# The Effect of Agglomeration on the Electrical and Mechanical Properties of Polymer Matrix Nanocomposites Reinforced with Carbon Nanotubes

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Samples Preparation

#### 2.2. Experimental Procedure

#### 2.3. Numerical Procedure

#### 2.4. Digimat FE Modelling

#### 2.5. MATLAB Modelling

## 3. Results and Discussion

#### 3.1. Mechanical Properties

#### 3.2. Electrical Properties

^{−7}(S/cm) to 2.123 × 10

^{−5}(S/cm). This phenomenon was confirmed with a fraction of 1 wt.%, achieving a final electrical conductivity of 5.195 × 10

^{−4}(S/cm). Thereafter, there was a sharp increase in the conductivity at 2 wt.%, where the value increased to 0.2512 (S/cm). At this percentage, the percolation threshold was achieved. Thereafter the addition of CNTs induced small increases in the final electrical properties, where 3.472 (S/cm) and 5.549 (S/cm) were achieved at 4 and 5%, respectively. This phenomenon is portrayed in Figure 6, where the percolation threshold is highlighted with a red line. The percolation threshold is a phenomenon that is related to the formation of carbon nanotubes networks [22].

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Tamayo-Vegas, S.; Muhsan, A.; Tarfaoui, M.; Lafdi, K.; Chang, L. Effect of CNT additives on the electrical properties of derived nanocomposites (experimentally and numerical investigation). Mater. Today Proc.
**2021**, 52, 3–9. [Google Scholar] [CrossRef] - Tarfaoui, M.; Lafdi, K.; El Moumen, A. Mechanical properties of carbon nanotubes based polymer composites. Compos. Part B Eng.
**2016**, 103, 113–121. [Google Scholar] [CrossRef] - Tamayo-Vegas, S.; Lafdi, K. Experimental and modelling of temperature-dependent mechanical properties of CNT/polymer nanocomposites. Mater. Today Proc.
**2022**, 57, 607–614. [Google Scholar] [CrossRef] - Maghsoudlou, M.A.; Barbaz Isfahani, R.; Saber-Samandari, S.; Sadighi, M. Effect of interphase, curvature and agglomeration of SWCNTs on mechanical properties of polymer-based nanocomposites: Experimental and numerical investigations. Compos. Part B Eng.
**2019**, 175, 107119. [Google Scholar] [CrossRef] - Alian, A.R.; El-Borgi, S.; Meguid, S.A. Multiscale modeling of the effect of waviness and agglomeration of CNTs on the elastic properties of nanocomposites. Comput. Mater. Sci.
**2016**, 117, 195–204. [Google Scholar] [CrossRef] - Gong, S.; Zhu, Z.H.; Meguid, S.A. Carbon nanotube agglomeration effect on piezoresistivity of polymer nanocomposites. Polymer
**2014**, 55, 5488–5499. [Google Scholar] [CrossRef] - Manta, A.; Tserpes, K.I. Numerical computation of electrical conductivity of carbon nanotube-filled polymers. Compos. Part B Eng.
**2016**, 100, 240–246. [Google Scholar] [CrossRef] - Bao, W.S.; Meguid, S.A.; Zhu, Z.H.; Pan, Y.; Weng, G.J. A novel approach to predict the electrical conductivity of multifunctional nanocomposites. Mech. Mater.
**2012**, 46, 129–138. [Google Scholar] [CrossRef] - Nilsson, F.; Krückel, J.; Schubert, D.W.; Chen, F.; Unge, M.; Gedde, U.W.; Hedenqvist, M.S. Simulating the effective electric conductivity of polymer composites with high aspect ratio fillers. Compos. Sci. Technol.
