Contrasting Fates: pH Dynamics as the Master Variable in Pharmaceutical Sorption on Biochar

This study presents a comprehensive analysis of the sorption kinetics of four ionizable organic pollutants (Acetaminophen, Diclofenac, Tramadol, and Sulfamethoxazole) onto biochar under varying pH conditions. Moving beyond empirical curve-fitting, we show that the observed kinetics are mechanistically explained by a site-matching model in which the rate and extent of sorption are governed by the pH-dependent properties of both the pollutant and the sorbent surface. The biochar surface charge reverses from predominantly anionic at high pH (9.4) to cationic at low pH (5.0), while pollutants transition between charged and neutral states according to their pKa values. We formalize this with pH-dependent state vectors for the surface and for each pollutant that interact through a universal 3 × 3 interaction matrix encoding electrostatic attraction, repulsion, and hydrophobic partitioning. Critically, we demonstrate via Bayesian Information Criterion (BIC) analysis that standard empirical models (Sips, T´oth) are statistically invalidated (ΔBIC > 70) in the alkaline regime, where the system exhibits stiff, multi-timescale dynamics. The proposed HARMONIA framework resolves this stiffness, achieving a > 99.9% Akaike probability of being the correct model. Independent spectroscopic measurements (Raman, FTIR) corroborate the mechanism, linking kinetic rate constants directly to the availability of aromatic domains and oxygenated surface groups. This work establishes a rigorous physical basis for predicting sorption performance in complex, variable-pH environments.