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Percolation Threshold of the Thermal, Electrical and Optical Properties of Carbonyl-Iron Microcomposites

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Abstract

Composites made up of microparticles embedded in a polymeric matrix have attracted increasing attention due to the possibility of tailoring their physical properties by adding the adequate quantity of fillers. As the concentration of these fillers increases, their connectivity changes drastically at a given threshold and therefore the electrical, thermal and optical properties of these composites are expected to exhibit a percolation effect. In this work, the thermal and electrical conductivities along with the emissivity of composites composed of carbonyl-iron microparticles randomly distributed in a polyester resin matrix are measured, for volume fractions ranging from 0 to 0.55. It is shown that both the thermal and electrical conductivities increase with the particles’ concentration, such that their percolation threshold appears at volume fractions of 0.46 and 0.38, respectively. The emissivity, on the other hand, decreases as the fillers’ concentration increases, such that it exhibits a substantial decay at a volume fraction of 0.41. The percolation threshold of the emissivity is thus higher than that of the thermal conductivity, but lower than the electrical conductivity one. This dispersion on the percolation concentration is justified by the different physical mechanisms required to activate the electrical, thermal, and optical responses of the considered composites. The obtained results thus show that the percolation phenomenon can efficiently be used to enhance or reduce the physical properties of particulate composites.

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References

  1. Zweben, C.: Advances in composite materials for thermal management in electronic packaging. JOM. 50, 47–51 (1998). https://doi.org/10.1007/s11837-998-0128-6

    Article  CAS  Google Scholar 

  2. Kim, J., Yim, B.S., Kim, J.M., Kim, J.: The effects of functionalized graphene nanosheets on the thermal and mechanical properties of epoxy composites for anisotropic conductive adhesives (ACAs). Microelectron. Reliab. 52, 595–602 (2012). https://doi.org/10.1016/j.microrel.2011.11.002

    Article  CAS  Google Scholar 

  3. Li, C., Liang, T., Lu, W., Tang, C., Hu, X., Cao, M., Liang, J.: Improving the antistatic ability of polypropylene fibers by inner antistatic agent filled with carbon nanotubes. Compos. Sci. Technol. 64, 2089–2096 (2004). https://doi.org/10.1016/j.compscitech.2004.03.010

    Article  CAS  Google Scholar 

  4. Zhang, X., Ma, Y., Zhao, C., Yang, W.: High dielectric constant and low dielectric loss hybrid nanocomposites fabricated with ferroelectric polymer matrix and BaTiO 3 nanofibers modified with perfluoroalkylsilane. Appl. Surf. Sci. 305, 531–538 (2014). https://doi.org/10.1016/j.apsusc.2014.03.131

    Article  CAS  Google Scholar 

  5. Wang, Y., Hou, Y., Deng, Y.: Effects of interfaces between adjacent layers on breakdown strength and energy density in sandwich-structured polymer composites. Compos. Sci. Technol. 145, 71–77 (2017). https://doi.org/10.1016/j.compscitech.2017.04.003

    Article  CAS  Google Scholar 

  6. Huang, H., Liu, C.H., Wu, Y., Fan, S.: Aligned carbon nanotube composite films for thermal management. Adv. Mater. 17, 1652–1656 (2005). https://doi.org/10.1002/adma.200500467

    Article  CAS  Google Scholar 

  7. Vadivelu, M.A., Kumar, C.R., Joshi, G.M.: Polymer composites for thermal management: a review. Compos. Interfaces. 23, 847–872 (2016). https://doi.org/10.1080/09276440.2016.1176853

    Article  CAS  Google Scholar 

  8. Prasher, R.: Thermal interface materials: Historical perspective, status, and future directions. Proc. IEEE. 94, 1571–1586 (2006). https://doi.org/10.1109/JPROC.2006.879796

    Article  CAS  Google Scholar 

  9. Fei, Y., Chen, F., Fang, W., Xu, L., Ruan, S., Liu, X., Zhong, M., Kuang, T.: High-strength, flexible and cycling-stable piezo-resistive polymeric foams derived from thermoplastic polyurethane and multi-wall carbon nanotubes. Compos. B. Eng. 199, 108279 (2020). https://doi.org/10.1016/j.compositesb.2020.108279

