turkmath.org

In nanotechnology, the size and shape control of nanoparticles is crucial as their properties are highly dependent on their morphology. This obliges researchers to work on obtaining uniform size and shape distribution in synthesized particles so that their electrical, optical, and magnetic properties remain uniform within the same batch. This brings the problem of how to quantify the shape and size of nanoparticles in the most accurate way. The most common way to determine size distribution is using UV-vis spectrometry; however, this method disregards the existence of agglomerated particles and may sometimes give an incorrect measurement. Therefore a technique that can obtain this data directly from the transmission electron microscopy (TEM) images of particles would be more reliable as it would capture data for every single particle in the batch. In a classical statistical sense, our interest is the shape and size distribution of nanoparticles. In this paper, we quantify the size and shape of nanoparticles using the statistical techniques applied on TEM images of particles: Functional Data and Shape Analysis. By using this shape theory we obtain the geodesic distances not only between the particles but also among the frames. We further cluster the nanoparticles in terms of their similarities. We want to emphasize the importance of the deformation and how it is done from one nanoparticle onto another.