Detecting Carbon Nanotube Orientation with Topological Analysis of Scanning Electron Micrographs

Abstract

As the aerospace industry is increasingly demanding stronger, lightweight materials, ultra-strong carbon nanotube (CNT) composites with highly aligned CNT network structures could be the answer. In this work, a novel methodology applying topological data analysis (TDA) to scanning electron microscope (SEM) images was developed to detect CNT orientation. The CNT bundle extensions in certain directions were summarized algebraically and expressed as visible barcodes. The barcodes were then calculated and converted into the total spread function, V(X, θ), from which the alignment fraction and the preferred direction could be determined. For validation purposes, the random CNT sheets were mechanically stretched at various strain ratios ranging from 0 to 40%, and quantitative TDA was conducted based on the SEM images taken at random positions. The results showed high consistency (R2 = 0.972) compared to Herman’s orientation factors derived from polarized Raman spectroscopy and wide-angle X-ray scattering analysis. Additionally, the TDA method presented great robustness with varying SEM acceleration voltages and magnifications, which might alter the scope of alignment detection. With potential applications in nanofiber systems, this study offers a rapid and simple way to quantify CNT alignment, which plays a crucial role in transferring the CNT properties into engineering products.

Multiscale Characterisation of Staple Carbon Fibre-Reinforced Polymers

“…In the literature, a vast number of methods exist that have been explored within the field of fibre-reinforced composite materials, such as fibre orientation [30][31][32], fibre length [33,34], interfibre spacing [35], fibre diameter [36], fibre connectivity [37], fibre curvature [37], fibre volume fraction (FVF) [38], and porosity [39,40]. Each microstructural descriptor is measured using individual approaches by destructive methods, e.g., optical microscopy, including bright-field and polarised light microscopy [41,42] and mechanical testing, such as tensile testing or compression testing [11,21,27]; or non-destructive methods, e.g., X-raybased techniques, such as X-ray diffraction [43], X-ray computed tomography [35,37,[44][45][46][47] and ultrasound computed tomography [48]; ultrasonic testing [49][50][51], nuclear magnetic resonance spectroscopy and Raman spectroscopy [52,53]; image analysis using different algorithms, such as Fourier analysis [54], gradient-based methods, and structure tensor methods. Destructive testing provides precise measurements but destroys the sample, while non-destructive testing preserves sample integrity and allows for in situ applications but may offer less detailed information and require specialized equipment.…”

Inverse projection of axisymmetric orientation distributions

“…Fibre orientation can also be studied by direct three-dimensional imaging techniques such as computed tomography [24]. However, it is more common to employ image analysis methods based on optical or scanning electron micrograph (SEM) images using the Fourier transform [25][26][27][28], the Hough transform [29,30], direct fibre tracking [27,31] or topological data analysis [32] as a fast and facile alternative to a full three-dimensional analysis.…”

“…In both cases, using the three-dimensional order parameters to quantify alignment is inappropriate as the ODF is not truly threedimensional. Incorrectly treating the two-dimensional ODF as a three-dimensional one and using it to calculate three-dimensional order parameters will lead to values which deviate from other experimental techniques such as XRD [20,32]. Rather, the ODF should be treated as two-dimensional and mean values of the Chebyshev polynomials T m should be used as order parameters instead [25,28,35].…”