# Strength and Deformation Behavior of Graphene Aerogel of Different Morphologies

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## Abstract

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## 1. Introduction

## 2. Simulation Details

## 3. Results and Discussion

#### 3.1. Effect of Temperature

#### 3.2. Effect of Loading Direction

#### 3.3. Elasticity

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GA | graphene aerogel |

MD | molecular dynamics |

CNT | carbon nanotubes |

## References

- Yu, C.; Song, Y.S. Analysis of Thermoelectric Energy Harvesting with Graphene Aerogel-Supported Form-Stable Phase Change Materials. Nanomaterials
**2021**, 11, 2192. [Google Scholar] [CrossRef] [PubMed] - Tafreshi, O.; Mosanenzadeh, S.; Karamikamkar, S.; Saadatnia, Z.; Park, C.; Naguib, H. A review on multifunctional aerogel fibers: Processing, fabrication, functionalization, and applications. Mater. Today Chem.
**2022**, 23, 100736. [Google Scholar] [CrossRef] - Zhu, L.; Wang, J.; Zhang, T.; Ma, L.; Lim, C.W.; Ding, F.; Zeng, X.C. Mechanically Robust Tri-Wing Graphene Nanoribbons with Tunable Electronic and Magnetic Properties. Nano Lett.
**2010**, 10, 494–498. [Google Scholar] [CrossRef] [PubMed] - Zhang, Z.; Kutana, A.; Yang, Y.; Krainyukova, N.V.; Penev, E.S.; Yakobson, B.I. Nanomechanics of carbon honeycomb cellular structures. Carbon
**2017**, 113, 26–32. [Google Scholar] [CrossRef] - Kawai, T.; Okada, S.; Miyamoto, Y.; Oshiyama, A. Carbon three-dimensional architecture formed by intersectional collision of graphene patches. Phys. Rev. B
**2005**, 72, 035428. [Google Scholar] [CrossRef] - Pang, Z.; Gu, X.; Wei, Y.; Yang, R.; Dresselhaus, M.S. Bottom-up Design of Three-Dimensional Carbon-Honeycomb with Superb Specific Strength and High Thermal Conductivity. Nano Lett.
**2016**, 17, 179–185. [Google Scholar] [CrossRef] [PubMed] - Yu, C.; Youn, J.R.; Song, Y.S. Reversible thermo-electric energy harvesting with phase change material (PCM) composites. J. Polym. Res.
**2021**, 28, 279. [Google Scholar] [CrossRef] - Wang, H.; Lu, W.; Di, J.; Li, D.; Zhang, X.; Li, M.; Zhang, Z.; Zheng, L.; Li, Q. Ultra-Lightweight and Highly Adaptive All-Carbon Elastic Conductors with Stable Electrical Resistance. Adv. Funct. Mater.
**2017**, 27, 1606220. [Google Scholar] [CrossRef] - Thakur, A. Graphene aerogel based energy storage materials—A review. Mater. Today Proc.
**2022**, 65, 3369–3376. [Google Scholar] [CrossRef] - Gibson, L.J.; Ashby, M.F. Cellular Solids; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar] [CrossRef]
- Schaedler, T.A.; Jacobsen, A.J.; Torrents, A.; Sorensen, A.E.; Lian, J.; Greer, J.R.; Valdevit, L.; Carter, W.B. Ultralight Metallic Microlattices. Science
**2011**, 334, 962–965. [Google Scholar] [CrossRef] - Yang, J.; Li, X.; Han, S.; Zhang, Y.; Min, P.; Koratkar, N.; Yu, Z.Z. Air-dried, high-density graphene hybrid aerogels for phase change composites with exceptional thermal conductivity and shape stability. J. Mater. Chem. A
**2016**, 4, 18067–18074. [Google Scholar] [CrossRef] - Jing, J.; Qian, X.; Si, Y.; Liu, G.; Shi, C. Recent Advances in the Synthesis and Application of Three-Dimensional Graphene-Based Aerogels. Molecules
**2022**, 27, 924. [Google Scholar] [CrossRef] [PubMed] - Hu, H.; Zhao, Z.; Wan, W.; Gogotsi, Y.; Qiu, J. Ultralight and Highly Compressible Graphene Aerogels. Adv. Mater.
