What can the use of well-defined statistical functions of pollutants sorption kinetics teach us? A case study of cyanide sorption onto LTA zeolite nanoparticles

This study demonstrates that the introduction of a fractal time yields a more clear description of the kinetics in the case of the aqueous phase sorption of cyanide onto LTA zeolite nanoparticles. The two best-known fractal models, the Brouers-Sotolongo (BSf(n,α)) fractal model and kinetics formula based on the Riemann-Liouville fractional derivative theory, are compared. These two models give very similar results and we present arguments for our preference for the former one. Another commonly employed model, the Elovich equation, is discussed. We justify that its continued use in its approximate form is currently not required, as it is inaccurate particularly for small uptake. Its exact expression produces results similar to the two former ones only for part of the kinetics curve, but it is unsuitable as it asymptotically yields an infinite value of the uptake. Besides, an extension of the BSf(n,α) is proposed by introducing a time-dependent fractal coefficient, which more clearly explains the evolution of the kinetics in detail and enables a more accurate calculation of the time-dependent rate, typical of non-exponential kinetics. The results reveal that, in this particular case of cyanide sorption onto zeolite, this model is the best fit to the experimental kinetics data.