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

J Appl Crystallogr. 2023 Sep 1;56(Pt 5):1381-1391. doi: 10.1107/S160057672300691X. eCollection 2023 Oct 1.

Abstract

A Monte Carlo (MC) method was introduced into a state-of-the-art model used to analyse small-angle X-ray scattering (SAXS) data of SBA-15, an ordered mesoporous material with many applications. With this new procedure, referred to herein as the SBA-15+MC model, it is possible to retrieve the size distribution of the mesopores, D(r), in a free modelling approach. To achieve this, two main points were addressed: (i) based on previous implementations, the method was adapted to work with long core-shell cylinders; (ii) since the MC model requires longer processing times, strategies to speed up the calculations were developed, which included a simplified version of the original model used to analyse SAXS data of SBA-15 (referred to as the SBA-15 model) as well as the determination of several structural features from the SAXS curve prior to the fit. The new model was validated with simulated data and later used to fit experimental SAXS curves of SBA-15. The obtained results show that the SBA-15 model only works well because the mesopore size distribution of SBA-15 is narrow, whereas the new approach can be successfully used in cases where D(r) is wider and/or has a more complex profile, such as SBA-15 with expanded mesopores. Even though a specific SAXS example was chosen to prove the model, the strategies presented herein are general and suitable for inclusion in other models aimed at the analysis of SBA-15 and similar ordered mesoporous materials.

Keywords: Monte Carlo methods; SAXS; SBA-15; data modelling; small-angle X-ray scattering.

Grants and funding

CLPO and MCAF are CNPq fellows. BBG and PLOF acknowledge FAPESP fellowships and grants (project Nos. 2017/17844-8, 2018/05888-3, 2020/02192-8, 2019/12301-1 and 2020/13204-7). The experiment carried out by XT and HNB at MAX IV was financed by the Danish Agency for Science, Technology and Innovation through DANSCATT. Research conducted at MAX IV, a Swedish national user facility, is supported by the Swedish Research Council under contract No. 2018-07152, the Swedish Governmental Agency for Innovation Systems under contract No. 2018-04969, and Formas under contract No. 2019-02496.