Accurate measurement of pitch-based carbon fiber electrical resistivity

Caroline Jovine Bouças Guimarães Alcino Palermo de Aguiar Alexandre Taschetto de Castro About the authors

Abstract

This study investigated the appropriate methodology required to measure single carbon fibers electrical resistivity. Two- and four-probe methods were evaluated for this measurement. Comparing results for single filaments of pitch-based and PAN-based fibers shows that the two-probe method gives acceptable results for PAN-based fibers, but much higher deviations from adjusted resistivity for pitch-based fibers (>15%). The four-probe method shows small deviations (<1%) for both precursors and is the most suitable for measurements of pitch-based carbon fibers. The four-probe method gives higher accuracy than the two-probe for all samples tested.

Keywords:
carbon fiber; four-probe method; mesophase-pitch; electrical resistivity

1. Introduction

Mesophase pitch-based carbon fibers have higher transport properties than most polymers, because of the mesophase pitch's ability to form highly ordered graphite domains[11 Singer, L. S. (1977). US Patent 4,005,183. United States. from https://patents.google.com/patent/ US4005183A/en
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3 Singer, L. S. (1978). The mesophase and high modulus carbon fibers from pitch. Carbon, 16(6), 409-415. http://dx.doi.org/10.1016/0008-6223(78)90085-4.
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4 Bright, A. A., & Singer, L. S. (1979). The electronic and structural characteristics of carbon fibers from mesophase pitch. Carbon, 17(1), 59-69. http://dx.doi.org/10.1016/0008- 6223(79)90071-X.
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5 Singer, L. S. (1981). Carbon fibres from mesophase pitch. Fuel, 60(9), 839-847. http://dx.doi.org/10.1016/0016-2361(81)90147-2.
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6 Matsumoto, T. (1985). Mesophase pitch and its carbon fibers. Pure and Applied Chemistry, 57(11), 1553-1562. http://dx.doi.org/10.1351/pac198557111553.
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-77 Rogers, D. K., Jones, S. P., Fain, C. C., & Edie, D. D. (1993). Graphitization of a high-sulfur mesophase pitch-based fiber. Carbon, 31(2), 303-313. http://dx.doi.org/10.1016/0008- 6223(93)90035-9.
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]. Therefore, they are used as thermal and electrical management materials in applications such as high thermal conductivity radiators[88 Goncharov, K., Panin, Y., Balykin, M., & Khmelnitsky, A. (2016). High thermal conductive carbon fiber radiators with controlled loop heat pipes. In 46th International Conference on Environmental Systems (pp. 10-14). Vienna, Austria: ICES Steering Committee, American Institute of Chemical Engineers - AIChE, American Society of Mechanical Engineers - ASME, ICES International Committee - INT. Retrieved in 2020, September 29, from http://hdl.handle.net/2346/67639
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,99 Yamada, K., Nagano, H., Kobayashi, Y., & Totani, T. (2014). Heat Storage Panel Using a Phase-change Material Encapsulated in a High-thermal conductivity CFRP for Micro Satellites. In 44th International Conference on Environmental Systems (pp. 13– 17). Tucson, Arizona: ICES Steering Committee, ICES International Committee – INT. Retrieved in 2020, September 29, from http://hdl.handle.net/2346/59577
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], electronic packaging[1010 Zweben, C. (1998). Advances in composite materials for thermal management in electronic packaging. Journal of the Minerals, 50(6), 47-51. http://dx.doi.org/10.1007/s11837-998- 0128-6.
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], electromagnetic interference shielding[1111 Lee, J., Liu, Y., Liu, Y., Park, S. J., Park, M., & Kim, H. Y. (2017). Ultrahigh electromagnetic interference shielding performance of lightweight, flexible, and highly conductive copper-clad carbon fiber nonwoven fabrics. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 5(31), 7853-7861. http://dx.doi.org/10.1039/C7TC02074K.
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], heat storage[99 Yamada, K., Nagano, H., Kobayashi, Y., & Totani, T. (2014). Heat Storage Panel Using a Phase-change Material Encapsulated in a High-thermal conductivity CFRP for Micro Satellites. In 44th International Conference on Environmental Systems (pp. 13– 17). Tucson, Arizona: ICES Steering Committee, ICES International Committee – INT. Retrieved in 2020, September 29, from http://hdl.handle.net/2346/59577
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], and radar absorption[1212 Neo, C. P., & Varadan, V. K. (2004). Optimization of carbon fiber composite for microwave absorber. IEEE Transactions on Electromagnetic Compatibility, 46(1), 102-106. http://dx.doi.org/10.1109/TEMC.2004.823618.
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].

