Predicting pH-dependent phosphate adsorption isotherms without in-situ pH control

Adsorption isotherms serve as the cornerstone for evaluating adsorbent performance and elucidating interfacial mechanisms. For pollutants with proton-binding capacity, such as phosphate (P), the adsorption process itself often induces significant pH shifts, making the accurate determination of such pH-dependent isotherms crucial yet challenging. The conventional method for its determination – maintaining a constant pH through in-situ intermittent manual adjustments – suffers from a critical lack of standardized protocols, undermining the reproducibility and inter-laboratory comparability of published data. This study introduces and validates a predictive framework that constructs accurate P adsorption isotherms at specific equilibrium pH (pH eq ) values using a matrix of simple, reproducible initial pH (pH ini ) control experiments. Layered double hydroxide (LDH), a material with pH-responsive surface chemistry, was used as a model adsorbent to validate the framework. A robust relationship was established between the pH eq and the equilibrium P adsorption amount ( q e ). This experimentally derived pH eq - q e map allowed for the accurate construction of Langmuir isotherms across target pH eq values (5 to 10) via interpolation. The predicted values for q e and equilibrium concentration ( c e ) showed excellent agreement with experimental data, with relative root mean squared errors (RRMSE) of only 3.72% and 4.42%, respectively. Multi-stage pH adjustment experiments further confirmed the framework's robustness, showing less than 2.5% deviation from predicted values. By addressing the standardization issue in pH-dependent adsorption studies, this predictive framework establishes a more reliable foundation for systematic adsorbent comparison, mechanistic investigation, and rational design of adsorption-based water treatment technologies.