Revealing nanoscale sorption mechanisms of gases in highly porous silica aerogel

Geological formations provide a promising environment for the long-term and short-term storage of gases, including carbon dioxide, hydrogen and hydrocarbons, controlled by the rock-specific small-scale pore structure. This study investigates the nanoscale structure and gas uptake in a highly porous silica aerogel (a synthetic proxy for natural rocks) using transmission electron microscopy, X-ray diffraction, and small-angle and ultra-small-angle neutron scattering with a tracer of deuterated methane (CD4) at pressures up to 1000 bar. The results show that the adsorption of CD4 in the porous silica matrix is scale dependent. The pore space of the silica aerogel is fully accessible to the invading gas, which quickly equilibrates with the external pressure and shows no condensation on the sub-nanometre scale. In the 2.5–50 nm pore size region a classical two-phase adsorption behaviour is observed. The structure of the aerogel returns to its original state after the CD4 pressure has been released.


Appendix A. SANS intensity of pressurized CD4 at p=500 bar
The (unbound) incoherent scattering cross section of 2 H, the nucleus of deuterium (2.0•10 -24 cm 2 ), is much smaller than its counterpart for hydrogen, 1 H, (80.2•10 -24 cm 2 ); its contribution to the large-Q background scattering of rocks, with the typically accessible porosity of the order of several per cent, is of the order of 0.001 cm -1 at pressures about 1 kbar.This is markedly lower than the typical large-Q SANS background for geological materials (varying from ca. 0.01cm -1 for sandstones to ca. 1 cm -1 for organic-rich shale and coal) and can be safely neglected during the analysis of CM SANS results obtained using pressurized CD 4 (Zhang et al., 2015;Bahadur et al., 2018;Blach et al., 2021;Sun et al., 2022), compared to other contributions to the large-Q background (in particular, the molecular-scale compositional inhomogeneity and incoherent scattering on hydrogen nuclei bound in the organic matter, clays and formation fluids).
The situation for the silica aerogel is different: it is chemically homogeneous and its porosity is exceptionally large (ca.96%), hence the contribution of the 2 H incoherent scattering to the large-Q SANS intensity background may be significant even at the relatively low pressures of CD 4 .Its magnitude at 500 bar is estimated to be 7⋅10 -3 cm -1 , since (dΣ/dΩ) incoh = 1/4π×ρ/M×σ i N A F A , where σ i = 8.2⋅10 24 cm 2 is the incoherent cross section for 2 H bound in CD 4 , ρ = 0.345 g/cm 3 is the bulk density of CD 4 at 500 bar, M is the molar mass of CD 4 , N A is Avogadro's number and F A = 0.97 is the CD 4 -accessible volume fraction inside the aluminium sample holder (accounting for the incomplete filling of the cell volume by the silica aerogel sample).
To verify this prediction, an additional control experiment -SANS measurement of the empty cell (without the Si-aerogel sample) -has been performed in vacuum and at the CD 4 pressure of 500 bar (above the contrast matching pressure of 415 bar).SANS intensity for the pressurized CD 4 fluid was calculated by comparing the two I(Q) curves of the empty cell at vacuum and under 500 bar of CD 4 .The experimental SANS curves and the calculated scattering intensity of the bulk CD 4 fluid confined in the cell at p=500 bar (with and without the aluminium sample holder installed) are shown in Figure S1; the results indicate an unexpectedly large, Q-dependent scattering signal.
In particular, in the large-Q limit, the differential scattering cross sections measured at p=500 bar with and without the aluminium sample holder installed in the sample compartment are ~0.2 cm -1 and ~5⋅10 - 2 cm -1 , respectively, which is 25 and seven times larger than the theoretically predicted incoherent scattering value of 7⋅10 -3 cm -1 .
In the small-Q range (from 0.001 Å -1 to 0.01 Å -1 ), the SANS intensity decreases from ~10 4 cm -1 to ~1 cm -1 , roughly according to the power law with the negative slope of -4.
The origin of the Q-dependent background scattering which so significantly exceeds the incoherent scattering of deuterium is not clear.Most likely it is caused by the heterogeneity of the scattering contrast on the sub-micrometre scale, due either to the density fluctuations of the supercritical CD 4 or scattering on the gas-metal interfaces inside the sample compartment, internal windows and the sample-window spacers exposed to the neutron beam.The latter hypothesis is supported by the fact that the intensity of the CD 4 scattering curves measured with and without the aluminium sample container in place are significantly different; it is examined in detail in the following sections.

