Large-scale reverse Monte Carlo analysis for the morphologies of silica nanoparticles in end-modified rubbers based on ultra-small-angle X-ray scattering data

Differences in the morphologies of silica nanoparticles (NPs) in end-modified styrene-butadiene rubber (SBR) and non-modified SBR were analyzed by comparing ultra-small-angle X-ray scattering (USAXS) experiments and transmission electron microscopy (TEM) images. To perform 3D topological data analysis on NPs, a modeling method for the 3D positions of NPs is essential. Reverse Monte Carlo (RMC) analysis is an effective tool for modeling the 3D configuration of NPs from the USAXS data. It was previously reported that the difference in the scattering intensity I(q) between the end-modified and the non-modified SBR can be observed at a q-range of 0.0015–0.06 nm−1. To take such a low q value into account in the RMC analysis, both a large system and a large number of NPs are required. In this study, a large-scale RMC analysis for 33,554,432 NPs, for a wide q-range from 0.0014 to 0.17 nm−1, was performed. The 3D topological data analyses were conducted using the histograms of neighboring particles and the volumes of the Voronoi cells. The results reveal that NPs in the end-modified SBR are better dispersed than those in the non-modified SBR. The histograms of the neighboring particles show that the average size of the aggregated NPs for the modified SBR is smaller than that for the non-modified SBR. From the histograms of the volumes of the Voronoi cells, it is observed that the fraction of the large free volume among the aggregated NPs for the non-modified SBR is larger than that for the modified SBR.