Thermodynamic and Molecular Analysis of Polar Adsorption Enthalpy: Modeling of Lewis Acid-Base Energetics at Solid...

A unified energetic framework for Lewis acid-base interactions at solid surfaces is developed through a new model, which integrates linear, amphoteric, and polarization contributions of the polar adsorption enthalpy (-ΔH^p) into a quadratic thermodynamic expression by introducing explicit coupling and curvature terms, allowing simultaneous representation of donor-acceptor charge transfer, mutual polarization, and surface deformation (-ΔH_p) = K_ADN + K_DAN - KDN × AN + K_2A(DN)² +K_2D(AN)², where AN and DN are respectively the acceptor and donor numbers of solvents, K_A and K_D represent the Lewis acid and base coefficients of the solid, K is the coupling amphoteric constant, whereas K_2A and K_2D are the new second order surface parameters, respectively representing the quadratic curvature terms for acid and base centers. Using inverse gas chromatography (IGC), adsorption energetics were investigated on a broad range of solids─silica, alumina, ZnO, Zn, PMMA, β-zeolite, Rh-doped zeolites, and PMMA/silica hybrid interfaces. Statistical analysis (R², RMSE, AIC, BIC) across hierarchical models (2-5 parameters) revealed a universal convergence toward the five-parameter formulation, yielding R² ≥ 0.97 and significantly reduced RMSE values. The inclusion of amphoteric coupling (K) and bidirectional curvature (K_2A, K_2D) terms was found essential to reproduce experimental linearity and capture the physical duality of real surfaces. The new model thus transforms adsorption thermodynamics from an empirical linear model into a physically interpretable, statistically validated law. This formulation provides a unified energetic basis for describing the amphoteric and polarizable nature of oxides, polymers, and hybrid materials, and offers a predictive platform for future studies on temperature-dependent adsorption and electronic structure-surface energy correlations.