Hi, If I could understand carefully your question there is my answer .
there is a theoretically difference between these models. You have to be ensure that which mechanisms do you want to identify. you have to know about your sorption phenomena (It is mostly Physical or Chemical sorption). you can do it by value of "e" parameter which calculate from Temkin model. So you can discuss about sorption and models. and I suggest to know about your adsorbent and sorbed ions.
you can use this paper:
Article Modelling and Interpretation of Adsorption Isotherms
From what point of view? From a mathematical point of view, the L isotherm is a hyperbolic function, the F isotherm is a power function, and the T isotherm is a logarithmic function. From a practical point of view, only the L isotherm can be used to determine the maximum adsorption capacity, the other two not. Moreover, the L and T isotherms are based on a physicochemical basis, while the F isotherm is not.
Imen Abidli, On the basis of the compatibility of a given function with the equilibrium or kinetic data, I would avoid inferring about the adsorption mechanism. Here, the physicochemical tests of the adsorbent surface are decisive.
- "Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review". Hai Nguyen Tran, Sheng-Jie You, Ahmad Hosseini-Bandegharaei, Huan-Ping Chao.DOI: 10.1016/j.watres.2017.04.014
- "Modelling and Interpretation of Adsorption Isotherms". Nimibofa Ayawei, Augustus Newton Ebelegi, and Donbebe Wankasi. https://doi.org/10.1155/2017/3039817.
I suggest you to have a look at the following paper that presents an overall review of the applications of adsorption isotherms, the use of linear regression analysis, nonlinear regression analysis, and error functions for optimum adsorption data analysis:
-Modelling and Interpretation of Adsorption Isotherms
Nimibofa Ayawei , Augustus Newton Ebelegi, and Donbebe Wankasi
Journal of Chemistry, Volume 2017 |Article ID 3039817
Available at: https://www.hindawi.com/journals/jchem/2017/3039817/
Adsorption isotherm is the most extensively employed method for representing the equilibrium states of an adsorption system. Langmuir, Freundlich, and Temkin are isotherm models, and everyone has own assumptions. For instance:
Langmuir model assumes that the solid surface is uniform and contains a finite number of binding sites with equivalent sorption activation energies and that there is no interaction between adsorbed molecules.
Freundlich model assumes that the surface of the adsorbent is heterogeneous and active sites and their energies distribute exponentially.
Temkin model presumes that adsorption is a multilayer process. Its equation is better for predicting the gas phase equilibrium rather than liquid-phase equilibrium.
To summarize: you can differentiate between these models in:
mono or multilayer process,
physisorption or chemisorption,
if there is interaction between adsorbed molecules.. etc.
I would suggest you take a really good look at the following papers: