Deformation of Microporous Carbons during N₂, Ar, and CO₂ Adsorption: Insight from the Density Functional Theory

Abstract

Using the nonlocal density functional theory, we investigate adsorption of N2 (77 K), Ar (77 K), and CO2 (273 K) and respective adsorption-induced deformation of microporous carbons. We show that the smallest micropores comparable in size and even smaller than the nominal molecular diameter of the adsorbate contribute significantly to the development of the adsorption stress. While pores of approximately the nominal adsorbate diameter exhibit no adsorption stress regardless of their filling level, the smaller pores cause expansive adsorption stresses up to almost 4 GPa. Accounting for this effect, we determined the pore-size distribution of a synthetic microporous carbon by simultaneously fitting its experimental CO2 adsorption isotherm (273 K) and corresponding adsorption-induced strain measured by in situ dilatometry. Based on the pore-size distribution and the elastic modulus fitted from CO2 data, we predicted the sample's strain isotherms during N2 and Ar adsorption (77 K), which were found to be in reasonable agreement with respective experimental data. The comparison of calculations and experimental results suggests that adsorption-induced deformation caused by micropores is not limited to the low relative pressures typically associated with the micropore filling, but is effective over the whole relative pressure range up to saturation pressure.

Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica—Effect of Pore-Level Anisotropy

“…The removal of the microporosity is essential, since microporosity was shown to potentially affect adsorption-induced deformation over the whole relative pressure range even when micropore filling is essentially completed. 4 The sample preparation described above is one of very few successful approaches to a material exhibiting well-defined cylindrical mesopores and being available in monolithic form, which is required for in situ dilatometry measurements of adsorption-induced deformation. The sintered sample was investigated by scanning electron microscopy (SEM) (Ultra Plus, Carl-Zeiss NTS) and N 2 adsorption analysis at 77 K (ASAP2020, Micromeritics).…”

“…With respect to the theoretical understanding of adsorption-induced deformation, a considerable number of studies were performed in recent years, e.g., refs (4, 5, and 28−50). One of the prevailing concepts in these studies is the adsorption stress approach proposed by Ravikovitch and Neimark; 29 it was used to elucidate the specifics of adsorption-induced deformation of zeolites, 29 carbons, 5,34,39 metal–organic frameworks, 40 and mesoporous solids.…”

Adsorption-induced deformation of nanoporous materials—A review

“…Despite the number of strong assumptions, this "thermodynamic approach" made it possible to calculate strain isotherms for various other microporous systems, e.g., activated carbons, 108 synthetic carbon monoliths, 50 coal, 95,109 and even breathing MOFs. 101 The key part is that the grand potential of the system (and therefore its derivative) is calculated based on a theory of adsorption in a rigid pore.…”

“…50 They employed DFT calculations to derive adsorption and adsorption stress isotherms for carbon micropores and the adsorbates N 2 (77 K), Ar (77 K), and CO 2 (273 K), and compared the results to the experimental data reported earlier. 127 One of the important features of this work was the consideration of micropores smaller than the nominal molecular diameter of the adsorbates, which are typically disregarded.…”

Relationship between pore-size distribution and flexibility of adsorbent materials: statistical mechanics and future material characterization techniques

“…Relationships between an adsorbent’s PSD and its structural deformation have been considered previously for carbonaceous materials [2, 41], but the alteration of a PSD due to structural deformation was not explicitly taken into account. Although it should be clear that the PSD of a deformable material depends on both the material’s properties and the imposed thermodynamic conditions, we are unaware of any rigorous statistical mechanical description of the PSD of a flexible adsorbent material.…”