Measurement of the cleavage energy of graphite

The basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene and carbon nanotubes. Nonetheless, a wide range of values for the CE has been reported and no consensus has yet emerged. Here we report the first direct, accurate experimental measurement of the CE of graphite using a novel method based on the self-retraction phenomenon in graphite. The measured value, 0.37±0.01 J m−2 for the incommensurate state of bicrystal graphite, is nearly invariant with respect to temperature (22 °C≤T≤198 °C) and bicrystal twist angle, and insensitive to impurities from the atmosphere. The CE for the ideal ABAB graphite stacking, 0.39±0.02 J m−2, is calculated based on a combination of the measured CE and a theoretical calculation. These experimental measurements are also ideal for use in evaluating the efficacy of competing theoretical approaches.

[1]  A. H. R. Palser,et al.  Interlayer interactions in graphite and carbon nanotubes , 1999 .

[2]  P. Hyldgaard,et al.  Van der Waals density functional for layered structures. , 2003, Physical review letters.

[3]  J. Hirth,et al.  Theory of Dislocations (2nd ed.) , 1983 .

[4]  S. Lebègue,et al.  Binding and interlayer force in the near-contact region of two graphite slabs: experiment and theory. , 2013, The Journal of chemical physics.

[5]  Kwon,et al.  Unusually high thermal conductivity of carbon nanotubes , 2000, Physical review letters.

[6]  V. Vítek,et al.  Intrinsic stacking faults in body-centred cubic crystals , 1968 .

[7]  Vivek B Shenoy,et al.  Anomalous Strength Characteristics of Tilt Grain Boundaries in Graphene , 2010, Science.

[8]  Friedhelm Bechstedt,et al.  Semiempirical van der Waals correction to the density functional description of solids and molecular structures , 2006 .

[9]  Qing Chen,et al.  Superlubricity in centimetres-long double-walled carbon nanotubes under ambient conditions. , 2013, Nature nanotechnology.

[10]  Sang Wook Lee,et al.  Breakdown of the interlayer coherence in twisted bilayer graphene. , 2012, Physical review letters.

[11]  Moon J. Kim,et al.  Electron microscopy analyses of natural and highly oriented pyrolytic graphites and the mechanically exfoliated graphenes produced from them , 2010 .

[12]  A. Beese,et al.  In situ scanning electron microscope peeling to quantify surface energy between multiwalled carbon nanotubes and graphene. , 2014, ACS nano.

[13]  D. Rocca,et al.  Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods. , 2007, The Journal of chemical physics.

[14]  J F Dobson,et al.  Cohesive properties and asymptotics of the dispersion interaction in graphite by the random phase approximation. , 2010, Physical review letters.

[15]  Andre K. Geim,et al.  The rise of graphene. , 2007, Nature materials.

[16]  P. Ming,et al.  Ab initio calculation of ideal strength and phonon instability of graphene under tension , 2007 .

[17]  R. Needs,et al.  van der Waals interactions between thin metallic wires and layers. , 2007, Physical Review Letters.

[18]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[19]  Hendrik Ulbricht,et al.  Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons , 2004 .

[20]  J. Bell,et al.  Experiment and Theory , 1968 .

[21]  A. Geim,et al.  Two-dimensional gas of massless Dirac fermions in graphene , 2005, Nature.

[22]  C. N. Lau,et al.  Superior thermal conductivity of single-layer graphene. , 2008, Nano letters.

[23]  J. Kysar,et al.  Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene , 2008, Science.

[24]  D. Srolovitz,et al.  Atomistic, generalized Peierls–Nabarro and analytical models for (1 1 1) twist boundaries in Al, Cu and Ni for all twist angles , 2014 .

[25]  M. Heggie,et al.  Elasticity of carbon allotropes. III. Hexagonal graphite: Review of data, previous calculations, and a fit to a modified anharmonic Keating model , 2003 .

[26]  Steven G. Louie,et al.  MICROSCOPIC DETERMINATION OF THE INTERLAYER BINDING ENERGY IN GRAPHITE , 1998 .

[27]  E. Lacaze,et al.  Dislocation networks in graphite: a scanning tunnelling microscopy study , 1992 .

[28]  T. L. Hill,et al.  Theory of Physical Adsorption , 1952 .

[29]  Ireneusz W. Bulik,et al.  Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence. , 2013, The Journal of chemical physics.

[30]  Jacobsen,et al.  Simulations of atomic-scale sliding friction. , 1996, Physical review. B, Condensed matter.

[31]  Kyuho Lee,et al.  Higher-accuracy van der Waals density functional , 2010, 1003.5255.

[32]  D. Srolovitz,et al.  Structure and energy of (111) low-angle twist boundaries in Al, Cu and Ni , 2013 .

[33]  M. Hirano,et al.  Dynamics of friction: superlubric state , 1993 .

[34]  N. Peres,et al.  Fine Structure Constant Defines Visual Transparency of Graphene , 2008, Science.

[35]  Masayuki Hasegawa,et al.  Semiempirical approach to the energetics of interlayer binding in graphite , 2004 .

[36]  Zhiping Xu,et al.  Observation of high-speed microscale superlubricity in graphite. , 2013, Physical review letters.

[37]  A. Rydberg,et al.  Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system , 2006 .

[38]  E. Weinan,et al.  A Generalized Peierls-Nabarro Model for Curved Dislocations and Core Structures of Dislocation Loops in Al and Cu , 2008 .

[39]  J. Charlier,et al.  Graphite Interplanar Bonding: Electronic Delocalization and van der Waals Interaction , 1994 .

[40]  Hirano,et al.  Atomistic locking and friction. , 1990, Physical review. B, Condensed matter.

[41]  Q. Zheng,et al.  Interlayer binding energy of graphite: A mesoscopic determination from deformation , 2012 .

[42]  Sheng Wang,et al.  Self-retracting motion of graphite microflakes. , 2007, Physical review letters.

[43]  Georg Kresse,et al.  Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory , 2008 .

[44]  John P. Perdew,et al.  Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works , 1980 .

[45]  Lifeng Wang,et al.  Extreme anisotropy of graphite and single-walled carbon nanotube bundles , 2007 .

[46]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[47]  F. Nabarro Dislocations in a simple cubic lattice , 1947 .

[48]  J. Frenken,et al.  Superlubricity of graphite. , 2004, Physical review letters.

[49]  Quanshui Zheng,et al.  Observation of microscale superlubricity in graphite. , 2012, Physical review letters.

[50]  Anthony J. Stone,et al.  The Theory of Intermolecular Forces , 2013 .

[51]  R. Peierls The size of a dislocation , 1940 .