Entropy-driven structure and dynamics in carbon nanocrystallites

Research Paper


New carbon composite materials are being developed that contain carbon nanocrystallites in the range of 5–17 Å in radius dispersed within an amorphous carbon matrix. Evaluating the applicability of these materials for use in battery electrodes requires a molecular-level understanding of the thermodynamic, structural, and dynamic properties of the nanocrystallites. Herein, molecular dynamics simulations reveal the molecular-level mechanisms for such experimental observations as the increased spacing between carbon planes in nanocrystallites as a function of decreasing crystallite size. As the width of this spacing impacts Li-ion capacity, an explanation of the origin of this distance is relevant to understanding anode performance. It is thus shown that the structural configuration of these crystallites is a function of entropy. The magnitude of out-of-plane ripples, binding energy between layers, and frequency of characteristic planar modes are reported over a range of nanocrystallite sizes and temperatures. This fundamental information for layered carbon nanocrystallites may be used to explain enhanced lithium ion diffusion within the carbon composites.


Nanocrystallite Carbon Entropy Graphene Nanoparticle Composite Modeling and simulation Energy applications 



Q.W. was supported by the Joint Directed Research and Development program (JDRD) of the University of Tennessee Science Alliance. N.M. was supported by a grant from the Oak Ridge Associated Universities High Performance Computing Program and by a grant from the Sustainable Energy Education and Research Center of the University of Tennessee. This research project used resources of the National Institute for Computational Sciences (NICS) supported by NSF under agreement number: OCI 07-11134.5. This research was also sponsored in part by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy. We thank Dr. Don Nicholson for invaluable advice during the preparation of this manuscript.