**2016**, 132, 16–23. [Google Scholar] [CrossRef] - Bao, W.S.; Meguid, S.A.; Zhu, Z.H.; Meguid, M.J. Modeling electrical conductivities of nanocomposites with aligned carbon nanotubes. Nanotechnology
**2011**, 22, 485704. [Google Scholar] [CrossRef] - Zeng, X.; Xu, X.; Shenai, P.M.; Kovalev, E.; Baudot, C.; Mathews, N.; Zhao, Y. Characteristics of the electrical percolation in carbon nanotubes/polymer nanocomposites. J. Phys. Chem. C
**2011**, 115, 21685–21690. [Google Scholar] [CrossRef] - Bauhofer, W.; Kovacs, J.Z. A review and analysis of electrical percolation in carbon nanotube polymer composites. Compos. Sci. Technol.
**2009**, 69, 1486–1498. [Google Scholar] [CrossRef] - Hu, N.; Masuda, Z.; Yan, C.; Yamamoto, G.; Fukunaga, H.; Hashida, T. The electrical properties of polymer nanocomposites with carbon nanotube fillers. Nanotechnology
**2008**, 19, 215701. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hu, N.; Karube, Y.; Yan, C.; Masuda, Z.; Fukunaga, H. Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater.
**2008**, 56, 2929–2936. [Google Scholar] [CrossRef][Green Version] - Kirkpatrick, S. Percolation and Conduction. Rev. Mod. Phys.
**1973**, 45, 574–588. [Google Scholar] [CrossRef] - Kirkpatrick, S. Classical Transport in Disordered Media: Scaling and Effective-Medium Theories. Phys. Rev. Lett.
**1971**, 27, 1722. [Google Scholar] [CrossRef] - Mohiuddin, M.; Hoa, S.V. Estimation of contact resistance and its effect on electrical conductivity of CNT/PEEK composites. Compos. Sci. Technol.
**2013**, 79, 42–48. [Google Scholar] [CrossRef] - Ounaies, Z.; Park, C.; Wise, K.E.; Siochi, E.J.; Harrison, J.S. Electrical properties of single wall carbon nanotube reinforced polyimide composites. Compos. Sci. Technol.
**2003**, 63, 1637–1646. [Google Scholar] [CrossRef] - Meguid, S.A.; Weng, G.J. Micromechanics and Nanomechanics of Composite Solids; Springer: New York, NY, USA, 2017. [Google Scholar]
- Simoes, R.; Silva, J.; Vaia, R.; Sencadas, V.; Costa, P.; Gomes, J.; Lanceros-Méndez, S. Low percolation transitions in carbon nanotube networks dispersed in a polymer matrix: Dielectric properties, simulations and experiments. Nanotechnology
**2009**, 20, 035703. [Google Scholar] [CrossRef] - Chanteli, A.; Tserpes, K.I. Finite element modeling of carbon nanotube agglomerates in polymers. Compos. Struct.
**2015**, 132, 1141–1148. [Google Scholar] [CrossRef] - Taherian, R. Experimental and analytical model for the electrical conductivity of polymer-based nanocomposites. Compos. Sci. Technol.
**2016**, 123, 17–31. [Google Scholar] [CrossRef] - Govorov, A.; Wentzel, D.; Miller, S.; Kanaan, A.; Sevostianov, I. Electrical conductivity of epoxy-graphene and epoxy-carbon nanofibers composites subjected to compressive loading. Int. J. Eng. Sci.
**2018**, 123, 174–180. [Google Scholar] [CrossRef] - Karevan, M.; Pucha, R.V.; Bhuiyan, M.A.; Kalaitzidou, K. Effect of Interphase Modulus and Nanofiller Agglomeration on the Tensile Modulus of Graphite Nanoplatelets and Carbon Nanotube Reinforced Polypropylene Nanocomposites. Carbon Lett.
**2010**, 11, 325–331. [Google Scholar] [CrossRef][Green Version] - Shi, D.L.; Feng, X.Q.; Huang, Y.Y.; Hwang, K.C.; Gao, H. The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J. Eng. Mater. Technol. Trans. ASME
**2004**, 126, 250–257. [Google Scholar] [CrossRef] - Romanov, V.S.; Lomov, S.V.; Verpoest, I.; Gorbatikh, L. Stress magnification due to carbon nanotube agglomeration in composites. Compos. Struct.
**2015**, 133, 246–256. [Google Scholar] [CrossRef] - Loos, M. Carbon Nanotube Reinforced Composites, 1st ed.; William Andrew: Oxford, UK, 2015; Volume 3, ISBN 9781455778980. [Google Scholar]
- Atlukhanova, L.B.; Kozlov, G.V. A carbon nanotubes aggregation in polymer nanocomposites. Mater. Sci. Forum
