Hi Hadjer

Providing a good answer to your main question would take some time, but we briefly introduced the basic assumptions behind some of these equations in Sect. 3.1 of this paper:

Article Outlook and challenges for hydrogen storage in nanoporous materials

That was in the context of H2 adsorption. I think Ref. [57] in the paper is worth looking up.

To answer your more specific questions, about explaining your results, etc, I think we would need more information (what system are you studying, for example, and under what conditions?) and perhaps to see the fits.

In general, for real adsorbents, I would expect to see better fits for equations with more fitting parameters, so that the dual site Langmuir, for instance, may always be expected to fit real data better than the standard Langmuir equation, regardless of its physical applicability. The same goes for the Toth, Sips, UNILAN and Jenson-Seaton expressions.

To comment more specifically, however, I think we would need both more information and to look at the quality of the fits - not just the SSE or similar figures-of-merit for the fitting process.

Another important point is the purpose of performing the fits in the first place, i.e. what do you wish to do with the results? In some cases - for example, for process modelling - mathematical simplicity is a priority and so if the Langmuir equation provides an adequate fit, even if it is not perfect, this may be a better choice than the more complex options (e.g. Sips, Toth, UNILAN and Jenson-Seaton).

Best regards,

Darren

• Darren Paul Broom , What do you see the exact reason of applying these models to our data and call them the best fit ?
• As I assume it validate your adsorption data, but what is the point Any adsorption can be indifferent to each other. So why to prove them ?
• Does it guarantees any model which followed with R2 value 0.9999 will be having same adsorption site , same pore types which model follows?
• Hadjer Bekhti you have applied lot of models. What do you exactly predict on the basis of it ?
• Thanks in advance

Hi Mihir

I think there are a few possible reasons for fitting data to an isotherm model.

I mentioned process modelling in my first answer. It's essential in that case, as input to a model for a separation process; for example, in pressure swing adsorption (PSA). In that case, you have to fit the isotherm data. You can't just put the raw data into the model or simulation.

Also, when calculating the isosteric enthalpy of adsorption, it is necessary to extract the pressures at which equal amounts of adsorbate are adsorbed. One way of doing that is to fit the data to an isotherm equation. We tested the use of different equations in this paper, for example:

Article Characterisation of porous hydrogen storage materials: Carbo...

However, for a long time, there was a lot of work carried out on analysing isotherms to try to extract physical information about the process. See, for example, the book by Rudzinski and Everett:

https://www.elsevier.com/books/adsorption-of-gases-on-heterogeneous-surfaces/rudzinski/978-0-12-601690-1

So, depending on the (adsorbate-adsorbent) system you are looking at, in principle, you may be able to extract some information about the nature of the process by fitting models to the data. In practice, however, you need to be very careful not to read too much into the fitted variables.

On a cruder level, maybe fitting the same isotherm model to data from two different adsorbents (two activated carbons, for example) may allow a simple comparison between them, i.e. the adsorption process is then parameterised in some way.

A good example is the fitting of either the Sips (Langmuir-Freundlich) or Toth equations to data and comparing the exponent, which is supposed to be related to the level of heterogeneity. In both cases, if the exponent is 1, then the models reduce to the Langmuir equation, which describes adsorption on a homogeneous surface. The further away from 1 the exponent gets, the greater the heterogeneity. That's the idea, anyway, although I would still be very careful about reading too much into such parameters.

Following on from this, to your question "Does it guarantees any model which followed with R2 value 0.9999 will be having same adsorption site , same pore types which model follows?", I would say no, it doesn't.

A nice test was carried out and described in one of the old adsorption books from the 1960s (Ross and Olivier, 1964), in which adsorption on a heterogeneous surface was simulated, in some way, with various assumptions that specifically do not agree with the Langmuir model of adsorption, such as the presence of strong adsorbate-adsorbate intermolecular interactions. The simulated isotherm data were then fitted using the linearised form of the Langmuir equation, and good agreement was found. This was an excellent demonstration of the fact that just because an equation may fit your data, it does not mean the model from which it was derived accurately describes the underlying physical process...

Best regards,

Darren

Hello,

i will reply you breively, you should change your minimization function error SSE.

Good Luck

Here is link

https://youtu.be/wWIZyxrp04I

You can differentiate among various isotherm mdels here: https://www.youtube.com/watch?v=hb8tJmHCsTo&list=PLxbTf96DhNSSZtzz1OEK5_oOR4Mb05hvU