  1. Aga RS, Fu CL, Krcmar M, Morris JR (2007) Theoretical investigation of the effect of graphite interlayer spacing on hydrogen absorption. Phys Rev B 76:165404CrossRefGoogle Scholar
  2. Baker DA, Gallego NC, Baker FS (2012) On the characterization and spinning of an organic-purified lignin toward the manufacture of low-cost carbon fiber. J Appl Polym Sci 124(1):227–234CrossRefGoogle Scholar
  3. Balandin AA, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau CN (2008) Superior thermal conductivity of single-layer graphene. Nano Lett 8(3):902–907CrossRefGoogle Scholar
  4. Dienwiebel M, Verhoeven GS, Pradeep N, Frenken JWM, Heimberg JA, Zandbergen HW (2004) Superlubricity of graphite. Phys Rev Lett 92:126101CrossRefGoogle Scholar
  5. Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2004) Van der Waals density functional for general geometries. Phys Rev Lett 92:246401CrossRefGoogle Scholar
  6. Dmowski W, Contescu CI, Llobet A, Gallego NC, Egami T (2012) Local atomic density of microporous carbons. J Phys Chem C 116(4):2946–2951CrossRefGoogle Scholar
  7. Fileti EE, Dalpian GM, Rivelino R (2010) Liquid separation by a graphene membrane. J Appl Phys 108(11):113527CrossRefGoogle Scholar
  8. Filippov AE, Dienwiebel M, Frenken JWM, Klafter J, Urbakh M (2008) Torque and twist against superlubricity. Phys Rev Lett 100:046102CrossRefGoogle Scholar
  9. Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6(3):183–191CrossRefGoogle Scholar
  10. Hasegawa M, Nishidate K, Iyetomi H (2007) Energetics of interlayer binding in graphite: the semiempirical approach revisited. Phys Rev B 76:115424CrossRefGoogle Scholar
  11. Hawaldar R, Merino P, Correia MR, Bdikin I, Gracio J, Mendez J, Martin-Gago JA, Singh MK (2012) Large-area high-throughput synthesis of monolayer graphene sheet by hot filament thermal chemical vapor deposition. Sci Rep 2:682CrossRefGoogle Scholar
  12. Hirano M, Shinjo K (1990) Atomistic locking and friction. Phys Rev B 41(17):11837–11851CrossRefGoogle Scholar
  13. Iijima T, Suzuki K, Matsuda Y (1995) Electrodic characteristics of various carbon materials for lithium rechargeable batteries. Synth Met 73(1):9–20CrossRefGoogle Scholar
  14. Jorgensen WL, Maxwell DS, Tirado-Rives J (1996) Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chem Soc 118(45):11225–11236CrossRefGoogle Scholar
  15. Langford JI, Wilson AJC (1978) Scherrer after 60 years—survey and some new results in determination of crystallite size. J Appl Crystallogr 11(Apr):102–113CrossRefGoogle Scholar
  16. Lebedeva IV, Knizhnik AA, Popov AM, Lozovik YE, Potapkin BV (2011) Interlayer interaction and relative vibrations of bilayer graphene. Phys Chem Chem Phys 13(13):5687–5695CrossRefGoogle Scholar
  17. Leontyev IN, Beenov SV, Guterman VE, Haghi-Ashtiani P, Shaganov AP, Dkhil B (2011) Catalytic activity of carbon-supported Pt nanoelectrocatalysts. Why reducing the size of Pt nanoparticles is not always beneficial. J Phys Chem C 115(13):5429–5434. doi: 10.1021/jp1109477 CrossRefGoogle Scholar
  18. Liu YH, Xue JS, Zheng T, Dahn JR (1996) Mechanism of lithium insertion in hard carbons prepared by pyrolysis of epoxy resins. Carbon 34(2):193–200CrossRefGoogle Scholar
  19. Marquez A (2007) Molecular dynamics studies of combined carbon/electrolyte/lithium–metal oxide interfaces. Mater Chem Phys 104(1):199–209CrossRefGoogle Scholar
  20. Marquez A, Balbuena PB (2001) Molecular dynamics study of graphite/electrolyte interfaces. J Electrochem Soc 148(6):A624–A635CrossRefGoogle Scholar
  21. Marquez A, Vargas A, Balbuena PB (1998) Computational studies of lithium intercalation in model graphite in the presence of tetrahydrofuran. J Electrochem Soc 145(10):3328–3334CrossRefGoogle Scholar
  22. Meyer JC, Geim AK, Katsnelson MI, Novoselov KS, Obergfell D, Roth S, Girit C, Zettl A (2007) On the roughness of single- and bi-layer graphene membranes. Solid State Commun 143(1–2):101–109CrossRefGoogle Scholar
  23. Nicklow R, Smith HG, Wakabayashi N (1972) Lattice-dynamics of pyrolytic-graphite. Phys Rev B 5(12):4951–4962CrossRefGoogle Scholar
  24. Noel M, Suryanarayanan V (2002) Role of carbon host lattices in Li-ion intercalation/de-intercalation processes. J Power Sources 111(2):193–209CrossRefGoogle Scholar
