Statistical Mechanics-Driven Adhesion of 2,4-Dichlorophenoxyacetic Acid (2,4-D) and Carbofuran for Water Disinfection

To address the issue of wastewater decontamination, this meticulous study leverages the concepts of probabilistic physics formalism to depict the adsorptive equilibrium data of two widely used pesticides: 2,4-dichlorophenoxyacetic acid (2,4-D) and carbofuran on phosphoric acid-activated peach stone biochar. Numerically, we proposed three advanced modelsmonoenergetic linking monolayer scenario, bienergetic linking monolayer scenario, and multilayer linking with saturation scenarioto fit the experimental data. The analysis of data-theory accuracy through χ_red ² and R _adj ² reveals that the adhesion of both toxic compounds occurs through a single monolayer at a single energy level. Based on the most probable scenario, our investigation demonstrates that an increase in temperature enhances retention on activated carbon, enabling a more optimized purification process. Regarding the equilibrium adsorption, a higher adsorption capacity is observed for 2,4-D (500 mg·g^-1) compared to carbofuran (250 mg·g^-1). Steric analysis further indicates that the number of adsorbate molecules per site, n, ranges from 2.46 to 1.65 for 2,4-D and from 1.29 to 1.68 for carbofuran over the temperature range of 25-65 °C. These values suggest multimolecular adsorption, in which a single binding site accommodates multiple adsorbate molecules, often with nonparallel anchoring orientations. As the temperature rises from 25 to 65 °C, the density of adsorption sites, n _m, increases by a factor of 1.9 for 2,4-D and by a factor of 1.3 for carbofuran, reflecting a more pronounced temperature-dependent availability of active sites for 2,4-D and suggesting enhanced adsorption capacity at elevated temperatures. At 65 °C, energetic analysis indicates that the adsorption mechanism for both pesticides is primarily physisorption, with adsorption energies not exceeding 40 kJ·mol^-1. Specifically, the adsorption energy for 2,4-D is approximately 17 kJ·mol^-1, while for carbofuran, it is around 9 kJ·mol^-1, reflecting weaker interactions with the adsorbent surface in the case of carbofuran. Pore size distribution characterization indicates that the smaller pore size ranges observed correspond to the microporous region (<2 nm) for both pesticides, while adsorption energy distribution confirms that van der Waals forces are the primary contributors to molecular adhesion. This study concludes that (2,4-D) is preferentially removed compared to carbofuran when in contact with activated carbon, highlighting its superior efficacy for wastewater treatment applications.