A modified Langmuir-Freundlich isotherm model for simulating pH-dependent adsorption effects.

Analytical isotherm equations such as Langmuir and Freundlich isotherms are widely used for modeling adsorption data. However, these isotherms are primarily useful for simulating data collected at a fixed pH value and cannot be easily adapted to simulate pH-dependent adsorption effects. Therefore, most adsorption studies currently use numerical surface-complexation models (SCMs), which are more complex and time consuming than traditional analytical isotherm models. In this work, we propose a new analytical isotherm model, identified as the modified Langmuir-Freundlich (MLF) isotherm, which can be used to simulate pH-dependent adsorption. The MLF isotherm uses a linear correlation between pH and affinity coefficient values. We validated the proposed MLF isotherm by predicting arsenic adsorption onto two different types of sorbents: pure goethite and goethite-coated sand. The MLF model gave good predictions for both experimental and surface complexation-model predicted datasets for these two sorbents. The proposed analytical isotherm framework can help reduce modeling complexity, model development time, and computational efforts. One of the limitations of the proposed method is that it is currently valid only for single-component systems. Furthermore, the model requires a system-specific pH. vs. affinity coefficient relation. Despite these limitations, the approach provides a promising analytical framework for simulating pH-dependent adsorption effects.