Volume resistivity is an important performance indicator for carbon fibers, applied to the evaluation of process parameters along its production steps: spinning[1313 Hamada, T., Nishida, T., Sajiki, Y., Matsumoto, M., & Endo, M. (1987). Structures and physical properties of carbon fibers from coal tar mesophase pitch. Journal of Materials Research, 2(6), 850-857. http://dx.doi.org/10.1557/JMR.1987.0850.
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14 Barnes, A. B., Dauché, F. M., Gallego, N. C., Fain, C. C., & Thies, M. C. (1998). As- spun orientation as an indication of graphitized properties of mesophase-based carbon fiber. Carbon, 36(7-8), 855-860. http://dx.doi.org/10.1016/S0008-6223(97)00166-8.
https://doi.org/10.1016/S0008-6223(97)00...
-1515 Gallego, N. C., & Edie, D. D. (2001). Structure property relationships for high thermal conductivity carbon fibers. Composites. Part A, Applied Science and Manufacturing, 32(8), 1031-1038. http://dx.doi.org/10.1016/S1359-835X(00)00175-5.
https://doi.org/10.1016/S1359-835X(00)00...
], stabilization[1616 Beauharnois, M. E., Edie, D. D., & Thies, M. C. (2001). Carbon fibers from mixtures of AR and supercritically extracted mesophases. Carbon, 39(14), 2101-2111. http://dx.doi.org/10.1016/S0008-6223(01)00045-8.
https://doi.org/10.1016/S0008-6223(01)00...
,1717 Yuan, G., Li, X., Xiong, X., Dong, Z., Westwood, A., Li, B., Ye, C., Ma, G., Cui, Z., Cong, Y., Zhang, J., & Li, Y. (2017). A comprehensive study on the oxidative stabilization of mesophase pitch-based tape-shaped thick fibers with oxygen. Carbon, 115, 59-76. http://dx.doi.org/10.1016/j.carbon.2016.12.040.
https://doi.org/10.1016/j.carbon.2016.12...
], carbonization[1818 Karacan, I., & Meşeli, H. (2018). Characterization of amorphous carbon fibers produced from thermally stabilized polyamide fibers. Journal of Industrial Textiles, 47(6), 1185-1211. http://dx.doi.org/10.1177/1528083716682922.
https://doi.org/10.1177/1528083716682922...
,1919 Shi, K., Yang, J., Li, J., Zhang, X., Wu, W., Liu, H., Yoon, S. H., & Li, X. (2020). Effect of oxygen-introduced pitch precursor on the properties and structure evolution of isotropic pitch-based fibers during carbonization and graphitization. Fuel Processing Technology, 199, 106291. http://dx.doi.org/10.1016/j.fuproc.2019.106291.
https://doi.org/10.1016/j.fuproc.2019.10...
], and graphitization[1919 Shi, K., Yang, J., Li, J., Zhang, X., Wu, W., Liu, H., Yoon, S. H., & Li, X. (2020). Effect of oxygen-introduced pitch precursor on the properties and structure evolution of isotropic pitch-based fibers during carbonization and graphitization. Fuel Processing Technology, 199, 106291. http://dx.doi.org/10.1016/j.fuproc.2019.106291.
https://doi.org/10.1016/j.fuproc.2019.10...

20 Jones, S. P., Fain, C. C., & Edie, D. D. (1997). Structural development in mesophase pitch-based carbon fibers produced from naphthalene. Carbon, 35(10-11), 1533-1543. http://dx.doi.org/10.1016/S0008-6223(97)00106-1.
https://doi.org/10.1016/S0008-6223(97)00...

