I'm trying to fit my equilibrium data to the Hill de Boer and Fowler-Guggenheim models. I've found a paper
Article Modeling of adsorption isotherms of phenol and chlorophenols...
which mentioned about this models as follows:
" It is important to notice that the Hill–de Boer isotherm is applicable only for the values of surface coverage calculated using the theoretical maximum adsorption capacity"
" It is important to notice that the Fowler–Guggenheim isotherm is only applicable for
fractional coverage < 0.6 when the Langmuir and Freundlich maximum adsorption capacities are used."
There is another way to calculate the theoretical maximum adsorption capacity? It is wrong if i use the qm obtained from Langmuir model to calculate the fractional coverage for Hill de Boer and Fowler-Guggenheim?
Hello,
I think you can use the qmax from Langmuir model or even from Langmuir-Freundlich model. It will be interesting to see if you'll find the same value.
hello, Recently I worked on a complete analytical expression of the isotherm (which goes beyond the limits of the Langmur model (see: Journal of Physical Chemistry C 2018 122 (42), 24103-24109, and the articles cited there). I do not think that there theoretically exists a maximum value for adsorption: it depends on the competition between the affinity of the substrate with respect to the adsorbed species and the repulsion of the adsorbed species between them.
The Langmuir (L), LF-Freundlich (LF) and Fowler-Guggenheim (FG) models are based on localised adsorption. In principle, the maximum adsorption is, in this case, determined by the number of adsorption sites. The Hill-deBoer model is for mobile adsorption, so based on different premisses than L, FL, FG. Here the theoretical maximum is, in principle, determined by the size of the molecules and the specific surface area. The two maxima should not be confused. With the FG model the lateral interaction parameter can only be obtained when the maximum adsorption is known.
In practice, isotherms often show a pseudo-maximum determined by a limited concentration range or lateral repulsion between the adsorbate molecules (see also the comment by Sidi Souvi).
See also my review on adsorption (from solution) in
Advances in Colloid and Interface Science 280 (2020) 102138; Article Equilibrium mono- and multicomponent adsorption models: From...
Bruna Steffens, No wonder that the values of qm determined with the help of different isotherms differ. Properties of individual mathematical functions are decisive, but we should not forget about different behaviors of particular numerical methods. The possibility of correlation between qm and other parameters is also important. I would also pay attention to the number of points, which should be correspondingly greater in the case of multi-parameter functions. And finally, I would check if a given isotherm was derived for the liquid-solid system (this is what you mean), or if it is valid only for the gas-solid system. If the latter, then with regard to the liquid-solid system, these are only empirical functions, and qm is their upper limit. One more thing, the data doesn't match the function just the other way around. Once, in some reviews, I wrote: "this is a way for perfect fit".
To the best of my knowledge it's better to check in and explore more about it in research paper of top ten publishing house and Q1 rated high impact factor journal of physical chemistry related to adsorption
The isotherm equations apply both for Gas-Solid systems and for Liquid-Solid systems. However, the meaning of the interaction parameters is for the SL systems more complicated.The Freundlich model is in both cases empirical, but it is a limiting form of both the LF, FG, and Hill equation (low adsorption values).A theoretical base of the LF equation is provided by Sips.
Hello,
Take this paper guide where I calculated both theoretical and experimental
https://idp.springer.com/authorize/casa?redirect_uri=https://link.springer.com/article/10.1007/s11356-019-06530-y&casa_token=M0knPL2BmQcAAAAA:4phgZ8dpaVY_BXvyg4J-uJm2qVoGIm6s7DaRTDidVE8i7xDgxxKVA708d0Gd3blnOdXcbMa6kqUuqIWN
In general the isotherms have been derived for the gas-solid systems. To liquid-solid systems they have been adopted by statistics. There are, of course, exceptions. H, L, and LF isotherms can be derived based on the low of mass action, but not F, Temkin or Jovanovic isotherms. In liquid-solid systems, numerous side effects may also occur, which should be kept in mind.
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