**2018**, 935, 55–60. [Google Scholar] [CrossRef] - Hosseinpour, K.; Ghasemi, A.R. Agglomeration and aspect ratio effects on the long-term creep of carbon nanotubes/fiber/polymer composite cylindrical shells. J. Sandw. Struct. Mater.
**2021**, 23, 1272–1291. [Google Scholar] [CrossRef] - Chen, X.; Alian, A.R.; Meguid, S.A. Modeling of CNT-reinforced nanocomposite with complex morphologies using modified embedded finite element technique. Compos. Struct.
**2019**, 227, 111329. [Google Scholar] [CrossRef] - Golbang, A.; Famili, M.H.N.; Shirvan, M.M.M. A method for quantitative characterization of agglomeration degree in nanocomposites. Compos. Sci. Technol.
**2017**, 145, 181–186. [Google Scholar] [CrossRef] - Yang, Q.S.; He, X.Q.; Liu, X.; Leng, F.F.; Mai, Y.W. The effective properties and local aggregation effect of CNT/SMP composites. Compos. Part B Eng.
**2012**, 43, 33–38. [Google Scholar] [CrossRef] - Pan, J.; Bian, L. Influence of agglomeration parameters on carbon nanotube composites. Acta Mech.
**2017**, 228, 2207–2217. [Google Scholar] [CrossRef] - Yellampalli, S. (Ed.) Functionalization of Carbon Nanotubes; IntechOpen: London, UK, 2011. [Google Scholar]
- Hirsch, A. Functionalization of Single-Walled Carbon Nanotubes. Angew. Chemie-Int. Ed.
**2002**, 41, 1853–1859. [Google Scholar] [CrossRef] - Khare, K.S.; Khabaz, F.; Khare, R. Effect of carbon nanotube functionalization on mechanical and thermal properties of cross-linked epoxy-carbon nanotube nanocomposites: Role of strengthening the interfacial interactions. ACS Appl. Mater. Interfaces
**2014**, 6, 6098–6110. [Google Scholar] [CrossRef] [PubMed] - Rahmat, M.; Hubert, P. Carbon nanotube-polymer interactions in nanocomposites: A review. Compos. Sci. Technol.
**2011**, 72, 72–84. [Google Scholar] [CrossRef] - Goyal, R.K. Nanomaterials and Nanocomposites: Synthesis, Properties, Characterization Techniques, and Applications; CRC Press: Boca Raton, FL, USA, 2017; ISBN 9781498761673. [Google Scholar]
- Jarali, C.S.; Basavaraddi, S.R.; Kiefer, B.; Pilli, S.C.; Lu, Y.C. Modeling of the effective elastic properties of multifunctional carbon nanocomposites due to agglomeration of straight circular carbon nanotubes in a polymer matrix. J. Appl. Mech. Trans. ASME
**2014**, 81, 021010. [Google Scholar] [CrossRef] - Zare, Y.; Rhee, K.Y. The mechanical behavior of CNT reinforced nanocomposites assuming imperfect interfacial bonding between matrix and nanoparticles and percolation of interphase regions. Compos. Sci. Technol.
**2017**, 144, 18–25. [Google Scholar] [CrossRef] - Ajayan, B.P.M.; Schadler, L.S.; Giannaris, C.; Rubio, A. Single-Walled Carbon Nanotube-Polymer Composites: Strength and Weakness. Adv. Mater.
**2000**, 12, 750–753. [Google Scholar] [CrossRef] - Zare, Y.; Rhee, K.Y. A power model to predict the electrical conductivity of CNT reinforced nanocomposites by considering interphase, networks and tunneling condition. Compos. Part B Eng.