21 Wu, G.-P., Li, D.-H., Yang, Y., Lu, C.-X., Zhang, S.-C., Li, X.-T., Feng, Z.-H., & Li, Z. H. (2012). Carbon layer structures and thermal conductivity of graphitized carbon fibers. Journal of Materials Science, 47(6), 2882-2890. http://dx.doi.org/10.1007/s10853-011- 6118-z. PMid:25170190.
https://doi.org/10.1007/s10853-011- 6118...
-2222 Qian, X., Zhi, J., Chen, L., Zhong, J., Wang, X., Zhang, Y., & Song, S. (2018). Evolution of microstructure and electrical property in the conversion of high strength carbon fiber to high modulus and ultrahigh modulus carbon fiber. Composites Part A: Applied Science and Manufacturing, 112, 111-118. http://dx.doi.org/10.1016/j.compositesa.2018.05.030.]. It can also be applied in the evaluation of pre and post-processing steps such as intercalation[2323 Gaier, J. R. (1984). Stability of bromine intercalated graphite fibers. Boston: American Physical Society - APS.,2424 Lee, W. D., Davis, G. P., & Vogel, F. L. (1985). Electrical resistivity and magneto resistance of carbon/graphite fibers intercalated with nitric acid and arsenic pentafluoride. Carbon, 23(6), 731-737. http://dx.doi.org/10.1016/0008-6223(85)90235-0.
https://doi.org/10.1016/0008-6223(85)902...
], annealing[2525 Yang, H., Yoon, S. H., Korai, Y., Mochida, I., & Katou, O. (2003). Improving graphitization degree of mesophase pitch-derived carbon fiber by solid-phase annealing of spun fiber. Carbon, 41(3), 397-403. http://dx.doi.org/10.1016/S0008-6223(02)00320- 2.
https://doi.org/10.1016/S0008-6223(02)00...
], and coating[2626 Ryu, S. K., Kim, S. Y., Gallego, N., & Edie, D. D. (1999). Physical properties of silver-containing pitch-based activated carbon fibers. Carbon, 37(10), 1619-1625. http://dx.doi.org/10.1016/S0008-6223(99)00086-X.
https://doi.org/10.1016/S0008-6223(99)00...

27 Tzeng, S. S., & Chang, F. Y. (2001). Electrical resistivity of electroless nickel coated carbon fibers. Thin Solid Films, 388(1-2), 143-149. http://dx.doi.org/10.1016/S0040-6090(01)00809-4.
https://doi.org/10.1016/S0040-6090(01)00...

28 Tzeng, S. S., & Chang, F. Y. (2001). EMI shielding effectiveness of metal-coated carbon fiber-reinforced ABS composites. Materials Science and Engineering A, 302(2), 258-267. http://dx.doi.org/10.1016/S0921-5093(00)01824-4.
https://doi.org/10.1016/S0921-5093(00)01...
-2929 Xing-Wen, J., Xin, Z., Jun-Meng, L., & Ping, W. (2018). Conductivity and conducting stability of copper-coated carbon-fiber-reinforced cement-based composite. Materials Research Express, 5(9), 095705. http://dx.doi.org/10.1088/2053-1591/aad98b.
https://doi.org/10.1088/2053-1591/aad98b...
]. Hence, many researchers use single fiber methods to find the correlation between electrical resistivity and other physical properties[3030 Lavin, J. G., Boyington, D. R., & Lahijani, J. (1993). The correlation of thermal conductivity with electrical resistivity in mesophase pitch-based carbon fiber. Carbon, 31(6), 1001-1002. http://dx.doi.org/10.1016/0008-6223(93)90207-Q.
https://doi.org/10.1016/0008-6223(93)902...

31 Zhang, X., Fujiwara, S., & Fujii, M. (2000). Measurements of thermal conductivity and electrical conductivity of a single carbon fiber. International Journal of Thermophysics, 21(4), 965-980. http://dx.doi.org/10.1023/A:1006674510648.
https://doi.org/10.1023/A:1006674510648...
-3232 Ouyang, Q., Liu, D., Jiang, X., Ma, H., Chen, Y., & He, L. (2018). Quantitative structure–property relationships of polyacrylonitrile-based graphite fibers revealed by laser confocal Raman spectroscopy. Spectroscopy Letters, 51(2), 89-95. http://dx.doi.org/10.1080/00387010.2018.1425304.
https://doi.org/10.1080/00387010.2018.14...
].

