## Results and Discussion

Figure 2 shows the values of the relative density function p(q) for «-hexane in APETA, calculated with Eq. (6) from the data of Figure 1. On immersion in liquid hexane all the pores fill, including those at low q. The contribution of the latter to the total adsorption is, however, small. (Values of p(q) in excess of unity in the low q region may be an instrumental artefact.) The sharp cut-off at the highest values of q indicates that hexane molecules do not penetrate into spaces smaller than 4.5 A [15]. At values of q below 1 A-1 the effective density of the hexane in the pores rises quickly to its bulk value. At the relative pressurep/p0 = 0.4, the larger pores (q < 0.1 A-1) are less populated and filling drops to zero in the largest cavities. In interpreting Figure 2, however, it should be recalled that larger pores scatter more strongly than smaller pores. The volume filling of the pores is thus defined not by p(q) but by q2p(q). Figure 2 thus implies that the carbon is almost completely saturated with hexane at p/p0 = 0.4.

Water molecules, being smaller than hexane, can penetrate into smaller spaces. Figure 3 shows the density functions p(q) calculated for water vapour at 43% relative humidity in APETA and APETB. In both samples,

Figure 3. Relative density p(q) in APETA (O) and in APETB (x) with water vapour at p/po = 0.43.

Figure 3. Relative density p(q) in APETA (O) and in APETB (x) with water vapour at p/po = 0.43.

p(q) is effectively zero at q « 2.1 A-1, corresponding to a limiting size d = 2n/q « 3 A. This result agrees with the critical size of the water molecule, 2.92 A [15].

The different SAXS responses of APETA and APETB reflect their different surface treatment. In APETB, p(q) in the nanopore region of the spectrum (0.3 A-1 < q < 1.5 A-1, i.e. 20 A > d > 4 A) rises to only 40-50% of the density of bulk water. In the next larger pore size range (q « 0.1 A-1, d « 60 A), filling reaches 90%, although these pores, owing the q2 weighting factor, contribute little to the total amount of adsorbed water. The response of APETA to water vapour is markedly different. At the same relative humidity the sample displays a broad q region of apparently negative values of p(q). As noted earlier, this is the signature of cluster formation. Since the sign of the third term in Eq. (3) is not positive for all q, it cannot be concluded from this figure alone that the filling in the nanoporous region is higher in APETA than in APETB. Figures 2 and 3 illustrate how the adsorption profiles of hexane and water vapour are qualitatively different and that water is highly sensitive to the surface chemistry of the carbon.

The pseudo-binary model, which quantifies the adsorption of wetting fluids, also reveals non uniform adsorption mechanisms, due either to surface chemistry or polarity of the probe molecules. The general case of water vapour equilibrated systems, however, requires independent information, such as water vapour adsorption isotherms, to refine the above results.

Figure 4a and b shows the direct SAXS spectra of APETA for various values of RH. At low RH small amounts of water condense initially in the micropores (q > 0.2 A-1), while cluster formation develops in the more open surfaces. Between 33% and 43% RH the amount of condensed water in the micropores increases significantly, while at low q, cluster formation becomes more pronounced. A simple estimate of the contribution from the clusters can be made based on a lognormal distribution of cluster sizes. This yields the broad bell-shaped curve on the lower left in Figure 4b. Subtraction of this function, centred at q = 0.036 Ä-1, from the experimental spectrum, yields the flat plateau region shown as a dashed line. It can be seen from the figure, however, that the approximation underestimates the broad q-range of

Figure 4a. SAXS response for APETA in the dry state and in water vapour at three degrees of relative humidity. Scattering intensity in excess of that of the dry sample is visible for q < 0.2 A-1 even at RH = 23%.

Figure 4b. SAXS from same sample showing in addition spectrum at 76% RH. Bell shaped curve is estimate for the third term in Eq. (3) (based on a lognormal function and divided by 10 for clarity), chosen to yield a plateau in the difference curve at q ~ 0.1 A-1. Dashed curve is the resulting difference between the full 43% curve and the lognormal function.

Figure 4b. SAXS from same sample showing in addition spectrum at 76% RH. Bell shaped curve is estimate for the third term in Eq. (3) (based on a lognormal function and divided by 10 for clarity), chosen to yield a plateau in the difference curve at q ~ 0.1 A-1. Dashed curve is the resulting difference between the full 43% curve and the lognormal function.

the scattering from clusters, since the intensity of the water vapour samples exceeds that of the dry carbon at much lower q. The cluster size distribution is therefore much wider than that of a simple lognormal distribution.

For the more oxidized APETB sample the various stages of the SAXS response as a function of RH are shown in Figure 5. Adsorption starts already at the lowest RH in the smallest pores (q « 1 A-1), but the corresponding values of p(q) indicate that even at RH = 76% complete filling is not achieved. Occupation of pores in the nanometre size range is limited to less than to -60%. For both APETA and APETB, access to the pores can be blocked by water clusters developing around functional groups located at the entrance of the pores, thus hindering the passage of further adsorbates.

The SAXS curves of Figure 5 indicate that cluster formation is not dominant in the highly oxidized sample for RH < 0.5. Above this value, however, the intensity of the plateau at q « 0.1 A-1 starts to increase monotonically. This unexpected finding shows that scattering from clusters becomes stronger at high relative humidity.

Figure 5. Pore filling sequence in APETB with increasing RH as observed by SAXS. 5. Conclusions q (A '>

Figure 5. Pore filling sequence in APETB with increasing RH as observed by SAXS. 5. Conclusions

The chemical character of both the adsorbent and the adsorbate influences the wetting mechanism of the adsorbing vapour. The presence of adsorbed molecules changes the intensity of the small angle x-ray scattering (SAXS) response in a way that depends on how the pores are filled. Two carbon samples of different surface polarity were investigated. For the wetting fluid «-hexane, the dispersion interaction ensures progressive filling in both carbons. For water vapour the degree of filling in the smaller pores and the cluster formation in the wider pores depend on the extent of oxidation. In the highly oxidized sample a cooperative mechanism enhances the filling of even larger pores.

The pseudo-binary model employed gives a satisfactory quantitative description at p/p0 « 0.4 for both surfaces with hexane, while with water it gives quantitative results only for the highly oxidized sample. In the latter case the contribution of the water-air interfaces, corresponding to the cross term in the full scattering expression, cannot be neglected. Quantitative evaluation of this situation can be obtained only with the help of contrast variation, such as afforded by solvent deuteration in SANS.

In conclusion, firstly, the nature of the wetting liquid and of the surface chemistry is of major importance in the pore filling process. Secondly, competition between the non-polar molecules and water can be significant at high RH values.

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