Freundlichisotherm

The Freundlich isotherm, named after Herbert Freundlich, is an empirical model used to describe adsorption on heterogeneous surfaces. It relates the amount of solute adsorbed per unit mass of adsorbent, q_e, to the equilibrium concentration of solute in the liquid, C_e.

Its most common mathematical form is q_e = K_F C_e^(1/n). The logarithmic form is log q_e = log K_F + (1/n) log C_e. Here K_F is the Freundlich adsorption constant (an indicator of adsorption capacity), and n is the heterogeneity factor. The term 1/n describes adsorption intensity; for most systems, 0 < 1/n ≤ 1 (equivalently n ≥ 1) indicates favorable adsorption.

The Freundlich model is empirical and commonly applied to adsorption on heterogeneous surfaces and to multilayer adsorption. It can describe adsorption over a wide range of concentrations and is often used when the surface energy is not uniform. The model does not predict a finite saturation capacity, and parameter values may depend on temperature.

Limitations include lack of a theoretical basis for all systems, poor extrapolation beyond studied concentration ranges, and its inability to describe saturation at high concentrations. Parameters K_F and n are empirical and should be evaluated under the same conditions.

Compared with the Langmuir isotherm, which assumes a homogeneous surface and a monolayer, Freundlich better describes adsorption on heterogeneous solids but lacks a finite adsorption capacity.