A Generalized Law of Corresponding States for the Physisorption of Classical Gases with Cooperative Adsorbate–Adsorbate Interactions

Abstract

The Law of Corresponding States for classical gases is well established. Recent attempts at developing an analogous Law of Corresponding States for gas physisorption, however, have had limited success, in part due to the omission of relevant adsorption considerations such as the adsorbate volume and cooperative adsorbate-adsorbate interactions. In this work, we modify a prior Law of Corresponding States for gas physisorption to account for adsorbate volume, and test it with experimental data and a generalized theoretical approach. Furthermore, we account for the recently-reported cooperative adsorbate-adsorbate interactions on the surface of zeolite-templated carbon (ZTC) with an Ising-type model, and in doing so, show that the Law of Corresponding States for gas physisorption remains valid even in the presence of atypically enhanced adsorbate-adsorbate interactions.

A thermodynamic investigation of adsorbate‐adsorbate interactions of carbon dioxide on nanostructured carbons

“…This heat capacity is larger than the heat capacity of liquid carbon dioxide (∼94 J•mol −1 K −1 ) and is suggestive of a phase transition. This suggests that the origin of the enhanced adsorbate‐adsorbate interactions may be an adsorbed‐phase clustering transition as previously noted in other systems . Once again this suggests that cooperative carbon dioxide adsorbate‐adsorbate interactions are better optimized for the micropore distribution of MSC‐30 than ZTC or CNS‐201.…”

“…The micropore volumes of MSC‐30, CNS‐201, and ZTC were determined to be 1.54, 0.45, and 1.66 mL•g −1 , respectively. The theoretical maximum possible carbon dioxide adsorption ( n m ) was estimated as the product of the micropore volume and the density of liquid carbon dioxide at its triple point, yielding estimated n m values of 41.3, 12, and 44.5 mmol•g −1 for MSC‐30, CNS‐201, and ZTC, respectively. MSC‐30 and CNS‐201 have skeletal densities of 2.1 g•mL −1 , while ZTC has a lower skeletal density of 1.8 g•mL −1 due to a higher hydrogen content …”

“…The reduced temperature and reduced pressure are defined as the ratios of the system temperature to the gas critical temperature, and the system pressure to the gas critical pressure, respectively. We have recently reported an extension to the Law of Corresponding States that applies to physisorbed molecules . Specifically:…”

“…However, recent investigations of nonideal gases adsorbed on carbonaceous materials at high pressures have shown that in some systems, strong lateral intermolecular interactions between adsorbate molecules can lead to an isosteric heat of adsorption that increases with increasing occupancy near ambient temperatures – . This effect is realized in adsorbent materials with optimal surface structure and a narrow distribution of binding‐site energies . At high pressures, carbon dioxide gas has strong intermolecular interactions and nonideal behavior, and is therefore a candidate for this effect.…”

Optimal fluids for adsorptive cooling and heating

“…However, as observed in a number of cases [44][45][46], many adsorption materials exhibit a characteristic curve which can describe the relative adsorption (q/qs) of fluids having similar thermodynamic properties. In an attempt of extending the corresponding state principle to adsorption, it has been demonstrated in [32] that for isotherms that can be reduced to the form (ln(P/Psat) = J(T) X ψ(θ)), where one temperature dependent term and one composition dependent term can be distinguished, the characteristic curve is defined by the following dimensionless group:…”