Langmuirisotermen

Langmuirisotermen is a term used in adsorption science to denote the Langmuir isotherm family, named after Irving Langmuir. These models describe how a sorbate distributes between a bulk phase and a solid surface at equilibrium, under the assumption that adsorption occurs on a finite number of identical, independent sites and forms a single molecular layer. They are widely applied to gas and solution-phase systems to estimate surface properties from adsorption data.

The core relation of Langmuirisotermen expresses the amount adsorbed q as a function of pressure or concentration. Using q_max for the maximum monolayer capacity and b as the affinity constant, the common form is q = q_max b p / (1 + b p) for gas-phase systems, or q = q_max b c / (1 + b c) in solutions, where p or c is pressure or concentration. The fractional coverage θ = q/q_max simplifies to θ = (b p)/(1 + b p). The constant b reflects adsorption/desorption kinetics and is temperature dependent, while q_max reflects surface capacity.

Assumptions underlying Langmuirisotermen include a homogeneous surface with equivalent adsorption sites, no interaction between adsorbed molecules, and reversibility of adsorption. Under these conditions the model yields a simple, monotonic rise of adsorption with increasing p or c, approaching a plateau at q_max.

Applications span surface science and chemical engineering, including estimation of surface area, catalyst characterization, and modeling of gas adsorption on activated carbons or nanoporous materials. Limitations arise from real surfaces that are heterogeneous or promote lateral interactions, or when multilayer adsorption occurs. In such cases, extensions or alternative models, such as Freundlich or BET, are employed.