Characterization of the adsorption site energies and heterogeneous surfaces of porous materials

Characterization of the guest-host interactions and the heterogeneity of porous materials is essential across the physical and biological sciences, for example for gas sorption and separation, pollutant removal from wastewater, biological systems (protein-ligand binding) and molecular recognition materials such as molecularly imprinted polymers. Information about the guest-host interactions can be obtained from calorimetric experiments. Alternatively, more detailed information can be obtained by properly analysing the experimentally acquired adsorption equilibrium data. Adsorption equilibrium is usually interpreted using theoretical adsorption isotherms that correlate with the equilibrium concentration of the adsorbate in the solid phase and in the bulk fluid at a constant temperature. Such theoretical isotherms or expressions can accurately predict the adsorbent efficiency (at equilibrium) as a function of process variables such as the initial adsorbate concentration, adsorbent mass, reactor volume and temperature. Detailed analysis of the adsorption isotherms permits the calculation of the number density of the adsorbent sites, their binding energy for the guest molecules and information about the distribution of adsorption site binding energies. These analyses are discussed in this review. A critical evaluation of the analytical and numerical methods that can characterize the heterogeneity and guest-host interactions involved in terms of discrete or continuous binding site affinity distribution was performed. Critical discussion of the limitations and the advantages of these models is provided. An overview of the experimental techniques that rely on calorimetric and chromatographic principles to experimentally measure the binding energy and characteristic properties of adsorbent surfaces is also included. Finally, the potential use of site energy distribution functions and their potential to provide new information about the binding energy of adsorbents for a specific guest molecule application is discussed. Heterogeneity of porous structures is an important material property involved during the design of adsorbents, catalysts and molecular recognition materials. This review discusses the mathematical methods that can characterize adsorption site energies and surface heterogeneity from the adsorption isotherms.