Langmuirisothermeconcept

The Langmuir isotherm is a mathematical model in surface chemistry that describes adsorption of a gas or solute on a solid surface to form a monolayer. It assumes a homogeneous surface with a finite number of identical adsorption sites, where each site can hold at most one adsorbate molecule and there are no interactions between adsorbed molecules. The model is most applicable to chemisorption on surfaces with uniform energy sites.

The Langmuir equation expresses the amount adsorbed, q, as a function of the (relative) pressure or concentration, p: q = (q_max b p)/(1 + b p). Here q is the amount adsorbed per unit mass of adsorbent, q_max is the maximum monolayer capacity, and b is an affinity constant related to the adsorption energy. It predicts a saturating, hyperbolic isotherm as pressure increases. In terms of surface coverage θ = q/q_max, the equation becomes θ = (b p)/(1 + b p).

A common linear form is p/q = (1/(q_max b)) + (p/q_max), allowing straightforward determination of q_max and b from a plot of p/q versus p. This linearization, and others, enable estimation of monolayer capacity and adsorption affinity from experimental data.

The Langmuir model, proposed by Irving Langmuir in 1918, provides a foundational framework for analyzing adsorption on solid surfaces. It is widely used to characterize gas adsorption on materials such as activated carbon, silica, and metal-organic frameworks. It also serves as a basis for comparing with more complex models, like the Freundlich and BET isotherms. Limitations include the assumption of surface homogeneity and the neglect of lateral interactions or multilayer formation, which can lead to deviations for real, heterogeneous surfaces.