Structural thermodynamics of adsorption on UiO-66 Metal–organic frameworks: A unified thermodynamic framework for surface energetics, Lewis acid–base interactions, and polar surface energy

Abstract

A comprehensive thermodynamic framework is developed for the structural and energetic characterization of the UiO-66 family of metal–organic frameworks using inverse gas chromatography at infinite dilution. Pristine UiO-66 together with amino-, formic acid-, and acetic acid-functionalized derivatives were investigated over the temperature range 313.15– 383.15 K. The standard Gibbs free energy of adsorption is expressed as a unified function of temperature and specific surface area, demonstrating that adsorption thermodynamics depends intrinsically on the structural characteristics of the adsorbent. This approach leads to the generalized structural thermodynamic equation, Δ𝐺 0 𝑎(𝑇,𝑆) = Δ𝐻 0 𝑎(𝑆) ― 𝑇Δ𝑆 0 𝑎(𝑆), establishing that the standard adsorption enthalpy and entropy become continuous functions of the specific surface area rather than universal constants for a family of porous materials. The effective molecular surface area of adsorbed solvents is likewise shown to depend simultaneously on temperature and surface structure, revealing the continuous evolution of molecular organization within the adsorption layer. Lewis acid–base interactions were analyzed using the Hamieh fiveparameter thermodynamic model applied independently to adsorption enthalpy and entropy. Statistical analysis demonstrates the superiority of nonlinear higher-order models over conventional linear approaches and reveals strong correlations among the Lewis acidic, basic, amphoteric, and cooperative interaction parameters. Post-synthetic functionalization markedly modifies Lewis acidity, Lewis basicity, and polar surface energy while only slightly affecting the London dispersive contribution. A new methodology is further introduced for determining the polar surface energy of adsorbed solvent molecules, demonstrating that the adsorbed phase itself possesses well-defined thermodynamic surface properties governed by cooperative solvent–framework interactions. The proposed framework provides a unified description of adsorption thermodynamics, molecular organization, Lewis acid–base interactions, and surface energetics, offering a general methodology for the thermodynamic characterization and rational design of advanced porous materials.