Hi Shabboo Rahimi

In your case I recommend using Langmuir equation and determining the "qm" by the lineal equation: (1/q) = 1/qm + 1/Kqm x (1/C)

Dear Trino Romero ,

Thank you for your response.

But my adsorption is obviously not monolayer, so I do not think Langmuir isotherm can describe this adsorption properly.

Dear Lee Xin Jiat ;

Thanks for sharing your knowledge.

I know that all these isotherms can have linear form... but as you mentioned, I have not seen before that 3 or more isotherms be linear at the same time!

I have repeated the experiment meticulously and used 3 replications each time. my results were consistent with my other result!

Dear Lee Xin Jiat ;

Thank you for your precious answer!

Yes, I think my adsorbent (a novel protein/clay nanocomposite) is not like conventional rigid adsorbents, because it exhibited a hydrogel form in the (dyes) solution. also, I used the adsorbent in flake form, instead of powder form...

The article was interesting, however, I did not understand how you assessed 4 isotherms in Fig. 3?

about your explanation of unfavorable adsorption (with a concave shape), you are right. unfavorable means that to achieve economic adsorption, you need a high concentration or pressure! However, based on some references (e.g. Ayawei et al, Modelling and Interpretation of Adsorption Isotherms) I assume this to be related to Langmuir isotherm and the adsorbents that are following this model.

My adsorbent is able to remove the dye in a wide range of concentrations and based on linear(Nernst) isotherm can be described well.

your answer would help me a lot.

Thanks again,

Shabboo

I obserbed that the monolayer is between C = 4 mg/L and 7 mg/L above this value is the multilayer. It should generate 2 or 3 values in that area.

Dear Trino Romero ;

Thanks for your answer.

I am not sure I understand what you exactly mean. Could you please provide me with one reference to read about that?

it maybe helpful to note that based on the BET results, my adsorbent does not form a distinctive monolayer (no B-point in the plot).

Regards,

Shabboo

Dear Lee Xin Jiat ;

Thank you for your explanation. :)

Nice approach!

Good Luck.

Shabboo Rahimi Aghdam, Langmuir, Freundlich and Temkin isotherms are non-linear functions. It does not matter whether the form of these functions is explicit (in relation to the variable q) or implicit. So, none of the isotherms listed is "precisely linear".

Looking at the first graph, the only reasonable solution is Henry's isotherm. We will reach a similar conclusion by analyzing the second graph. However, if we compare the two graphs, which, according to the author, differ only in the process time (48 and 168 hours), we can see a significant shift of the points towards higher Ce values with a relatively small decrease in the qe value. Before explaining the reason for this behavior, the description of the equilibrium data by any function is unjustified.

Dear Mirosław Grzesik ,

That is right and we think that Henry's isotherm (Nernst or linear isotherm) would be the best for our case. Thank you.

about your 2nd part of your answer, I have to mention that: from 48 to 168 h, Ce has decreased from 16.5 to 9.1 mg/l, which I assume that we cannot consider a significant shift. because our initial concentration has been 250 mg/l, and ~7 mg/l has not had a significant influence on our qe amount.

Best regards

Dear Shabboo Rahimi Aghdam, Some remarks: The equilibrium data can only be approximated by a linear function in the range you are examining. I believe that if you increase Co the straight line will start to bend to the right. There are no adsorbents with unlimited adsorption capacity. Unfortunately, if you significantly increase Co, the likelihood of pore blockage increases, which will falsify the results. The difference between the values of C close to the equilibrium state for t = 48 h and 168 h is significant and is about 43%. The error must not be referred to Co = 250 mg/dm3. It is also worth explaining why this significant change in the current adsorbate concentration is. This may be related to the continuation of adsorption, but may be related to particle decay due to prolonged mechanical exposure.

Dear Mirosław Grzesik ,

Thank you for your useful remarks.

I was just wondering how did you calculate this 43% of adsorbate concentration?!

after 48 h R% are: 83.6 88.4 93.1 96.1 97.1 97.8 97.8

and after 196h : 90.9 95.2 97.9 98.6 98.8 98.6 98.6

The maximum R% change hear is ~7%

Dear Shabboo Rahimi Aghdam, Very simple: 100%(16.5-9.1)/16.5=45% (I wrote 3 instead of 5 by mistake). We are talking here about an equilibrium curve, not kinetic curves. Regards,

Dear Mirosław Grzesik ,

This is interesting that you look at the process differently.

Thank you for sharing your precious knowledge and experience.

Couldn't this be related to the macroscopic size of the adsorbent?

You mentioned that "Unfortunately, if you significantly increase Co, the likelihood of pore blockage increases, which will falsify the results."

The results of the adsorption in 100mg/l with 250mg/l were comparable. But as you mentioned increasing the Co more than 250 could be tricky. what about decreasing the adsorbent dosage?

Best regards

Dear Shabboo Rahimi Aghdam, Adsorption can be related to internal mass transport and parallel surface phenomena. Adsorption can also be accompanied by various adverse side effects. I have only indicated such a possibility, nothing more. You have two options. Either you will perform supplementary tests for higher Co values, or you will perform new tests for a lower value of the adsorbent dosage (I'm guessing), e.g. for 0.5 g/dm3 with a wide range of Co changes. You may also have to reduce the time to get a wider range of %removal changes. Of course, the possessed kinetic data can be described by means of empirical functions, however, in the case of describing each curve separately, it will only be data archiving. But reviewers like this kind of scientifically worthless archiving. Or you can describe several curves together for different Co. You will find information on how to do this in every chemical kinetics textbook. Regards,

Dear Rahimi Aghdam

Miroslaw Grzesik has explained what you need to do to better understand your experiment. Isotherms are linear. You can observe its isotherm by extending its scale and graphing from 0 to 5 mg/L. Then you can select the type of isotherm taking into account the specifications of each one of them.

Shabboo Rahimi Aghdam, As you wanted, I wrote a comment on your work. I'm sorry it's not very nice. But this is science. Your results are unacceptable, especially negative k1 or qecal for PFO much smaller than qeexp. R2 should also be counted for data in the q vs t coordinate system, and not for nonlinear transformed data. Then you definitely won't get R2 close to 1 and find that PSO, i.e. empirical hyperbolic function, is the best.

Useful link

https://youtu.be/b6sqSPhv-HI

Asif Ayub, The above presentation concerns the Temkin isotherm. For equilibrium data like above, I don't think the logarithmic function is useful. Try not to mislead others, similar to the useless presentation of the calculations for PFO and PSO.