First proposed by Wenner[3333 Wenner, F. (1915). A method of measuring earth resistivity. National Bureau of Standards, US Government Printing Office. 12, 478-496.] in 1915, and adjusted for small, fragile compounds by Coleman[3434 Coleman, L. B. (1975). Technique for conductivity measurements on single crystals of organic materials. The Review of Scientific Instruments, 46(8), 1125-1126. http://dx.doi.org/10.1063/ 1.1134370.
https://doi.org/10.1063/ 1.1134370...
] in 1975, the four-probe method is commonly used by carbon fiber researchers[1414 Barnes, A. B., Dauché, F. M., Gallego, N. C., Fain, C. C., & Thies, M. C. (1998). As- spun orientation as an indication of graphitized properties of mesophase-based carbon fiber. Carbon, 36(7-8), 855-860. http://dx.doi.org/10.1016/S0008-6223(97)00166-8.
https://doi.org/10.1016/S0008-6223(97)00...

15 Gallego, N. C., & Edie, D. D. (2001). Structure property relationships for high thermal conductivity carbon fibers. Composites. Part A, Applied Science and Manufacturing, 32(8), 1031-1038. http://dx.doi.org/10.1016/S1359-835X(00)00175-5.
https://doi.org/10.1016/S1359-835X(00)00...

16 Beauharnois, M. E., Edie, D. D., & Thies, M. C. (2001). Carbon fibers from mixtures of AR and supercritically extracted mesophases. Carbon, 39(14), 2101-2111. http://dx.doi.org/10.1016/S0008-6223(01)00045-8.
https://doi.org/10.1016/S0008-6223(01)00...

17 Yuan, G., Li, X., Xiong, X., Dong, Z., Westwood, A., Li, B., Ye, C., Ma, G., Cui, Z., Cong, Y., Zhang, J., & Li, Y. (2017). A comprehensive study on the oxidative stabilization of mesophase pitch-based tape-shaped thick fibers with oxygen. Carbon, 115, 59-76. http://dx.doi.org/10.1016/j.carbon.2016.12.040.
https://doi.org/10.1016/j.carbon.2016.12...

18 Karacan, I., & Meşeli, H. (2018). Characterization of amorphous carbon fibers produced from thermally stabilized polyamide fibers. Journal of Industrial Textiles, 47(6), 1185-1211. http://dx.doi.org/10.1177/1528083716682922.
https://doi.org/10.1177/1528083716682922...

19 Shi, K., Yang, J., Li, J., Zhang, X., Wu, W., Liu, H., Yoon, S. H., & Li, X. (2020). Effect of oxygen-introduced pitch precursor on the properties and structure evolution of isotropic pitch-based fibers during carbonization and graphitization. Fuel Processing Technology, 199, 106291. http://dx.doi.org/10.1016/j.fuproc.2019.106291.
https://doi.org/10.1016/j.fuproc.2019.10...
-2020 Jones, S. P., Fain, C. C., & Edie, D. D. (1997). Structural development in mesophase pitch-based carbon fibers produced from naphthalene. Carbon, 35(10-11), 1533-1543. http://dx.doi.org/10.1016/S0008-6223(97)00106-1.
https://doi.org/10.1016/S0008-6223(97)00...
,2323 Gaier, J. R. (1984). Stability of bromine intercalated graphite fibers. Boston: American Physical Society - APS.

24 Lee, W. D., Davis, G. P., & Vogel, F. L. (1985). Electrical resistivity and magneto resistance of carbon/graphite fibers intercalated with nitric acid and arsenic pentafluoride. Carbon, 23(6), 731-737. http://dx.doi.org/10.1016/0008-6223(85)90235-0.
https://doi.org/10.1016/0008-6223(85)902...

25 Yang, H., Yoon, S. H., Korai, Y., Mochida, I., & Katou, O. (2003). Improving graphitization degree of mesophase pitch-derived carbon fiber by solid-phase annealing of spun fiber. Carbon, 41(3), 397-403. http://dx.doi.org/10.1016/S0008-6223(02)00320- 2.
https://doi.org/10.1016/S0008-6223(02)00...

