Langmuir and Freundlich adsorption Isotherm models are from different assumptions like the former from monolayer and the second multilayer, to state one;But I have observations that both models fitted for same data. anyone to help
Dear Fekadu,
during my research on adsorption of Pb by modified powdered activated carbon I got results which fitted both models and it was observed by many others because an adosrbate can bind to more than one surface
Dear Ahmed, thank you. but still in need of further explanation how. can i assume that if Freundlich and Langmuir fits then the tendency of being multilayer formation is not significant but exists not to miss langmuir assumption of mono-layer formation. I am talking by considering only one of their assumptions
Freundlich isotherm is a special case of Langmuir isotherm at intermediate pressure. At intermediate pressure , y=kPn where n =1 to 0 , y =mass of gas adsorbed per unit area or mass of adsorbent .
Possibly for this reason your data fits in both the isotherms.
hi fekadu melak
you should be find amount of Mean Square Error and Average Absolute Deviation for both of Langmuir and Freundlich isotherm equation,and then Compare result of MSE and AAD
in order to find more information read attached paper
regards
Article Designing a commercial scale pressure swing adsorber for hyd...
Langmuir isotherm assumes monolayer coverage on a homogeneous surface with identical adsorption sites. But these assumptions are valid for gas adsorption on solid surface. In solution-solid systems, with the hydration forces, mass transport effects etc. the system is much more dynamic and complicated, and obeying the isotherm does not necessarily reflect the validity of the aforementioned assumptions. In such systems the isotherm adequacy can be seriously affected by the experimental conditions, in particular, the range of concentration of the solute/adsorbate.
From my experience, both of Langmuir and Freundlich isothems might adequately describe the same set of liquid-solid adsorption data at certain concentration ranges, in particular if the concentration is small and the adsorption capacity of the solid is large enough to make both isotherm equations approach a linear form.
My suggestion to you is to increase the concentration range significantly, and check again the isotherm validity using both models, you will most probably observe than one of the two isotherms correlates better with the data. Best wishes
I would vote for the answer from Talal Shahwan. Physically and conceptually the Langmuir and Freundlich models are different. When no preference is found between the models applied to the same data set, this means that either (1) the method of the data fitting evaluation is not appropriate or (2) the data is not sensitive, and various physical pictures are consistent with your reality, in this second case you cannnot decide whether you have a monolayer or a variety of sorption sites. However, very often the problem comes from the wrong evaluation of the data fitting, and here I agree with Hossein Anisi. However, even Mean Square Error and Average Absolute Deviation and RMSE may appear similar for different models. What should be done is the examination of the distribution of residuals (experimental sorbed concentration minus fitted sorbed concentration) along the isotherm. This is a simplest way to see whether there is a tendency in the distribution of deviations. For example, often, the low concentration range is underestimated, the intermediate concentration range is overestimated, and then, the highest concentration range is again underestimated. Such a tendency of the residual distribution when the residuals are plotted against a concentration (vapor pressure) shows a non-random shape, i.e., the bell-shape. If you got it, regardless to anything you could think, your fit is inadequate, even being very good in terms of the resduals. There is n important factor not accounted by a given model. Then, of course, the lack-of-fit analysis could be quantified by roughly comparing the deviatioins with your experimental reproducibility.
During my research modified activated carbon by ZnCl2 , I got both model fitted. But I got more favour for Langmuir than Frienflich isotherm
The hyperbolic function (here Langmuir equation) fulfills the boundary conditions in zero and infinity, and the power function (here the Freundlich equation) only in zero. I advise against using the power function to describe equilibrium data for the batch adsorption process in liquid-solid system. Regards,
This is happening when the adsorbent has different types of functional groups. In most of cases the adsorption process occurs until a monolayer coverage is formed, but due to the different affinity of functional groups for metal ions from aqueous solution, the Freundlich isotherm model fit also well the experimental data.
A limited mass of the adsorbate is dissolved in the solution. The adsorbed mass cannot increase to infinity. Thus, the power function (Freundlich isotherm) can only be used to locally approximate the adsorption isotherm.