Mostly I use the Langmuir, Freundlich and Sips model for the describe the isotherm database but I don't know how to use D-R and Tempkin isotherm models
Thanks for raising this query. Input the non-linear equation as a newly defined equation and input the equations for DR/Tempkin. Then, while you are "fitting" your data points in non-linear fit, find the equation you have previously input.
It requires few experience to actually have the parameters diverged, but you need to play with the initial values and input the values of the constants manually to actually diverging them. In this way, we are actually forcing the fit to diverge until we get the statistical parameters to the extent we require.
TIP: start with previous studies done on your sorbents, and utilize the initial parameters for input from the previous papers. Feel free to write to me back.
I disagree with the answer by Ahmed above: why would you use the non-linear form of the equations? This would complicate all the procedure. For example, you would need initial parameters.
Just find the correct forms of the Temkin and DR equations (trivial) and do the linear regression in a software of your choice.
This paper has a proper example of all these linearizations:
Article Modelling and Interpretation of Adsorption Isotherms
Thank you Fernando Vallejos-Burgos for pointing it out. However, the non-linear/linear fit depends on the user. For some scenarios, we need to use the non-linear fitting even if requires complications, we need to assign parameters values for both. Linearizing all the equations solely depends on the user and the applicability.
Tran, H. N., You, S. J., Hosseini-Bandegharaei, A., & Chao, H. P. (2017). Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review. Water Research, 120, 88–116. https://doi.org/10.1016/j.watres.2017.04.014
This one says it all about adsorption and the distinction about linear and non-linear fits usage.
Thanks again!
Cheers!
Ashiq
Thank you Hai Nguyen Tran
, our group utilizes your paper as a hint for our models. There is still, a lot of room for learning on using the different parameters and playing with them to get the right fit and mechanisms.Thanks to Fernando Vallejos-Burgos for sharing another paper on interpreting the models. This helped.
I recommend Dr Hai Nguyen Tran
answer, however, I am not sure if the equation in the picture he provides is missing something?.Should it be qe=qDR*2.7182818284^(-KDR*(0.00831*298*(ln(1+(1/Ce)))^2)
Not qe=qDR*2.7182818284^(-KDR*(0.00831*298*(ln(1+(1/Ce)))
very valuable opinions.. I usually use non-linear equations, but some days ago I tried to apply D-R non-linear model, but it didn`t fit, I plotted qe vs epsilon^2.
Then I tryed with the linear form of D-R equation and I got it. I did it in Matlab curve fitting app. I will try again with the non-linear D-R function shared by Dr. Hai Nguyen Tran
It would be useful if the experts summarise the advantages and disadvantages of using non-linear or linear equations.
Hai Nguyen Tran
Using 0.00831*298*(ln(1+(1/Ce)) seems incorrect. It is well-known that logarithmic expression (ln [1+(1/Ce)]) does not have any unit. The conversion of mg to mole for Ce does not solve this problem as some do. In this conversion, ln [1+(1/Ce)] has a unit!!!
In literature, many article results published about Dubinin-Radushkevich isotherm model are incorrect. Please read the original article of Dubinin-Radushkevich isotherm model
haha, it was an error--new version is being made
The adsorption potential theory reflected the change in the Gibbs free energy of an adsorbent after adsorbing a unit molar mass of adsorbate
E=RTln(Ps/P); where ps (atm.) and p (atm.) are the saturation vapor pressure and the equilibrium pressure of adsorbate molecules at the temperature T, respectively. Based on this, the change in the Gibbs free energy for solute will be
E=RTln(Cs/Ce); where Cs is the solubility and Ce is the equilibrium concentration of the adsorbate.
Article Application of Dubinin–Radushkevich isotherm model at the so...
Goerge William Kajjumba, thank you for your contributiion. So, Cs is the adsorbate water solubility at the temperature, pressure, etc) of the experimentation? If so, where could I get these values for heavy metals? thank you for repply
Byron Lapo https://www.researchgate.net/post/The_dubinin-radushkevich_isotherm_model?isAnswerFieldFocused=true
May be helpful "Adsorption of hexavalent chromium onto alkali modified biochar derived from lepironia articulata: Kinetic, equilibrium and thermodynamic study
George William Kajjumba , thank you for your valuable information
if I am studying the hormone adsorption:
- from where I can get the Cs for each hormone?
- if I am doing my study at the maximum concentration of hormones (highest possible solubility) and the adsorption capacity of the adsorbent is very high, in your opinion is it still possible to use the D-R model (according to the Qili Hu, Zhenya Zhang paper C ≪ 1, but in my case, the Ce and Cs are close to each other.
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