26 Ryu, S. K., Kim, S. Y., Gallego, N., & Edie, D. D. (1999). Physical properties of silver-containing pitch-based activated carbon fibers. Carbon, 37(10), 1619-1625. http://dx.doi.org/10.1016/S0008-6223(99)00086-X.
https://doi.org/10.1016/S0008-6223(99)00...

27 Tzeng, S. S., & Chang, F. Y. (2001). Electrical resistivity of electroless nickel coated carbon fibers. Thin Solid Films, 388(1-2), 143-149. http://dx.doi.org/10.1016/S0040-6090(01)00809-4.
https://doi.org/10.1016/S0040-6090(01)00...
-2828 Tzeng, S. S., & Chang, F. Y. (2001). EMI shielding effectiveness of metal-coated carbon fiber-reinforced ABS composites. Materials Science and Engineering A, 302(2), 258-267. http://dx.doi.org/10.1016/S0921-5093(00)01824-4.
https://doi.org/10.1016/S0921-5093(00)01...
]. However, the carbon fiber resistivity international standard method, ISO 13913, specifies a two-probe measurement[3535 International Organization for Standardization – ISO. Carbon fibre — Determination of volume resistivity ISO 13931. (2013). Switzerland: ISO.], and many authors use which[3636 Owston, C. N. (1970). Electrical properties of single carbon fibres. Journal of Physics. D, Applied Physics, 3(11), 1615-1626. http://dx.doi.org/10.1088/0022-3727/3/11/309.
https://doi.org/10.1088/0022-3727/3/11/3...

37 Sundaray, B., Subramanian, V., & Natarajan, T. S. (2005). Electrical Properties of Electrospun Poly(Ethylene Oxide) - Polypyrrole Composite Fibers. MRS Online Proceedings Library, 889, 308. http://dx.doi.org/10.1557/PROC-0889-W03-08.
https://doi.org/10.1557/PROC-0889-W03-08...

38 Castellanos-Gomez, A. (2013). A simple method to characterize the electrical and mechanical properties of micro-fibers. European Journal of Physics, 34(6), 1547-1554. http://dx.doi.org/10.1088/0143-0807/34/6/1547.
https://doi.org/10.1088/0143-0807/34/6/1...

39 Gant, P., Niu, Y., Svatek, S. A., Agraït, N., Munuera, C., García-Hernández, M., Frisenda, R., de Lara, D. P., & Castellanos-Gomez, A. (2017). Lithography-free electrical transport measurements on 2D materials by direct microprobing. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 5(43), 11252-11258. http://dx.doi.org/10.1039/C7TC01203A.
https://doi.org/10.1039/C7TC01203A...

40 Niu, Y., Frisenda, R., Svatek, S. A., Orfila, G., Gallego, F., Gant, P., Agraït, N., Leon, C., Rivera-Calzada, A., De Lara, D. P., Santamaria, J., & Castellanos-Gomez, A. (2017). Photodiodes based in La0.7Sr0.3MnO3/single layer MoS2 hybrid vertical heterostructures. 2D Materials, 4(3), 034002. http://dx.doi.org/10.1088/2053-1583/aa797b
https://doi.org/10.1088/2053-1583/aa797b...

41 Yanhong, T., Weizhe, H., & Xuejun, Z. (2017). Comparison of methods for the measurement of the resitivity of carbon fibers. Journal of Beijing University of Chemical Technology, 44, 34-37.
-4242 Mizuno, Y., Shindo, Y., Kawakita, K., Kusashi, Y., Ohsawa, Y., Satou, H., Akama, H., & Horie, H. (2018). US Patent 2018/0,090,762. United States. from https://patents. justia.com/patent/20180090762
https://patents. ...
].

