Reconstruction of adsorption potential in Polanyi-based models and application to various adsorbents

The equilibrium Polanyi adsorption potential was reconstructed as ε = -RT ln(Ca(or H)/δ) to correlate the characteristic energy (E) of Polanyi-based models (qe = f[ε/E]) with the properties or structures of absorbates, where qe is the equilibriumn adsorption capacity, Ca(or H) is the converted concentration from the equilibrium aqueous concentration at the same activity and corresponds to the adsorption from the gas or n-hexadecane (HD) phase by the water-wet adsorbent, and "δ" is an arbitrary divisor to converge the model fitting. Subsequently, the modified Dubinin-Astakhov model based on the reconstructed ε was applied to aqueous adsorption on activated carbon, black carbon, multiwalled carbon nanotubes, and polymeric resin. The fitting results yielded intrinsic characteristic energies Ea, derived from aqueous-to-gas phase conversion, or EH, derived from aqueous-to-HD phase conversion, which reflect the contributions of the overall or specific adsorbate-adsorbent interactions to the adsorption. Effects of the adsorbate and adsorbent properties on Ea or EH then emerge that are unrevealed by the original characteristic energy (Eo), i.e., adsorbates with tendency to form stronger interactions with an adsorbent have larger Ea and EH. Additionally, comparison of Ea and EH allows quantitative analysis of the contributions of nonspecific interactions, that is, a significant relationship was established between the nonspecific interactions and Abraham's descriptors for the adsorption of all 32 solutes on the four different adsorbents: (Ea - EH) = 24.7 × V + 9.7 × S - 19.3 (R(2) = 0.97), where V is McGowan's characteristic volume for adsorbates, and S reflects the adsorbate's polarity/polarizability.