How to fit adsorption isotherm models using Microsoft Excel

Link to Excel spreadsheet: doi.org/10.5281/zenodo.4521579
This tutorial video teaches you how to fit adsorption isotherm models (Langmuir and Freundlich) to experimental data using Microsoft Excel. The video demonstrates both linearised and non-linear fitting, using the LINEST function and the Solver Add In.
Please get in touch with any questions and suggestions. I hope this video benefits the community.
Excel spreadsheet: doi.org/10.5281/zenodo.4521579
Data set: doi.org/10.5281/zenodo.3689692
Original paper: doi.org/10.1016/j.jcis.2020.0...
00:00 linearised Langmuir fitting
07:20 non-linear Langmuir fitting
11:50 linearised Freundlich fitting
14:14 non-linear Freundlich fitting
15:40 comparing the goodness-of-fit
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Google Scholar: scholar.google.com/citations?...
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[@waddema]

wow, this will definetly pimp my masterthesis to another level. Thank you sooooo much for this tutorial and your excel sheets :*

[@rawan4297]

I like how you explain, i never understood these models till i saw your video, thank you very sooo much

[@hiramob]

Very clear explanation. Exactly what i needed! I see it was uploaded 2y ago but id love to see more uploads like this.

[@King_Daud]

Thanks Sir, I was struggling this for the past six months. Thanks a lot sir

[@patino.gelver]

Thanks a lot Jay...great help for the community

[@sandervanduinen6248]

Thank you for the amazing and clear explanation.

[@isaacvicentini5747]

This was such a good explanation. Thankyou so much for putting out such educational content

[@riantempany543]

you are my saviour, great vid

[@SasaCecaSole]

Thank you! Very well explained.

[@MegaPad2]

Excellent explanation! Thanks.

[@chandrabhan2715]

Thank you sir, this is well explained concept.

[@azanhk1]

great tutorials... so many thesis compared the R-squared between models in their linearized forms..

[@Aminulchem]

Good job!

[@wijisena9214]

Great it helped a lot cheers😊

[@abdelazizkadri6973]

Thank you very very very much

[@nabilahabdulsamad1772]

Thank you for a great tutorial. May I know, can excel solver able to solve when ln (MR-C) = ln a - Kt when we only have data for MR and t and need to find the constant value which is a, K and C?

[@vahidmousalou8870]

you are a genus man (like), plz calculate a fit an 3 parameter and more isotherm like Sips and... plzzzz.

[@lucaslima5731]

Do you have any videos about the Freundlich-Langmuir (Sips) isotherm? I am in doubt about getting the Ks and ns parameters of the regression.

[@dosentekim]

thank you sir

[@Orian366]

Hello thank you for the nice video. I would like to ask if you happen to know how to fit data of multicomponent adsorption systems to modified extended langmuir model, SRS and extended freundich model in excel. I wonder is it possible to find the eg. interaction factor η of modified extended langmuir model with the excel solver you showed here?Thank you

[@refalka4970]

i think the first langmuir equation is also can be linearized and it can be fitted to the y = mx+c also. But the m value you got is different with the second equation...

[@g_silver_3549]

Thanks a lot :)

[@lucaslima5731]

Salvou minha vida! obrigado :)

[@jaybullen2887]

De nada - estou feliz que foi util

[@archanasailypainuly7841]

VERY INFORMATIVE VIDEO , COULD YOU PLEASE EXPLAIN THE BET ISOTHERM AS WELL

[@mahamajmal5495]

which data is required to applying langmuir adsorption isotherm?

[@williamtchabo1310]

How to obtain the K value?

[@DebashisBandyopadhyay-ow3mj]

Nice explanation. How to apply it in case of hydrogen adsorption using Freundlich Isotherm model??

[@Javsaful]

To determine the value of qe a volume is needed, this volume influences the final result of qm and I have seen that some authors use 1 liter and a better qm is obtained. Is this feasible? thanks for the reply

[@fridtjofsobanski359]

My master thesis is saved! Thanks a lot!!!

[@King_Daud]

Me 2

[@priyankakhare4469]

Sir Plesae make vedio tutorial for dubnin non linear isotherm..

[@aminnaifar4442]

thanks a lot Could you give us another example please

[@herculesdf9748]

First of all, thank you for the video. In non-linear models, having followed all your steps, when I draw a scatter diagram and configure the trendlines, the graph continues to be linear and a small R^2 is obtained. On the contrary, the calculated R^2 from the square differences is above 0.96. I notice to you that the final trendlines are non-linear. What did you choose in the trendlines menu?

[@jaybullen]

@@herculesdf9748 In the non-linear model, we do NOT add a trendline. The black dotted line that you see at 11:40 of the video is not a trendline, but it is actually the Langmuir adsorption isotherm model. The data used for this dotted line is Ce (column B) and qe (column G). When you plot this data, you will get the curved line with the Langmuir adsorption isotherm shape. If you have any difficulties, please download my Excel spreadsheet template (linked in the video description). I hope this helps you - Please do leave a comment to say how your modelling went!