    Article  CAS  Google Scholar 

  10. Ju, J., Kuang, T., Ke, X., Zeng, M., Chen, Z., Zhang, S., Peng, X.: Lightweight multifunctional polypropylene/carbon nanotubes/carbon black nanocomposite foams with segregated structure, ultralow percolation threshold and enhanced electromagnetic interference shielding performance. Compos. Sci. Technol. 193, 108116 (2020). https://doi.org/10.1016/j.compscitech.2020.108116

    Article  CAS  Google Scholar 

  11. Kuang, T., Chang, L., Chen, F., Sheng, Y., Fu, D., Peng, X.: Facile preparation of lightweight high-strength biodegradable polymer/multi-walled carbon nanotubes nanocomposite foams for electromagnetic interference shielding. Carbon. 105, 305–313 (2016). https://doi.org/10.1016/j.carbon.2016.04.052

    Article  CAS  Google Scholar 

  12. Lebovka, N., Lisunova, M., Mamunya, Y.P., Vygornitskii, N.: Scaling in percolation behaviour in conductive-insulating composites with particles of different size. J. Phys. D. Appl. Phys. 39, 2264–2271 (2006). https://doi.org/10.1088/0022-3727/39/10/040

    Article  CAS  Google Scholar 

  13. Lee, G.-W., Park, M., Kim, J., Lee, J.I., Yoon, H.G.: Enhanced thermal conductivity of polymer composites filled with hybrid filler. Compos. Part A Appl. Sci. Manuf. 37, 727–734 (2006). https://doi.org/10.1016/j.compositesa.2005.07.006

    Article  CAS  Google Scholar 

  14. Clerc, J.P., Giraud, G., Roussenq, J., Blanc, R., Carton, J.P., Guyon, E., Ottavi, H., Stauffer, D.: La percolation. Ann. Phys. (Paris) 8, 3–105 (1983). https://doi.org/10.1051/anphys/198308080003

    Article  CAS  Google Scholar 

  15. Vigolo, B.: An experimental approach to the percolation of sticky nanotubes. Science. 309, 920–923 (2005). https://doi.org/10.1126/science.1112835

    Article  CAS  Google Scholar 

  16. Kargar, F., Barani, Z., Salgado, R., Debnath, B., Lewis, J.S., Aytan, E., Lake, R.K., Balandin, A.A.: Thermal percolation threshold and thermal properties of composites with high loading of graphene and boron nitride fillers. ACS Appl. Mater. Interfaces. 10, 37555–37565 (2018). https://doi.org/10.1021/acsami.8b16616

    Article  CAS  Google Scholar 

  17. Kim, B., Pfeifer, S., Park, S. H., Bandaru, P.R.: The experimental determination of the onset of electrical and thermal conductivity percolation thresholds in carbon nanotube-polymer composites. MRS. Proc. 1312 (2011). https://doi.org/10.1557/opl.2011.114

  18. Yin, R., Zhang, Y., Zhao, W., Huang, X., Li, X., Qian, L.: Graphene platelets/aluminium nitride metacomposites with double percolation property of thermal and electrical conductivity. J. Eur. Ceram. Soc. 38, 4701–4706 (2018). https://doi.org/10.1016/j.jeurceramsoc.2018.06.036

    Article  CAS  Google Scholar 

  19. Kwon, S.Y., Kwon, I.M., Kim, Y.-G., Lee, S., Seo, Y.-S.: A large increase in the thermal conductivity of carbon nanotube/polymer composites produced by percolation phenomena. Carbon N. Y. 55, 285–290 (2013). https://doi.org/10.1016/j.carbon.2012.12.063

    Article  CAS  Google Scholar 

  20. Sun, K., Zhang, Z.D., Qian, L., Dang, F., Zhang, X.H., Fan, R.H.: Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites. Appl. Phys. Lett. 108, 061903 (2016). https://doi.org/10.1063/1.4941758

    Article  CAS  Google Scholar 

  21. Shenogina, N., Shenogin, S., Xue, L., Keblinski, P.: On the lack of thermal percolation in carbon nanotube composites. Appl. Phys. Lett. 87, 133106 (2005). https://doi.org/10.1063/1.2056591

