Type I adsorption may be modeled using Langmuir or Freundlich Adsorption isotherm models. But how do I analyse a system that does not follow the Type I adsorption mechanism?
you will have to apply several sorption models to your data set then on bases of r2 values you can conclude it to some extent.
Apart from Langmuir and Freundlich models which are the most popular ones, there are other two which you might use your data for. They are Dubinin-Radushkevich (D-R) model and the Temkin model. Try them and based on the R2 values, you can really decide which model does your data follow.
Thank you so much Z. Aly for your suggestion and input. This will surely help.
Examples of equations and fittings in order to get see which one works best are given in the attachment. I am sure you will find there the equation you need.
Alain
This is an old question, but I don't think that attacking the problem immediately from the numeric side (brute force calculation of statistical parameters and R-squares) is the good (or elegant solution).
I think everything starts by identifying the behavior of your system: you can see from the shape of the isotherm which kind it is. Whether it is type-I, type-II or type-III can be clearly recognized from the overall shape. Only after this you should choose the appropriate model. This can be validated comparing interactions energies of the adsorbate-adsorbent vs. adsorbate-adsorbate (low adsorbate-adsorbent energies will lead to type-II, while high ones (or nanopores) would lead to type-I).
If you want to select best fitted model on the basis of R Square, You should must confined the values of parameters in realistic limits.