Mechanistic Insights Into Nickel(II) Adsorption–Diffusion on Sulfamoylbenzamide‐Modified Hydrous Zirconium Oxide for Wastewater Treatment

This study systematically investigates the adsorption and diffusion‐based kinetics of Ni(II) uptake onto N‐(((2‐((2‐aminoethyl)amino)ethyl)amino)methyl)‐4‐sulfamoylbenzamide‐impregnated hydrous zirconium oxide (AESB/HZO) within the temperature range of 303–333 K. Fractal‐like pseudo‐second‐order (FPSO) and fractal‐like pseudo‐first‐order (FPFO) models were employed to elucidate the adsorption mechanism, with FPSO demonstrating superior correlation (R 2 > 0.9995), confirming a chemisorptive rate‐controlling process. The Elovich model (R 2 > 0.9952) further validated surface heterogeneity in adsorption kinetics. Diffusion‐based models revealed that Ni(II) ions were initially transported to the external surface via external mass transfer (Mathews‐Weber and Furusawa‐Smith models), followed by intraparticle diffusion as the primary rate‐limiting step (Fick's law, R 2 > 0.9958). The Urano and Tachikawa model reinforced this, whereas the Boyd film diffusion model (R 2 < 0.8421) showed limited film diffusion influence. The Biot number (BN > 100) confirmed intraparticle diffusion dominance, while the Bangham pore diffusion model indicated significant pore diffusion contributions. The dual exponential model indicated that both external mass transport and internal pore diffusion contributed to the overall adsorption process. Statistical physics models provided deeper adsorption insights, with Model 2 yielding the best fit (R 2 > 0.999, 𝜒 2 < 0.00021), suggesting multi‐docking and multimolecular adsorption mechanisms. Ni(II) ions adopted horizontal and vertical orientations, with the first receptor site playing a dominant role. The total saturation capacity (95.792–117.173 mg g −1 ) closely aligned with experimental values (96.030–117.825 mg g −1 ), validating model accuracy. Adsorption energy analysis indicated stronger chemisorptive interactions at the primary site (22.310–28.451 kJ mol −1 ) and weaker physisorption at the secondary site (12.623–15.844 kJ mol −1 ). Arrhenius and Eyring analyses revealed activation energies for FPSO (29.292 kJ mol −1 ) and intraparticle diffusion (35.321 kJ mol −1 ), confirming their synergistic contribution. The adsorption process was endothermic (ΔH > 0) with reduced randomness (ΔS < 0), emphasizing structured Ni(II) uptake. This mechanistic understanding facilitates the optimization of AESB/HZO for efficient Ni(II) removal in environmental applications.