English

Nanoscale Mechanism of Microstructure-Dependent Thermal Diffusivity in Thick Graphene Sheets

• Tianqi Bai ^{1, 2, †,} ,
• Kun Huang ^{3, 4, †,} ,
• Fachen Liu ^{1, 2,} ,
• Ruochen Shi ^{1, 5,} ,
• Wencai Ren ^{3, 4,} ,
• Songfeng Pei ^{3, 4, ,} ,
• Peng Gao ^{1, 2, 5, 6, 7, 8, ,} ,
• Zhongfan Liu ^{6, 9, ,}

• 1.

  Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China

• 2.

  Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China

• 3.

  Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

• 4.

  School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

• 5.

  International Center for Quantum Materials, Peking University, Beijing 100871, China

• 6.

  Beijing Graphene Institute, Beijing 100095, China

• 7.

  Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

• 8.

  Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing 100871, China

• 9.

  National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China

Corresponding author: Email: pgao@pku.edu.cn (P.G.); Email: sfpei@imr.ac.cn (S.P.); Email: zfliu@pku.edu.cn (Z.L.)

• Received Date: 17 April 2024
  Accepted Date: 17 June 2024
  Revised Date: 13 June 2024
  Available Online: 15 March 2025
• Fund Project:

  the National Natural Science Foundation of China 

  the National Natural Science Foundation of China 

  the National Natural Science Foundation of China 

  the National Natural Science Foundation of China 

Abstract: The rapid advancement in the integration density of electronic components has led to a pressing need for effective thermal management solutions. Among the promising materials in this regard, graphene stands out due to its exceptional thermal conductivity properties. Currently, the production of ultra-high thermally conductive thick graphene sheets primarily involves the reduction of graphene oxide. However, despite significant progress, the impact of defects on thermal properties remains inadequately understood, limiting the achievement of thermal conductivity exceeding 1500 W·m^-1·K^-1. During the preparation process of reduced graphene oxide-based graphene sheets, hole structures are inevitably formed, reducing the overall density and thus decreasing thermal conductivity. However, the influencing factors on thermal diffusivity, one of the determining factors of thermal conductivity, have not been reported. Thus, we defined the intrinsic thermal diffusivity specific to materials with internal holes and further investigated the correlation between the intrinsic thermal diffusivity of thick graphene sheets and microstructure through various electron microscopy characterization, thermal diffusivity measurements, and simulations. We aim to elucidate the factors and mechanisms affecting the thermal diffusivity and hence thermal conductivity. Our research reveals subtle insights, particularly regarding the impact of holes of different sizes and quantities on thermal diffusivity. Notably, our simulation results show that a real dense-small-holes structure in graphene sheets can reduce thermal diffusivity by 39.4%, more than twice the reduction caused by a single-large-hole structure (16.1%). Statistical conclusions obtained through three-dimensional reconstruction also perfectly match these computational results. We emphasize that the presence of dense-small-holes structures disrupt the original high-speed heat transfer paths more severely, while the effect of single-large-hole structures are relatively weaker, primarily reducing overall density and thus thermal conductivity. Additionally, we found that the out-of-plane crystallinity has a significant impact on thermal diffusivity, further enhancing our understanding of microstructural factors affecting thermal diffusivity. By elucidating these mechanisms, our findings make significant contributions to the technological advancement of producing ultra-high thermally conductive thick graphene sheets. A deeper understanding of the interaction between microstructure and thermal performance brings hope for the development of next-generation electronic device thermal management solutions. Through continued research in this field, we anticipate further improvements in the performance and efficiency of graphene thermal management systems, ultimately driving innovation in electronic device design and manufacturing.

