Study of self-organized structure in carbon nanotube forest by fractal dimension and lacunarity analysis

In this work, a fractal analysis of a morphology of carbon nanotube (CNT) forest was conducted. A self-similarity between the formation of catalyst nanoparticles, low and high-density CNT forest growth, and Raman mapping was investigated, for a catalyst thickness of 0.8, 1.0, and 1.2 nm. To explain reasons behind fluctuations of the CNT forest structure, a fractal dimension (D-f) and lacunarity (Lambda) were calculated, using a box-counting method. During the fractality analysis of catalyst particles, the highest D-f was obtained for the 0.8-nm-thick film (D-f = 1.91), while the lowest one was noted for the Fe catalyst thickness of 1.2 nm (D-f = 1.72). The progressive increase of the catalyst thickness affected the dewetting, Ostwald ripening and diffusion processes, affecting the catalyst size distribution and arrangement. The same thickness variation led to a similar decreasing trend of D-f changes, which was observed in the planar and linear analysis of the distribution of CNTs and in the I-G/I-D ratio distribution in Raman mapping, confirming the complexity and the self-organizing properties of CNT forest. The self-similarity and scaling of properties of self-organized CNT forest structure were proved by the analysis of fractal dimension and lacunarity analysis and revealed different stages of the catalyst annealing.