**2013**, 25, 2219–2223. [Google Scholar] [CrossRef] [PubMed] - Nardecchia, S.; Carriazo, D.; Ferrer, M.L.; Gutiérrez, M.C.; del Monte, F. Three dimensional macroporous architectures and aerogels built of carbon nanotubes and/or graphene: Synthesis and applications. Chem. Soc. Rev.
**2013**, 42, 794–830. [Google Scholar] [CrossRef] - Kashani, H.; Ito, Y.; Han, J.; Liu, P.; Chen, M. Extraordinary tensile strength and ductility of scalable nanoporous graphene. Sci. Adv.
**2019**, 5, eaat6951. [Google Scholar] [CrossRef] - Afroze, J.D.; Tong, L.; Abden, M.J.; Yuan, Z.; Chen, Y. Hierarchical honeycomb graphene aerogels reinforced by carbon nanotubes with multifunctional mechanical and electrical properties. Carbon
**2021**, 175, 312–321. [Google Scholar] [CrossRef] - Peng, X.; Wu, K.; Hu, Y.; Zhuo, H.; Chen, Z.; Jing, S.; Liu, Q.; Liu, C.; Zhong, L. A mechanically strong and sensitive CNT/rGO–CNF carbon aerogel for piezoresistive sensors. J. Mater. Chem. A
**2018**, 6, 23550–23559. [Google Scholar] [CrossRef] - Wasalathilake, K.C.; Galpaya, D.G.; Ayoko, G.A.; Yan, C. Understanding the structure-property relationships in hydrothermally reduced graphene oxide hydrogels. Carbon
**2018**, 137, 282–290. [Google Scholar] [CrossRef] - Shang, J.J.; Yang, Q.S.; Liu, X. New Coarse-Grained Model and Its Implementation in Simulations of Graphene Assemblies. J. Chem. Theory Comput.
**2017**, 13, 3706–3714. [Google Scholar] [CrossRef] - Si, Y.; Wang, X.; Dou, L.; Yu, J.; Ding, B. Ultralight and fire-resistant ceramic nanofibrous aerogels with temperature-invariant superelasticity. Sci. Adv.
**2018**, 4, eaas8925. [Google Scholar] [CrossRef] - Fan, Z.; Gong, F.; Nguyen, S.T.; Duong, H.M. Advanced multifunctional graphene aerogel–Poly (methyl methacrylate) composites: Experiments and modeling. Carbon
**2015**, 81, 396–404. [Google Scholar] [CrossRef] - Zheng, B.; Liu, C.; Li, Z.; Carraro, C.; Maboudian, R.; Senesky, D.G.; Gu, G.X. Investigation of mechanical properties and structural integrity of graphene aerogels via molecular dynamics simulations. Phys. Chem. Chem. Phys.
**2023**, 25, 21897–21907. [Google Scholar] [CrossRef] [PubMed] - Lei, J.; Liu, Z. The structural and mechanical properties of graphene aerogels based on Schwarz-surface-like graphene models. Carbon
**2018**, 130, 741–748. [Google Scholar] [CrossRef] - Qin, Z.; Jung, G.S.; Kang, M.J.; Buehler, M.J. The mechanics and design of a lightweight three-dimensional graphene assembly. Sci. Adv.
**2017**, 3, e1601536. [Google Scholar] [CrossRef] [PubMed] - Xu, Z.; Zhang, Y.; Li, P.; Gao, C. Strong, Conductive, Lightweight, Neat Graphene Aerogel Fibers with Aligned Pores. ACS Nano
**2012**, 6, 7103–7113. [Google Scholar] [CrossRef] [PubMed] - Ha, H.; Shanmuganathan, K.; Ellison, C.J. Mechanically Stable Thermally Crosslinked Poly(acrylic acid)/Reduced Graphene Oxide Aerogels. ACS Appl. Mater. Interfaces
**2015**, 7, 6220–6229. [Google Scholar] [CrossRef] - Hong, J.Y.; Yun, S.; Wie, J.J.; Zhang, X.; Dresselhaus, M.S.; Kong, J.; Park, H.S. Cartilage-inspired superelastic ultradurable graphene aerogels prepared