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

• Published in: Materials characterization 2020-02, Vol.160, p.110086, Article 110086
• Main Authors: Pander, Adam, Onishi, Takatsugu, Hatta, Akimitsu, Furuta, Hiroshi
• Format: Article
• Language: English
• Subjects: Carbon nanotube; Catalyst particles; Fractal dimension; Lacunarity; Ostwald ripening; Raman mapping
• ISSN: 1044-5803; 1873-4189
• DOI: 10.1016/j.matchar.2019.110086

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 (Df) and lacunarity (Λ) were calculated, using a box-counting method. During the fractality analysis of catalyst particles, the highest Df was obtained for the 0.8-nm-thick film (Df = 1.91), while the lowest one was noted for the Fe catalyst thickness of 1.2 nm (Df = 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 Df changes, which was observed in the planar and linear analysis of the distribution of CNTs and in the IG/ID 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. [Display omitted] •High self-similarity of physical properties of self-organized CNT forest is proved.•Thin catalyst for uniform CNT growth has high fractal dimension and low lacunarity.•Scaling law was observed for fractal analysis for particles, CNTs, and Raman maps.•Dewetting is critical for catalyst formation from thinner films.•Ostwald ripening is more important for catalyst formation from thicker films.