Abstract
The present paper suggests an equation for the average contact number of carbon nanotubes (CNTs) in CNT-reinforced polymer nanocomposites (PCNT) by two developed equations for electrical conductivity. Several novel parameters in PCNT such as CNT size, CNT concentration, network fraction, interphase depth, tunneling effect, and CNT wettability by the polymer medium are considered to define the average contact number (m). “m” is calculated for some samples and the variation of “m” is explored over a range of parameters’ values. The results show that dense interphase, high fraction of networked CNTs, reedy and short CNTs, low CNT surface energy, high polymer surface energy, low tunneling distance, and small contact diameter increase the “m” improving the conductivity. Moreover, tunneling distance and CNT contact diameter have the greatest effects on the “m”. The optimized level for “m” is necessary to control the nanocomposite’s conductivity.
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References
Vinyas M, Harursampath D, Kattimani S (2020) On vibration analysis of functionally graded carbon nanotube reinforced magneto-electro-elastic plates with different electro-magnetic conditions using higher order finite element methods. Def Technol (2020)
Vinyas M (2019) A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods. Compos B Eng 158:286–301
Vinyas M, Harursampath D (2020) Nonlinear vibrations of magneto-electro-elastic doubly curved shells reinforced with carbon nanotubes. Compos Struct 253:112749
Mahesh V, Harursampath D (2020) Nonlinear vibration of functionally graded magneto-electro-elastic higher order plates reinforced by CNTs using FEM. Eng Comput 1–23
Mallek H, Jrad H, Algahtani A, Wali M, Dammak F (2019) Geometrically non-linear analysis of FG-CNTRC shell structures with surface-bonded piezoelectric layers. Comput Methods Appl Mech Eng 347:679–699
Mallek H, Jrad H, Wali M, Kessentini A, Gamaoun F, Dammak F (2020) Dynamic analysis of functionally graded carbon nanotube–reinforced shell structures with piezoelectric layers under dynamic loads. J Vib Contr 26:1157–1172
Mellouli H, Jrad H, Wali M, Dammak F (2020) Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method. Comput Math Appl 11:3160
Ebrahimi F, Mahesh V (2019) Chaotic dynamics and forced harmonic vibration analysis of magneto-electro-viscoelastic multiscale composite nanobeam. Eng Comput 1–14
Ghassabi M, Zarastvand M, Talebitooti R (2019) Investigation of state vector computational solution on modeling of wave propagation through functionally graded nanocomposite doubly curved thick structures. Eng Comput 1–17
Hajmohammad MH, Nouri AH, Zarei MS, Kolahchi R (2019) A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal environment. Eng Comput 35:1141–1157
Zidan HM, Abdelrazek EM, Abdelghany AM, Tarabiah AE (2019) Characterization and some physical studies of PVA/PVP filled with MWCNTs. J Mat Res Technol 8:904–913
Hassanzadeh-Aghdam MK, Mahmoodi MJ, Ansari R, Mehdipour H (2019) Effects of adding CNTs on the thermo-mechanical characteristics of hybrid titanium nanocomposites. Mech Mat 131:121–135
Mallek H, Jrad H, Wali M, Dammak F (2019) Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory. Eng Comput 1–19
Ebrahimi F, Habibi M, Safarpour H (2019) On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell. Eng Comput 35:1375–1389
Rostami A, Vahdati M, Alimoradi Y, Karimi M, Nazockdast H (2018) Rheology provides insight into flow induced nano-structural breakdown and its recovery effect on crystallization of single and hybrid carbon nanofiller filled poly (lactic acid). Polymer 134:143–154
Rostami A, Eskandari F, Masoomi M, Nowrouzi M (2019) Evolution of microstructure and physical properties of PMMA/MWCNTs nanocomposites upon the addition of organoclay. J Oil Gas Petrochem Technol (2019)
