Reconstruction
of Adsorption Potential in Polanyi-Based
Models and Application to Various Adsorbents
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Abstract
The equilibrium Polanyi
adsorption potential was reconstructed
as ε = −<i>RT</i> ln(<i>C</i><sub>a(or H)</sub>/δ) to correlate the characteristic energy
(<i>E</i>) of Polanyi-based models (<i>q</i><sub>e</sub> = <i>f</i>[ε/<i>E</i>]) with the
properties or structures of absorbates, where <i>q</i><sub>e</sub> is the equilibriumn adsorption capacity, <i>C</i><sub>a(or H)</sub> is the converted concentration from the equilibrium
aqueous concentration at the same activity and corresponds to the
adsorption from the gas or <i>n</i>-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 <i>intrinsic</i> characteristic energies <i>E</i><sub>a</sub>, derived from aqueous-to-gas phase conversion, or <i>E</i><sub>H</sub>, 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 <i>E</i><sub>a</sub> or <i>E</i><sub>H</sub> then emerge that are unrevealed by the original characteristic
energy (<i>E</i><sub>o</sub>), i.e., adsorbates with tendency
to form stronger interactions with an adsorbent have larger <i>E</i><sub>a</sub> and <i>E</i><sub>H</sub>. Additionally,
comparison of <i>E</i><sub>a</sub> and <i>E</i><sub>H</sub> 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: (<i>E</i><sub>a</sub> – <i>E</i><sub>H</sub>) = 24.7 × <i><b>V</b></i> + 9.7
× <i><b>S</b></i> – 19.3 (<i>R</i><sup>2</sup> = 0.97), where <i><b>V</b></i> is McGowan’s
characteristic volume for adsorbates, and <i><b>S</b></i> reflects the adsorbate’s polarity/polarizability
