Modelling single compound adsorption onto porous and non-porous sorbents using a deformed Weibull exponential isotherm

A new isotherm equation, the Brouers–Sotolongo isotherm (BSI), a deformed (Weibull) exponential equation was used to describe adsorption equilibrium of phenol and methylene blue (MB), respectively onto a non-porous adsorbent, Posidonia oceanica fibres and two porous adsorbents, chemically and physically activated carbons (ACs) prepared from vetiver roots. The adsorption characteristic parameters obtained were also calculated using classical adsorption isotherm, i.e. the Langmuir isotherm (LI), Freundlich isotherm (FI) and Redlich–Peterson isotherm (RPI). Using only R2 to determine the best-fitting model was not sufficient, calculation of the error deviation using both the Marquardt's percent standard error (MPSE) and the average relative error (ARE) was also done. For the case of phenol, and among all studied models, the BSI involving adsorption on a heterogeneous surface is definitely the most suitable one to satisfactorily describe biosorption of phenol on posidonia, but as well adsorption of phenol on the ACs giving the highest squared correlation coefficients and the lowest MPSE. For posidonia and as well for the ACs, when MB is the adsorbate, the RPI is the best-fitting model.