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

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.