    Article  CAS  Google Scholar 

  22. Biercuk, M.J., Llaguno, M.C., Radosavljevic, M., Hyun, J.K., Johnson, A.T., Fischer, J.E.: Carbon nanotube composites for thermal management. Appl. Phys. Lett. 80, 2767–2769 (2002). https://doi.org/10.1063/1.1469696

    Article  CAS  Google Scholar 

  23. Garboczi, E.J., Snyder, K.A., Douglas, J.F., Thorpe, M.F.: Geometrical percolation threshold of overlapping ellipsoids. Phys. Rev. E. 52, 819–828 (1995). https://doi.org/10.1103/PhysRevE.52.819

    Article  CAS  Google Scholar 

  24. Balberg, I., Anderson, C.H., Alexander, S., Wagner, N.: Excluded volume and its relation to the onset of percolation. Phys. Rev. B. 30, 3933–3943 (1984). https://doi.org/10.1103/PhysRevB.30.3933

    Article  Google Scholar 

  25. Kim, B.-W., Park, S.-H., Kapadia, R.S., Bandaru, P.R.: Evidence of percolation related power law behavior in the thermal conductivity of nanotube/polymer composites. Appl. Phys. Lett. 102, 243105 (2013). https://doi.org/10.1063/1.4811497

    Article  CAS  Google Scholar 

  26. Tjong, S.C., Liang, G.D., Bao, S.P.: Electrical properties of low-density polyethylene/ZnO nanocomposites: The effect of thermal treatments. J. Appl. Polym. Sci. 102, 1436–1444 (2006). https://doi.org/10.1002/app.24294

    Article  CAS  Google Scholar 

  27. Wang, Y., Shan, J.W., Weng, G.J.: Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling. J. Appl. Phys. 118, 065101 (2015). https://doi.org/10.1063/1.4928293

    Article  CAS  Google Scholar 

  28. Pech-May, N.W., Vales-Pinzn, C., Vega-Flick, A., Cifuentes, Oleaga, A., Salazar, A., Alvarado-Gil, J.J.: Study of the thermal properties of polyester composites loaded with oriented carbon nanofibers using the front-face flash method. Polym. Test. 50, 255–261 (2016). https://doi.org/10.1016/j.polymertesting.2015.12.011

  29. Pech-May, N.W., Cifuentes., Mendioroz, A., Oleaga, A., Salazar, A.: Simultaneous measurement of thermal diffusivity and effusivity of solids using the flash technique in the front-face configuration. Meas. Sci. Technol. 26, 085017 (2015). https://doi.org/10.1088/0957-0233/26/8/085017

  30. Abate, J., Whitt, W.: A Unified Framework for Numerically Inverting Laplace Transforms. INFORMS J. Comput. 18, 408–421 (2006). https://doi.org/10.1287/ijoc.1050.0137

    Article  Google Scholar 

  31. Marquardt, D.W.: An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 11, 431–441 (1963). https://doi.org/10.1137/0111030

    Article  Google Scholar 

  32. Forero-Sandoval, I.Y., Pech-May, N.W., Alvarado-Gil, J.J.: Measurement of the thermal transport properties of liquids using the front-face flash method. Infrared Phys. Technol. 93, 9–15 (2018). https://doi.org/10.1016/j.infrared.2018.07.009

    Article  CAS  Google Scholar 

  33. Rahaman, M., Aldalbahi, A., Govindasami, P., Khanam, N., Bhandari, S., Feng, P., Altalhi, T.: A new insight in determining the percolation threshold of electrical conductivity for extrinsically conducting polymer composites through different sigmoidal models. Polymers (Basel). 9, 527 (2017). https://doi.org/10.3390/polym9100527

  34. Merzouki, A., Haddaoui, N.: Electrical Conductivity Modeling of Polypropylene Composites Filled with Carbon Black and Acetylene Black. ISRN Polym. Sci. 2012, 1–7 (2012). https://doi.org/10.5402/2012/493065

    Article  CAS  Google Scholar 

  35. Yaman, K., Taga.: Thermal and electrical conductivity of unsaturated polyester resin filled with copper filler composites. Int. J. Polym. Sci. 2018, 1–10 (2018). https://doi.org/10.1155/2018/8190190

