Quantitative characterization of the average structure of dense nanoparticle assemblies and aggregates is a common problem in nanoscience. Small-angle scattering is a suitable technique, but it is usually limited to not too big assemblies due to the limited experimental range, low concentrations to avoid interactions, and monodispersity to keep calculations tractable. In the present paper, a straightforward analysis of the generally available scattered intensity – even for large assemblies, at high concentrations – is detailed, providing information on the local volume fraction of polydisperse particles with hard sphere interactions. It is based on the identical local structure of infinite homogeneous nanoparticle assemblies and their subsets forming finite-sized clusters. This approach is extended to polydispersity, using Monte-Carlo simulations of hard and moderately sticky hard spheres. As a result, a simple relationship between the observed structure factor minimum – termed the correlation hole – and the average local volume fraction κ on the scale of neighboring particles is proposed and validated through independent aggregate simulations. This relationship shall be useful as an efficient tool for the structural analysis of arbitrarily aggregated colloidal systems.

中文翻译：

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测定多分散纳米颗粒组件的局部密度

致密纳米颗粒组装体和聚集体的平均结构的定量表征是纳米科学中的一个普遍问题。小角度散射是一种合适的技术，但由于实验范围有限，避免相互作用的低浓度以及使计算易于处理的单分散性，通常将其限制在不太大的组件中。在本文中，详细分析了通常可用的散射强度-即使对于大型装配体，在高浓度下也是如此-详细介绍了具有硬球相互作用的多分散颗粒的局部体积分数信息。它基于无限均匀的纳米粒子组件及其形成有限大小簇的子集的相同局部结构。这种方法扩展到了多分散性，使用硬和中等粘性硬球的蒙特卡罗模拟。结果，观察到的最小结构因子（称为相关孔）与平均局部体积分数之间存在简单的关系提出了在邻近粒子尺度上的κ，并通过独立的聚集体仿真对其进行了验证。这种关系应作为一种有效的工具，用于对任意聚集的胶体系统进行结构分析。