Numerical characterization method for dispersion state of carbon nanotube based on fractal dimension

A numerical characterization method for the dispersion states of carbon nanotubes based on fractal dimension, comprising:

• (1) adopting different dispersion conditions to disperse carbon nanotubes for obtaining various dispersion states of carbon nanotubes, and diluting the dispersion liquids to obtain the sample solutions;
• (2) putting the certain amount of the diluted sample solution on a clean silicon wafer, and using a scanning electron microscope to image the dispersion states of the carbon nanotubes on the silicon wafer after the solvent is completely volatilized;
• (3) performing a black and white binary process on the image obtained by the scanning electron microscope, and extracting the boundary of individual carbon nanotubes or carbon nanotube agglomerates in the image;
• (4) obtaining a series of corresponding numbers of boxes Ni, by constantly varying the side size δi of boxes covering the boundary of carbon nanotube in the image, and thereby calculating the fractal dimension of the processed image by box-count algorithm to achieve the quantitative characterization of the dispersion state of the carbon nanotubes, wherein the equation of the box-count algorithm is:
• D
• =
• Lim
• i
• →
• ∞
• ⁢
• ln
• ⁢
• ⁢
• N
• i
• ln
• ⁢
• ⁢
• δ
• i
• ⁢
• wherein δi is the side size of a box, Ni, is the total number of boxes with the side size of δi covering a region occupied by the boundary of individual carbon nanotubes or carbon nanotubes agglomerates in the processed image, and D is the fractal dimension.