LangmuirIsothermen

Langmuir isotherms describe the adsorption of a solute onto a solid surface, forming a monolayer. They were developed by Irving Langmuir in 1918 and are based on the idea of a homogeneous adsorbent with a finite number of equivalent adsorption sites, each capable of binding one molecule. The model assumes no interactions between adsorbed molecules and that adsorption occurs at constant temperature and pressure.

The relationship between the amount adsorbed and the equilibrium concentration is given by the Langmuir equation: q_e = (q_max b C_e) / (1 + b C_e). In this formulation, q_e is the amount adsorbed per unit mass of adsorbent, q_max is the maximum monolayer capacity, C_e is the equilibrium concentration of the solute in solution, and b is the Langmuir constant related to the affinity of the adsorption sites. The equation predicts a saturation plateau as all sites become occupied.

For data analysis, several linear forms are commonly employed, such as 1/q_e versus 1/C_e and C_e/q_e versus C_e, which allow the parameters q_max and b to be determined by linear regression. A related measure is the separation factor RL = 1/(1 + b C_0), which indicates adsorption favorability (0 < RL < 1), linear behavior (RL ≈ 1), or unfavorable adsorption (RL > 1).

Limitations of the Langmuir isotherm arise from its core assumptions: a homogeneous surface, equivalent adsorption sites, and no interaction between adsorbate molecules. Real adsorbents often exhibit surface heterogeneity and multilayer adsorption, for which models such as Freundlich, Temkin, or Sips are more appropriate. Nonetheless, the Langmuir isotherm remains a fundamental model for understanding monolayer adsorption processes and provides a useful benchmark for comparing adsorption systems.