by the selective gluing of intersheet joints. Nanoscale
**2016**, 8, 12900–12909. [Google Scholar] [CrossRef] - Chen, Y.; Yang, Y.; Xiong, Y.; Zhang, L.; Xu, W.; Duan, G.; Mei, C.; Jiang, S.; Rui, Z.; Zhang, K. Porous aerogel and sponge composites: Assisted by novel nanomaterials for electromagnetic interference shielding. Nano Today
**2021**, 38, 101204. [Google Scholar] [CrossRef] - Ren, W.; Cheng, H.M. When two is better than one. Nature
**2013**, 497, 448–449. [Google Scholar] [CrossRef] - Guo, F.; Jiang, Y.; Xu, Z.; Xiao, Y.; Fang, B.; Liu, Y.; Gao, W.; Zhao, P.; Wang, H.; Gao, C. Highly stretchable carbon aerogels. Nat. Commun.
**2018**, 9, 881. [Google Scholar] [CrossRef] - Wang, H.; Cao, Q.; Peng, Q.; Liu, S. Atomistic Study of Mechanical Behaviors of Carbon Honeycombs. Nanomaterials
**2019**, 9, 109. [Google Scholar] [CrossRef] [PubMed] - Tong, H.; Chen, H.; Zhao, Y.; Liu, M.; Cheng, Y.; Lu, J.; Tao, Y.; Du, J.; Wang, H. Robust PDMS-based porous sponge with enhanced recyclability for selective separation of oil-water mixture. Colloids Surf. A Physicochem. Eng. Asp.
**2022**, 648, 129228. [Google Scholar] [CrossRef] - Yu, X.; Liang, X.; Zhao, T.; Zhu, P.; Sun, R.; Wong, C.P. Thermally welded honeycomb-like silver nanowires aerogel backfilled with polydimethylsiloxane for electromagnetic interference shielding. Mater. Lett.
**2021**, 285, 129065. [Google Scholar] [CrossRef] - Sun, H.; Xu, Z.; Gao, C. Multifunctional, Ultra-Flyweight, Synergistically Assembled Carbon Aerogels. Adv. Mater.
**2013**, 25, 2554–2560. [Google Scholar] [CrossRef] [PubMed] - Park, O.K.; Tiwary, C.S.; Yang, Y.; Bhowmick, S.; Vinod, S.; Zhang, Q.; Colvin, V.L.; Asif, S.A.S.; Vajtai, R.; Penev, E.S.; et al. Magnetic field controlled graphene oxide-based origami with enhanced surface area and mechanical properties. Nanoscale
**2017**, 9, 6991–6997. [Google Scholar] [CrossRef] [PubMed] - Cao, L.; Fan, F. Deformation and instability of three-dimensional graphene honeycombs under in-plane compression: Atomistic simulations. Extrem. Mech. Lett.
**2020**, 39, 100861. [Google Scholar] [CrossRef] - Morris, B.; Becton, M.; Wang, X. Mechanical abnormality in graphene-based lamellar superstructures. Carbon
**2018**, 137, 196–206. [Google Scholar] [CrossRef] - Meng, F.; Chen, C.; Hu, D.; Song, J. Deformation behaviors of three-dimensional graphene honeycombs under out-of-plane compression: Atomistic simulations and predictive modeling. J. Mech. Phys. Solids
**2017**, 109, 241–251. [Google Scholar] [CrossRef] - Shokrieh, M.M.; Rafiee, R. A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites. Mech. Compos. Mater.
**2010**, 46, 155–172. [Google Scholar] [CrossRef] - Young, R.J.; Kinloch, I.A.; Gong, L.; Novoselov, K.S. The mechanics of graphene nanocomposites: A review. Compos. Sci. Technol.
**2012**, 72, 1459–1476. [Google Scholar] [CrossRef] - Yang, Y.; Shi, E.; Li, P.; Wu, D.; Wu, S.; Shang, Y.; Xu, W.; Cao, A.; Yuan, Q. A compressible mesoporous SiO
_{2}sponge supported by a carbon nanotube network. Nanoscale**2014**, 6, 3585. [Google Scholar] [CrossRef] - Fan, Z.; Tng, D.Z.Y.; Lim, C.X.T.; Liu, P.; Nguyen, S.T.; Xiao, P.; Marconnet, A.; Lim, C.Y.; Duong, H.M. Thermal and electrical properties of graphene/carbon nanotube aerogels. Colloids Surf. A Physicochem. Eng. Asp.
