I'm fitting my isotherm data to linearized langmuir and freundlich isotherm models. But they didn't have a good fit with these models. But data showed a good fit with dubinin-radushkevich and Temkin isotherm models is it possible?
Sure ! So many models were developed because a single one is never able to fit to all possible experimental data. However, some of them should be used with care, as they are phenomenologic, i.e. are able to fit data but their physical meaning is not so clear.
Just have a look to the attached paper for a selection of models. Probably one of these will fit your data better than Langmuir of Freundlich.
Alain
Yes, it is very possible. Quite a number of adsorption systems especially in solution do not obey Langmuir. You can also check some of my publications on this issue. The papers are there on my page within this community.
If I may ask what was the basis of your fitting?
Thanks.
One additional caution. When you fit to a linearized equation, in all but very special cases, you loose any way to obtain true uncertainty values on the fitting parameters. Absent such uncertainty values, no one can ever make any objective comparisons of the results from your experiments to their results. The use of R^2 to show "best fit" is over-abused if not totally meaningless in this regard. I would not even teach this result to a first year student in college any more, let alone accept it in for publication in a research journal (unless the person doing the work really knew what to do with the R^2 value).
Whatever isotherm model you choose, I strongly encourage you to do non-linear regression fitting and report your fitting coefficients +/- their uncertainty values.
I will also say "Yes" sure! But, could you give some idea about your adsorbent/ adsorbate system? This may ease the selection.
I'm fitting both linear and nonlinear equations for metal adsorption on to plant materials.
For the fitting I'm using Origin software.
Dr Jeffrey J Weimer, I noticed a clear difference in parameters when I fitted my data to linearized and nonlinear equations. Nonlinear fitting showed good agreement with data. Linearized models showed low R^2 values for langmuir and freundlich models but for nonlinear analysis showed high R^2 values. it confused me
R^2 is valid as a test of the goodness of fit for one model to multiple data sets. It confirms whether the proposed linear model fits one data set better than another. That is all it does. It offers no measure of the true uncertainties of the coefficients of fitting.
When your base equation is linear, this is a reasonable tool. When your base equation is non-linear, the best that linearized fitting does is offer a ranking. Be aware that, within the bounds of the uncertainties in your data, even differences in R^2 of +/- 1% or less may have absolutely no meaning. IOW, suppose you have linear Model A and linear Model B, both with total relative uncertainties in slope of about +/- 5%. In this case stating that R^2 values of 0.9996 and 0.9988 proves one model is better than the other will be ... rather naive.
Linear coefficients and non-linear coefficients will be different in all but a very restricted situation. The non-linear fitting is a "truer" representation. For non-linear fitting, you will do better to consider the magnitude of the chi^2 value ... the R^2 value has a far more complex behavior.
You might do well to read some background on statistical analysis of data. Even reading in wikipedia can serve as a start.
http://en.wikipedia.org/wiki/Coefficient_of_determination
You might also consider what physical behavior best models your system. Langmuir assumes uniform, monolayer adsorption with no dependence of adsorption energy on site density. Freundlich relaxes the assumption of uniform adsorption energy (adding one more degree of freedom). Tempkin and other models also add additional degrees of freedom.
A useful analogy is, the Langmuir model is like the ideal gas law (no intermolecular interactions), while other models include molecular interactions or site/site exclusion principles equivalent to what the van der Waals equation of state for gases does.
Adsorption is a surface phenomenon. Some of the earlier work was developed for gas solid systems and have many assumptions made for justifying their application. For a start, yours is a liquid-solid system and an involve more than just mono-layer adsorption. It may also involve some chemisorption with certain surface active groups. These reactions can change the surface charge and attract or repel more of the metals to the surface.
If if the solution you are using has other anions present, there is further potential for layering to occur, hence you could experience multiple layering in certain surfaces due to van der Waal forces.
Please find the following manuscript and you will find the correct answer as well as nature of different adsorption isotherms:
http://journals.tubitak.gov.tr/chem/issues/kim-12-36-2/kim-36-2-2-1110-6.pdf
Although Langmuir and Freundlich isotherm models are often discussed,these models cannot be applied for S-shape or LS-shape adsorption isotherms. If adsorption takes place into porous structure, two model above cannot use.
In various case, two-step adsorption model with general adsorption isotherm equation can be used.
You should try to learn two-step model.
I see that the author of the question is working with different biosorbents, so I would like to ask - what is the reason, why Langmuir model is applied? As it is not likely that "biosorption system" does comply with the assumptions of the Langmuir model (for example, all surface sites have the same energy or equal affinity for the adsorbate).
These videos can answer your questions: https://www.youtube.com/channel/UC5MiS3nMoji95OZ7uE1V8qw/playlists?view=50&sort=dd&shelf_id=6
This video shows how to fit Jovanovic isotherm model nonlinear equation easily using originpro. #aminulcheminnovation #chemcolony #aminulsir #aminulchem https://youtu.be/1w7kNbDabyg