Uncertainty impact of isotherm models on liquid-phase adsorption thermodynamics: A bayesian inference perspective

Abstract

Liquid-phase adsorption, a fundamental process where molecules in a liquid medium adhere to a solid surface, plays a crucial role in various chemical engineering applications such as wastewater decontamination and solvent recovery. These phenomena can be described by equilibrium models, which offer insight into adsorption capacity and thermodynamic properties, such as enthalpy and entropy variations, yet parameter uncertainty often undermines their accuracy. This study applies a Bayesian approach to assess uncertainties within adsorption models quantitatively and qualitatively. Through Bayesian analysis, substantial parameter variability was identified in the Sips model, with posterior distributions for thermodynamic parameters revealing broad uncertainty regions and a high likelihood of exothermic enthalpy values (i.e. $P\left(\Delta H^{\circ }<0\right)>0.5$), which often deviate from established thermodynamic expectations across different systems. Despite achieving good fit statistics (e.g., R² ≈ 0.99), this flexibility in the Sips model does not consistently translate into reliable thermodynamic interpretations. In contrast, the Langmuir model yields more stable estimates, offering narrower and thermodynamically consistent probability distributions for equilibrium constants (e.g., ΔH° > 0 and ΔS° > 0) and Gibbs free energy changes across temperature variations, albeit with slightly lower fit statistics (e.g., R² ≈ 0.97). These findings highlight the need for uncertainty analysis in model selection and advise caution in attributing physical significance to isotherm-derived parameters. This study advocates for a balanced approach to model choice, incorporating uncertainty quantification to enhance the reliability of adsorption predictions in both research and industrial applications.