Appendix B. Pressure dependence of SANS intensity in the large-Q region
In the large-Q range (from 0.1 to 0.5 Å -1 ) the SANS intensity rapidly increases at the first pressure step from vacuum to 50 bar (Figure 6) and then remains relatively stable (at the level of about 0.1 cm -1 ) with increased pressure; the SANS intensity tends to plateau rather than follow a V-shaped pressure dependence characteristic for a two-phase system subjected to contrast matching.
Importantly, the SANS patterns measured at p = 500 bar for the CD 4 fluid (acquired at ANSTO) and the CD 4 -invaded silica aerogel sample (acquired at ILL) are similar (parallel and linear on the log-log plot), 3 with the slope value of -0.24.The intensities without the silica aerogel scale with a factor of 2.4 and 0.82 with and without the aluminium sample container installed, respectively, to the SANS data of the pressurized silica aerogel (Figure S2).
Following these observations, we postulate that in the large-Q region, the scattering intensity of silica aerogel invaded with pressurized CD 4 is dominated by the nano-scale heterogeneities of the scattering contrast which are not related to the presence of the aerogel sample hence they carry no useful silica aerogel structural information.
The scattering cross section measured at various pressures in the large-Q region is modelled using the power-law formula where α is the scattering intensity at Q = 1 Å -1 and exponent β is the slope on the log-log plot.Parameters α and β fitted to Equation (S1) are shown in Figure S3 and listed in Table S1.S2 Parameters β (intersect with the vertical axis at Q = 1 Å -1 ) and α (slope) obtained from fitting Equation (S1) to the low-Q SANS intensity for the silica aerogel.S3.The CM pressures are 415 bar for the silica aerogel matrix (SLD=3.2·10 10 cm -2 , marked CM1), 288 bar for TiO 2 (SLD=2.6·10 10 cm -2 , marked CM2) and 209 bar for Al (SLD=2.1·10 10 cm -2 , marked CM3 in the plot).The CM pressure for Al 2 O 3 (>2 kbar) is outside of the experimental range; titanium has a negative SLD which cannot be matched using CD 4 .CM conditions close to CM1 are observed in the mid-Q pore size range of 2.5 nm to 25 nm (Figure 12; nearly full contrast match) and those close to the combined CM2 and CM3 are seen for the ~125 nm pore sizes (Figure 8, the largest pore size investigated; about 70% contrast match)

Figure S1
Figure S1 Comparison of SANS intensity measured for the evacuated empty cell and at 500 bar of CD 4 and the calculated scattering cross section of pressurized CD 4 .The large-Q region detail is shown in the inset.(a) and (b) show SANS data for the empty cell with and without the aluminium sample holder installed in the sample compartment, respectively; the scattering intensities of CD 4 were calculated by subtracting the empty cell scattering measured in vacuum from that measured under the pressure of 500 bar, and are markedly different in magnitude.

Figure S2
Figure S2 Comparison of SANS intensity measured at the CD 4 pressure of 500 bar for the empty cell, the empty cell with the aluminium container installed, and the silica aerogel sample mounted in the aluminium container.Inset shows details in the large-Q region; dashed lines represent power-law fits.

Figure S3
Figure S3 Parameters α and modulus of β obtained by fitting Equation (S1) to the pressure-dependent large-Q SANS data for the silica aerogel, as a function of SLD(CD 4 )

Figure S4 Q
Figure S4 Q dependence of the silica-aerogel-independent background at the CD 4 pressure of 150 bar; it is the sum of extrapolated power-law scattering intensities fitted in the low-Q and large-Q regions: (a) calculated for SANS results acquired at p(CD 4 ) = 150 bar; (b) colour map of the background for various pressures of CD 4 .

Figure S5
Figure S5 Pressure dependence of the square root of the Porod Invariant calculated after the subtraction of two different backgrounds from the original SANS results.Main panel: small-Q powerlaw (350-1000 bar) plus large-Q power-law (50-1000 bar); Inset: small-Q power-law (50-1000 bar) plus large-Q power-law (50-1000 bar), shown previously in Figure 11.

Figure S6
Figure S6 Diagram showing the pressures of CD 4 and corresponding SLD values at the contrast match (CM) points (where appropriate) with titanium, titanium oxide, aluminium, aluminium oxide and the silica aerogel solid matrix.Data for CD 4 were taken from the NIST Chemistry WebBook (NIST Chemistry WebBook); SLDs for solids are listed in TableS3.The CM pressures are 415 bar for the silica

Table S1
Parameters β (intersect with the vertical axis at Q = 1 Å -1 ) and α (slope) obtained from fitting Equation (S1) to the large-Q SANS intensity for the silica aerogel.

Table S3
SLD values for the Textor et al., 2001)etal components exposed to pressurized CD 4 .Ranges of thicknesses of the naturally formed surface layers of oxides are the typical values, reported after exposure to air at room temperature for times from days to a year(Chen et al., 1997;Textor et al., 2001).Values of SLD were calculated using the NIST calculator (NIST Center for Neutron Research).