Despite being a simple alternative[4343 Rebouillat, S., & Lyons, M. E. G. (2011). Measuring the electrical conductivity of single fibres. International Journal of Electrochemical Science, 6(11), 5731-5740.], the two-probe method may be sensitive to contact and lead resistances[4444 Miccoli, I., Edler, F., Pfnür, H., & Tegenkamp, C. (2015). The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems. Journal of Physics Condensed Matter, 27(22), 223201. http://dx.doi.org/10.1088/0953-8984/27/22/223201. PMid:25985184.
https://doi.org/10.1088/0953-8984/27/22/...
] (Figure 1). Some authors recommend this method only when resistance values are high[4545 Yanhong, T., Weizhe, H., & Xuejun, Z. (2017). Research on measuring method of volume resistivity of carbon fiber bundle. Journal of Beijing University of Chemical Technology, 44(1), 34-37. http://dx.doi.org/10.1016/j.compositesa.2014.10.015.
https://doi.org/10.1016/j.compositesa.20...
] or when accuracy is not required, as it has a known systematic bias (20–800 Ω)[3838 Castellanos-Gomez, A. (2013). A simple method to characterize the electrical and mechanical properties of micro-fibers. European Journal of Physics, 34(6), 1547-1554. http://dx.doi.org/10.1088/0143-0807/34/6/1547.
https://doi.org/10.1088/0143-0807/34/6/1...

39 Gant, P., Niu, Y., Svatek, S. A., Agraït, N., Munuera, C., García-Hernández, M., Frisenda, R., de Lara, D. P., & Castellanos-Gomez, A. (2017). Lithography-free electrical transport measurements on 2D materials by direct microprobing. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 5(43), 11252-11258. http://dx.doi.org/10.1039/C7TC01203A.
https://doi.org/10.1039/C7TC01203A...

40 Niu, Y., Frisenda, R., Svatek, S. A., Orfila, G., Gallego, F., Gant, P., Agraït, N., Leon, C., Rivera-Calzada, A., De Lara, D. P., Santamaria, J., & Castellanos-Gomez, A. (2017). Photodiodes based in La0.7Sr0.3MnO3/single layer MoS2 hybrid vertical heterostructures. 2D Materials, 4(3), 034002. http://dx.doi.org/10.1088/2053-1583/aa797b
https://doi.org/10.1088/2053-1583/aa797b...
-4141 Yanhong, T., Weizhe, H., & Xuejun, Z. (2017). Comparison of methods for the measurement of the resitivity of carbon fibers. Journal of Beijing University of Chemical Technology, 44, 34-37.]. Thus, this information suggests the reference standard single carbon-fiber resistivity test method has some limitations, and it could be inadequate for carbon fibers' electrical resistivity measurements with highly ordered graphite domains such as mesophase pitch-based carbon fibers.

Figure 1
Two-probe method equivalent circuit representation.

To investigate whether the two methods used in literature are suitable, applied the two- and four-probe to measuring PAN- and pitch-based carbon fibers’ electrical resistivity and testing the effect of contact resistance through the linear fitting sample resistances for different gauge lengths. The results were compared with the datasheet values and literature reports.

2. Materials and Methods

Standard and high-modulus grades of PAN- and pitch-based carbon fibers were selected (Table 1). For each sample, electrical resistivity measurements for ten single filaments, obtained at room temperature by the two- and four-point methods, were averaged and compared to the manufacturer datasheet values.

Table 1
Electrical resistivity (ρ0), Young Modulus (E), and diameter (D) of commercial fibers specification[4646 SOLVAY. P-25 Technical Data Sheet. (2020). Retrieved in 2020, September 29, from www.cytec.com
www.cytec.com...

47 TORAY. T300 Technical Data Sheet Rev 6: Updated April 13, 2018. Retrieved in 2020, September 29, from www.toraycma.com
www.toraycma.com...

48 TORAY. M46J Technical Data Sheet Rev. 1: Updated April 13, 2018. Retrieved in 2020, September 29, from www.toraycma.com
www.toraycma.com...
-4949 SOLVAY. K1100 Technical Data Sheet. Retrieved in 2020, September 29, from www.cytec.com
www.cytec.com...
].

Individual filaments were straightened and glued to the specific mounting tab of each method. The two-probe mounting template is a 0.3 mm thickness cardboard, with a 25 mm hole cut out. The four-probe arrangement is a printed circuit board with four parallel copper conduction paths, with the two inner trails separated by 25 mm and the two outer trails by 35 mm. Each carbon monofilament lay on the standard support following a centerline of the mounting template, fixed with a conductive adhesive (Figure 2).

