An overview of the most correct mathematical models for describing the thermal conductivity of polymer-carbon nanotube systems, which characterize percolation behavior, is given. It is shown that the Landauer model, which does not take into account the presence of a percolation transition at low filler concentrations, is in poor agreement with the experiment. The sigmoidal model describes experimental data well, but is purely empirical. Zhang's model turned out to be incorrect for this type of system, as it was designed for a system with a high filler content. The scaling model showed good agreement with experimental data for a system with a low percolation threshold.
thermal conductivity, carbon nanotubes, thermal conductivity models, polymer nanocomposites, percolation behavior
- Chena, H., Ginzburg, V.V., Yang, J. et. al. (2016), “Thermal conductivity of polymer-based composites: Fundamentals and applications”, Progress in Polymer Science, Vol. 59, рр. 41–85.
- Han, Z. and Fina, A. (2011), “Thermal Conductivity of Carbon Nanotubes and their Polymer Nanocomposites: A Review”, Progress in Polymer Science, Vol. 36, pp. 914–944.
- Hu, J., Huang, Y., Yao, Y. et. al. (2017), “A Polymer Composite with Improved Thermal Conductivity by Constructing Hierarchically Ordered Three-Dimensional Interconnected Network of BN”, ACS Applied Materials & Interfaces, Vol. 9, no. 15, рр. 13544–13553.
- Huxtable, S.T., Cahill, D.G., Shenogin, S. et. al. (2003). “Interfacial heat flow in carbon nanotube suspensions”, Nature Materials, Vol. 2, no. 11, pp. 731–734.
- Aalilija, A., Gandin, Ch.-A. and Hachem, E. (2021), “A simple and efficient numerical model for thermal contact resistance based on diffuse interface immersed boundary method”, International Journal of Thermal Sciences, Vol. 166, pp. 106817.
- He, C. and Xu, J. (2020) “Finite element analysis of the thermal conductivity and the specific heat of Carbon Fiber Reinforced Plastic (CFRP) composites”, 2020 International Conference on Artificial Intelligence and Electromechanical Automation (AIEA), рр. 771–774.
- Fiedler, Th., Pesetskaya, E., Öchsner, A. and Grácio, J. (2005), “Numerical and analytical calculation of the orthotropic heat transfer properties of fibre reinforced materials”, Materialwissenschaft und Werkstofftechnik, Vol. 36, no. 10, рр. 602–607.
- Kwon, S.Y., Kwon, I.M., Kim, Y.-G., Lee, S. and Seo, Y.-S. (2013), “A large increase in the thermal conductivity of carbon nanotube/polymer composites produced by percolation phenomena”, Carbon, Vol. 55, pp. 285–290.
- Kim, B.-W., Park, S.-H., Kapadia, R.S. and Bandaru, P.R. (2013), “Evidence of percolation related power law behavior in the thermal conductivity of nanotube/polymer composites”, Applied Physics Letters, Vol. 102, pp. 243105.
- Zhang, G., Xia, Y., Wang, H., Tao, Y., Tao, G. and Tu, S. (2010), “A Percolation Model of Thermal Conductivity for Filled Polymer Composites”, Journal of Composite Materials, Vol. 44, no. 8, pp. 963–970.
- Lysenkov, Е.А. and Dinzhos, R.V. (2019), “Theoretical analysis of thermal conductivity of polymer systems filled with carbon nanotubes”, Journal of Nano- and Electronic Physics, Vol. 11, no. 4, рр. 04004.
- Lysenkov, Е.А. (2019), “Simulation of thermal conductivity of polymer nanocomposites, using models based on thermal-electrical analogy”, Nanosistemi, Nanomateriali, Nanotehnologii, Vol. 17, no. 4, pp. 761–772.
- Landauer, R. (1952), “The Electrical Resistance of Binary Metallic Mixtures”, Journal of Applied Physics, Vol. 23, no. 7, рр. 779–784.
- Tjørve, E. (2003), “Shapes and functions of species–area curves: a review of possible models”, Journal of Biogeography, Vol. 30, no. 6, pp. 827–835.
- Taherian, R. (2014), “Development of an Equation to Model Electrical Conductivity of Polymer-Based Carbon Nanocomposites”, ECS Journal of Solid State Science and Technology, Vol. 3, no. 6, pp. M26–M38.
- Sun, K., Zhang, Z.D., Qian, L., Dang, F., Zhang, X.H. and Fan, R.H. (2016), “Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites”, Applied Physics Letters, Vol. 108, pp. 061903.
- Lysenkov, Е.A. and Klepko, V.V. (2015), “Characteristic features of the thermophysical properties of a system based on polyethylene oxide and carbon nanotubes”, Journal of Engineering Physics and Thermophysics, Vol. 88, no. 4, рр. 1008–1014.
- Forero-Sandoval, I., Cervantes-Alvarez, F., Ramirez-Rincon, J. et. al. (2021), “Percolation threshold of the thermal, electrical and optical properties of carbonyl-iron microcomposites”, Applied Composite Materials, Vol. 28, no. 2, pp. 447–454.