[@herculesdf9748]

@@jaybullen I understood my mistake and you confirmed it to me. Finally, the model that was created fits well with the original and I have 0.96 R^2. But I have one question, this moment maybe my mind is tired but I wonder if after the work is done we copy and paste the initial values ​​of Qe to the Qe values ​​of the model we will obviously have R^2= 1, but the qmax and KL values ​​remain the same. does all this make sense? Thank you very much for your help

[@herculesdf9748]

@@jaybullen One last question. The name of the method you re following in non-linear models, is it called regression or least square method? Or both maybe? Thanks a lot

[@tamarapozo4204]

Hello! first of all thank you very much for the video! and the second thing is to ask a question, I do not understand very well the difference between the qe used at the beginning to calculate the y-axis (Ce/qe) in the linear regression graph, and the qe calculated later from the data obtained from the first one. Thank you!

[@drsaqibscienceacademy]

The qe value calculated earlier (using Ce/qe) is derived from your experimental data, while the qe value, which is theoretical, is determined based on the Langmuir model. Therefore, they differ in terms of being experimental and calculated values, respectively.

[@SIAHSI]

Thank you for the explanation. I have a question, what is the unit of KF, I can't deduce it, hope you can give me some hints. Waiting for good news.

[@jaybullen2887]

Imagine that qe (mg g-1) = KF (UNITS) * Ce (ug L-1)^(1/n). We can rearrange to get KF (UNITS) = qe (mg g-1) / [Ce (ug L-1)]^(1/n). This is the same as KF (UNITS) = [qe (mg g-1)]*[Ce (ug L-1)]^(-1/n). If we look at the units only, we see that the units for KF will be equal to (mg g-1)*(ug L-1)^(-1/n). Or more generically, the units are (aqueous concentration units)*(adsorbed adsorbate units)*(-1/n). These units are very strange indeed!

[@sufiasiddiqui]

I have a question. It's written that R2=1-(sum of squared differences between model and experiment/sum of square differences between model and average). However, in the excel sheet in the denominator the term is calculated for sum of square differences between experiment and average. Can you please clarify?

[@jaybullen2887]

Hi there - great question. We want to compare the quality of our optimised model with optimised parameters k and qe with a very poor model. The poor model is a simple average of all y-values (i.e. no model at all!). So we calculate (a) sum of squared differences between experiment and model, and then calculate (b) sum of squared differences between experiment and average of all y-values. And we compare the two. Further explanation can be found elsewhere: www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/regression-and-correlation/coefficient-of-determination-r-squared.html

[@zxcvb2003]

hello! I am following this video, and the intercept value is negative, so the KL value is also negative. No matter how much I think about it, I don't know why, so I'm leaving a comment. Do you know anything about this issue? Thank you and have a good day!!

[@eduardotcb]

Rifas machín chicharrín!

[@menglizhang5176]

How can we know the original qmax when we fitting non-linear Langmuir adsorption model?

[@jaybullen2887]

Thanks for the question. When you use non-linear fitting with Microsoft Excel's Solver feature, you have to take an initial guess of the parameters Qmax and KL (the Langmuir constant). For Qmax, choose a value of where you think that the adsorption isotherm will plateau. In the graph of experimental data in this video, you can see that the reaction has reached a plateau with qe ~ 9.5 mg g-1, so I would use this as an initial guess. Then you need to guess the value of KL. You can choose any number, and see how the shape of your model compares to the experimental data. Next, change this number a bit and see if the shape of the model improves or gets worse. Keep doing this until you have the rough shape of the experimental data. Then use the Solver function to optimise Qmax and KL to improve the R^2 value!

[@menglizhang5176]

@@jaybullen2887 Thank you for your reply! Now I can understand well and this video is very useful for me! Thank you very much!

[@karunratsakulnarmrat7993]

I've tried solver for 4 unknowns to optimize value. Two times run with exactly data have got different values. Do you have any suggestion please?

[@jaybullen2887]

Hi there, what is the model you're trying to fit? Is it an adsorption isotherm with 4 fitting parameters? When we increase the number of fitting parameters, we increase the probability that the Solver algorithm fails to find the true best fit, and instead it finds a not-so-good fit. If you can, try to simplify the problem so that you can optimise just two unknowns first. After you know what those two unknowns are, you can use them in the model and calculate the other two unknowns.

[@karunratsakulnarmrat7993]

@@jaybullen2887 Thank very much for your suggestion. I used Peleg's model (MC = A(aw)^C + B(aw)^D; C1) for sorption isotherm.

