Multiscale Tomographic Analysis for Micron-Sized Particulate Samples.

The three-dimensional characterization of distributed particle properties in the micro- and nanometer range is essential to describe and understand highly specific separation processes in terms of selectivity and yield. Both performance measures play a decisive role in the development and improvement of modern functional materials. In this study, we mixed spherical glass particles (0.4–5.8 μm diameter) with glass fibers (diameter 10 μm, length 18–660 μm) to investigate a borderline case of maximum difference in the aspect ratio and a significant difference in the characteristic length to characterize the system over several size scales. We immobilized the particles within a wax matrix and created sample volumes suitable for computed tomographic (CT) measurements at two different magnification scales (X-ray micro- and nano-CT). Fiber diameter and length could be described well on the basis of the low-resolution micro-CT measurements on the entire sample volume. In contrast, the spherical particle system could only be described with sufficient accuracy by combining micro-CT with high-resolution nano-CT measurements on subvolumes of reduced sample size. We modeled the joint (bivariate) distribution of fiber length and diameter with a parametric copula as a basic example, which is equally suitable for more complex distributions of irregularly shaped particles. This enables us to capture the multidimensional correlation structure of particle systems with statistically representative quantities.