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

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 (-ΔHp) 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 (-ΔHp) = KADN + KDAN - KDN × AN + K2A(DN)2 +K2D(AN)2, where AN and DN are respectively the acceptor and donor numbers of solvents, KA and KD represent the Lewis acid and base coefficients of the solid, K is the coupling amphoteric constant, whereas K2A and K2D 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 (K2A, K2D) 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.