Adsorption Isotherms and Kinetics

Core Idea

Langmuir, Freundlich, and BET isotherms model how adsorbate coverage changes with pressure or concentration at constant T. Langmuir assumes monolayer adsorption with a single binding site type; BET extends to multilayers. Kinetics involve forward adsorption (collision/activation limited) and reverse desorption (Arrhenius-like). Together, isotherms and kinetics characterize adsorbent capacity, selectivity, and rates for separations and catalysis.

Explainer

Building on what you know about adsorption isotherms and surface thermodynamics, we can now connect the equilibrium description of adsorption (how much sticks at a given pressure) to the kinetic description (how fast it sticks and unsticks). This connection is essential because real applications — catalytic converters, gas masks, chromatography columns — operate under dynamic conditions where both the extent and the rate of adsorption matter.

The Langmuir isotherm is the simplest physically motivated model. It treats the surface as a collection of identical, independent binding sites. At equilibrium, the fraction of occupied sites θ = KP/(1 + KP), where K is the equilibrium constant for adsorption and P is gas pressure. At low pressure, θ grows linearly with P (every molecule that hits the surface finds an empty site). At high pressure, θ approaches 1 — the surface is full, and additional gas molecules have nowhere to land. The shape is a hyperbola, identical in form to Michaelis-Menten enzyme kinetics, and for the same mathematical reason: a saturable process with first-order uptake competing against a fixed capacity. The key Langmuir assumptions — uniform sites, no lateral interactions, monolayer only — are often violated in practice, but the model remains the essential starting point.

The Freundlich isotherm (θ ∝ P^1/n) is empirical and handles heterogeneous surfaces where some sites bind strongly and others weakly. It fits many real systems well over intermediate pressure ranges but lacks Langmuir's saturation behavior — it predicts infinite adsorption at infinite pressure, which is unphysical. The BET isotherm extends Langmuir to multilayer adsorption: once the first layer forms, additional layers can stack on top. BET is the standard method for measuring surface area of porous materials; the characteristic S-shaped isotherm reflects monolayer formation followed by multilayer condensation.

On the kinetic side, the rate of adsorption depends on collision frequency (from kinetic molecular theory) multiplied by a sticking probability — the fraction of collisions that actually lead to binding. This sticking probability may include an activation energy barrier (chemisorption) or be nearly unity (physisorption). Desorption follows Arrhenius kinetics: rate ∝ exp(−E_des/RT), where E_des is the desorption activation energy. At equilibrium, the rates of adsorption and desorption are equal, and you recover the Langmuir isotherm from the kinetic expressions — this is a satisfying consistency check. For catalysis, the kinetic picture is crucial: a catalyst that binds reactants too weakly never accumulates enough surface coverage, while one that binds too strongly cannot release products fast enough. The optimal catalyst sits at the peak of a volcano plot, balancing adsorption and desorption rates — a principle known as the Sabatier principle that directly follows from the kinetics of adsorption.