Directional Statistics of Preferential Orientations of Two Shapes in Their Aggregate and Its Application to Nanoparticle Aggregation

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.

KEYWORDS:

• Orientation of shapes
• Point-set-based shape representation
• Shape alignment
• Statistical analysis of circular data

Acknowledgments

The authors acknowledge support through the Laboratory Directed Research and Development (LDRD) Program Chemical Imaging Initiative at Pacific Northwest National Laboratory (PNNL) as performed in the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research at PNNL. PNNL is a multiprogram national laboratory operated by Battelle for the U.S. Department of Energy (DOE) under Contract DE-AC05-76RL01830. This work is also supported by the National Science Foundation under NSF-1334012, the Air Force Office of Scientific Research under FA9550-13-1-0075 and FA9550-16-1-0110, and FSU COFRS 039921.