Key words:
• Thick graphene sheets
•  /  Intrinsic thermal diffusivity
•  /  Single large hole
•  /  Dense small holes
•  /  Out-of-plane crystallinity

• 1. [1]

     Moore, A. L.; Shi, L. Mater. Today 2014, 17 (4), 163. doi: 10.1016/j.mattod.2014.04.003

  2. [2]

     Garimella, S. V. Microelectron. J. 2006, 37 (11), 1165. doi: 10.1016/j.mejo.2005.07.017

  3. [3]

     Pop, E. Nano Res. 2010, 3 (3), 147. doi: 10.1007/s12274-010-1019-z

  4. [4]

     Balandin, A. A.; Ghosh, S.; Bao, W.; Calizo, I.; Teweldebrhan, D.; Miao, F.; Lau, C. N. Nano Lett. 2008, 8 (3), 902. doi: 10.1021/nl0731872

  5. [5]

     Ghosh, S.; Calizo, I.; Teweldebrhan, D.; Pokatilov, E. P.; Nika, D. L.; Balandin, A. A.; Bao, W.; Miao, F.; Lau, C. N. Appl. Phys. Lett. 2008, 92 (15), 151911. doi: 10.1063/1.2907977

  6. [6]

     Zhang, P.; Ma, L.; Fan, F.; Zeng, Z.; Peng, C.; Loya, P. E.; Liu, Z.; Gong, Y.; Zhang, J.; Zhang, X.; et al. Nat. Commun. 2014, 5 (1), 3782. doi: 10.1038/ncomms4782

  7. [7]

     Stöberl, U.; Wurstbauer, U.; Wegscheider, W.; Weiss, D.; Eroms, J. Appl. Phys. Lett. 2008, 93 (5), 051906. doi: 10.1063/1.2968310

  8. [8]

     马英杰, 智林杰. 物理化学学报, 2022, 38 (1), 2101004. doi: 10.3866/PKU.WHXB202101004Ma, Y.; Zhi, L. Acta Phys. -Chim. Sin. 2022, 38 (1), 2101004. doi: 10.3866/PKU.WHXB202101004

  9. [9]

     Renteria, J. D.; Nika, D. L.; Balandin, A. A. Appl. Sci. 2014, 4 (4), 525. doi: 10.3390/app4040525

  10. [10]

      Fu, Y.; Hansson, J.; Liu, Y.; Chen, S.; Zehri, A.; Samani, M. K.; Wang, N.; Ni, Y.; Zhang, Y.; Zhang, Z. -B.; et al. 2D Mater. 2020, 7 (1), 012001. doi: 10.1088/2053-1583/ab48d9

  11. [11]

      Park, S.; Ruoff, R. S. Nat. Nanotechnol. 2009, 4 (4), 217. doi: 10.1038/nnano.2009.58

  12. [12]

      Stankovich, S.; Dikin, D. A.; Piner, R. D.; Kohlhaas, K. A.; Kleinhammes, A.; Jia, Y.; Wu, Y.; Nguyen, S. T.; Ruoff, R. S. Carbon 2007, 45 (7), 1558. doi: 10.1016/j.carbon.2007.02.034

  13. [13]

      Pei, S.; Cheng, H. -M. Carbon 2012, 50 (9), 3210. doi: 10.1016/j.carbon.2011.11.010

  14. [14]

      Huh, S. H. Phys. Appl. Graphene: Exp. 2011, 19, 73. doi: 10.5772/14156

  15. [15]

      Teng, C.; Xie, D.; Wang, J.; Yang, Z.; Ren, G.; Zhu, Y. Adv. Funct. Mater. 2017, 27 (20), 1700240. doi: 10.1002/adfm.201700240

  16. [16]

      Ding, J.; Zhao, H.; Wang, Q.; Dou, H.; Chen, H.; Yu, H. Nanoscale 2017, 9 (43), 16871. doi: 10.1039/c7nr06667hScopus

  17. [17]

      Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; et al. Science 2006, 312 (5777), 1191. doi: 10.1126/science.1125925

  18. [18]

      Berger, C.; Song, Z.; Li, T.; Li, X.; Ogbazghi, A. Y.; Feng, R.; Dai, Z.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; et al. J. Phys. Chem. B 2004, 108 (52), 19912. doi: 10.1021/jp040650f

