Fractal and digital image processing to determine the degree of dispersion of carbon nanotubes

The degree of dispersion is an important parameter to quantitatively study properties of carbon nanotube composites. Among the many methods for studying dispersion, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy are the most commonly used, intuitive, and convincing methods. However, they have the disadvantage of not being quantitative. To overcome this disadvantage, the fractal theory and digital image processing method can be used to provide a quantitative analysis of the morphology and properties of carbon nanotube composites. In this paper, the dispersion degree of carbon nanotubes was investigated using two fractal methods, namely, the box-counting method and the differential box-counting method. On the basis of the results, we propose a new method for the quantitative characterization of the degree of dispersion of carbon nanotubes. This hierarchical grid method can be used as a supplementary method, and can be combined with the fractal calculation method. Thus, the accuracy and effectiveness of the quantitative characterization of the dispersion degree of carbon nanotubes can be improved. (The outer diameter of the carbon nanotubes is about 50 nm; the length of the carbon nanotubes is 10–20 μm.)