Quantifying Nanoparticle Dispersion by Using The Area Disorder of Delaunay Triangulation

Abstract

Summary.Characterising dispersion quality of nanocomposites presents a challenging statistical problem for which no direct method has been fully adopted. A high precision, statistically well grounded measure is required suitable for dealing with a single non-stationary particle pattern obtained from the material. Our approach uses the Delaunay Network of particles to measure the Area Disorder, AD Del , which can be further used to categorised a material sample into well or poorly dispersed. AD Del analysis is applied to several micrographs of nanoparticle-modified materials and found to reliably classify the type of dispersion. Select spatial point processes are employed to estimate expected imprecision in observed measurements.

Direct formation of gold nanorods on surfaces using polymer-immobilised gold seeds

“…3. Delaunay triangulation was used for calculating the nearest neighbour distance of the nanoparticles [39]. The average distance between nanoparticles in the P1-20 sample is 800 nm while for P2-20 and P1-60 nanocomposite it is 500 nm with a wide distribution (±500 nm).…”

Tunable and label-free virus enrichment for ultrasensitive virus detection using carbon nanotube arrays

“…The average particle-to-particle distance was calculated by applying the Delaunay triangle selection to determine the closest neighbor particles, then represented as the mean of the three edges r 1 , r 2 , and r 3 (fig. S16) ( 63 ).…”

Quantifying nanoparticle dispersion: application of the Delaunay network for objective analysis of sample micrographs

“…Hence we would disregard these findings as suspect because the simple arguments used for defining the RHM become invalid for small N . The actual value for µ R (A f = 0) becomes strongly dependent on N and approaches 0 with decreasing particle number [21].…”

“…A detailed mathematical description has been provided in concurrent work [20,21]. This paper considers how it may be applied in a materials science context.…”