#
Molecular Dynamics Modeling of Mechanical Properties of Polymer Nanocomposites Reinforced by C_{7}N_{6} Nanosheet

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## Abstract

**:**

## 1. Introduction

## 2. Simulation Methodology

#### 2.1. Potential and Uniaxial Tensile for ${C}_{7}{N}_{6}$ Monolayer

#### 2.2. ${C}_{7}{N}_{6}/P3HT$ Nanocomposite Mechanical Test

#### 2.3. Cohesive Model for ${C}_{7}{N}_{6}$—$P3HT$ Interface Investigation

## 3. Results and Discussion

#### 3.1. ${C}_{7}{N}_{6}$ Mechanical Properties and Thermal Stability Test

#### 3.2. ${C}_{7}{N}_{6}$ Fracture Analysis

#### 3.3. ${C}_{7}{N}_{6}/P3HT$ Composite Deformation

#### 3.4. Interfacial Mechanical Properties

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Atomic Structures in VASP POSCAR Format

`C7N6`

`1.00000000000000`

`6.7943948564804693 0.0000000000000000 0.0000000000000000`

`3.3971974282402351 5.8841185491832784 0.0000000000000000`

`0.0000000000000000 0.0000000000000000 15.0000000000000000`

`C N`

`7 6`

`Direct`

`0.9998100576047193 0.0002509396813224 0.5000000000000000`

`0.9331640163519950 0.7159702217766863 0.5000000000000000`

`0.9331204068991781 0.3511955830278453 0.5000000000000000`

`0.7155979589857679 0.9335029314294445 0.5000000000000000`

`0.7155586812735208 0.3512017827147176 0.5000000000000000`

`0.3507638336030467 0.9335002995972488 0.5000000000000000`

`0.3507380370779813 0.7159747027046279 0.5000000000000000`

`0.1110737155275103 0.1115015469972604 0.5000000000000000`

`0.1110716970172021 0.7777302000807538 0.5000000000000000`

`0.9928516147958462 0.5037223459642206 0.5000000000000000`

`0.7772919263856721 0.1115054214509428 0.5000000000000000`

`0.5034145543584359 0.9930456207717029~0.5000000000000000`

## Appendix B. Tersoff Potential to Simulate Mechanical Properties of C 7 N 6

`# DATE: 2013-03-21 CONTRIBUTOR: Cem Sevik CITATION: Kinaci, Haskins, Sevik and Cagin, Phys Rev B, 86, 115410 (2012)`

`# Tersoff parameters for B, C, and~BN-C hybrid based graphene like nano structures`

`# multiple entries can be added to this file, LAMMPS reads the ones it~needs`

`# these entries are in LAMMPS "metal" units:`

`# A,B = eV; lambda1,lambda2,lambda3 = 1/Angstroms; R,D = Angstroms`

`# other quantities are~unitless`

`# Cem Sevik (csevik at anadolu.edu.tr) takes full blame for this`

`# file. It specifies B-N, B-C, and~N-C interaction parameters`

`# generated and published by the reseacrh group of Prof. Tahir~Cagin.`

`# 1. Physical Review B 84, 085409 2011`

`# Characterization of thermal transport in low-dimensional boron nitride nanostructures,`

`#`

`# 2. Physical Review B 86, 075403 2012`

`# Influence of disorder on thermal transport properties of boron nitride nanostructures`

`#`

`# 3. Physical Review B 86, 075403 2012, Please see for further information about B-C and N-C parameters`

`# Thermal conductivity of BN-C nanostructures`

`#`

`# The file also specifies C-C, interaction parameters`

`# generated and published by the reseacrh group of Dr. D. A. Broido`

`# Physical Review B 81, 205441 2010`

`# Optimized Tersoff and Brenner empirical potential parameters for`

`# lattice dynamics and phonon thermal transport in carbon nanotubes and~graphene`

`# Users in referring the full parameters can cite the full parameter paper (3) as:`

`# A. Kinaci, J. B. Haskins, C. Sevik, T. Cagin, Physical Review B 86, 115410 (2012)`

`# Thermal conductivity of BN-C nanostructures`

`#`

`# format of a single entry (one or more lines):`

`# element 1, element 2, element 3,`

`# m, gamma, lambda3, c, d, costheta0, n, beta, lambda2, B, R, D, lambda1, A`

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**Figure 1.**Schematic illustration of the uniaxial tensile of ${C}_{7}{N}_{6}$ structure via VESTA [26]; (

**a**) ${C}_{7}{N}_{6}$ monolayer with a size of $164.75$ × $67.94$ Å; (

**b**) the single lattice structure of ${C}_{7}{N}_{6}$; (

**c**) boundary condition of ${C}_{7}{N}_{6}$ for uniaxial tensile.

**Figure 2.**Normal stress-strain of ${C}_{7}{N}_{6}$ with different temperatures and constant strain rate ($2.0\times {10}^{9}$ s${}^{-1}$); (

**a**) the uniaxial tensile in X-direction, the critical strain state related to maximum stress and different temperatures are respectively as follows: 0.146 (300 K), 0.123 (500 K), 0.108 (700 K), 0.101 (900 K), 0.090 (1100 K); and (

**b**) uniaxial tensile in Y-direction, the corresponding critical strains are: 0.161 (300 K), 0.152 (500 K), 0.135 (700 K), 0.126 (900 K), 0.087 (1100 K).

