On validity, physical meaning, mechanism insights and regression of adsorption kinetic models

The study of adsorption kinetics is ubiquitous when reporting new adsorbent materials in the literature. The information these tests provide are no doubt valuable, but the conclusions drawn from adsorption kinetic models are many times contradictory between papers. In this work, the validity and meaning of common kinetic models are reviewed from literature dealing with their mathematical development, and are discussed. It is found that the most common models, the pseudo second order and pseudo first order models, have the ability to fit to kinetic data originating from systems limited by the surface reaction and by diffusion. Thus, these models are not associated with just one adsorption mechanism and further precautions when analyzing the data should be taken. Other less common models are also discussed, as they can be used to gain clearer insights into the rate limiting step. Another important topic discussed is the type of regression used. Linear regression has a bias toward the pseudo second order model and the estimated parameters can be very bad, which is particularly true for the pseudo-first order model. Thus, the wrong kinetic model is more easily chosen. The benefits of employing nonlinear regression and criteria for model selection are elaborated upon, using case studies reporting the adsorption of different solutes as examples.