Miroslaw, the key words in your question are "scientific value." How do you define "scientific" in this particular case? Yurii

Yurii, There are at least two keywords or phrases there, namely "physical meaning" and "scientific value". In case of adsorption the most important is adsorbent and its properties. Important are the reliable results of equilibrium and kinetic tests, but quantitative description of them is of secondary importance. However, if someone intends to do it, it should be well thought-out, preferably based on theoretical foundations. This is how I understand the "scientific value" here. Best regards, Mirosław

Can you provide a link to the RG article?

I'm curious if this is referring to adsorption isotherms. If so, then it seems the two types of polynomial you describe are for mono- and multi-layer adsorption etc.

Whether there is scientific value and if the properties of the adsorbent are more important than the adsorbed material depends on the application.

Consider a process like aggregation of suspended matter for water treatment. Quantitatively determining the minimum amount to promote aggregation can save a lot of money given the large scale of the operation. The adsorption behavior depends not only on the properties of the adsorbent but also the continuous phase including the adsorbing material. Sometimes you have no control over the properties of the adsorbent and so you need to understand scientifically what is happening in order to find the most cost effective option.

Miroslaw,

In general I agree with you. Here is my own understanding. If you want to describe whatever process, you need a set of mathematical equations. This equations might be obtained by fitting experimental data by a polynomial equations and use them to solve the problem. I would still call this approach as "scientific,'" because it's based on experimental data and can be confirmed experimentally. However, such approach is not based on "physical" meaning of each equation and does not help to understand the process. Therefore, the "scientific value" of such approach is very low.

John Francis Miller

I will not give the link. It's easy to get to work through my RG website. I wrote a few comments to it.

I am not a specialist in adsorption, but I fully realize that the adsorption process is conditioned both by the properties of the adsorbent and the mixture in which it is dispersed. The equilibrium curve can increase (for smaller initial concentrations) and then decrease (for larger ones). One can give many reasons for this behavior, but it is not necessary to describe such a curve with a mathematical function, in particular a polynomial. Especially since here it will almost certainly be replacing several experimental points with three numbers. That's the view I represent. Regards,

Yurii,

It is generally difficult to undermine the scientific value of the results of a given experiment. I was convinced of this for a long time, until I started reading works on batch adsorption in a liquid-solid system. Recently, I wrote comments to over a dozen works in this field. In a few of them, it seems to me that the material tested was unstable. Hence, various "surprising" behaviors. And then, in my opinion, both the results of such experiments and their description are of little value. In the case of reliable results, the description by equations may be, but not necessarily. However, as far as the description of data on kinetics and equilibrium of batch adsorption is concerned, I am slowly becoming convinced that it is unnecessary littering of usually valuable works. Mirosław