**Figure 3.**(

**a**) Stress-strain response for ${C}_{7}{N}_{6}$ monolayer with different strain rates in uniaxial tensile (X-direction) at 300 K; and (

**b**) isotropic modulus and anisotropic strength behavior: axis X, and Y-direction comparing for ${C}_{7}{N}_{6}$ monolayer in 300 K with a constant strain rate of $2.0\times {10}^{9}$ s${}^{-1}$.

**Figure 4.**Fracture evaluation of ${C}_{7}{N}_{6}$ monolayer from (

**a**–

**d**) the uniaxial tensile is under a constant strain rate of $2.0\times {10}^{9}$ s${}^{-1}$ at 300 K, the loading was carried out in the X-direction, graph (

**c**,

**d**) shows the zoom of the crack zone.

**Figure 5.**Fracture evaluation of ${C}_{7}{N}_{6}$ monolayer from (

**a**–

**d**) the uniaxial tensile is under a constant strain rate of $2.0\times {10}^{9}$ s${}^{-1}$ at 300 K, the loading was carried out in the Y-direction, graph (

**c**,

**d**) shows the zoom of the crack zone.

**Figure 6.**(

**a**) Stress-strain curve of ${C}_{7}{N}_{6}/P3HT$ composite at 300K and pure $P3HT$ polymer, with a constant strain rate of $6.0\times {10}^{9}$ s${}^{-1}$, the load was carried in X-direction; (

**b**) ${C}_{7}{N}_{6}/P3HT$ nanocomposite with the volume fraction from $5\%$ to $15\%$ cubic structure.

**Figure 7.**Cohesive model test for ${C}_{7}{N}_{6}$ separated from $P3HT$ polymer matrix; (

**a**) comparing between a theoretical method with molecular dynamics simulation; (

**b**) Cohesive structure of ${C}_{7}{N}_{6}$ monolayer and matrix.

**Table 1.**Parameters for atoms in the cohesive model. The mole ratio represents the type of atoms for each unit or each single lattice structure.

Types | Mass (g/mol) | $\mathit{\sigma}$ (Å) | $\mathit{\epsilon}$ (kcal/mol) | Mole Ratio | Comment | |
---|---|---|---|---|---|---|

${C}_{7}{N}_{6}$ | c | 12.011 | 0.054 | 4.010 | 7/13 | generic $S{p}^{3}$ carbon |

n | 14.007 | 0.096 | 3.830 | 1/13 | generic $S{p}^{2}$ carbon | |

n2 | 14.007 | 0.050 | 4.010 | 3/13 | generic nitrogen | |

n3 | 14.007 | 0.015 | 3.720 | 2/13 | generic nitrogen | |

P3HT | c3a | 12.011 | 0.068 | 3.915 | 6/25 | generic $S{p}^{3}$ carbon |

s2a | 32.064 | 0.125 | 4.047 | 1/25 | generic sulphur | |

h1 | 1.008 | 0.032 | 2.878 | 14/25 | generic hydrogen | |

c4 | 12.011 | 0.062 | 4.010 | 4/25 | generic $S{p}^{2}$ carbon |

**Table 2.**Temperature influence comparing for ${C}_{7}{N}_{6}$ monolayer in different loading directions. The maximum tensile stress unit is GPa.nm.

Loading Direction | X | Y | ||
---|---|---|---|---|

Temperatures (K) | Stress $\left({\mathbf{\sigma}}_{\mathit{xx}}\right)$ | Strain $\left({\mathbf{\epsilon}}_{\mathit{xx}}\right)$ | Stress $\left({\mathbf{\sigma}}_{\mathit{xx}}\right)$ | Strain $\left({\mathbf{\epsilon}}_{\mathit{xx}}\right)$ |

300 | 18.101 | 0.146 | 19.908 | 0.161 |

500 | 15.815 | 0.123 | 17.306 | 0.152 |

700 | 12.997 | 0.108 | 14.465 | 0.135 |

900 | 11.317 | 0.101 | 12.391 | 0.126 |

1100 | 9.388 | 0.090 | 8.942 | 0.087 |

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**MDPI and ACS Style**

Zhang, Q.; Mortazavi, B.; Aldakheel, F.
Molecular Dynamics Modeling of Mechanical Properties of Polymer Nanocomposites Reinforced by *C*_{7}*N*_{6} Nanosheet. *Surfaces* **2021**, *4*, 240-254.
https://doi.org/10.3390/surfaces4030019

**AMA Style**

Zhang Q, Mortazavi B, Aldakheel F.
Molecular Dynamics Modeling of Mechanical Properties of Polymer Nanocomposites Reinforced by *C*_{7}*N*_{6} Nanosheet. *Surfaces*. 2021; 4(3):240-254.
https://doi.org/10.3390/surfaces4030019

**Chicago/Turabian Style**

Zhang, Qinghua, Bohayra Mortazavi, and Fadi Aldakheel.
2021. "Molecular Dynamics Modeling of Mechanical Properties of Polymer Nanocomposites Reinforced by *C*_{7}*N*_{6} Nanosheet" *Surfaces* 4, no. 3: 240-254.
https://doi.org/10.3390/surfaces4030019