  25. Phillips JM, Shrimpton N (1992) Molecular-dynamics study of interlayer incommensurability in adsorbed multilayers. Phys Rev B 45(7):3730–3734CrossRefGoogle Scholar
  26. Plimpton S (1995) Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 117(1):1–19CrossRefGoogle Scholar
  27. Popov AM, Lebedeva IV, Knizhnik AA, Lozovik YE, Potapkin BV (2011) Molecular dynamics simulation of the self-retracting motion of a graphene flake. Phys Rev B 84:245437CrossRefGoogle Scholar
  28. Popov AM, Lebedeva IV, Knizhnik AA, Lozovik YE, Potapkin BV (2012) Barriers to motion and rotation of graphene layers based on measurements of shear mode frequencies. Chem Phys Lett 536:82–86CrossRefGoogle Scholar
  29. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in FORTRAN: the art of scientific computing, vol 1, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  30. Qi WH, Huang BY, Wang MP, Yin ZM, Li J (2009) Molecular dynamic simulation of the size- and shape-dependent lattice parameter of small platinum nanoparticles. J Nanopart Res 11:575–580CrossRefGoogle Scholar
  31. Rai A, Warrier M, Schneider R (2009) A hierarchical multi-scale method to simulate reactive-diffusive transport in porous media. Comput Mater Sci 46(2):469–478CrossRefGoogle Scholar
  32. Sasaki N, Kobayashi K, Tsukada M (1996) Atomic-scale friction image of graphite in atomic-force microscopy. Phys Rev B 54(3):2138–2149CrossRefGoogle Scholar
  33. Savchenko DV, Ionov SG (2010) Physical properties of carbon composite materials with low percolation threshold. J Phys Chem Solids 71(4):548–550CrossRefGoogle Scholar
  34. Sharma RK, Wooten JB, Baliga VL, Lin XH, Chan WG, Hajaligol MR (2004) Characterization of chars from pyrolysis of lignin. Fuel 83(11–12):1469–1482CrossRefGoogle Scholar
  35. Shimizu A, Tachikawa H (2003) Molecular dynamics simulation for sodium atom in and on the two layers of C150H30 graphite plane. J Phys Chem Solids 64(12):2397–2402CrossRefGoogle Scholar
  36. Stuart SJ, Tutein AB, Harrison JA (2000) A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys 112(14):6472–6486CrossRefGoogle Scholar
  37. Tenhaeff WE, Rios O, More K, McGuire MA (2014) Highly robust lithium ion battery anodes from lignin: an abundant, renewable, and low-cost material. Adv Funct Mater 24(1):86–94CrossRefGoogle Scholar
  38. Tsai JL, Tu JF (2010) Characterizing mechanical properties of graphite using molecular dynamics simulation. Mater Des 31(1):194–199CrossRefGoogle Scholar
  39. Tuckerman M, Berne BJ, Martyna GJ (1992) Reversible multiple time scale molecular-dynamics. J Chem Phys 97(3):1990–2001CrossRefGoogle Scholar
  40. Verhoeven GS, Dienwiebel M, Frenken JWM (2004) Model calculations of superlubricity of graphite. Phys Rev B 70:165418CrossRefGoogle Scholar
  41. Wang YC, Scheerschmidt K, Gosele U (2000) Theoretical investigations of bond properties in graphite and graphitic silicon. Phys Rev B 61(19):12864–12870CrossRefGoogle Scholar
  42. Wang QF, Keffer DJ, Petrovan S, Thomas JB (2010) Molecular dynamics simulation of poly(ethylene terephthalate) oligomers. J Phys Chem B 114(2):786–795CrossRefGoogle Scholar
  43. Warrier M, Schneider R, Salonen E, Nordlund K (2005) Multi-scale modeling of hydrogen isotope transport in porous graphite. J Nucl Mater 337(1–3):580–584CrossRefGoogle Scholar
  44. Winter M, Besenhard JO, Spahr ME, Novak P (1998) Insertion electrode materials for rechargeable lithium batteries. Adv Mater 10(10):725–763CrossRefGoogle Scholar
  45. Yoo EJ, Kim J, Hosono E, Zhou H, Kudo T, Honma I (2008) Large reversible Li storage of graphene nanosheet families for use in rechargeable lithium ion batteries. Nano Lett 8(8):2277–2282CrossRefGoogle Scholar
  46. Zacharia R, Ulbricht H, Hertel T (2004) Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys Rev B 69:155406CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • N. W. McNutt
    • 1
  • Q. Wang
    • 1
  • O. Rios
    • 2
  • D. J. Keffer
    • 3
  1. 1.Department of Chemical and Biomolecular EngineeringUniversity of TennesseeKnoxvilleUSA
  2. 2.Materials Science and Technology DivisionOak Ridge National LaboratoryOak RidgeUSA
  3. 3.Department of Materials Science and EngineeringUniversity of TennesseeKnoxvilleUSA

Personalised recommendations