**2018**, 155, 11–18. [Google Scholar] [CrossRef] - Zare, Y.; Rhee, K.Y.; Hui, D. Influences of nanoparticles aggregation/agglomeration on the interfacial/interphase and tensile properties of nanocomposites. Compos. Part B Eng.
**2017**, 122, 41–46. [Google Scholar] [CrossRef] - Poorsolhjouy, A.; Naei, M.H. Effects of carbon nanotubes’ dispersion on effective mechanical properties of nanocomposites: A finite element study. J. Reinf. Plast. Compos.
**2015**, 34, 1315–1328. [Google Scholar] [CrossRef] - Tornabene, F.; Fantuzzi, N.; Bacciocchi, M.; Viola, E. Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells. Compos. Part B
**2016**, 89, 187–218. [Google Scholar] [CrossRef] - Zare, Y. Study of nanoparticles aggregation/agglomeration in polymer particulate nanocomposites by mechanical properties. Compos. Part A Appl. Sci. Manuf.
**2016**, 84, 158–164. [Google Scholar] [CrossRef] - Ward, B. A Numerical Resistor Network Model for the Determination of Electrical Properties of Nanocomposites. Master Dissertation, Rice University, Huston, TX, USA, 2011. [Google Scholar]
- Fang, W.; Jang, H.W.; Leung, S.N. Evaluation and modelling of electrically conductive polymer nanocomposites with carbon nanotube networks. Compos. Part B Eng.
**2015**, 83, 184–193. [Google Scholar] [CrossRef] - Halpin, J.; Kardos, J. The Halpin-Tsai equations: A review. Polym. Eng. Sci.
**1976**, 16, 344–352. [Google Scholar] [CrossRef] - Ayatollahi, M.R.; Shadlou, S.; Shokrieh, M.M.; Chitsazzadeh, M. Effect of multi-walled carbon nanotube aspect ratio on mechanical and electrical properties of epoxy-based nanocomposites. Polym. Test.
**2011**, 30, 548–556. [Google Scholar] [CrossRef] - Silva, J.; Lanceros-Mendez, S.; Simoes, R. Effect of cylindrical filler aggregation on the electrical conductivity of composites. Phys. Lett. Sect. A Gen. At. Solid State Phys.
**2014**, 378, 2985–2988. [Google Scholar] [CrossRef] - Kovacs, J.Z.; Velagala, B.S.; Schulte, K.; Bauhofer, W. Two percolation thresholds in carbon nanotube epoxy composites. Compos. Sci. Technol.
**2007**, 67, 922–928. [Google Scholar] [CrossRef][Green Version] - Sandler, J.; Shaffer, M.S.P.; Prasse, T.; Bauhofer, W.; Schulte, K.; Windle, A.H. Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties. Polymer
**1999**, 40, 5967–5971. [Google Scholar] [CrossRef] - Sandler, J.K.W.; Kirk, J.E.; Kinloch, I.A.; Shaffer, M.S.P.; Windle, A.H. Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites. Polymer
**2003**, 44, 5893–5899. [Google Scholar] [CrossRef] - Kilbride, B.E.; Coleman, J.N.; Fraysse, J.; Fournet, P.; Cadek, M.; Drury, A.; Hutzler, S.; Roth, S.; Blau, W.J. Experimental observation of scaling laws for alternating current and direct current conductivity in polymer-carbon nanotube composite thin films. J. Appl. Phys.
**2002**, 92, 4024–4030. [Google Scholar] [CrossRef] - Celzard, A.; McRae, E.; Deleuze, C.; Dufort, M. Critical concentration in percolating systems containing a high-aspect-ratio filler. Phys. Rev. B-Condens. Matter Mater. Phys.
**1996**, 53, 6209–6214. [Google Scholar] [CrossRef] [PubMed] - Munson-Mcgee, S.H. Estimation of the critical concentration in an anisotropic percolation network. Phys. Rev. B
**1991**, 43, 3331–3336. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Generation of RVEs as a function of the percentage of nanofillers. (

