Unified thermodynamic modeling of adsorption and London dispersive surface energy on Rh-modified H-β zeolite: Coupled effects of temperature, metal loading, and specific surface area

A comprehensive thermomechanical and electronic characterization of solvent adsorption on Rh-modified H-β zeolite was performed using inverse gas chromatography. The adsorbed molecular surface area a(T,θ,S) and the London dispersive surface energy γ _s ^d(T,θ,S) were quantified as functions of temperature, Rh loading (θ), and specific surface area (S). A unified second-order bivariate model was developed, enabling direct extraction of the temperature derivatives, cross-coupling terms, and structural sensitivity coefficients for every system. The results show that Rh loading enhances the electronic polarizability density of the zeolite surface, leading to increased γ _s ^d and amplified temperature sensitivity through negative dispersive surface entropy ε _s ^d(θ). Moderate Rh content (0.5–1 wt%) maximizes the adsorbed molecular footprint due to cooperative strengthening of dispersion interactions without excessive pore blocking. In contrast, variations in S act primarily through geometric effects: high S decreases γ _s ^d due to polarizability dilution but significantly increases the adsorbed footprint by reducing confinement and allowing greater molecular deformation with temperature. Comparison of Rh and S models demonstrates that adsorption on Rh/H-β-zeolites is governed by two independent mechanisms: electronic enrichment (θ-dependent) and geometric deconfinement (S-dependent). Their interplay determines both interaction strength and conformational freedom of adsorbed molecules. This unified framework provides fundamental insight into adsorption thermodynamics on metal-modified zeolites and offers predictive design rules for optimizing catalysts, sorbents, and surface-engineered porous materials.