**2014**, 445, 48–53. [Google Scholar] [CrossRef] - Qiu, L.; Liu, J.Z.; Chang, S.L.; Wu, Y.; Li, D. Biomimetic superelastic graphene-based cellular monoliths. Nat. Commun.
**2012**, 3, 1241. [Google Scholar] [CrossRef] - Zhu, C.; Han, T.Y.J.; Duoss, E.B.; Golobic, A.M.; Kuntz, J.D.; Spadaccini, C.M.; Worsley, M.A. Highly compressible 3D periodic graphene aerogel microlattices. Nat. Commun.
**2015**, 6, 6962. [Google Scholar] [CrossRef] [PubMed] - Hyun, S.; Torquato, S. Effective elastic and transport properties of regular honeycombs for all densities. J. Mater. Res.
**2000**, 15, 1985–1993. [Google Scholar] [CrossRef] - Grima, J.N.; Oliveri, L.; Attard, D.; Ellul, B.; Gatt, R.; Cicala, G.; Recca, G. Hexagonal Honeycombs with Zero Poisson’s Ratios and Enhanced Stiffness. Adv. Eng. Mater.
**2010**, 12, 855–862. [Google Scholar] [CrossRef] - Goldstein, R.V.; Gorodtsov, V.A.; Lisovenko, D.S. The elastic properties of hexagonal auxetics under pressure. Phys. Status Solidi (B)
**2016**, 253, 1261–1269. [Google Scholar] [CrossRef] - Goldstein, R.; Lisovenko, D.; Chentsov, A.; Lavrentyev, S. Experimental study of defects influence on auxetic behavior of cellular structure with curvilinear elements. Lett. Mater.
**2017**, 7, 355–358. [Google Scholar] [CrossRef] - Yang, M.; Zhao, N.; Cui, Y.; Gao, W.; Zhao, Q.; Gao, C.; Bai, H.; Xie, T. Biomimetic Architectured Graphene Aerogel with Exceptional Strength and Resilience. ACS Nano
**2017**, 11, 6817–6824. [Google Scholar] [CrossRef] - Available online: https://www.lammps.org (accessed on 24 November 2023).
- Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys.
**1995**, 117, 1–19. [Google Scholar] [CrossRef] - Thompson, A.P.; Aktulga, H.M.; Berger, R.; Bolintineanu, D.S.; Brown, W.M.; Crozier, P.S.; in ’t Veld, P.J.; Kohlmeyer, A.; Moore, S.G.; Nguyen, T.D.; et al. LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun.
**2022**, 271, 108171. [Google Scholar] [CrossRef] - Stuart, S.J.; Tutein, A.B.; Harrison, J.A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys.
**2000**, 112, 6472–6486. [Google Scholar] [CrossRef] - Patil, S.P.; Shendye, P.; Markert, B. Molecular Investigation of Mechanical Properties and Fracture Behavior of Graphene Aerogel. J. Phys. Chem. B
**2020**, 124, 6132–6139. [Google Scholar] [CrossRef] - Baimova, J.; Rysaeva, L.; Rudskoy, A. Deformation behavior of diamond-like phases: Molecular dynamics simulation. Diam. Relat. Mater.
**2018**, 81, 154–160. [Google Scholar] [CrossRef] - Shang, J.; Yang, Q.S.; Liu, X.; Wang, C. Compressive deformation mechanism of honeycomb-like graphene aerogels. Carbon
**2018**, 134, 398–410. [Google Scholar] [CrossRef] - Rysaeva, L.K.; Baimova, J.A.; Lisovenko, D.S.; Gorodtsov, V.A.; Dmitriev, S.V. Elastic Properties of Fullerites and Diamond-Like Phases. Phys. Status Solidi (B)
**2018**, 256, 1800049. [Google Scholar] [CrossRef] - Safina, L.; Baimova, J.; Krylova, K.; Murzaev, R.; Mulyukov, R. Simulation of metal-graphene composites by molecular dynamics: A review. Lett. Mater.
**2020**, 10, 351–360. [Google Scholar] [CrossRef] - Wei, Y.; Wu, J.; Yin, H.; Shi, X.; Yang, R.; Dresselhaus, M. The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene. Nat. Mater.
