# Review on Molecular Dynamics Simulations of Effects of Carbon Nanotubes (CNTs) on Electrical and Thermal Conductivities of CNT-Modified Polymeric Composites

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fundamental Concepts

#### 2.1. Dispersion of Carbon Nanotubes

#### 2.2. Thermal Conductivity

#### 2.3. Electrical Conductivity

#### 2.4. Chirality of CNTs

**R**= m

**a**

**+ n**

_{1}**a**

**represents the chirality and diameter of SWNTs, where**

_{2}**R**is the lattice vector of two-dimensional graphene, m and n are integers;

**a**and

_{1}**a**are the unit vectors of the graphene. The schematic diagram of the chirality of a graphene is shown in Figure 1, and the diameter of a SWNT is defined as

_{2}**R**and the orientation of the zigzag SWNT [34,35]. It is represented as

#### 2.5. Some of the MD Techniques Used in the Literatures of This Review

^{REBO}potential was developed by Brenner. Here, the E

^{REBO}used to describe the interactions between covalent atoms has the same form as in [43,44] and has the same coefficients as the Brenner potential function, that is:

^{LJ}term, defined as [45]:

^{TORTION}term.

_{0}is the Fermi–Dirac distribution, μ is the Fermi level, and${E}_{qr}\left(E\right)$ is the transport coefficients defined as

_{i,q}is the velocity of the ith band along q, N

_{k}is the number of k-points over the cell volume V, and the lifetime, τ, is 1 fs for all studied systems. The conductivity is shown as the summation of the α and β spin states [49,50].

#### 2.6. Effectivity of Hydrogen Bonding for CNT Alignment

^{−1}), where S is 1/ohm.

_{B}is the Boltzmann constant, and m

_{k}and v

_{k}are the atomic mass and velocity of the atom k, respectively [54].

## 3. Results and Discussion

#### 3.1. Effects of CNT Chirality and Length

^{3}to 15 × 10

^{3}, the electrical conductivity is much higher than that of the zigzag SWNTs. For lower amounts of CNTs, the electrical conductivities of the armchair and the zigzag SWNTs have increased sharply with the increase in the CNT volume fraction, but this upward trend continues as the slop of higher volume fraction decreases. For a high-volume fraction of CNTs, the electrical conductivity starts to decrease, mainly because CNTs cannot be distributed well in the matrix of the composite material very well [66,68,69,70].

^{−7}, −37.12, 31.43, and −394.3 for zigzag CNTs, respectively. σ

_{c}represents electrical conductivity and V

_{f}stands for volume fraction of CNTs.

_{c}represents electrical conductivity and L stands for length of CNTs.

#### 3.2. Effect of CNT Overlap Length by Hydrogen Bonds

_{2}O and 75% polyurethane/25% H

_{2}O containing 4.5 wt.% MWNT-OH are 80 and 4.1 Ω·cm, respectively, 8 times and 207 times lower than the resistivities of the samples without H

_{2}O, respectively. Therefore, the composites of 75% polycrylic/25%H

_{2}O and 75% polyurethane/ 25% H

_{2}O with 4.5 wt.% MWNT-OH have a higher electrical conductivity than that of the samples without H

_{2}O. Table 3 shows the effect of H

_{2}O on the electrical conductivity and resistivity of CNT-modified composites [51,81,82].

_{2}O with the same MWNT-OH concentration, the thermal conductivity increases by 82.6%.

_{2}O does not always help increase the thermal conductivity of the f-CNT reinforced samples. When adding 25 wt.% H

_{2}O to a polyurethane sample with 4.5 wt.% MWNT-OH, the thermal conductivity did not increase significantly. The reason is that as the concentration of carbon nanofillers increases, H

_{2}O acts more like hydrogen bonding auxiliary than a dispersing aid, while extra hydrogen bonds are conducive to electrical conductivity rather than thermal conductivity [83,84]. Therefore, as the gaps between the tubes and the fibers decrease, the thermal conductivity will not increase, and physical contact needs to improve the thermal energy transport.

^{−8}WK

^{−1}to 1.64 × 10

^{−8}WK

^{−1}. For f-CNTs, hydrogen bonds are formed on the junction, and the thermal conductivity mainly depends on the number of hydrogen bonds. Therefore, as the overlap length increases, the hydrogen bond increases and the thermal conductivity increases.

**Table 3.**Measured electric resistivities and conductivities of polyurethane and polycrylic-based coatings containing 4.5%wt CNTs nanocomposites, with or without H

_{2}O [86].

Base Coating | Resistivity (Ω cm) | Electrical Conductivity (S/cm) |
---|---|---|

Polyurethane | 850 | 1.2 × 10^{−3} |

75% Polyurethane/25% H_{2}O | 4.1 | 0.24 |

Polycrylic | 690 | 1.45 × 10^{−3} |

75% Polycrylic/25% H_{2}O | 80 | 0.0125 |

#### 3.3. Other Factors’ Effects on Thermal and Electrical Properties of CNTs

## 4. Conclusions

_{2}O, and with the increase in hydrogen bonds, the electrical conductivity increases and the resistivity decreases. However, for thermal conductivity, it depends on the composites; in some cases, the thermal conductivity increases in the presence of H

_{2}O, but not in others. So, the extra hydrogen bonds are beneficial for electrical conductivity, but not always good for the thermal conductivity. In addition, the overlap length of the CNTs by hydrogen bonds affects the thermal conductivity, since the thermal conductivity also depends on the number of hydrogen bonds, and the thermal conductivity increases with the increase in the overlap length and the increase in the hydrogen bonds.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the chirality of a graphene hexagonal lattice with lattice vectors

**𝑎**and

_{1}**𝑎**.

