Thermodynamic and Molecular Characterization of Adsorption on Zeolites: A Unified Framework Combining Inverse Gas Chromatography, Hamaker Theory, and Nonlinear Lewis Acid–Base Modeling

A comprehensive thermodynamic and molecular-level investigation of adsorption on MgY and NH4Y zeolites is presented using inverse gas chromatography at infinite dilution (IGC-ID), combined with a Hamaker-based formalism and an extended five-parameter Lewis acid–base model. The study introduces a unified framework that integrates dispersive, polar, and donor–acceptor interactions while explicitly accounting for temperature-dependent intermolecular geometry. The results demonstrate that the London dispersive free energy exhibits a highly linear temperature dependence (R2 > 0.999), while the corresponding surface energy decreases linearly with temperature (e.g., γsd(T)=−0.297T+189.48 mJ·m−2 for MgY), reflecting the progressive weakening of dispersion forces. Simultaneously, the intermolecular separation distance follows a linear relation r(T)=r0+αeffT, with αeff values on the order of (2–3) × 10−3 Å·K−1 for MgY, enabling the determination of intrinsic contact distances r0 at 0 K, varying between 4.00 Å and 6.60 Å. A major finding is that the molecular surface area of adsorbed probes is not constant but follows a quadratic temperature dependence with excellent accuracy (R2 > 0.999), establishing adsorption cross-section as a thermodynamic variable. The comparison between MgY and NH4Y reveals two distinct adsorption regimes: MgY exhibits a structured and strongly dispersive interaction field associated with Mg2+ cations, whereas NH4Y displays enhanced polarity, stronger specific interactions, and greater molecular flexibility driven by hydrogen bonding and protonic effects. Thermodynamic analysis of Lewis acid–base interactions shows that classical linear models are insufficient. Statistical evaluation (R2 ≈ 0.986, minimum AIC/BIC, lowest RMSE) demonstrates that the five-parameter Hamieh model provides the most accurate and physically meaningful description, capturing nonlinear donor–acceptor interactions and amphoteric coupling effects. Overall, this work establishes a novel thermodynamic methodology that quantitatively links macroscopic surface energetics to microscopic interaction parameters, providing new insight into adsorption mechanisms and a robust framework for the rational design of porous materials in catalysis, separation, and energy applications.