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

Measuring quantitatively the nanoparticle dispersion of a composite material requires more than choosing a particular parameter and determining its correspondence to good and bad dispersion. It additionally requires anticipation of the measure's behaviour towards imperfect experimental data, such as that which can be obtained from a limited number of samples. It should be recognised that different samples from a common parent population can give statistically different responses due to sample variation alone and a measure of the likelihood of this occurring allows a decision on the dispersion to be made. It is also important to factor into the analysis the quality of the data in the micrograph with it: (a) being incomplete because some of the particles present in the micrograph are indistinguishable or go unseen; (b) including additional responses which are false. With the use of our preferred method, this article investigates the effects on the measured dispersion quality of nanoparticles of the micrograph's magnification settings, the role of the fraction of nanoparticles visible and the number of micrographs used. It is demonstrated that the best choice of magnification, which gives the clearest indication of dispersion type, is dependent on the type of nanoparticle structure present. Furthermore, it is found that the measured dispersion can be modified by particle loss, through the limitations of micrograph construction, and material/microscope imperfections such as cut marks and optical aberrations which could lead to the wrong conclusions being drawn. The article finishes by showing the versatility of the dispersion measure by characterising various different spatial features.