  36. Genetti, W.B., Yuan, W.L., Grady, B.P., Orear, E.A., Lai, C.L., Glatzhofer, D.T.: Polymer matrix composites: Conductivity enhancement through polypyrrole coating of nickel flake. J. Mater. Sci. 33, 3085–3093 (1998). https://doi.org/10.1023/A:1004387621165

    Article  CAS  Google Scholar 

  37. Marsden, A.J., Papageorgiou, D.G., Valls, C., Liscio, A., Palermo, V., Bissett, M.A., Young, R.J., Kinloch, I.A.: Electrical percolation in graphene–polymer composites. 2D Mater. 5, 032003 (2018). https://doi.org/10.1088/2053-1583/aac055

  38. Ukshe, A., Glukhov, A., Dobrovolsky, Y.: Percolation model for conductivity of composites with segregation of small conductive particles on the grain boundaries. J. Mater. Sci. 55, 6581–6587 (2020). https://doi.org/10.1007/s10853-020-04408-w

    Article  CAS  Google Scholar 

  39. Parker, W.J., Jenkins, R.J., Butler, C.P., Abbott, G.L.: Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 32, 1679–1684 (1961). https://doi.org/10.1063/1.1728417

    Article  CAS  Google Scholar 

  40. Sofian, N.M., Rusu, M., Neagu, R., Neagu, E.: Metal powder-filled polyethylene composites. V. Thermal properties. J. Thermoplast. Compos. Mater. 14, 20–33 (2001). https://doi.org/10.1106/9N6K-VKH1-MHYX-FBC4

  41. Rusu, M., Sofian, N., Rusu, D., Neagu, E., Neagu, R.: Properties of iron powder filled high density polyethylene. J. Polym. Eng. 21, 469–487 (2001). https://doi.org/10.1515/POLYENG.2001.21.5.469

    Article  CAS  Google Scholar 

  42. Pech-May, N., Vales-Pinzon, C., Vega-Flick, A., Oleaga, A., Salazar, A., Yanez-Limon, J., Alvarado-Gil, J.: Heat transport in epoxy and polyester carbonyl iron microcomposites: The effect of concentration and temperature. J. Compos. Mater. 52, 1331–1338 (2018). https://doi.org/10.1177/0021998317723694

    Article  CAS  Google Scholar 

  43. Bevington, P., Robinson, D.K.: Data reduction and error analysis for the physical sciences. McGraw-Hill Higher Education, New York (2002)

    Google Scholar 

  44. Zhang, G., Xia, Y., Wang, H., Tao, Y., Tao, G., Tu, S., Wu, H.: A percolation model of thermal conductivity for filled polymer composites. J. Compos. Mater. 44, 963–970 (2010). https://doi.org/10.1177/0021998309349690

    Article  CAS  Google Scholar 

  45. Almond, D.P., Patel, P.M.: Photothermal science and techniques. vol 10. Springer Science & Business Media (1996)

  46. Elimat, Z.M., AL-Aqrabawi, F.S., Hazeem, T.A., Ramadin, Y., Zihlif, A.M.: Effect of iron particle size and concentration on thermal conductivity of iron/polystyrene composites. Int. J. Thermophys. 34, 2009–2018 (2013). https://doi.org/10.1007/s10765-013-1499-7

  47. Boudenne, A., Ibos, L., Fois, M., Gehin, E., Majeste, J.C.: Thermophysical properties of polypropylene/aluminum composites. J. Polym. Sci. Part. B. Polym. Phys. 42, 722–732 (2004). https://doi.org/10.1002/polb.10713

    Article  CAS  Google Scholar 

  48. Ramirez-Rincon, J.A., Ares-Muzio, O., Macias, J.D., Estrella-Gutierrez, M.A., Lizama-Tzec, F.I., Oskam, G., Alvarado-Gil, J.J.: On the use of photothermal techniques for the characterization of solar-selective coatings. Appl. Phys. A. 124, 252 (2018). https://doi.org/10.1007/s00339-018-1667-5

    Article  CAS  Google Scholar 

  49. Houtz, D.A., Gu, D.: A measurement technique for infrared emissivity of epoxy-based microwave absorbing materials. IEEE Geosci. Remote Sens. Lett. 15, 48–52 (2018). https://doi.org/10.1109/LGRS.2017.2772783

