Useful informations can be fount in the paper: L. (Negrilă) Nemeş, Laura Bulgariu, Optimization of process parameters for heavy metals biosorption onto mustard waste biomass, Open Chemistry, 14, (2016), 175-187
The various adsorption isotherm equations apply roughly speaking to different degrees of non ideality of the adorbed phase (layer). This applies to both adsorption from solution and to gas adsorption. Below some examples of isotherm equations (apply at contant temp) arementioned. So the choice of an equation should in principle be based on how ideal/non-ideal the system behaves.
Monolayer adsorption monocomponent systems (dilute solutions, low gas pressure)
- Langmuir=ideal monolayer with only interaction with the homogeneous surface; --Frumkin-Fowler-Guggenheim (FFG)= Langmuir extended with lateral interactions in the adsorbed layer;
--Freundlich= adsorption on heterogeneous surfaces in a monolayer without lateral interaction and low coverage; originally seen as a purely empirical equation.
- Langmuir-Freundlich or Sips= same as Freundlich but for adorption up to a complete mono layer
--Stern or Langmuir-Stern= same as langmuir but also electrostatic interaction (with surface and laterally)
These equations have also more complicated analoges for multicomponent adsorption.
Multilayer adsorption (monocomponent, gas pressures up to saturation; not directly for solute adsorption)
--BET=Langmuir like but with multilayer formation with the same adsorption energy for layers>1.
--Frankel-Halsey-Hill (FHH)= multilayer adsorption with gradual decay of the adsorption enthalpy (energy)with distance to the surface, better description for multilayer adsorption than BET
- Polaniy theory= multilayer adsorption, like the FHH (can also be used for solute ads).