Adsorption of Cd(II) ions on magnetic graphene oxide/cellulose modified with β-cyclodextrin: Analytical interpretation via statistical physics modeling and fractal like kinetic approach

Monolayer Adsorption of Ciprofloxacin on Magnetic Inulin/Mg–Zn–Al Layered Double Hydroxide: Advanced Interpretation of the Adsorption Process

“…The conventional isotherm models are not sufficient to provide relevant insights into the adsorption process. Advanced statistical physics model has been applied to assess the adsorption process at macroscopic and microscopic levels . The measured data were assessed by statistical physics models (models 1, 2, 3, and 4) and their equations are given in Table .…”

“…The endothermic nature of the adsorption process was suggested by positive values of adsorption energies. Additionally, the adsorption energies were below 40 kJ/mol that demonstrated the involvement of weak forces (physical) in the uptake of ciprofloxacin …”

“…Kopelman has shown that the rate coefficient of the adsorption process diminishes as the time increases (fractal-like kinetics). The relationship between measured rate coefficient, k inst , (time-dependent) and rate coefficient, k ′, (time-independent) is given as k normali normaln normals normalt = k ′ t − h goodbreak0em3em⁣ 0 ≤ h ≤ 1 , goodbreak0em3em⁣ t ≥ 1 where h refers to the heterogeneity of the sorbent surface. The parameter h can be related to fractional time index (α) by eq α = ( 1 − h ) …”

“…Advanced statistical physics model has been applied to assess the adsorption process at macroscopic and microscopic levels . The measured data were assessed by statistical physics models (models 1, 2, 3, and 4) and their equations are given in Table . The plots of statistical physics models are shown in Figure .…”

“…If the value of n < 1, then the binding of one ion/molecule occurs onto numerous active sites of the material (multidocking mechanism). If n > 1, then several ions/molecules can be taken up by one binding site of the adsorbent (multimolecular mechanism) . The n value also provides information regarding the orientation of adsorbed ions/molecules on the adsorbent surface.…”