Retrieving the size distribution of SBA-15 mesopores from small-angle X-ray scattering data using a Monte Carlo method

Tan, X.; Gerbelli, B.B.; Fantini, M.C.A.; Oliveira, C.L.P.; Bordallo, H.N.; Oseliero Filho, P.L.

doi:10.1107/S160057672300691X

Figure 1
(a) Modelling of SBA-15, where the mesopores are represented by cylinders with length L arranged in a 2D-hexagonal lattice. (b) Front view of modelled SBA-15 with lattice parameter a considering an ideal lattice, represented by the red crosses, in which the cylinder centres coincide with the lattice points. The mesopores have average inner and outer radii R and $[{R_{\rm out}}]$ , respectively, with $[{R_{\rm out}} = R + T]$ , where T is the average thickness of the shell. Core and shell have electron-density contrasts $[\Delta {\rho _{\rm core}}]$ and $[\Delta {\rho _{\rm shell}}]$ , respectively. (c) In a more realistic scenario, besides polydispersity of R and $[{R_{\rm out}}]$ , the lattice can be distorted, i.e. the centre of each cylinder does not coincide with the lattice points (red crosses). (d) Black filled circles correspond to the SAXS experimental curve of SBA-15 obtained at the CoSAXS beamline (MAX IV, Lund, Sweden), where it is possible to observe Bragg reflections whose indexing is compatible with a 2D-hexagonal lattice (Losito et al., 2021a

). The red continuous line is the fit with equation (1)

, which is quite satisfactory. The other continuous lines represent the form factor P(q ) (blue) and the structure factor S(q ) (orange). The green, purple and magenta dashed–dotted lines show the function Z(q ) [equation (10)

], the Porod term and the polymer scattering [equation (21)

], respectively. (e) The normalized volume-weighted size distribution of the core radius, D(r ), and the shell thickness, D(t ), obtained from the fit, with averages and standard deviations (R, $[{\sigma _R}]$ ) and (T, $[{\sigma _T}]$ ), respectively.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 56| Part 5| October 2023| Pages 1381-1391

https://doi.org/10.1107/S160057672300691X

Open

access

Search IUCr Journals		doi		Advanced search
Author		volume	page