Figure 2
Two and four-probe mounting tab for single filament.

A Mitutoyo CD-6” AX-B digital caliper was used to measure the distances between the two inner points (L) at which the fiber no longer touches the conductive adhesive. An Olympus BX41 confocal microscope was used to measure the diameter (D) at three distinct points along the filament length at 1000x magnification. In the two-probe method, a Fluke 87 V digital multimeter the electrical resistance (R) of individual filaments. Meanwhile, in the four-probe method, the external contacts were connected through a Keithley's 6221 DC source, and the internal contacts connected through a Keithley's 2182A high impedance nano voltmeter connected the others. Thermal voltage's effects were eliminated by reversing the polarity and averaging the two values[5050 Cigoy, D. (2010). Accurate low-resistance measurements start with identifying sources of error. Cleveland, Ohio: Keithley Instruments, Inc. Retrieved in 2020, September 29, from https://download.tek.com/document/LLResistWhitePaper.pdf
https://download.tek.com/document/LLResi...
]. Electrical resistance was obtained according to Equation 1.

ρ = π D 2 4 L R (1)

The resistance of each sample was also measured by both methods, at different lengths in the 2–15 mm range (Figure 3) to estimate the contact resistance (Rc) and the adjusted resistivity value (ρa). These parameters can be obtained by linearly fitting the resistance (R*) of different gauge lengths (L*), according to Equation 2, assuming that the cross-sectional carbon fiber area (A) and the contact resistance are constant. The adjusted electrical resistivity values were compared to the averages electrical resistivity at the fixed 25 mm distance.

Figure 3
Mounting tab with different gauge length sample for two and four-probe method.
R * = ρ a L * A + R c (2)

3. Results and Discussions

Table 2 shows the average electrical resistivity (ρ¯i) and relative deviation (Di) from the manufacturers' values (ρ0) of each carbon fiber for both tested methods. For the two-probe method, the electrical resistivity relative deviations of the PAN-based fibers are less than 4%, while the pitch-based deviations exceed 10%. In contrast, all relative deviations for the four-probe method are less than 2%. Besides that, at 95% confidence interval Student's t-test[5151 Montgomery, D. (2019). Introduction to Statistical Quality Control. Arizona, USA: John Wiley & Sons.] results in no statistically significant difference between the manufacturers' values (ρ0) and the four-probe method electrical resistivity (ρ¯IV) (Table 2), since t-values (tIV) modulus are less than the critical t-value (tcrit = 2.26[5151 Montgomery, D. (2019). Introduction to Statistical Quality Control. Arizona, USA: John Wiley & Sons.]). On the other hand, the two-probe showed a significant difference between these values for K-1100 and P-25 fiber since the t-values modulus is higher than the t-critical. These results suggest that pitch-based carbon fiber manufacturers do not follow the single filament method proposed by ISO 13913 international standards.

Table 2
Average electrical resistivity (ρ¯i), manufacturers declared value (ρ0), standard deviation (σi), relative deviation (RDi) from manufacturers provided value, t and F values.

The four-probe standard deviations are smaller than the two-probe for all samples (Table 2). Besides, the former, by statistical F-test[5151 Montgomery, D. (2019). Introduction to Statistical Quality Control. Arizona, USA: John Wiley & Sons.], provide better precision at 95% confidence level, since all samples F-value (Table 2) are superior to the critical F-value (Fcrit = 3.31[5151 Montgomery, D. (2019). Introduction to Statistical Quality Control. Arizona, USA: John Wiley & Sons.]). These results suggest that the four-probe is more accurate than the two-probe method.

Table 3 shows each carbon fiber's literature data electrical resistivity (ρL). Comparing these to two- and four-probe the electrical resistivity (ρIIandρIV) by Student's t-test concludes that is no statistically significant difference in a 95% confidence interval (Table 3) since the t-values (tIV) modulus are less than the critical t-value for all sample. On the other hand, there is a significant difference between literature data and two-probe electrical resistivity values for K-1100 fiber since t-values modulus is higher than the t-critical. This result indicates that the two-probe may not be a suitable method to estimate the pitch-based carbon fibers' electrical properties.

Table 3
Literature data (ρL), standard deviation (σi), and t values for two- and four- probe results.

