Real-space modeling for complex structures based on small-angle X-ray scattering.

Kazuhiko Omote,Tomoyuki Iwata

doi:10.1107/s1600576721006701

Kazuhiko Omote, Tomoyuki Iwata

Open Access

https://doi.org/10.1107/s1600576721006701

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Abstract

A three-dimensional real-space model has been created for hierarchical materials by matching observed and simulated small-angle X-ray scattering patterns. The simulation is performed by arranging the positions of small primary particles and constructing an aggregate structure in a finite-sized cell. In order to avoid the effect of the finite size of the cell, the cell size is extended to infinity by introducing an asymptotic form of the long-range correlations among the primary particles. As a result, simulations for small-angle X-ray scattering patterns can be performed correctly in the low-wavenumber regime (<0.1 nm-1), allowing the model to handle hundred-nanometre-scale structures composed of primary particles of a few nanometres in size. An aerogel structure was determined using this model, resulting in an excellent match with the experimental scattering pattern. The resultant three-dimensional model can generate cross-sectional images similar to those obtained by transmission electron microscopy, and the calculated pore-size distribution is in accord with that derived from the gas adsorption method.

Highlights

Many functional materials have a hierarchical structure, e.g. catalyst carriers, hybrid polymer composites, highperformance rubber tires, aerogels and so forth
Transmission and scanning electron microscopy (TEM and SEM, respectively) are powerful tools to investigate the precise structure of these primary units; it is difficult to investigate such hierarchical complex structures using TEM and SEM because the materials can be destroyed during sample preparation, e.g. slicing and thinning
The purpose of this paper is to construct three-dimensional structural models composed of primary particles, which are fitted to Small-angle X-ray scattering (SAXS) experiments on the basis of reverse Monte Carlo (RMC) simulation (McGreevy & Pusztai, 1988)

Summary

Introduction

Many functional materials have a hierarchical structure, e.g. catalyst carriers, hybrid polymer composites, highperformance rubber tires, aerogels and so forth. They are composed of complex formations of atomic-scale or nanometre-sized primary units. It was assumed that the constituent primary particles were identical, and the structure factor could be factored from the form factor. This simulation exhibits oscillatory fringes corresponding to the size (diameter) of the primary particles. The experimental scattering patterns do not show such

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Discussion

Conclusion