[@jaybullen2887]

@@karunratsakulnarmrat7993 I'm not familiar with the Peleg sorption isotherm model. Looking at a paper called "Comparison of the Sorption Properties of Fruit Powder Shampoos Using the BET, GAB, and Peleg Models" - They use a Monte Carlo algorithm to solve the non-linear regression and optimise all four constants. This should avoid the algorithm getting stuck in a local minimum rather than the true minimum. Unfortunately I don't know how to do this using Microsoft Excel's Solver without a lot of manual work (i.e. constrain two parameters, optimise the second two parameters, write down R^2, change the first two parameters, and repeat the optimisation, and generate a whole table of R^2 values then choose the best) - If you solve the problem, then please do share your progress. Good luck!

[@karunratsakulnarmrat7993]

@@jaybullen2887 Thanks for your information. I recalculate Peleg model same as your way. But this time I change the initial value (previously assigned as "1" for 4 unknows). After I run the solver the results look good. I will try Monte Carlo in order to compare the results. Highly appreciate your time and suggestion.

[@jaybullen2887]

@@karunratsakulnarmrat7993 Thanks for the update. Glad that you're making progress. You can also make a very nice graph where the x-axis is the value you fix unknown 1 or unknown 2 to be, and the y-axis is the R^2 value after you optimise unknown 3 and unknown 4. You change unknown 1 and 2 to many different values, and write down the R^2 results. Let us know how you get on with the Monte Carlo method and how you implement it.

[@martljn6431]

Why can't you use the excel function to calculate R²? Isn't that an easier method to determine the R² if you got the calculated qe values?

[@jaybullen2887]

Definitely! But in this spreadsheet, we show all the mathematical steps, one by one, to improve our understanding of what R^2 is and what it means and how we calculate it :-)

[@fajin8992]

Why you use Ln instead of Log?

[@jaybullen2887]

You should get the same answer either way, whether you use natural logs or base 10.

[@md.nahidpervez8525]

Can I get your email to discuss about my data

[@ry8361]

This is for single adsorption system. How to fit Binary-Adsorption isotherm models??

[@jaybullen2887]

Hi there, when you say binary adsorption isotherm models, do you mean (a) two different adsorbates, (b) two different adsorbent materials, or (c) two different adsorption mechanisms, e.g. monolayer adsorption followed by multilayer adsorption-surface precipitation?

[@ry8361]

@@jaybullen2887 Thank you for your reply. I mean adsorption of two different adsorbates. How can I use non-linear method to fit the data to different multiple adsorption models such as extended Langmuir model, modified Langmuir model and so forth?

[@jaybullen2887]

@@ry8361 Perhaps you could provide the equation that you would like to model? I am not familiar with multi-adsorbate Langmuir adsorption isotherms and I imagine that there are many different approaches. Perhaps contact the author from a recent paper than interests you. Looking at the "Non-modified Langmuir multi-component isotherm" in the following paper: pubs.rsc.org/en/content/articlelanding/2019/ra/c9ra04865k the authors provide the following adsorption isotherm equation: qe,j = Qmax,j * (KL,j * Ce,j) / (1 + Σ,j (KL,j * Ce,j)) where parameter j refers to either adsorbate A, adsorbate B or adsorbate C etc... (It's very hard to write the equation in KZbin so please refer to the paper!) You could model an adsorption isotherm using this equation in Microsoft Excel, using the Solver function. You would add extra columns since for a binary system you don't just have one independent variable (Ce) and one dependent variable (qe), but you instead have two independent variables (Ce,A and Ce,B) and two dependent variables (qe,A and qe,B). Just like the single-adsorbate system, you would run the Solver and try to improve the R^2 value. The challenge is that you now have 4 fitting parameters instead of 2 (KL,A and KL,B and Qmax,A and Qmax,B). The Solver function is likely to fail to give the best fit, since the algorithm may get stuck at a local minima rather than the universal minimum when trying to minimise the error between the experimental data and the model. To solve this, you could first determine KL,A and Qmax,A by fitting an experimental adsorption isotherm where you only have adsorbate A, and there is zero adsorbate B. Then you can constrain (fix) the values of KL,A and Qmax,A in the binary model to the results from your single-adsorbate experiment, and you will only have to optimise the fitting parameters KL,B and Qmax,B. When you are dealing with complex systems with multiple adsorbates and multiple adsorbents, you may wish to consider using a Surface Complexation Model (SCM) instead. In an SCM, you calculate adsorption equilibrium constants for one adsorbate and one adsorbent at a time, then you combine your experimental parameters with a database of literature parameters to achieve a model that is sensitivity to many factors: not just adsorbate concentration but also pH, ionic strength and competitor ions. I have a short tutorial article about surface complexation modelling here: www.researchgate.net/publication/349947876_Surface_complexation_modelling_Building_tools_to_understand_and_predict_adsorption