Quantifying Nanoparticle Mixing State to Account for Both Location and Size Effects
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2017 American Statistical Association and the American Society for Quality. Ripleys K function is commonly used to characterize the homogeneity of spatial point distribution. Not surprisingly, it becomes a favored tool in quantifying the nanoparticles mixing state in composite materials, a parameter that material scientists believe is of close relevance to certain properties of the nanoparticle-embedding material. Ripleys K function assumes that the spatial points are dimensionless. In reality, the nanoparticles, once mixed in a host material, form clusters or agglomerates of various sizes and shapes. Our analysis shows that using the original K function falls short of ranking or distinguishing the homogeneity of nanoparticle mixing. We therefore propose to revise the K function to account for both particle location and size effects. We apply the revised function to electron microscopy images of material samples and conduct analysis and comparison of nanoparticle mixing. The analysis shows that the revised function is a better index to quantify the mixing states.