Apparent lattice expansion in ordered nanoporous silica during capillary condensation of fluids

Ordered nanoporous silica materials containing cylindrical pores on a two-dimensional hexagonal lattice are known to deform upon adsorption and condensation of fluids. These sorption strains can be measured by in situ small-angle X-ray scattering by analysing the shift of the Bragg peaks from the ordered pore lattice. Besides the real lattice deformation due to the interaction of the solid pore walls with the fluid, a hitherto unexplained apparent lattice expansion is found experimentally in SBA-15 nanoporous silica in a narrow pressure region for three different fluids (pentane, perfluoropentane and water). It is shown that the Bragg peak shift in this region results partly from a subtle contrast effect. The pore form factor changes during capillary condensation owing to the sequential filling of pores according to their diameter. Together with the structure factor from a lattice of finite size, this leads to an effective shift of the Bragg peaks, resulting in the measured apparent lattice strain. Two simple models are presented, which aim to quantitatively describe these apparent strains. The first model employs cylindrical pores with a size distribution on a two-dimensional hexagonal lattice. Filling of pores is achieved by changing the contrast between the pores of a certain size with respect to the surrounding matrix, and the peak shift is calculated from the power spectrum of this lattice. The second model derives analytical expressions for the peak shifts as a function of pore filling fraction by using a Taylor expansion of the pore form factor and a uniform pore size distribution. Both models are able to reproduce the experimental results satisfactorily, providing the possibility to separate these apparent lattice strains from real pore wall deformation in nanoporous materials.