Figure 4 shows the correlations between measured electrical resistance and gauge length, fitted by a straight line, for both methods. Contact resistance is given by the vertical axis intercept, and electrical resistivity by the line slope (Table 4). All correlation coefficients (R2) were higher than 0.999, representing a good fit.

Figure 4
Commercial carbon fibers fit of (a) two-probe and (b) four-probe methods.
Table 4
Contact resistance (Rc), adjusted electrical resistivity (ρa), and coefficient of determination (R2)

Contact resistances varied from about 20 – 220 Ω, with the highest values from PAN-based carbon fibers. For these fibers, there was no significant difference between two and four probes contact resistance. However, for pitch-based carbon fibers, the contact resistance obtained by the two-probe method is significantly higher than by the four-probe method. These results confirm the higher accuracy of the four-probe method[4444 Miccoli, I., Edler, F., Pfnür, H., & Tegenkamp, C. (2015). The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems. Journal of Physics Condensed Matter, 27(22), 223201. http://dx.doi.org/10.1088/0953-8984/27/22/223201. PMid:25985184.
https://doi.org/10.1088/0953-8984/27/22/...
].

For all samples, the adjusted electrical resistivity obtained by the two and four-probe methods were identical. Comparison of average values for the adjusted electrical resistivity (ρa) and the electrical resistivity (ρ¯i) obtained by the four-probe method, by Student's t-test[5151 Montgomery, D. (2019). Introduction to Statistical Quality Control. Arizona, USA: John Wiley & Sons.] show no statistically significant difference in a 95% confidence interval. For the two-probe method, on the other hand, there is a significant difference between these values for K-1100 and P-25 fibers, which are both pitch-based.

Besides having low resistivity, the P-25 and K-1100 fibers' electrical resistances are the lowest because they have the largest diameter (Table 1), so its values are more affected by contact resistance (Table 5). The lowest electrical resistance fiber, K-1100, presented the highest relative deviation from adjusted resistivity, while the highest electrical resistance fiber, M46J, presented the smallest difference. This effect is more prominent in two-probe measurements, which is the method that has higher contact resistances.

Table 5
Average electrical resistance (R¯), relatives deviation (RD) from adjusted resistivity, and relative standard deviation (RSD).

The coefficient of variation (Table 5), variability estimator, from pitch-based carbon fibers is higher than PAN-based; this occurs because pitch-based fibers tend to be more heterogeneous than PAN-based[5656 Huson, M. G., Church, J. S., Kafi, A. A., Woodhead, A. L., Khoo, J., Kiran, M. S. R. N., Bradby, J. E., & Fox, B. L. (2014). Heterogeneity of carbon fibre. Carbon, 68, 240-249. http://dx.doi.org/10.1016/j.carbon.2013.10.084.
https://doi.org/10.1016/j.carbon.2013.10...
], which intensifies measurement noise.

4. Conclusions

The two-probe method specified by ISO resulted in up to 2% relative deviation from adjusted resistivity for PAN-based fibers and over 15% deviation for pitch-based fibers. On the other hand, the four-probe method achieved less than 1% relative deviation from adjusted resistivity for all tested fibers, producing accurate and consistent results, even when measuring low resistances.

We conclude that the two-probe method is particularly inadequate for determining pitch-based carbon fiber's electrical resistivity due to its inability to measure low electrical resistances accurately. For PAN-based fibers, the two-probe method gives acceptable results, but with lower accuracy than the four-probe method unless its values are corrected by linear fitting of the resistance of different gauge lengths.

5. Acknowledgements

We thank the Brazilian Army Technological Center (Centro Tecnológico do Exército - CTEx) for supporting this work.

  • How to cite: Guimarães, C. J. B., Aguiar, A. P., & Castro, A. T. (2021). Accurate measurement of pitch-based carbon fiber electrical resistivity. Polímeros: Ciência e Tecnologia, 31(1), e2021011. https://doi.org/10.1590/0104-1428.08720

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Publication Dates

  • Publication in this collection
    28 May 2021
  • Date of issue
    2021

History

  • Received
    29 Sept 2020
  • Reviewed
    26 Feb 2021
  • Accepted
    21 Mar 2021
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