Statistical physics and fractal like kinetic modelling for adsorption of acetaminophen on MgO/aminated β-cyclodextrin: Variables optimization using Box-Behnken Design

Abstract

Magnesium oxide/aminated β-cyclodextrin (MgO/β-CD-O-C₂H₄-NH₂) was synthesized for the elimination of acetaminophen from water. The material was characterized using various analytical techniques. Box-Behnken design (BBD) combined with response surface methodology (RSM) was employed to optimize key adsorption parameters (contact time = 70 min, adsorbent dose = 15 mg, pH = 6.5, and initial acetaminophen concentration = 125 mg/L) to achieve the maximum removal efficiency (99.28 %). Equilibrium data were analyzed using classical isotherm and statistical physics models. Among the classical isotherm models, Langmuir model (R² = 0.9996–0.9997) fitted best to adsorption data with the maximum saturation capacity of 213.84 mg/g at 298 K. Statistical physics model (M 2: monolayer with two energies) revealed that acetaminophen adsorption occurred on two distinct receptor sites, supported by adsorption energies (E₁ = 28.35–35.36 kJ/mol; E₂ = 11.97–13.03 kJ/mol), indicating physical forces primarily govern the uptake of acetaminophen. The kinetic data were best fitted to the fractal-like pseudo-first-order model (R² = 0.9927–0.9998), revealing energetic heterogeneity. Diffusion-based models (Weber-Morris and Boyd) confirmed the involvement of both intraparticle and film diffusion mechanisms. The material demonstrated excellent reusability, maintaining high acetaminophen removal efficiency over eight adsorption–desorption cycles.