**a**) 0.5 wt.%; (

**b**) 1 wt.%; (

**c**) 2 wt.% (

**d**) 4 wt.%; (

**e**) 5 wt.%.

**Figure 5.**SEM characterization sample CNT 4%wt: (

**a**) CNTs agglomeration, (

**b**) high magnification of CNT agglomeration, (

**c**) interface adhesion CNT and epoxy resin, and (

**d**) CNTs and porosity characterization, Yellow arrows represent the Porosity, White allow point the CNTs.

**Figure 6.**Experimental stress–strain curves of nanocomposites with different percentages of CNT. (

**a**) Epoxy. (

**b**) 0.5 wt.%. (

**c**) 1 wt.%. (

**d**) 2 wt.%. (

**e**) 4 wt.%. (

**f**) 5 wt.%.

Properties | Epoxy | MWCNT |
---|---|---|

Density (g/cm^{3}) | 1.21 | 2.1 |

Young’s modulus (MPa) | 1650 | 500,000 |

Poisson’s ratio | 0.3 | 0.261 |

Electrical conductivity (S/cm) | 2.1 × 10^{−7} | 5 × 10^{1}–5 × 10^{5} |

Samples | Experimental | FEA | 20% | 30% | 40% |
---|---|---|---|---|---|

0 wt.% | 1611 | 1611 | - | - | - |

0.5 wt.% | 2420 | 2131 | - | - | - |

1 wt.% | 2450 | 2320 | - | - | - |

2 wt.% | 2392 | 2416 | - | - | - |

4 wt.% | 659 | 679 | 1040 | 679 | 478 |

5 wt.% | 751 | 719 | 950 | 719 | 536 |

Samples | D1 = 0.3 (%) | D2 = 0.4 (%) | D3 = 0.5 (%) |
---|---|---|---|

0 wt.% | 0 | 0 | 0 |

0.5 wt.% | 8 | 10 | 10 |

1 wt.% | 12 | 18 | 26 |

2 wt.% | 47.27 | 98 | 98 |

4 wt.% | 96 | 100 | 100 |

5 wt.% | 100 | 100 | 100 |

Samples | Experimental | FEA | D1 = 0.3 | D2 = 0.4 | D3 = 0.5 |
---|---|---|---|---|---|

0 wt.% | 2.123 × 10^{−7} | 2.123 × 10^{−7} | |||

0.5 wt.% | 2.123 × 10^{−5} | 2.15 × 10^{−7} | 4.9 × 10^{−2} | 7.774 × 10^{−2} | 1.68 × 10^{−1} |

1 wt.% | 5.195 × 10^{−4} | 1.167 10^{−6} | 8.13 × 10^{−2} | 2.361 × 10^{−1} | 3.7754 × 10^{−1} |

2 wt.% | 0.2512 | 0.222 | 0.9300 | 1.5609 | 1.366 |

4 wt.% | 3.472 | 3.160 | 2.658 | 2.7572 | 4.161 |

5 wt.% | 5.549 | 5.2190 | 4.2644 | 5.2208 | 5.32 |

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**MDPI and ACS Style**

Tamayo-Vegas, S.; Muhsan, A.; Liu, C.; Tarfaoui, M.; Lafdi, K.
The Effect of Agglomeration on the Electrical and Mechanical Properties of Polymer Matrix Nanocomposites Reinforced with Carbon Nanotubes. *Polymers* **2022**, *14*, 1842.
https://doi.org/10.3390/polym14091842

**AMA Style**

Tamayo-Vegas S, Muhsan A, Liu C, Tarfaoui M, Lafdi K.
The Effect of Agglomeration on the Electrical and Mechanical Properties of Polymer Matrix Nanocomposites Reinforced with Carbon Nanotubes. *Polymers*. 2022; 14(9):1842.
https://doi.org/10.3390/polym14091842

**Chicago/Turabian Style**

Tamayo-Vegas, Sebastian, Ali Muhsan, Chang Liu, Mostapha Tarfaoui, and Khalid Lafdi.
2022. "The Effect of Agglomeration on the Electrical and Mechanical Properties of Polymer Matrix Nanocomposites Reinforced with Carbon Nanotubes" *Polymers* 14, no. 9: 1842.
https://doi.org/10.3390/polym14091842