pH-mediated adsorption of pharmaceuticals by biochar: Correlation between experiment and theory

• Adsorption kinetics bifurcate from fast electrostatic attraction in acidic regimes to stiff, diffusion-limited aromatic partitioning in alkaline regimes. • Standard empirical models (Sips, Tóth) are statistically invalidated Δ BIC > 70 for capturing multi-timescale sorption dynamics. • Raman and FTIR spectroscopy successfully anchor the kinetic model, replacing arbitrary curve-fitting with physically derived state vectors. • The HARMONIA framework predicts competitive adsorption in ternary mixtures without re-parameterization using a universal interaction matrix. Current adsorption modeling relies heavily on empirical formalisms (e.g., Pseudo-First/Second Order) that lack the physical basis to predict performance under transient conditions. This study aims to bridge this gap by establishing “HARMONIA”, a mechanistic state-matching framework that links sorption kinetics directly to pH-dependent surface chemistry and pollutant speciation. We quantified the uptake of four ionizable pharmaceuticals (Acetaminophen, Diclofenac, Tramadol, Sulfamethoxazole) on wood-derived biochar under acidic (pH 5.0) and alkaline (pH 9.4) regimes. Crucially, the model’s surface parameters were not arbitrarily fitted but anchored using Raman spectroscopy to quantify aromatic sp 2 domains and FTIR to track oxygenated functional groups. The results reveal a fundamental kinetic bifurcation: acidic conditions facilitate rapid, single-timescale electrostatic attraction, whereas alkaline conditions induce strong electrostatic repulsion, forcing uptake into a stiff, diffusion-limited aromatic partitioning mode. Bayesian Information Criterion (BIC) analysis confirms that standard models (Sips, Tóth) are statistically invalidated Δ BIC > 70 in this stiff regime, while HARMONIA achieves a >99.9% Akaike probability of correctness. Furthermore, the framework successfully predicted competitive removal in ternary mixtures without re-parameterization. This work demonstrates that a universal 3x3 nteraction matrix can unify diverse kinetic behaviors, providing a transferable engineering tool for optimizing contact times in complex, variable-pH effluents.