**2012**, 11, 759–763. [Google Scholar] [CrossRef] - O’Connor, T.C.; Andzelm, J.; Robbins, M.O. AIREBO-M: A reactive model for hydrocarbons at extreme pressures. J. Chem. Phys.
**2015**, 142, 024903. [Google Scholar] [CrossRef] - Du, Y.; Zhou, J.; Ying, P.; Zhang, J. Effects of cell defects on the mechanical and thermal properties of carbon honeycombs. Comput. Mater. Sci.
**2021**, 187, 110125. [Google Scholar] [CrossRef] - Hu, J.; Zhou, J.; Zhang, A.; Yi, L.; Wang, J. Temperature dependent mechanical properties of graphene based carbon honeycombs under tension and compression. Phys. Lett. A
**2021**, 391, 127130. [Google Scholar] [CrossRef] - Li, B.; Wei, Y.; Meng, F.; Ou, P.; Chen, Y.; Che, L.; Chen, C.; Song, J. Atomistic simulations of vibration and damping in three-dimensional graphene honeycomb nanomechanical resonators. Superlattices Microstruct.
**2020**, 139, 106420. [Google Scholar] [CrossRef] - Zhang, P.; Ma, L.; Fan, F.; Zeng, Z.; Peng, C.; Loya, P.E.; Liu, Z.; Gong, Y.; Zhang, J.; Zhang, X.; et al. Fracture toughness of graphene. Nat. Commun.
**2014**, 5, 3782. [Google Scholar] [CrossRef] [PubMed] - Zhao, H.; Min, K.; Aluru, N.R. Size and Chirality Dependent Elastic Properties of Graphene Nanoribbons under Uniaxial Tension. Nano Lett.
**2009**, 9, 3012–3015. [Google Scholar] [CrossRef] [PubMed] - Liu, Y.; Liu, J.; Yue, S.; Zhao, J.; Ouyang, B.; Jing, Y. Atomistic Simulations on the Tensile Deformation Behaviors of Three-Dimensional Graphene. Phys. Status Solidi (B)
**2018**, 255, 1700680. [Google Scholar] [CrossRef] - Jung, G.S.; Irle, S.; Sumpter, B.G. Dynamic aspects of graphene deformation and fracture from approximate density functional theory. Carbon
**2022**, 190, 183–193. [Google Scholar] [CrossRef] - Srinivasan, S.G.; van Duin, A.C.T.; Ganesh, P. Development of a ReaxFF Potential for Carbon Condensed Phases and Its Application to the Thermal Fragmentation of a Large Fullerene. J. Phys. Chem. A
**2015**, 119, 571–580. [Google Scholar] [CrossRef] - Zhao, H.; Aluru, N.R. Temperature and strain-rate dependent fracture strength of graphene. J. Appl. Phys.
**2010**, 108, 064321. [Google Scholar] [CrossRef] - Magnin, Y.; Rondepierre, F.; Cui, W.; Dunstan, D.; San-Miguel, A. Collapse phase diagram of carbon nanotubes with arbitrary number of walls. Collapse modes and macroscopic analog. Carbon
**2021**, 178, 552–562. [Google Scholar] [CrossRef] - Gu, X.; Pang, Z.; Wei, Y.; Yang, R. On the influence of junction structures on the mechanical and thermal properties of carbon honeycombs. Carbon
**2017**, 119, 278–286. [Google Scholar] [CrossRef] - Qi, P.; Zhu, H.; Borodich, F.; Peng, Q. A Review of the Mechanical Properties of Graphene Aerogel Materials: Experimental Measurements and Computer Simulations. Materials
**2023**, 16, 1800. [Google Scholar] [CrossRef] [PubMed] - Qiu, L.; Huang, B.; He, Z.; Wang, Y.; Tian, Z.; Liu, J.Z.; Wang, K.; Song, J.; Gengenbach, T.R.; Li, D. Extremely Low Density and Super-Compressible Graphene Cellular Materials. Adv. Mater.
**2017**, 29, 1701553. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Three morphologies of honeycomb graphene aerogel: honeycomb, re-entrant honeycomb, and arrow-honeycomb. (