    Article  Google Scholar 

  50. Hu, C., Xu, G., Shen, X., Shao, C., Yan, X.: The epoxy-siloxane/Al composite coatings with low infrared emissivity for high temperature applications. Appl. Surf. Sci. 256, 3459–3463 (2010). https://doi.org/10.1016/j.apsusc.2009.12.053

    Article  CAS  Google Scholar 

  51. Wu, G., Yu, D.: Preparation and characterization of a new low infrared-emissivity coating based on modified aluminum. Prog. Org. Coatings. 76, 107–112 (2013). https://doi.org/10.1016/j.porgcoat.2012.08.018

    Article  CAS  Google Scholar 

  52. Yu, H., Xu, G., Shen, X., Yan, X., Cheng, C.: Low infrared emissivity of polyurethane/Cu composite coatings. Appl. Surf. Sci. 255, 6077–6081 (2009). https://doi.org/10.1016/j.apsusc.2009.01.019

    Article  CAS  Google Scholar 

  53. Sherman, R.D., Middleman, L.M., Jacobs, S.M.: Electron transport processes in conductor-filled polymers. Polym. Eng. Sci. 23, 36–46 (1983). https://doi.org/10.1002/pen.760230109

    Article  Google Scholar 

  54. Albers, W.M., Karttunen, M., Wikstrm, L., Vilkman, T.: Effects of compression and filler particle coating on the electrical conductivity of thermoplastic elastomer composites. J. Electron. Mater. 42, 2983–2989 (2013). https://doi.org/10.1007/s11664-013-2689-6

    Article  CAS  Google Scholar 

  55. Balberg, I.: Tunneling and nonuniversal conductivity in composite materials. Phys. Rev. Lett. 59, 1305–1308 (1987). https://doi.org/10.1103/PhysRevLett.59.1305

    Article  CAS  Google Scholar 

  56. Huang, C., Qian, X., Yang, R.: Thermal conductivity of polymers and polymer nanocomposites. Mater. Sci. Eng. R Reports. 132, 1–22 (2018). https://doi.org/10.1016/j.mser.2018.06.002

    Article  Google Scholar 

  57. Hida, S., Hori, T., Shiga, T., Elliott, J., Shiomi, J.: Thermal resistance and phonon scattering at the interface between carbon nanotube and amorphous polyethylene. Int. J. Heat Mass Transf. 67, 1024–1029 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.068

    Article  CAS  Google Scholar 

  58. Wang, Y., Weng, G.J., Meguid, S.A., Hamouda, A.M.: A continuum model with a percolation threshold and tunneling-assisted interfacial conductivity for carbon nanotube-based nanocomposites. J. Appl. Phys. 115, 193706 (2014). https://doi.org/10.1063/1.4878195

    Article  CAS  Google Scholar 

  59. Shi, Y.D., Li, J., Tan, Y.J., Chen, Y.F., Wang, M.: Percolation behavior of electromagnetic interference shielding in polymer/multi-walled carbon nanotube nanocomposites. Compos. Sci. Technol. 170, 70–76 (2019). https://doi.org/10.1016/j.compscitech.2018.11.033

    Article  CAS  Google Scholar 

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Acknowledgements

This work was partially supported by projects SRE-AMEXCID-2016-1-278320 and Cinvestav Scientific Research and Technological Development Fund No. 98. F. C-A acknowledges the postdoctoral scholarship obtained from the project SEP-CB-2015-01-251882. N.W. P-M acknowledges support from the Adolf Martens fellowship at BAM Berlin. The FESEM analyzes were carried out by the M.C. Dora Huerta Quintanilla at the National Laboratory of Nano and Biomaterials, Cinvestav-IPN; financed by the projects FOMIX-Yucatán 2008-108160, CONACYT LAB-2009-01-123913, 292692, 294643, 188345 and 204822. The authors are grateful to J. Bante-Guerra for his technical assistance.

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Forero-Sandoval, I.Y., Cervantes-Alvarez, F., Ramirez-Rincon, J.A. et al. Percolation Threshold of the Thermal, Electrical and Optical Properties of Carbonyl-Iron Microcomposites. Appl Compos Mater 28, 447–463 (2021). https://doi.org/10.1007/s10443-021-09869-z

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