A Master Isotherm Model Approach to Quantify Defects in UiO-66 from Nitrogen Adsorption Isotherms

The presence of defects in metal-organic frameworks (MOFs) significantly impacts their adsorption and catalytic properties, yet noninvasive quantitative defect characterization remains challenging. In this study, we introduce a computational approach to estimate missing-cluster defect concentrations in UiO-66, a prototypical zirconium MOF, based on nitrogen adsorption isotherms at 77 K. By combining grand canonical Monte Carlo (GCMC) simulations and a statistical modeling framework, we construct composite models from unit-cell or 2 × 2 × 2 supercell pristine and defective models to reproduce the isotherms of larger test structures. We show that choosing 2 × 2 × 2 supercell models as the basis models outperformed unit-cell models by capturing a broader range of pore environments, enabling reliable defect prediction across a wide defect concentration range. This nondestructive, simulation-based method provides a generalizable platform for defect analysis in MOFs and other porous materials with well-defined local motifs.