Razavi R, Zare Y, Rhee KY (2019) The roles of interphase and filler dimensions in the properties of tunneling spaces between CNT in polymer nanocomposites. Polym Compos
Zare Y, Rhee KY, Park S-J (2019) Modeling the roles of carbon nanotubes and interphase dimensions in the conductivity of nanocomposites. Res Phys 15:102562
Zare Y, Rhee KY (2019) Following the morphological and thermal properties of PLA/PEO blends containing carbon nanotubes (CNTs) during hydrolytic degradation. Compos Part B Eng 175:107132
Maiti S, Shrivastava NK, Khatua B (2013) Reduction of percolation threshold through double percolation in melt-blended polycarbonate/acrylonitrile butadiene styrene/multiwall carbon nanotubes elastomer nanocomposites. Polym Compos 34:570–579
Sagalianov I, Vovchenko L, Matzui L, Lazarenko O (2017) Synergistic enhancement of the percolation threshold in hybrid polymeric nanocomposites based on carbon nanotubes and graphite nanoplatelets. Nanoscale Res Lett 12:140
Seidel G, Puydupin-Jamin A-S (2011) Analysis of clustering, interphase region, and orientation effects on the electrical conductivity of carbon nanotube–polymer nanocomposites via computational micromechanics. Mech Mater 43:755–774
Li C, Thostenson ET, Chou T-W (2007) Dominant role of tunneling resistance in the electrical conductivity of carbon nanotube-based composites. Appl Phys Lett 91:223114
Zare Y, Rhee KY (2017) A simple methodology to predict the tunneling conductivity of polymer/CNT nanocomposites by the roles of tunneling distance, interphase and CNT waviness. RSC Adv 7:34912–34921
Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H (2008) Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater 56:2929–2936
Bao W, Meguid S, Zhu Z, Weng G (2012) Tunneling resistance and its effect on the electrical conductivity of carbon nanotube nanocomposites. J Appl Phys 111:093726
Li J, Ma PC, Chow WS, To CK, Tang BZ, Kim JK (2007) Correlations between percolation threshold, dispersion state, and aspect ratio of carbon nanotubes. Adv Func Mater 17:3207–3215
Kim S, Zare Y, Garmabi H, Rhee KY (2018) Variations of tunneling properties in poly (lactic acid)(PLA)/poly (ethylene oxide)(PEO)/carbon nanotubes (CNT) nanocomposites during hydrolytic degradation. Sens Actuat A 274:28–36
Razavi R, Zare Y, Rhee KY (2017) A two-step model for the tunneling conductivity of polymer carbon nanotube nanocomposites assuming the conduction of interphase regions. RSC Adv 7:50225–50233
Zare Y, Rhee KY (2017) Development of a conventional model to predict the electrical conductivity of polymer/carbon nanotubes nanocomposites by interphase, waviness and contact effects. Compos Part A Appl Sci Manuf 100:305
Takeda T, Shindo Y, Kuronuma Y, Narita F (2011) Modeling and characterization of the electrical conductivity of carbon nanotube-based polymer composites. Polymer 52:3852–3856
Feng C, Jiang L (2013) Micromechanics modeling of the electrical conductivity of carbon nanotube (CNT)–polymer nanocomposites. Compos A Appl Sci Manuf 47:143–149
Zare Y, Rhee KY (2017) Multistep modeling of Young’s modulus in polymer/clay nanocomposites assuming the intercalation/exfoliation of clay layers and the interphase between polymer matrix and nanoparticles. Compos A Appl Sci Manuf 102:137–144
Zare Y (2016) “a” interfacial parameter in Nicolais–Narkis model for yield strength of polymer particulate nanocomposites as a function of material and interphase properties. J Colloid Interface Sci 470:245–249
Zare Y (2016) Study on interfacial properties in polymer blend ternary nanocomposites: role of nanofiller content. Comput Mater Sci 111:334–338
Zare Y (2016) Modeling the strength and thickness of the interphase in polymer nanocomposite reinforced with spherical nanoparticles by a coupling methodology. J Colloid Interface Sci 465:342–346
