A Critical Overview of Adsorption Models Linearization: Methodological and Statistical Inconsistencies

The linearization of adsorption equations is controversial. The estimation of fitting parameters strongly depends on the linearization method, magnitude of experimental error, and data range. Although many studies contrast linear versions of these equations with their non-linear counterparts, linearization is preferred due to its simplicity since a line could be represented with fewer experimental points than a curve. An in-depth analysis was carried out to compare the accuracy of linear and non-linear models. Although different transformations linearize Langmuir isotherms, only one form yields reliable fitting parameters. Linear transformations could also lead to a statistical bias, favoring a model that does not represent the experimental behavior. Similar observations are discussed regarding the pseudo-second-order kinetic model. Linearization of Freundlich isotherms, pseudo-first-order kinetic models, and fixed-bed adsorption models through logarithms implies that attention must be taken on the logarithm limits by properly selecting the data range. Linearization also promotes the incorrect interpretation of models due to oversimplification. The linearized van't Hoff equation would yield a reasonable fit with fewer experimental points than the non-linear regression, which requires more data to assure convergence. In this sense, there is convincing evidence that non-linear regression is a more robust and reliable tool for adsorption modeling.

Automated summary

The linearization of adsorption equations is controversial, with the estimation of fitting parameters strongly depending on the method of linearization, magnitude of experimental error, and data range. While linear transformation simplifies modeling, it may introduce statistical bias and oversimplify interpretations. Non-linear regression is shown to be a more robust and reliable tool for adsorption modeling.