Trade-off between quantum capacitance and thermodynamic stability of defected graphene: an implication for supercapacitor electrodes


Defects are inevitable most of the times either at the synthesis, handling or processing stage of graphene, causes significant deviation of properties. The present work discusses the influence of vacancy defects on the quantum capacitance as well as thermodynamic stability of graphene, and the nitrogen doping pattern needs to be followed to attain a trade-off between these two. Density Functional Theory (DFT) calculations have been performed to analyze various vacancy defects and different possible nitrogen doping patterns at the vacancy site of graphene, with an implication for supercapacitor electrodes. The results signify that vacancy defect improves the quantum capacitance of graphene at the cost of thermodynamic stability, while the nitrogen functionalization at the vacancy improves thermodynamic stability and quantum capacitance both. It has been observed that functionalizing all the dangling carbons at the defect site with nitrogen is the key to attain high thermodynamic stability as well as quantum capacitance. Furthermore, the results signify the suitability of these functionalized graphenes for anode electrode of high energy density asymmetric supercapacitors.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. Atomistix ToolKit—version 2016.4, QuantumWise A/S (

  2. Banhart F, Kotakoski J, Krasheninnikov AV (2010) Structural defects in graphene. ACS Nano 5(1):26–41

    Article  Google Scholar 

  3. Brandbyge M, Mozos J-L, Ordejon P, Taylor J, Stokbro K (2002) Density-functional method for nonequilibrium electron transport. Phys Rev B 65(16):165401

    Article  Google Scholar 

  4. El-Gendy DM, Ghany NAA, El Sherbini EF, Allam NK (2017) Adenine-functionalized Spongy Graphene for green and high-performance supercapacitors. Sci Rep 7:43104

    Article  Google Scholar 

  5. Hirunsit P, Liangruksa M, Khanchaitit P (2016) Electronic structures and quantum capacitance of monolayer and multilayer graphenes influenced by Al, B, N and P doping, and monovacancy: theoretical study. Carbon 108:7–20

    Article  Google Scholar 

  6. Jeong HM, Lee JW, Shin WH, Choi YJ, Shin HJ, Kang JK et al (2011) Nitrogen-doped graphene for high-performance ultracapacitors and the importance of nitrogen-doped sites at basal planes. Nano Lett 11(6):2472–2477

    Article  Google Scholar 

  7. Li D, Yu C, Wang M, Zhang Y, Pan C (2014) Synthesis of nitrogen doped graphene from graphene oxide within an ammonia flame for high performance supercapacitors. RSC Adv 4(98):55394–55399

    Article  Google Scholar 

  8. Liu L, Qing M, Wang Y, Chen S (2015) Defects in graphene: generation, healing, and their effects on the properties of graphene: a review. J Mater Sci Tech 31(6):599–606

    Article  Google Scholar 

  9. Luo G, Liu L, Zhang J, Li G, Wang B, Zhao J (2013) Hole defects and nitrogen doping in graphene: implication for supercapacitor applications. ACS Appl Mater Interfaces 5(21):11184–11193

    Article  Google Scholar 

  10. Mousavi-Khoshdel M, Targholi E, Momeni MJ (2015) First-principles calculation of quantum capacitance of codoped graphenes as supercapacitor electrodes. J Phys Chem C 119(47):26290–26295

    Article  Google Scholar 

  11. Paek E, Pak AJ, Hwang GS (2013a) A computational study of the interfacial structure and capacitance of graphene in [BMIM][PF6] ionic liquid. J Electrochem Soc 160(1):A1–A10

    Article  Google Scholar 

  12. Paek E, Pak AJ, Kweon KE, Hwang GS (2013b) On the origin of the enhanced supercapacitor performance of nitrogen-doped graphene. J Phys Chem C 117(11):5610–5616

    Article  Google Scholar 

  13. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865

    Article  Google Scholar 

  14. Ponomarenko LA, Yang R, Gorbachev RV, Blake P, Mayorov AS, Novoselov KS et al (2010) Density of states and zero Landau level probed through capacitance of graphene. Phys Rev Lett 105(13):136801

    Article  Google Scholar 

  15. Soler JM, Artacho E, Gale JD, Garcia A, Junquera J, Ordejon P et al (2002) The SIESTA method for ab initio order-N materials simulation. J Phys Condens Matter 14(11):2745

    Article  Google Scholar 

  16. Taluja Y, SanthiBhushan B, Yadav S, Srivastava A (2016) Defect and functionalized graphene for supercapacitor electrodes. Superlattices Microstruct 98:306–315

    Article  Google Scholar 

  17. Taylor J, Guo H, Wang J (2001) Ab initio modeling of quantum transport properties of molecular electronic devices. Phys Rev B 63(24):245407

    Article  Google Scholar 

  18. Troullier N, Martins JL (1991) Efficient pseudopotentials for plane-wave calculations. Phys Rev B 43(3):1993

    Article  Google Scholar 

  19. Wood BC, Ogitsu T, Otani M, Biener J (2013) First-principles-inspired design strategies for graphene-based supercapacitor electrodes. J Phys Chem C 118(1):4–15

    Article  Google Scholar 

  20. Yang GM, Zhang HZ, Fan XF, Zheng WT (2015) Density functional theory calculations for the quantum capacitance performance of graphene-based electrode material. J Phys Chem C 119(12):6464–6470

    Article  Google Scholar 

  21. Zhan C, Neal J, Wu J, Jiang DE (2015) Quantum effects on the capacitance of graphene-based electrodes. J Phys Chem C 119(39):22297–22303

    Article  Google Scholar 

  22. Zhan C, Zhang Y, Cummings PT, Jiang DE (2016) Enhancing graphene capacitance by nitrogen: effects of doping configuration and concentration. Phys Chem Chem Phys 18(6):4668–4674

    Article  Google Scholar 

  23. Zhan C, Lian C, Zhang Y, Thompson MW, Xie Y, Wu J et al (2017) Computational insights into materials and interfaces for capacitive energy storage. Adv Sci.

    Google Scholar 

  24. Zhang Y, Wang F, Zhu H, Zhou L, Zheng X, Li X et al (2017) Preparation of nitrogen-doped biomass-derived carbon nanofibers/graphene aerogel as a binder-free electrode for high performance supercapacitors. Appl Surf Sci 426:99–106

    Article  Google Scholar 

  25. Zhu J, Childress AS, Karakaya M, Dandeliya S, Srivastava A, Lin Y et al (2016) Defect-engineered graphene for high-energy-and high-power-density supercapacitor devices. Adv Mater 28(33):7185–7192

    Article  Google Scholar 

Download references


The authors would like to thank Atal Bihari Vajpayee—Indian Institute of Information Technology and Management, Gwalior for providing the infrastructural support for carrying out this research work. They would also like to thank Prof. De-en Jiang and Cheng Zhan of University of California, Riverside, and Brandon C. Wood of Lawrence Livermore National Laboratory, Livermore for the valuable scientific discussions.

Author information



Corresponding author

Correspondence to Anurag Srivastava.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Boddepalli SanthiBhushan is the first author.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 603 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Srivastava, A., SanthiBhushan, B. Trade-off between quantum capacitance and thermodynamic stability of defected graphene: an implication for supercapacitor electrodes. Appl Nanosci 8, 637–644 (2018).

Download citation


  • Supercapacitor
  • Graphene
  • Quantum capacitance
  • Thermodynamic stability
  • Defects