  19. [19]

      Emtsev, K. V.; Bostwick, A.; Horn, K.; Jobst, J.; Kellogg, G. L.; Ley, L.; McChesney, J. L.; Ohta, T.; Reshanov, S. A.; Röhrl, J.; et al. Nat. Mater. 2009, 8 (3), 203. doi: 10.1038/nmat2382

  20. [20]

      Yu, Q.; Lian, J.; Siriponglert, S.; Li, H.; Chen, Y. P.; Pei, S. -S. Appl. Phys. Lett. 2008, 93 (11), 113103. doi: 10.1063/1.2982585

  21. [21]

      Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; et al. Science 2009, 324 (5932), 1312. doi: 10.1126/science.1171245

  22. [22]

      Sun, J.; Chen, Y.; Priydarshi, M. K.; Chen, Z.; Bachmatiuk, A.; Zou, Z.; Chen, Z.; Song, X.; Gao, Y.; Rümmeli, M. H.; et al. Nano Lett. 2015, 15 (9), 5846. doi: 10.1021/acs.nanolett.5b01936

  23. [23]

      Rozada, R.; Paredes, J. I.; Villar-Rodil, S.; Martínez-Alonso, A.; Tascón, J. M. Nano Res. 2013, 6, 216. doi: 10.1007/s12274-013-0298-6

  24. [24]

      Wang, X.; Zhi, L.; Müllen, K. Nano Lett. 2008, 8 (1), 323. doi: 10.1021/nl072838r

  25. [25]

      Valles, C.; Nunez, J. D.; Benito, A. M.; Maser, W. K. Carbon 2012, 50 (3), 835. doi: 10.1016/j.carbon.2011.09.042

  26. [26]

      Chen, H.; Müller, M. B.; Gilmore, K. J.; Wallace, G. G.; Li, D. Adv. Mater. 2008, 20 (18), 3557. doi: 10.1002/adma.200800757

  27. [27]

      Akbari, A.; Cunning, B. V.; Joshi, S. R.; Wang, C.; Camacho-Mojica, D. C.; Chatterjee, S.; Modepalli, V.; Cahoon, C.; Bielawski, C. W.; Bakharev, P.; et al. Matter 2020, 2 (5), 1198. doi: 10.1016/j.matt.2020.02.014

  28. [28]

      Xu, F.; Chen, R.; Lin, Z.; Sun, X.; Wang, S.; Yin, W.; Peng, Q.; Li, Y.; He, X. J. Mater. Chem. C 2018, 6 (45), 12321. doi: 10.1039/C8TC04008G

  29. [29]

      Chen, X.; Deng, X.; Kim, N. Y.; Wang, Y.; Huang, Y.; Peng, L.; Huang, M.; Zhang, X.; Chen, X.; Luo, D.; et al. Carbon 2018, 132, 294. doi: 10.1016/j.carbon.2018.02.049

  30. [30]

      Zhang, P.; Hao, Y.; Shi, H.; Lu, J.; Liu, Y.; Ming, X.; Wang, Y.; Fang, W.; Xia, Y.; Chen, Y.; et al. Nano-Micro Lett. 2023, 16 (1), 58. doi: 10.1007/s40820-023-01277-1

  31. [31]

      Hao, Y.; Ming, X.; Lu, J.; Cao, M.; Zhang, P.; Shi, H.; Li, K.; Gao, Y.; Wang, L.; Fang, W.; et al. Adv. Funct. Mater. 2024, 34, 2400110. doi: 10.1002/adfm.202400110

  32. [32]

      Peng, L.; Xu, Z.; Liu, Z.; Guo, Y.; Li, P.; Gao, C. Adv. Mater. 2017, 29 (27), 1700589. doi: 10.1002/adma.201700589

  33. [33]

      Xin, G.; Sun, H.; Hu, T.; Fard, H. R.; Sun, X.; Koratkar, N.; Borca-Tasciuc, T.; Lian, J. Adv. Mater. 2014, 26 (26), 4521. doi: 10.1002/adma.201400951

