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 (-Δ<i>H</i>^<i>p</i>) 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 (-Δ<i>H</i>_p) = <i>K_ADN</i> + <i>K_DAN</i> - <i>KDN</i> × <i>AN</i> + <i>K_2A</i>(<i>DN</i>)² +<i>K_2D</i>(<i>AN</i>)², where <i>AN</i> and <i>DN</i> are respectively the acceptor and donor numbers of solvents, <i>K</i>_<i>A</i> and <i>K</i>_<i>D</i> represent the Lewis acid and base coefficients of the solid, <i>K</i> is the coupling amphoteric constant, whereas <i>K</i>_2<i>A</i> and <i>K</i>_2<i>D</i> 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 (<i>R</i>^<i>2</i><i>, RMSE, AIC, BIC</i>) across hierarchical models (2-5 parameters) revealed a universal convergence toward the five-parameter formulation, yielding <i>R</i>² ≥ 0.97 and significantly reduced <i>RMSE</i> values. The inclusion of amphoteric coupling (<i>K</i>) and bidirectional curvature (<i>K</i>_2<i>A</i>, <i>K</i>_2<i>D</i>) 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.