Directional Statistics of Preferential Orientations of Two Shapes in Their Aggregate and Its Application to Study Preferential Attachment of Nanoparticles

TL;DR

This paper introduces a statistical method to analyze the preferential orientations of nanoparticles during aggregation, providing quantitative insights into their oriented attachment behavior.

Contribution

It presents a novel statistical framework for quantifying and testing the orientation distributions of nanoparticles in aggregates, advancing beyond manual qualitative analysis.

Findings

Nanoparticles exhibit statistically significant preferential orientations.

The method successfully estimates orientation probability distributions.

Application confirms geometric dependence of aggregation orientations.

Abstract

Nanoscientists have long conjectured that adjacent nanoparticles aggregate with one another in certain preferential directions during a chemical synthesis of nanoparticles, which is referred to the oriented attachment. For the study of the oriented attachment, the microscopy and nanoscience communities have used dynamic electron microscopy for direct observations of nanoparticle aggregation and have been so far relying on manual and qualitative analysis of the observations. We propose a statistical approach for studying the oriented attachment quantitatively with multiple aggregation examples in imagery observations. We abstract an aggregation by an event of two primary geometric objects merging into a secondary geometric object. We use a point set representation to describe the geometric features of the primary objects and the secondary object, and formulated the alignment of two point sets to one point set to estimate the orientation angles of the primary objects in the secondary object. The estimated angles are used as data to estimate the probability distribution of the orientation angles and test important hypotheses statistically. The proposed approach was applied for our motivating example, which demonstrated that nanoparticles of certain geometries have indeed preferential orientations in their aggregates.