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Relationship between the microstructures and Young’s modulus of 3D-networked porous carbon material

  • Composites & nanocomposites
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Abstract

Herein, we prepared 3D-networked porous carbon materials (TNPCs) (porosity ≈ 70%, average pore size ≈ 10 μm, density ≈ 0.37 g cm–3) composed of glassy carbon via pyrolysis of porous phenolic precursors. A compressive test for TNPCs shows that the Young’s moduli and compressive strength of TNPCs ranged from 0.7 to 1.5 GPa and 11 to 30 MPa, respectively, which increased with increasing pore diameter. Although these moduli could not be accurately predicted using conventional periodic unit cell models, the homogenized Young’s moduli predicted using a 3D image-based model acquired by X-ray computed tomography and focused ion beam scanning electron microscopy were in good agreement with the experimental values. These results indicate that the method can be used to reliably investigate the microstructures and evaluate the Young’s modulus using 3D image-based modeling.

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Acknowledgements

This work was supported by the Nagoya University Microstructural Characterization Platform as part of the "Nanotechnology Platform" of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. We are grateful to Prof. S. Arai and T. Nakao of Nagoya University and H. Miyazaki (Hitachi High Technologies Corp.) for assistance with the FIB-SEM experiments, and we also thank M. Ikezaki (Nippon Rober) for helping us with the image analysis. This work was also supported by the Precise Measurement Technology Promotion Foundation (PMTP-F, K20-041) and Japan Keirin Autorace Foundation (JKA, 2020M-193).

Author information

Authors and Affiliations

  1. Department of Materials Science and Technology, Tokyo University of Science, 6-3-1, Niijyuku, Katsushika-ku, Tokyo, 125-8585, Japan

    Y. Arai, Y. Daigo, E. Kojo & Y. Kogo

  2. Department of Mechanical Engineering, Tokyo University of Science, 6-3-1, Niijyuku, Katsushika-ku, Tokyo, 125-8585, Japan

    R. Inoue

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  1. Y. Arai
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Appendices

Appendix A

Method for separating the carbon and pores in images and homogenization analysis

Figure 

Figure 12
figure 12

a Typical tomographic image of TNPC-3 obtained by X-ray CT. b Binarized image in (a) after masking

Full size image

12a and b shows typical images acquired by X-ray CT. The white and black regions correspond to the carbon and pores, respectively. In the reconstruction of 3D image-based models based on multiple tomographic images, accurate separation of carbon and pores is required. Generally, conventional methods such as the Otsu method can be used to determine the threshold brightness value. However, it is difficult to use this method for TNPCs because the brightness values of the carbon region in the X-ray CT image are not uniform. In the present study, carbon and pores were separated by the three following steps: First, the brightness values of all the tomographic images are adjusted. Second, the carbon regions with lower contrast than other carbon regions (see Fig. 12a) were filled with white using a graphic software. Finally, the binarization of the edited tomographic images was conducted using a constant threshold value (138; see Fig. 12b).

Figure 

Figure 13
figure 13

a Typical SEM image of TNPC-1 after ion milling. b Binarized image of (a) after masking of TNPC-1

Full size image

13a and b shows typical tomographic images obtained by FIB-SEM. The curtain effect, which is a trace shaved by FIB, was observed, and this makes the reconstruction of the 3D image-based models with the exact microstructures of the TNPCs difficult. To obtain a 3D image-based model of TNPC-1 and -2, the position of each tomographic image was aligned with an image analysis software after binarization. Then, the regions showing the curtain effect were filled with white, and the pore regions are filled with black to create the model. The 3D image-based models of the TNPCs were constructed by stacking these edited images.

To calculate the Young’s modulus using 3D image-based models, homogenization analysis was conducted. Figure 

Figure 14
figure 14

Schematic diagram for the procedure of analysis

Full size image

14 shows the schematic diagrams for the analysis. The constraint and loading conditions were set for direct modeling for the conventional finite element method, whereas a unit composed of complex structures was used to constructs a uniform model. The constraint and loading conditions were set to a uniform model for the homogenization analysis. The application of the finite element method for materials with minute and complex structures is possible by homogenization analysis. In particular, uniform models with a size of 50 × 50 × 100 voxel (10 × 10 × 20 mm) that have information on porous structures with 3345601 (TNPC-1), 6792881 (TNPC-2), and 34271453 (TNPC-3) voxels were prepared for calculation. After that, the center of the bottom face was fully constrained and other points on the bottom face were constrained in the z-direction. A compressive load was applied to the top face in the z-direction, which was simulated in the compressive test. The Young’s modulus of the TNPCs calculated from the stress–strain curve obtained by FEM is available.

Appendix B

Procedure for image analysis

The strut length, strut thickness, and joint diameter were measured as shown in Fig. 

Figure 15
figure 15

Flowchart for the microstructural analysis of an image-based model

Full size image

15. A 3D framework with one-voxel-thick struts was obtained by means of a 3D thinning algorithm for 3D binary images. This model contained an unconnected skeleton that was removed by application of a pruning filter. Finally, the joints of all struts were removed using 3D skeleton filters, and the framework was segmented.

Distance mapping was performed using a 3D distance mapping filter, and the boundary–pixel distance was translated into intensity, i.e., the intensity increased toward the strut framework. Multiplication of these two images provided a model containing distance information. The strut length was obtained by calculating the maximum fillet diameter, and the minimum strut thickness was determined by calculating the value of double minimum intensity, as struts were assumed to be cylindrical.

To extract framework joints, a 3D branching filter was applied to the image after pruning. Four or five interconnected pixels were considered as joints. Subsequently, the images were multiplied with the image processed using the distance mapping filter. Joints were assumed to be spherical, and the joint radius was obtained from the maximum joint intensity and joint volume fraction.

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Arai, Y., Daigo, Y., Kojo, E. et al. Relationship between the microstructures and Young’s modulus of 3D-networked porous carbon material. J Mater Sci 56, 10338–10352 (2021). https://doi.org/10.1007/s10853-021-05950-x

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