_{2}**Figure 2.**(

**a**) Schematic structure of a SWNT used in MD simulations and (

**b**) a typical temperature profile along the axial length of a SWNT with a chirality (12, 12).

**Figure 3.**(

**a**) The schematic diagram of the overlap of two parallel aligned CNTs by hydrogen bonds with an overlap length of 3.934 nm (Δx) and free boundary conditions in all directions. (

**b**) The temperature profile of the corresponding structure.

**Figure 4.**Chiral angle vs. thermal conductivity of smaller diameter shorter SWNTs with a tube length of 20 nm (Group A), larger diameter shorter SWNTs with a tube length of 20 nm (Group B), and smaller diameter longer SWNTs with a tube length of 50 nm (Group C).

**Figure 7.**Thermal conductance G, and thermal conductance per unit overlap length σ as a function of overlap length Δx.

Group A | Group B | Group C | |||
---|---|---|---|---|---|

Chiral Angle (°) | Thermal Conductivity (W/m·K) | Chiral Angle (°) | Thermal Conductivity (W/m·K) | Chiral Angle (°) | Thermal Conductivity (W/m·K) |

5.0 | 105.6 | 1.0 | 110.3 | 5.0 | 125.2 |

5.0 | 100.2 | ||||

12.5 | 112.5 | 7.5 | 118.1 | 13.0 | 130.2 |

12.5 | 130.4 | ||||

17.5 | 134.2 | 15.0 | 140.2 | 17.5 | 122.2 |

20.0 | 150.1 | ||||

22.5 | 130.3 | 22.5 | 125.1 | 23.0 | 132.1 |

25.0 | 140.3 | ||||

27.5 | 110.1 | 27.5 | 120.0 | 28.0 | 139.1 |

30.0 | 122.3 |

Length (mm) | Armchair Electrical Conductivity (m/s) | Zigzag Electrical Conductivity (m/s) |
---|---|---|

0.01 | 2 × 10^{−2} | 3 × 10^{−8} |

0.015 | 10^{−1} | 10^{−7} |

0.6 | 3.02 | 2 × 10^{−6} |

0.8 | 3.15 | 2.4 × 10^{−6} |

0.9 | 3.52 | 2.8 × 10^{−6} |

1.1 | 3.79 | 2.9 × 10^{−6} |

1.3 | 3.81 | 3 × 10^{−6} |

Volume Fraction | Armchair Electrical Conductivity (m/s) | Zigzag Electrical Conductivity (m/s) |

0.0005 | 10^{−1} | 10^{−7} |

0.00075 | 0.5 | 2 × 10^{−7} |

0.0010 | 1 | 10^{−6} |

0.0012 | 3 | 2 × 10^{−6} |

0.0015 | 5 | 2.5 × 10^{−6} |

0.0020 | 15 | 10^{−5} |

0.010 | 17 | 3 × 10^{−5} |

0.015 | 18 | 6 × 10^{−5} |

0.1 | 7.5 | 0.5 × 10^{−6} |

0.2 | 4.5 | 0.25 × 10^{−6} |

**Table 4.**Summary of MD simulations of thermal conductivity values at room temperature for the maximum length and different diameters.

Chirality | L (nm) | D (nm) | Thermal Conductivity (W/mK) | Electrical Conductivity (S/cm) | Simulation Method | Ref. |
---|---|---|---|---|---|---|

(10, 10) | <10 | 1.36 | 880 | 350 | EMD | [89] |

(10, 10) | <1500 | 1.351 | 355 | 80 | NEMD | [90] |

(10, 10) (18, 0) (14, 6) | 2.477–39.632 2.145–34.320 3.813–30.504 | 1.351 1.404 1.387 | 859 790 765 | 110 95 80 | EMD | [91] |

(5, 5) (10, 10) (15, 5) | Aspect ratio of 10–20 (~22 nm) | 0.68 1.36 1.41 | 4500 1700 1640 | 500 300 250 | NEMD | [92] |

(5, 5) (6, 6) (8, 8) (10, 10) | 12.2 and 24.4 | 0.68 0.81 1.08 1.35 | 410 435 365 300 | 105 120 103 100 | NEMD | [93] |

(5, 5) (10, 10) (15, 15) | 6–100 | 0.68 1.36 2.03 | ~1024 ~1023 ~1022 | 400 380 365 | EMD | [94] |

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## Share and Cite

**MDPI and ACS Style**

Najmi, L.; Hu, Z.
Review on Molecular Dynamics Simulations of Effects of Carbon Nanotubes (CNTs) on Electrical and Thermal Conductivities of CNT-Modified Polymeric Composites. *J. Compos. Sci.* **2023**, *7*, 165.
https://doi.org/10.3390/jcs7040165

**AMA Style**

Najmi L, Hu Z.
Review on Molecular Dynamics Simulations of Effects of Carbon Nanotubes (CNTs) on Electrical and Thermal Conductivities of CNT-Modified Polymeric Composites. *Journal of Composites Science*. 2023; 7(4):165.
https://doi.org/10.3390/jcs7040165

**Chicago/Turabian Style**

Najmi, Lida, and Zhong Hu.
2023. "Review on Molecular Dynamics Simulations of Effects of Carbon Nanotubes (CNTs) on Electrical and Thermal Conductivities of CNT-Modified Polymeric Composites" *Journal of Composites Science* 7, no. 4: 165.
https://doi.org/10.3390/jcs7040165