In my experiment, heavy metal removal from wastewater, I have obtained good fitting for both langmuir's and freundlich isotherms. There is very less difference such as difference of 0.02 only (0.99-0.97 = 0.02) How to explain this phenomena.
In addition to what Arpan said, calculation of determination coefficient (R^2) is considered to be a preliminary step to check the validity of a proposed model to fit the experimental data, so if the values are too close as in your case you can use more sophisticated method such as the Marquardt's percent standard deviation ( MPSD ) error function in order to determine and select the best model to fit your experimental data
To my opinion, these models are developed with the basis of some assumptions. The assumptions can vary from one model to another. We try to explain adsorption phenomenon by these models by considering that the process is governed by the assumptions considered in a certain model. However, the fact may differ from that and which we may not know. Nevertheless, to some extent these models can overlap depending upon some certain experimental conditions. May be in your case certain parametric values satisfy both the models you applied.
In addition to what Arpan said, calculation of determination coefficient (R^2) is considered to be a preliminary step to check the validity of a proposed model to fit the experimental data, so if the values are too close as in your case you can use more sophisticated method such as the Marquardt's percent standard deviation ( MPSD ) error function in order to determine and select the best model to fit your experimental data
You will see a difference if you can operate close to surface saturation. You may see a difference if you operate with a wide range of concentrations.
If you have a narrow range of concentrations, or your tests are using an adsorption bed where breakthrough is determined by rate of adsorption rather than by available sites, then you may well see that the two models perform in a similar manner.
Have a look at
https://www.researchgate.net/publication/6527344_Modeling_of_adsorption_isotherms_of_phenol_and_chlorophenols_onto_granular_activated_carbon_Part_I_Two-parameter_models_and_equations_allowing_determination_of_thermodynamic_parameters
Article Modeling of adsorption isotherms of phenol and chlorophenols...
Dear Renu
In both adsorption model, you have fitted your data, the differences are not significant. However. Langmuir adsorption would be considering multi layer adsorption; while Freundlich isotherm is projected by single layer adsorption. There are many more adsorption model you can try and find out which model is suitable for your work.
Dear Dr. Najafpour
One of the most known assumption related to Langmuir adsorption model is its mono-layer coverage. it means that each site can hold at most one molecule of adsorbate. And also the idea about Freundlich model is multi-layer adsorption.
As you mentioned above, there are a lot of isotherm models that can be used and the one with higher R2 shows the best model.
In some cases selecting a wrong isotherm model , will cause a great error in calculation of maximum adsorption capacity.
If the objective is to remove non-complexed ionic heavy metals from water/wastewater then there are more efficient and sustainable ways than adsorption such as their direct precipitation as insoluble metal-sulfides. We apply this proven method at full scale either chemically or biologically (to reduce available sulfate).
It's veryi mportant to study in this case the thermodynamic in order to conclude
Renu Bisht
for this particular experiment both method of assumption would be effective
Dear Renu,
In addition to all the comments, I want to mention that, if R2 value of both the models are very close and it was used to decide the type of model fitting well. Then, I would suggest you that you should calculate the maximum adsorption capacity obtained from the model by plotting the graph and compare it with the experimental adsorption capacity obtained for both the models. The model gives closer values of adsorption capacity is the best fit models. Secondly, if again you are not able to distinguish between two then o for thermodynamic study. If you get enthalpy value greater than 40 KJ/mol then it signifies chemisorption which is well explained by Freundlich isotherm. however, if enthalpy value less than 40 KJ/mol indicates physisorption which is well explained Langmuir isotherm for monolayer adsorption by Vander Waal forces of attraction.
Regards
Sumit
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