Capillary condensation, freezing, and melting in silica nanopores: A sorption isotherm and scanning calorimetry study on nitrogen in mesoporous SBA-15

Condensation, melting, and freezing of nitrogen in a powder of mesoporous silica grains (SBA-15) has been studied by combined volumetric sorption isotherm and scanning calorimetry measurements. Within the mean-field model of Saam and Cole for vapor condensation in cylindrical pores, a liquid nitrogen sorption isotherm is well described by a bimodal pore radius distribution. It encompasses a narrow peak centered at 3.3 nm, typical of tubular mesopores, and a significantly broader peak characteristic of micropores, located at 1 nm. The material condensed in the micropores as well as the first two adsorbed monolayers in the mesopores do not exhibit any caloric anomaly. The solidification and melting transformation affects only the pore condensate beyond approximately the second monolayer of the mesopores. Here, interfacial melting leads to a single peak in the specific-heat measurements. Homogeneous and heterogeneous freezing along with a delayering transition for partial fillings of the mesopores result in a caloric freezing anomaly similarly complex and dependent on the thermal history to that observed for argon in SBA-15. The axial propagation of the crystallization in pore space is more effective in the case of nitrogen than previously observed for argon, which we attribute to differences in the crystalline textures of the pore solids.

Figure 1

N${}_2$ sorption isotherm in SBA-15, measured at $77.9\mathrm{K}$. The dot-dashed, dashed, and solid lines represent sorption isotherms calculated based on the model of Saam and Cole for capillary condensation, while assuming a single radius, a unimodal, and a bimodal Gaussian pore radius distribution (as depicted in the inset and discussed in the text), respectively.

Figure 2

Specific-heat curves of cooling (solid line) and heating (dashed line) cycles for selected filling fractions $f$ indicated in the figure for N${}_2$. For the sake of readability, the curves are shifted vertically by an arbitrary offset.

Figure 3

Melting entropy (red, solid diamonds) and entropy related to the delayering transition (anomaly III) (blue, solid triangles) as a function of filling fraction $f$. The inset depicts a zoomed version of the anomaly III entropy as a function of filling fraction $f$. The dotted lines are guides for the eye.

Figure 4

Specific-heat freezing anomalies of Ar (solid lines) and ${\text{N}}_2$ (dashed lines) condensed in SBA-15 for selected filling fractions, as indicated in the figure, and plotted for a better comparison as a function of normalized temperature $\Theta$, where $\Theta =T/T_m$ and $T_m$ is the melting temperature of confined Ar and N${}_2$, respectively, defined by the peak of the melting anomaly in the case in which the pore condensate is assumed to be in contact with bulk crystallites ($f>1.10$).

Figure 5

Transition temperatures $T$ of the characteristic anomalies found in the specific heat of N${}_2$ in SBA-15 as a function of filling fraction and normalized to the bulk triple point $T_3$ of N${}_2$.

Figure 6

Incomplete freezing cycles as discussed in the text. The upper panels depict the freezing anomaly of complete freezing cycles for two selected filling fractions as references. The solid symbols indicate to which temperature, listed in the figure, the sample was cooled from 56.9 K before the heating scans (marked by numbers) started. The dotted lines represent the melting anomaly of a complete heating run with a virgin sample.

Figure 7

Incomplete melting cycles as discussed in the text. The upper panels depict the melting anomaly of complete freezing cycles for three selected filling fractions as references. The solid symbols indicate to which temperature, listed in the figure, the sample was heated before the cooling scans (indicated by numbers) started.