The role of methodological conditions and model interpretation in the adsorption of a nanomaterial on a volcanic soil

Abstract

Soil adsorption governs the environmental fate of nanomaterials, yet standard procedures often fail to fully capture adsorption behaviour through kinetic and isotherm models. This study proposes a comprehensive framework to enhance the reliability and interpretability of adsorption data by improving both experimental design and model analysis, using the adsorption of Cu₂O nanoparticles from the commercial pesticide NORDOX 75 WG (NOR) in Metrenco soil (Ultisol). Batch adsorption kinetics and isotherm experiments were conducted. NOR stability and supernatant pH were the most influential factors and were used to select a subset of consistent, comparable data. Transport-related parameters (e.g., kinetic rates) were more sensitive to NOR stability than bulk-adsorbent parameters (e.g., adsorption capacity). We applied a novel validation strategy combining traditional goodness-of-fit metrics (including adjusted $R^2$) with intra-model assumption checking, and inter-model comparison. While the linear Pseudo-Second Order model (PSO) achieved the highest $R_{\mathrm{adj}}^2$, a combined analysis of multiple nonlinear models provided stronger evidence for non-equilibrium condition and apparent instantaneous adsorption, in contrast to the interpretation derived from linear PSO parameters. This approach also led to the formulation of a modified PSO model equation, better aligned with the system behaviour and consistent with trends observed in other models. Unlike typical studies that rely on a single “best-fitting” model, our method enables deeper mechanistic insights, even from poorly fitting models. This addresses a widespread but overlooked issue in the literature and supports more robust modelling of complex adsorption systems to support environmental decision-making.