Environmental Fate and Stability of the AA-Hyp/β-CD-AgNPs Nanocomposite for Amoxicillin Removal: Insights through Fractal Kinetics, Statistical Physics, and Thermodynamic Investigations

The contamination of water with antibiotics such as amoxicillin (AMX) necessitates effective and sustainable remediation strategies. This study presents a novel nanocomposite adsorbent, acrylic acid hyperbranched polymer-grafted β-cyclodextrin embedded with silver nanoparticles (AA-Hyp/β-CD-AgNPs) developed for efficient AMX removal. The nanocomposite was thoroughly characterized using FTIR, XRD, SEM-EDX, BET, DLS, XPS, and TGA-DTA, confirming its porous structure, high thermal stability, and successful AgNP incorporation. Adsorption optimization using Definitive Screening Design (DSD) under Response Surface Methodology (RSM) revealed optimal conditions (90 min contact time, 30 mg L –1 AMX, pH 6.0, 0.015 g of adsorbent dose), achieving 98.43% removal efficiency. Isotherm modeling using classical and statistical physics models indicated multilayer adsorption on a heterogeneous surface. The Freundlich model showed the best fit, while statistical physics modeling confirmed adsorption site heterogeneity and nanoscale energetic interactions. Thermodynamic analysis revealed spontaneous (Δ G ° < 0), exothermic (Δ H ° < 0), and entropy-driven (Δ S ° > 0) adsorption. Fractal-like kinetics, using fractal pseudo-first- and second-order models, demonstrated that heterogeneous surface diffusion, involving both film and intraparticle diffusion, governed the rate-limiting step. The nanocomposite exhibited strong reusability, maintaining over 90% efficiency after five cycles. Environmental fate studies evaluated the stability of AgNPs under various pH levels, ionic strengths, and real water matrices, confirming minimal AgNP leaching. This immobilization within the polymer/β-CD framework mitigates nanoparticle release, reducing risks of secondary contamination. Real matrix tests showed >98% AMX removal from tap, municipal, and surface water. Overall, AA-Hyp/β-CD-AgNPs offers enhanced removal efficiency, structural stability, recyclability, and environmental safety compared to conventional nanoadsorbents, making it a promising candidate for sustainable antibiotic remediation in wastewater treatment systems.