June 19, 2019
Journal Article

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

James Evans
David Welch
Chiwoo Park
Roland Faller
Ali Sikaroudi
Taylor Woehl
Nanoscientists have long conjectured that adjacent nanoparticles aggregate with one another in certain preferential directions during chemical syntheses of nanoparticles, which is so called the oriented attachment. For the study of the oriented attachment phenomenon, the microscopy and nanoscience community have used dynamic electron microscopy for direct observations of nanoparticle aggregation and have been so far relying on the manual and qualitative analysis of the observations. In this paper, we present a statistical approach for studying the oriented attachment phenomenon with multiple aggregation examples observed by dynamic microscope data. We abstract a nanoparticle aggregation by an event of two primary geometric objects merging into a secondary geometric object. We define a metric space for geometrical bodies, and the endowed metric in the space allows us to define the likelihood function of the orientation angles of two primary objects within the corresponding secondary object. We maximize the likelihood to estimate the orientation angles. We fit a mixture of bivariate von Mises distributions to the estimated orientation angles for the density estimation. By analyzing the density estimate, we are able to demonstrate that nanoparticles of certain geometries have indeed preferential orientations in their aggregates.

Revised: June 19, 2019 | Published: May 14, 2018

Sikaroudi A.E., D.A. Welch, T.J. Woehl, R. Faller, J.E. Evans, N.D. Browning, and C. Park. 2018. "Directional Statistics of Preferential Orientations of Two Shapes in Their Aggregate and Its Application to Nanoparticle Aggregation." Technometrics 60, no. 3:332-344. PNNL-SA-110076. doi:10.1080/00401706.2017.1366949