**a**) Part of the simulation cell in projection to $xz$ plane. (

**b**) Part of the simulation cell on an enlarged scale as the projection to $xz$-plane and in perspective.

**Figure 2.**(

**a**) Stress–strain curves as the function of strain during tension along x-axis for honeycomb GA. The critical points on the stress–strain curve are labeled as 1–5. (

**b**) The snapshots of the structure as the projection on $xz$-plane at critical points for tension at 300 K. Part of the simulation cell is presented. (

**c**,

**d**) Stress ${\sigma}_{xx}$ per atom (

**c**) and potential energy per atom (

**d**) during tension. Part of the simulation cell (one honeycomb cell) is presented.

**Figure 3.**(

**a**) Stress–strain curves as the function of strain during tension along x-axis for re-entrant honeycomb GA. The critical points on the stress–strain curve are labeled as 1–7. (

**b**) The snapshots of the structure as the projection on $xz$-plane at critical points. Part of the simulation cell is presented.

**Figure 4.**(

**a**) Stress–strain curves during tension along x-axis for arrow-honeycomb. The critical points on the stress–strain curve were labeled as 1–5. (

**b**) The snapshots of the structure as the projection on $xz$-plane at critical points. Part of the simulation cell is presented. (

**c**,

**d**) Stress ${\sigma}_{xx}$ per atom (

**c**) and potential energy per atom (

**d**) during tension. Part of the simulation cell (one structural element) is presented.

**Figure 5.**Stress–strain curves as the function of strain during tension along x- and z-axis for (

**a**) honeycomb and re-entrant honeycomb; (

**b**) for arrow honeycomb.

**Table 1.**Density, tensile strength $\sigma $, and failure strain $\epsilon $ for all the considered GA.

Honeycomb | Re-Entrant | Arrow | |||||||
---|---|---|---|---|---|---|---|---|---|

GA Matrix | Flakes | CNT | GA Matrix | Flakes | CNT | GA Matrix | Flakes | CNT | |

$\rho $, g/cm${}^{3}$ | 0.58 | 0.86 | 0.92 | 1.01 | 1.31 | 1.58 | 0.69 | 1.21 | 1.0 |

$\sigma $, GPa | 190 | 156 | 110 | 180 | 160 | 101 | 31 | 27 | 33 |

$\epsilon $ | 0.79 | 0.76 | 0.72 | 0.8 | 0.76 | 0.7 | 0.36 | 0.37 | 0.38 |

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**MDPI and ACS Style**

Baimova, J.A.; Shcherbinin, S.A.
Strength and Deformation Behavior of Graphene Aerogel of Different Morphologies. *Materials* **2023**, *16*, 7388.
https://doi.org/10.3390/ma16237388

**AMA Style**

Baimova JA, Shcherbinin SA.
Strength and Deformation Behavior of Graphene Aerogel of Different Morphologies. *Materials*. 2023; 16(23):7388.
https://doi.org/10.3390/ma16237388

**Chicago/Turabian Style**

Baimova, Julia A., and Stepan A. Shcherbinin.
2023. "Strength and Deformation Behavior of Graphene Aerogel of Different Morphologies" *Materials* 16, no. 23: 7388.
https://doi.org/10.3390/ma16237388