Adsorption Thermodynamics and Kinetics of Simple and Complex Fluids: Physical Modeling of Surface Saturation, Reservoir Depletion, Lateral Interactions, and Collective Effects

Adsorption-based remediation techniques are promising methods for removing emerging pollutants from water. However, a major gap in the literature remains in modeling complex adsorption mechanisms. In this study, three key factors were identified and included for modeling adsorption thermodynamics and kinetics: surface saturation, reservoir depletion, and lateral interactions. While surface saturation is captured by the celebrated Langmuir model, reservoir depletion is crucial for assessing adsorption in batch and dynamic experiments. However, it is often neglected in classical kinetic models. Lateral interactions are also important for pollutants, like PFAS and certain PPCP with an aromatic ring, as they may undergo cooperative adsorption. A 2D lattice gas model with two- and three-body lateral interactions was solved using mean-field and quasi-chemical approximations. The resulting thermodynamic framework leads to a phase diagram predicting L-, S-, and LS-type adsorption isotherms as well as a first-order dilute to dense phase transition. Building on this, a mixed-order kinetic model, including surface saturation, reservoir depletion and lateral interactions, was built and solved in various cases. Both thermodynamic and kinetic models were successfully applied to experimental data for the adsorption of a self-aggregating antibiotic, a non-ionic surfactant, and two PFAS molecules.