Inorganic–organic hybrid materials through post-synthesis modification: Impact of the treatment with azides on the mesopore structure

Hybrid, hierarchically organized, monolithic silica gels, comprising periodically arranged mesopores and a cellular macroscopic network, have been prepared through a co-condensation reaction of tetrakis(2-hydroxyethyl)orthosilicate with chloromethyl-trimethoxysilane or 3-(chloropropyl)-triethoxysilane. Subsequent conversion of the chloro groups into azido groups, by nucleophilic substitution with NaN3 in N,N-dimethylformamide, was conducted upon preservation of the monolithic structure. However, treatment with NaN3 had a strong influence on the structure in the mesoporous regime, with changes such as an increase of mesopore diameter, pore volume and lattice constants, as well as a concomitant decrease of the pore wall thickness, as confirmed by small angle X-ray scattering, transmission electron microscopy, and nitrogen sorption analysis. Similar effects were observed for unmodified silica gels by simple ageing in azide-containing media, whether a relatively small or a sterically demanding counter ion (Na+ or (H3C)4N+) was used. The structural modification did not seem to depend greatly on whether an organic aprotic solvent (N,N-dimethylformamide, 1,1,3,3-tetramethylurea, 1,3-dimethyl-2-imidazolidinone) or a protic solvent that can form hydrogen bonds, such as water, was used.

: Schematic representation of a hexagonally organized pore system and the characteristic sizes From a geometrical point of view, one can consider the lattice constant a to be: a = D + t (1) with D being the mean pore-diameter and t the mean wall thickness between the pores. Variation of pore diameter and wall thickness leads to changes in the electron density distribution and thus to differences in the scattering intensities of the diffraction peaks.
According to Glatter and Kratky [1], the scattering intensity is proportional to the product of structure factor S(q) and the square of the scattering amplitude (form factor) P(q): For the case of a 2-D hexagonal lattice with spherical pores, S(q) is described as the sum of Gaussian functions with maxima located at the reciprocal lattice points. The reciprocal lattice points are equal to the positions of the  [2,3].
The form factor P(q) can be written as [4]: with R being the mean pore radius and J1 the Bessel function of the first kind.
The scattering intensity (2) was then convoluted with the resolution function of the equipment described by a Lorentzian curve and fitted to the experimental values. Fitting parameters were the pore diameter and the wall thickness as described above.

Electron density reconstruction:
A different approach is the reconstruction of the electron densities from a Fourier series and by the appropriate choice of the phases [5,6]. This has been experimentally and theoretically used to model the electron density across the pore for modified and unmodified MCM-41 and SBA-15 materials [7,8]. For a centrosymmetric unit cell, the electron density can be written as a Fourier series of cosines: With Aq being the Fourier coefficients, q  the scattering vector of the reciprocal lattice and r  a vector to the position in the unit cell.
The Fourier coefficients are determined from the peak intensities of the observed (h,k) reflections by , LP(qhk) being the Lorentz polarization-factor [9] and m the multiplicity of the respective reflection [5,6].
In order to obtain the integrated intensities I(q), the background scattering was subtracted from the data using a non-linear baseline. The remaining peaks were then fitted by a Gaussian function, from which the peak area was determined.
The next step in reconstructing the electron density is choosing the right phase. For centro-symmetric structures, this is equivalent to choosing the correct sign (+ or -) of the Fourier coefficients. The method, known as the "swelling method", was originally described by Stamatoff and Krimm [10] for lamellar phases ( α L ) and was extended by Turner and Gruner [5] to hexagonal phases: One compares two phases with slightly differing radii and therefore slightly differing X-ray patterns. Then all possible permutations of signs for the Aq's are calculated and compared, the proper phase set will have the closest correspondence (for more details see [5,6]). In our case, we did not use a swelling of phases, but compared the samples before and after nucleophilic substitution, which led also to slightly differing X-ray patterns. Finally, one has to check if the resulting phase is physically consistent. For example, if the origin was placed in the centre of the pore cross section, the electron density should be a minimum at this point. Towards the pore wall, the electron density should increase and reach a maximum in the silica phase between the pores.    Figure S3: Nitrogen isotherms and SAXS patterns of untreated silica gels, reference silica gels (solvent/60 °C) and azide-treated silica gels (solvent/NaN3/60 °C) in different solvents: TMU (top) and H2O (bottom) Figure S4: Electron-density reconstruction for unmodified silica gels exposed to DMI and DMI/NaN3 (top left), TMU and TMU/NaN3 (bottom left), H2O and H2O/NaN3 (bottom right) and for gels exposed to DMF and DMF/TMAA (top right).