Zare Y (2016) A two-step method based on micromechanical models to predict the Young’s modulus of polymer nanocomposites. Macromol Mater Eng 301:846–852
Li Y, Waas AM, Arruda EM (2011) A closed-form, hierarchical, multi-interphase model for composites—derivation, verification and application to nanocomposites. J Mech Phys Solids 59:43–63
Sevostianov I, Kachanov M (2007) Effect of interphase layers on the overall elastic and conductive properties of matrix composites. Applications to nanosize inclusion. Int J Solids Struct 44:1304–1315
Zare Y, Rhee KY (2017) Prediction of tensile modulus in polymer nanocomposites containing carbon nanotubes (CNT) above percolation threshold by modification of conventional model. Curr Appl Phys 17:873–879
Zare Y (2016) Development of Nicolais–Narkis model for yield strength of polymer nanocomposites reinforced with spherical nanoparticles. Int J Adhes Adhes 70:191–195
Zare Y, Rhee KY, Park S-J (2019) A developed equation for electrical conductivity of polymer carbon nanotubes (CNT) nanocomposites based on Halpin–Tsai model. Res Phys 14:102406
Zare Y, Rhee KY (2018) A multistep methodology for calculation of the tensile modulus in polymer/carbon nanotube nanocomposites above the percolation threshold based on the modified rule of mixtures. RSC Adv 8:30986–30993
Y. Zare, K.Y. Rhee, Accounting the reinforcing efficiency and percolating role of interphase regions in the tensile modulus of polymer/CNT nanocomposites, European Polymer Journal, (2017).
Weber M, Kamal MR (1997) Estimation of the volume resistivity of electrically conductive composites. Polym Compos 18:711–725
Taherian R (2016) Experimental and analytical model for the electrical conductivity of polymer-based nanocomposites. Compos Sci Technol 123:17–31
Maiti S, Suin S, Shrivastava NK, Khatua B (2013) Low percolation threshold in polycarbonate/multiwalled carbon nanotubes nanocomposites through melt blending with poly (butylene terephthalate). J Appl Polym Sci 130:543–553
Mai F, Habibi Y, Raquez J-M, Dubois P, Feller J-F, Peijs T, Bilotti E (2013) Poly (lactic acid)/carbon nanotube nanocomposites with integrated degradation sensing. Polymer 54:6818–6823
Kim YJ, Shin TS, Do Choi H, Kwon JH, Chung Y-C, Yoon HG (2005) Electrical conductivity of chemically modified multiwalled carbon nanotube/epoxy composites. Carbon 43:23–30
Lisunova M, Mamunya YP, Lebovka N, Melezhyk A (2007) Percolation behaviour of ultrahigh molecular weight polyethylene/multi-walled carbon nanotubes composites. Eur Polym J 43:949–958
Hassanzadeh-Aghdam M, Mahmoodi M, Ansari R, Darvizeh A (2018) Interphase influences on the mechanical behavior of carbon nanotube–shape memory polymer nanocomposites: a micromechanical approach. J Intell Mat Syst Struct 30:463
Amraei J, Jam JE, Arab B, Firouz-Abadi RD (2018) Modeling the interphase region in carbon nanotube–reinforced polymer nanocomposites. Polym Compos 40:E1219
Ashraf MA, Peng W, Zare Y, Rhee KY (2018) Effects of size and aggregation/agglomeration of nanoparticles on the interfacial/interphase properties and tensile strength of polymer nanocomposites. Nanoscale Res Lett 13:214
Zare Y, Rhee KY (2019) A simulation work for the influences of aggregation/agglomeration of clay layers on the tensile properties of nanocomposites. JOM 71:3989–3995
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This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Project number: 2020R1A2B5B02002203).
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Zare, Y., Rhee, K.Y. Estimation of average contact number of carbon nanotubes (CNTs) in polymer nanocomposites to optimize the electrical conductivity. Engineering with Computers 38 (Suppl 1), 243–253 (2022). https://doi.org/10.1007/s00366-020-01153-1
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DOI: https://doi.org/10.1007/s00366-020-01153-1