Dubinin isotherms versus the Brouers–Sotolongo family isotherms: A case study

Abstract

We show how the Dubinin isotherm and its extensions can be related to the isotherms derived from the general Brouers-Sotolongo isotherm. We compare them using benzene vapor adsorbed on activated carbon data from one of the original Dubinin's paper. We use the same procedure to analyze data from the thesis of Francois Marquez-Montesino on the adsorption on activated carbons prepared from Pinus caribaea saw dust. We conclude by proposing a simple methodology to determine the macroscopic information given by genuine statistical isotherms.

Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase transition from an isotherm

“…Such an approach has a clear advantage when the experimental adsorption isotherm can be successfully reproduced by the model and when the model assumptions reflect the surface structure and the behaviour of the adsorbates. However, this approach runs into difficulty when multiple different models can fit an experimental isotherm, [76][77][78][79] or when, despite successful fitting, the assumptions do not reflect the reality of the system. 9 This is when the alternative approach of ours, based on the principles of statistical thermodynamics free of model assumptions, can be useful in its ability to quantify adsorbate-adsorbate interactions directly from the isotherm data alone.…”

Synthesis of novel biocomposite powder for simultaneous removal of hazardous ciprofloxacin and methylene blue: Central composite design, kinetic and isotherm studies using Brouers-Sotolongo family models

“…The family of kinetics Brouers-Sotolongo model, based on the Burr-XII statistical distribution [47], is the most widespread fractal theory studied in the domain of kinetics adsorption of contaminants onto porous materials [48]. The statistical macroscopic model BSf (n,α) broadly integrates fractal diffusion and adsorption, irreversibility, and the nature of the nascence and ending (birth-death or sorption-desorption mechanism) of the procedure [49,50]. In the present study, Brouers-Sotolongo fractal BSf equation (n,α) was used in order to depict the biosorption kinetic data of the antibiotic and dye binary adsorption onto RR-ChR as was recommended in several previous works [36,37].…”

“…where , and , are the adsorbed amount at equilibrium and the saturation adsorbed amount at equilibrium respectively (mg/g) and is the adsorbate concentration in the liquid phase (mg/l). The coefficients (a) and (c) are related to the form and (b) represents a scale parameter [50]. The exponent (a) gives an idea about the shape and width of the adsorption energy distribution which is related to the substrate heterogeneity [57].…”

“…Hypothetically, this isotherm would imply that the decrease of the part of the unoccupied surface by the adsorbate particles is strictly proportional to a power of the adsorbate partial pressure [50,59].…”

“…n a l P r e -p r o o f[50,59].The BS isotherm was specifically used to describe the high heterogeneous and complex systems. This model considers a pattern of sorption energy distribution makes, that is why it is suitable to depict adsorption process implying sorbing materials even if they show various chemical and structural characteristics.…”