  34. [34]

      Kumar, P.; Shahzad, F.; Yu, S.; Hong, S. M.; Kim, Y. -H.; Koo, C. M. Carbon 2015, 94, 494. doi: 10.1016/j.carbon.2015.07.032

  35. [35]

      Zhao, J.; Pei, S.; Ren, W.; Gao, L.; Cheng, H. -M. ACS Nano 2010, 4 (9), 5245. doi: 10.1021/nn1015506

  36. [36]

      Wei, Q.; Pei, S.; Qian, X.; Liu, H.; Liu, Z.; Zhang, W.; Zhou, T.; Zhang, Z.; Zhang, X.; Cheng, H. -M.; et al. Adv. Mater. 2020, 32 (14), 1907411. doi: 10.1002/adma.201907411

  37. [37]

      宋厚甫, 康飞宇. 物理化学学报, 2022, 38 (1), 2101013. doi: 10.3866/PKU.WHXB202101013Houfu Song, F. K. Acta Phys. -Chim. Sin. 2022, 38 (1), 2101013. doi: 10.3866/PKU.WHXB202101013

  38. [38]

      Parker, W. J.; Jenkins, R. J.; Butler, C. P.; Abbott, G. L. J. Appl. Phys. 2004, 32 (9), 1679. doi: 10.1063/1.1728417

  39. [39]

      Shieh, S. R.; Hsieh, W. -P.; Tsao, Y. -C.; Crisostomo, C.; Hsu, H. J. Geophys. Res. : Planets 2022, 127 (3), e2022JE007180. doi: 10.1029/2022JE007180

  40. [40]

      Park, H. K.; Grigoropoulos, C. P.; Tam, A. C. Int. J. Thermophys. 1995, 16 (4), 973. doi: 10.1007/BF02093477

  41. [41]

      Groeber, M. A.; Haley, B. K.; Uchic, M. D.; Dimiduk, D. M.; Ghosh, S. Mater. Charact. 2006, 57 (4), 259. doi: 10.1016/j.matchar.2006.01.019

  42. [42]

      Nan, N.; Wang, J. Adv. Mater. Sci. Eng. 2019, 2019 (1), 8680715. doi: 10.1155/2019/8680715

  43. [43]

      Liu, Z.; Chen-Wiegart, Y. -C. K.; Wang, J.; Barnett, S. A.; Faber, K. T. Microsc. Microanal. 2016, 22 (1), 140. doi: 10.1017/S1431927615015640

  44. [44]

      Saini, P.; Sharma, R.; Chadha, N. Indian J. Pure Appl. Phys. 2017, 55 (9), 625. doi: 10.56042/ijpap.v55i9.16047

  45. [45]

      Nika, D. L.; Balandin, A. A. Rep. Prog. Phys. 2017, 80 (3), 036502. doi: 10.1088/1361-6633/80/3/036502

  46. [46]

      Wang, Y.; Vallabhaneni, A. K.; Qiu, B.; Ruan, X. Nanoscale Microscale Thermophys. Eng. 2014, 18 (2), 155. doi: 10.1080/15567265.2014.891680

  47. [47]

      Balandin, A. A. Nat. Mater. 2011, 10 (8), 569. doi: 10.1038/nmat3064

  48. [48]

      Sudhakar, K.; Plummer, G.; Tucker, G.; Barsoum, M. Carbon 2023, 213, 118221. doi: 10.1016/j.carbon.2023.118221

  49. [49]

      Badr, H. O.; Barsoum, M. W. Carbon 2023, 201, 599. doi: 10.1016/j.carbon.2022.09.042

  50. [50]

      Gruber, J.; Lang, A. C.; Griggs, J.; Taheri, M. L.; Tucker, G. J.; Barsoum, M. W. Sci. Rep. 2016, 6 (1), 33451. doi: 10.1038/srep33451

•