Thermodynamically consistent determination of surface energetics from IGC retention data: unified energetic–structural analysis of DVB and ZMOF/DVB composites

The determination of surface energetics from inverse gas chromatography (IGC) data has traditionally relied on simplified thermodynamic assumptions that neglect the temperature dependence of intermolecular and interfacial parameters. In this work, a thermodynamically consistent framework is developed to determine the energetic, structural, and functional properties of polymer and hybrid materials from IGC retention data at infinite dilution. The proposed approach revisits the definition of the adsorption equilibrium constant and explicitly incorporates temperature-dependent intermolecular separation distances, molecular surface areas, and dispersive interactions. Application to divinylbenzene (DVB) and 0.7% ZMOF/DVB monolithic composites reveals a linear decrease in the London dispersive surface energy with temperature, together with systematic variations in the intermolecular separation distance and adsorption molecular surface area. These results demonstrate that adsorption is governed by coupled energetic and structural effects and establish that the adsorption molecular surface area is a thermodynamic rather than a fixed geometric quantity. The polar contribution is described using a nonlinear five-parameter Lewis acid–base model that incorporates amphoteric coupling and second-order donor–acceptor interactions, providing a substantially improved description over classical models. DVB exhibits a predominantly basic surface character, whereas ZMOF incorporation promotes a more balanced amphoteric behavior and a more homogeneous adsorption environment. Overall, the proposed framework provides a unified thermodynamic–structural description of adsorption and establishes a physically consistent basis for the characterization and design of advanced polymeric and hybrid materials.