Abstract
Adsorption-induced deformation of a series of silica samples with hierarchical porosity has been studied by in situ small-angle neutron scattering (SANS) and in situ dilatometry. Monolithic samples consisted of a disordered macroporous network of struts formed by a 2D lattice of hexagonally ordered cylindrical mesopores and disordered micropores within the mesopore walls. Strain isotherms were obtained at the mesopore level by analyzing the shift of the Bragg reflections from the ordered mesopore lattice in SANS data. Thus, SANS essentially measured the radial strain of the cylindrical mesopores including the volume changes of the mesopore walls due to micropore deformation. A H2O/D2O adsorbate with net zero coherent neutron scattering length density was employed in order to avoid apparent strain effects due to intensity changes during pore filling. In contrast to SANS, the strain isotherms obtained from in situ dilatometry result from a combination of axial and radial mesopore deformation together with micropore deformation. Strain data were quantitatively analyzed with a theoretical model for micro-/mesopore deformation by combining information from nitrogen and water adsorption isotherms to estimate the water–silica interaction. It was shown that in situ SANS provides complementary information to dilatometry and allows for a quantitative estimate of the elastic properties of the mesopore walls from water adsorption.
Highlights
Adsorption-induced deformation describes the effect that porous materials tend to mechanically deform upon the adsorption of a fluid.[1]
While many theoretical and/or computational studies treat the detailed adsorbate−adsorbent interactions,[19] and numerous works have been published on the deformation of the pore space as a result of internal and external pressures,[20] the combined treatment of both aspects is more recent.[21−32] We have lately developed a general theoretical framework to describe the adsorption- and the strain isotherms for cylindrical mesopores by combining the Derjaguin−Broekhoff−de Boer (DBdB) theory,[33−35] the adsorption stress model,[17] and the mechanical model of a cylindrical tube.[14]
If a zero scattering length density (Z-SLD) fluid is adsorbed into a twophase system, the changes of the integrated small-angle neutron scattering (SANS) intensity can be directly translated to mesopore volume changes and/or to density changes within the mesopore walls
Summary
Adsorption-induced deformation describes the effect that porous materials tend to mechanically deform upon the adsorption of a fluid.[1]. The theoretical model does not take anisotropy of the elastic properties of the mesopore walls into account, which could be a consequence of directional, nonspherical micropores.[69−71] Yet, another qualitative explanation for the observed discrepancy may be reasonable as follows: The theoretical model for anisotropic deformation of cylindrical mesopores predicts the major differences between the axial and the radial strains in the hysteresis region of capillary condensation/evaporation, while for the film region the two strain components should be very similar, and for the completely filled pores they should be identical.[36] the determination of the parameter x will depend on the quality of the modeling in the capillary condensation/ evaporation regime It is seen already in the N2 isotherms of the sintered and calcined samples (see Figures S1 and S2) that the adsorption isotherm modeling is not as good as compared to the samples used in.[37] In particular, the condensation/ evaporation branches are strongly tilted. Such a scenario is far from being covered by the model of pure adsorption-induced deformation and will not be discussed further
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