# Investigation and Modeling of the Electrical Conductivity of Graphene Nanoplatelets-Loaded Doped-Polypyrrole

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Electrical Conductivity Models

- Aspect ratio is concerned with either shifting the percolation threshold leftward or upward; therefore, the aspect ratio can substitute the constant $a$ in the Sigmoidal equation.
- The filler roundness has an inverse relationship to the aspect ratio, as does the constant $a$ to ${x}_{o}$; in this case, the filler roundness replaced the constant ${x}_{o}$.
- The influence of surface energy on the composite is proportional to the orientation of the fillers in the matrix. This effect has an inverse impact on the electrical conductivity, as does the constant $b$. Therefore, the surface energy replaces the constant b.
- The volume fraction is taken as $x$.

## 3. Materials

^{2}/g, bulk density of 0.03–0.1 g/cm

^{3}, a diameter of 5 μm, an average thickness of 15 nm, and <1% oxygen content. The PPy has a 20 wt.% loading of carbon black. Deionized water was used for the experiment.

## 4. Processing of Polymer Composites

#### The Electrical Conductivity Measurement

## 5. Results and Discussion

#### 5.1. Morphology Analysis of the Hybrids

#### 5.2. Thermal Analysis of the Hybrids

#### 5.3. Structural Characterization

#### 5.4. HGPPy.CB_{20%} Electrical Conductivity

^{−3}S/m and 552 S/m, respectively. The electrical conductivity measurements for the $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ can be found in Figure 9. As shown in Figure 9, the electrical characteristics of the $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ changes as the weight fraction of the Gr changes. At Gr weight fraction of 0.15 wt.%, the hybrid begins continuous conduction, which connotes the percolation network formation. In other words, the percolation threshold of the hybrid occurred at 0.15 wt.%. At this point, there is a linear increment in the system’s electrical conductivity until 0.25 wt.%, when the hybrid begins to saturate. These results confirm the effectiveness and ability of Gr to improve polymers’ electrical conductivity at low or moderate quantity for diverse applications [32,55,56,57]. This, of course, can be attributed to the homogenous dispersion of Gr onto the $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$ matrix and the ability of Gr to link the carrier transport through the van der Waals force and the $\pi -\pi $ interactions exemplified by the materials [33,46].

#### 5.5. Measurement and Model Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**SEM graphs of (

**a**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 1:3 (

**b**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 3:7 (

**c**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 7:13.

**Figure 4.**Temperature of analysis of Gr and $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$. W-PPy.CB

_{20%}and W-Gr are the percentage weight curves. D-PPy.CB

_{20%}and D-Gr are the derivatives curves.

**Figure 5.**The hybrids temperature analysis: (

**a**–

**d**) percentage weight curve of $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 1:3, $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}3:7$, $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}7:13$, $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$ and (

**e**–

**h**) derivatives curve of $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$, $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 1:3, $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}3:7$, $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}7:13$.

**Figure 6.**DSC thermograms for $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$ and $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ (

**a**) $\mathrm{PPy}.{\mathrm{CB}}_{20\%}$ (

**b**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 1:3 (

**c**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 3:7 (

**d**) $\mathrm{HGPPy}.{\mathrm{CB}}_{20\%}$ 7:13.

Models | Parameter | Parameter Value | Standard Error | Per Unit Standard Error | R^{2} | R^{2}-Adj. |
---|---|---|---|---|---|---|

Weber | ${\beta}_{1}$ | 2.8504 | 0.1015 | 0.0453 | 0.923 | 0.907 |

Models | Parameters | Parameters Values | Standard Error | Per Unit Standard Error | R^{2} | R^{2}-Adj. |
---|---|---|---|---|---|---|

Clingerman | ${\alpha}_{1}$ | 1720.8 | 255.68 | 0.1486 | 0.964 | 0.927 |

${\alpha}_{2}$ | 3.8000 | 0.5413 | 0.1426 | |||

${\alpha}_{3}$ | 0.3000 | 0.0480 | 0.1594 | |||

${\alpha}_{4}$ | 1.1100 | 0.0132 | 0.0119 |

Models | Parameters | Parameters Values | Standard Error | Per Unit Standard Error | R^{2} | R^{2}-Adj. |
---|---|---|---|---|---|---|

Taherian | ${\gamma}_{1}{\sigma}_{f}$ | 2278 | 408 | 0.1789 | 0.967 | 0.950 |

${\gamma}_{2}$ | 10.54 | 2.96 | 0.2810 | |||

${\gamma}_{3}$ | 0.19 | 0.04 | 0.2270 |

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**MDPI and ACS Style**

Folorunso, O.; Hamam, Y.; Sadiku, R.; Ray, S.S.; Kumar, N.
Investigation and Modeling of the Electrical Conductivity of Graphene Nanoplatelets-Loaded Doped-Polypyrrole. *Polymers* **2021**, *13*, 1034.
https://doi.org/10.3390/polym13071034

**AMA Style**

Folorunso O, Hamam Y, Sadiku R, Ray SS, Kumar N.
Investigation and Modeling of the Electrical Conductivity of Graphene Nanoplatelets-Loaded Doped-Polypyrrole. *Polymers*. 2021; 13(7):1034.
https://doi.org/10.3390/polym13071034

**Chicago/Turabian Style**

Folorunso, Oladipo, Yskandar Hamam, Rotimi Sadiku, Suprakas Sinha Ray, and Neeraj Kumar.
2021. "Investigation and Modeling of the Electrical Conductivity of Graphene Nanoplatelets-Loaded Doped-Polypyrrole" *Polymers* 13, no. 7: 1034.
https://doi.org/10.3390/polym13071034