Model-Based and Molecular-Level Evaluation of Methyl Orange Adsorption onto a Hazelnut Shell-Based Carbonaceous Adsorbent

This study presents a combined model-based and molecular-level assessment of methyl orange uptake by a hazelnut shell-based carbonaceous adsorbent. Batch experiments were conducted under previously optimized conditions, namely a dye concentration of 42.65 mg/L, adsorbent loading of 1.29 g/L, temperature of 30.4 °C, and pH 3.0. Kinetic, diffusion, equilibrium, apparent thermodynamic, surface charge, Fourier-transform infrared spectroscopy, and density functional theory analyses were used to evaluate the macroscopic adsorption behavior and to support possible molecular interaction pathways. The nonlinear pseudo-first-order model provided the most suitable empirical description of the kinetic profile, yielding qe = 32.62 ± 0.51 mg/g, k1 = 1.28 × 10−2 ± 5.63 × 10−4 min−1, and R2 = 0.9963. Weber–Morris and Boyd analyses suggested that the uptake behavior was consistent with coupled surface attachment, film diffusion, and intraparticle diffusion rather than a single rate-controlling step. Freundlich modeling suggested a heterogeneous adsorption description, with the Freundlich constant increasing from 15.05 to 46.09 (mg/g)(L/mg)1/n and n rising from 2.24 to 3.37 with increasing temperature. Negative apparent Gibbs free energy changes and positive apparent enthalpy and entropy changes suggested a favorable, endothermic, and entropy-favored tendency under the investigated conditions. Surface charge measurements, infrared spectral changes, and quantum chemical results collectively supported the possibility that acidic conditions favored electrostatic attraction, while π–π stacking, dispersion forces, and localized hydrogen bonding may have contributed to stabilization of the adsorbed state. Overall, the hazelnut shell-based carbonaceous adsorbent exhibited effective dye-removal performance, as supported by combined experimental and computational evidence.