms for pressure-swing separation processes.
Can isotherms predict separation performance in a column?
Yes — isotherm shape directly determines how well a chromatographic or adsorption column separates mixtures. A favourable (concave) Langmuir isotherm produces a sharp self-sharpening front but a diffuse rear wavefront; an unfavourable (convex) isotherm produces the opposite. Linear isotherms give symmetric Gaussian peaks in chromatography. Industrial pressure-swing adsorption (PSA) processes for producing oxygen or hydrogen rely on steep isotherms that allow efficient cycling between adsorption and regeneration steps.