Modeling the temperature dependence of PFAS adsorption equilibria on activated carbon

In this study, temperature dependence was incorporated directly into four adsorption isotherm models: the Freundlich, Volmer, Jovanović, and power-law Jovanović models. The models were evaluated using previously published equilibrium data for three short-chain perfluoroalkyl substances (PFAS), specifically perfluorobutanesulfonic acid (PFBS), perfluoropentanoic acid (PFPeA), and hexafluoropropylene oxide dimer acid (GenX), adsorbed on activated carbon at 10, 20, and 30 °C. Each model was fitted simultaneously to the data at all three temperatures using a two-step parameter estimation procedure combining differential evolution and Levenberg–Marquardt optimization. Direct application of the original formulations resulted in numerical instability and convergence difficulties arising primarily from severe disparities in parameter magnitudes. Logarithmic and reference-temperature reparameterizations were therefore introduced to improve numerical conditioning while preserving the mathematical equivalence and predictive behavior of the original models. Among the four models, the reparameterized power-law Jovanović model provided the best overall description of the equilibrium data for all three PFAS, whereas the reparameterized Jovanović model exhibited the poorest performance. The results demonstrate that appropriate reparameterization is essential for reliable estimation of temperature-dependent isotherm parameters and that the power-law Jovanović model is a promising alternative for describing temperature-dependent PFAS adsorption. Its formulation also provides a practical basis for incorporating temperature-dependent equilibrium relationships into mechanistic adsorption models, including fixed-bed column models, for evaluating the effect of temperature on process performance.