Location and Dispersion Analysis

Material scientists have discovered that certain properties of a composite, for instance, the strength, conductivity or transparency, can be remarkably enhanced by blending nanoparticles into the host materials. The resulting improvement in material properties is believed to depend, to a large degree, on how uniformly nanoparticles are mixed into the host materials. This calls for data science methods to quantify the homogeneity of nanoparticles mixing state, also referred to the location and dispersion analysis of nanoparticles in a host material. This chapter covers two methods of quantifying the mixing state: the count-based approaches such as the quadrat method and the distance-based approaches such as Ripley’s K function. Aware that the real materials are 3D while the current nano images are mostly 2D, the last section of the chapter is dedicated to the discussion on the 2D-to-3D inference. We want to note that the importance of material mixing applies not only to nanoparticle-embedded materials but also to other types of material mixing involving a host and additive or reinforcing agents, endowing the methods discussed in this chapter with broader impacts beyond nanomaterials.