Exploiting the adsorption of simple gases O₂ and H₂ with minimal quadrupole moments for the dual gas characterization of nanoporous carbons using 2D-NLDFT models

Abstract

For years, the characterization of carbon pore size distribution (PSD) has been dominated by the analysis of N₂ isotherms. Recently, the IUPAC Technical Report (2015) recommended Ar as inert gas for this analysis. N₂ molecule due to its significant quadrupole moment may selectively interact with the polar surface sites and affect the isotherm measurement. CO₂, another gas that is often used for the characterization of microporous carbons exhibits even higher quadrupole moment than N₂. In the present study, we substitute N₂ and CO₂ with O₂ and H₂ gases that have much lower quadrupole moments. The PSD calculations are performed using molecular models based on classical and quantum corrected two-dimensional nonlocal density functional theory (2D-NLDFT).

We compare the results of the dual gas analysis methods by the simultaneous fit of our models to N₂ & CO₂, and O₂ & H₂ isotherms for several reference carbon samples and demonstrate consistency between the results derived from both pairs of isotherms.

A fundamental and practical benefit of using the dual gas analysis method is the ability to obtain the full micro and mesopore PSD by using a partial O₂ isotherm without low-pressure data in combination with full H₂ isotherm both measured at 77 K.

Introduction

For years, the characterization of carbon pore size distribution (PSD) has been dominated by the analysis of nitrogen (N₂) isotherms measured at its boiling point (77 K). From the scientific viewpoint, however, N₂ may not be the most appropriate molecular probe for the PSD evaluation. Its high quadrupole moment may affect the adsorption of N₂ molecules due to the interactions with polar surface sites.

The molecular models used in this work for the evaluation of carbon pore structure assume nonspecific interactions of gas molecules with carbon surface. Real carbon materials may contain various mineral contaminations and chemical surface sites that may interact with adsorbate molecules via specific interactions. If the experimental adsorption isotherms are distorted by such interactions it may affect the PSDs calculated from these isotherms.

To minimize such effects IUPAC Technical Report 2015 [1] recommended argon (Ar) as the most reliable for the PSD evaluation. However, Ar adsorption measurements using liquid Ar as a coolant are more costly than the standard N₂ analysis; therefore, from the practical viewpoint, Ar analysis is not a preferred one in a typical laboratory. As a replacement for argon, it was recently proposed to use oxygen (O₂) [2]. Oxygen was chosen because its quadrupole moment has about three times lower value than N₂. Moreover, it was shown for several representative carbon samples that their PSDs derived from adsorption measurements of N₂ and O₂ at 77 K and Ar at 87 K are in quantitative agreement.

On the other hand, the Report [1] recommended using CO₂ for the characterization of ultramicroporous carbons because, at the recommended temperature (273 K), CO₂ diffuses faster into micropores than N₂ at the cryogenic temperature. This recommendation, however, is inconsistent with the premise of using molecules with low sensitivity to interactions with polar sites, because the CO₂ quadrupole moment is even larger than that of N₂, which makes it sensitive to the carbon surface chemistry [3]. In the absence of polar sites, the use of CO₂ may be appropriate, and several authors applied CO₂ adsorption to study the porosity of microporous carbons and carbon molecular sieves [[4], [5], [6], [7], [8], [9]].

Another simple gas that diffuses faster into ultramicropores than N₂ at 77 K is H₂, which is supercritical at this temperature. Furthermore, the H₂ molecule has a small quadrupole moment and smaller diameter than CO₂, and it has been that H₂ adsorption data may provide meaningful PSD results in an extended range of pore sizes when analyzed alone [10] or simultaneously with argon data [11]. The grand canonical Monte Carlo (GCMC) model isotherms of H₂ and CO₂ were also used [12] to analyze simultaneously adsorption data of H₂ and CO₂

The values of the absolute quadrupole moments of the considered molecules are in the following order [13]: Ar < O₂ <H₂ <N₂ <CO₂ and their ratios to the value of N₂ are as follows 0.0 < 0.28< 0.46 < 1.0 <3.1. Other gases such as CH₄ [14], CF₄ and SF₆ [15] with symmetrical molecules, zero quadruple moments and different molecular diameters have been used for the carbon pore size analysis as well as for the evaluation of pore connectivity and molecular sieving effects.

In present work, we use molecular models based on the nonlocal density functional theory (NLDFT) to analyze O₂ and H₂ adsorption data simultaneously. We show comparisons of PSD results derived from O₂ and H₂ data and with those from N₂ and CO₂ data. The approach introduced in this work is advantageous compared to the earlier presented “dual analysis method” [16] based on N₂ and CO₂ data, due to the lower quadrupole moments of O₂ and H₂. It is also more practically convenient because of the same cryogen, liquid N₂, used for both analyses. The PSD analysis is executed using adsorption models incorporating surface roughness, and energetic heterogeneity derived based on the NLDFT [[17], [18], [19], [20]] in its two-dimensional version 2D-NLDFT-HS [21,22] herein referred to as 2D-HS where HS stands for the heterogeneous surface.