| Abstract
| - Adsorption in spherical cavities is studied by the nonlocal density functional theory (NLDFT). Theoreticalresults are compared with experimental data on ordered nanoporous materials with cubic Pm3n (SBA-1,HMM-3), cubic Im3m (SBA-16), and 3D hexagonal P63/mmc (SBA-2, SBA-12) cagelike structures.Quantitative comparison shows that capillary condensation of N2 at 77 K in sufficiently small cavities (porediameters 3 < D < 6 nm) occurs reversibly; the equilibrium condensation pressure is determined by thecavity diameter. In the case of hysteretic isotherms on materials with cavity diameters of >ca. 6 nm, thecapillary condensation step corresponds to the theoretical limit of stability of the metastable adsorptionfilm. For pores wider than ca. 10 nm, this limit is approximated by the macroscopic Derjaguin−Broekhoff−de Boer equations. Desorption from cavities of >6 nm is controlled by the size of the windows that connectthe cavity with the bulk fluid. If the diameter of the window is below ca. 4 nm, desorption occurs viaspontaneous cavitation of condensed liquid. We developed a NLDFT method for calculating pore sizedistributions (PSD) of cavities, the amount of intrawall porosity, and, in combination with X-ray diffraction,the wall thickness in siliceous materials with cagelike pores. We demonstrate that the adsorption methodallows one to differentiate between the materials of different morphological symmetry. For regular cagelikestructures, the NLDFT results are in remarkably good agreement with the estimates derived fromgeometrical considerations. In contrast, the conventional Barrett−Joyner−Halenda method of PSD analysis,based on the Kelvin equation, underestimates the pore sizes in cagelike nanopores by up to 100%.
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