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dc conductivity upon annealing

The electromagnetic properties of epoxy composites loaded with a small fraction of graphene nanoplatelets (GNP) have been studied between 20 Hz and 2 THz. The percolation threshold was found to be 2.9 wt%. According to low-temperature analysis, the electrical conductivity occurs by a tunneling mechanism. The figure shows the temperature dependence of the dc electrical conductivity measured on heating (solid symbols) and on cooling (open symbols) composite samples with different GNP concentrations. Annealing those samples that are close to and above the percolation threshold leads to dramatic increase of both permittivity and conductivity. The reason is a redistribution of the GNP clusters after which the average size and the separation between the conductive clusters has decreased. This leads to a huge rise of the conductivity and pulls the percolation threshold down to 1.4 wt%. Annealing is a simple way to improve significantly the shielding ability of GNP-based composites [A. Plyushch et al, Compos. Sci. Techno. 128 (2016) 75].

AFM image of pyrolitic graphite

Unlike graphene, pyrolytic carbon can be produced directly by CVD on a dielectric substrate such as silica. The AFM  topographic picture (figure) of a 5-nm-thick film of pyrolytic crabon grown on silica reveals a rough surface with correlation length less than 100 nm. Pyrolytic carbon is an interesting carbonaceous material for shielding applications, thanks to its good electrical conductivity [P. Kuzhir et al, Nanoscale Res. Lett. 8 (2013) 60]. In addition, it is relatively transparent in the visible and near infra-red domain (less than 20% absorption for a 5-nm thick film). Optical parameters of pyrolytic carbon with different thickness have been measured by vis-UV absorption spectroscopy [G. Dovbeshko et al, Nanoscale Res. Lett. 10 (2015) 234].

electromagnetic properties of a gr/PMMA multilayer

Variation of the transmittance T (dotted-line curve) and absorbance A(solid-line curve) of a graphene/PMMA multilayer on silica versus incidence angle θ for non-polarized RF radiations at 30 GHz. The number of graphene planes is 7. The s and p components of the absorbance are shown by the dashed-line and dot-dashed-line curves, respectively. The orientation of the system is the substrate facing the incidence medium. These calculations demonstrate that the absorbance and transmittance of the system remain remarkably constant in a wide interval of incidence angle [M. Lobet et al, Nanotechnology 26 (2015) 285702].

Curved structure of a pentaribbon

Using state-of-the art electronic total energy calculations, it has been shown that a perfect 2D crystal composed of pentagonal rings that mix multiple sp2/sp3 sublattices is unstable. The mechanical stress leads to the formation of uniformly curved repetitive structural units that can be combined in irregular nanoclusters of saddle shape, rings, tubes, or even foam for the largest structures. Contrasting the monolayer case, it was confirmed that bilayered AB pentagraphenes are structurally stable due to compensation of the stress by two perpendicular sets of mutually parallel sp2 carbon sublattices [P. Avramov et al, J. Phys. Chem. Lett. 6 (2015) 4525].

Conductivity of epoxy composite with modified nanotubes 

Chemical modification of multi-walled carbon nanotube (MWNT) surfaces has been realized with the aim of improving the characteristics of epoxy-nanotubes composites. At this end, in situ ultrasonic irradiation of the nanotubes was performed, either in polyethylene polyamine or in liquid epoxy resin, leading to amine-grafted or epoxy-grafted composites, respectively. The chemical modification of the MWNTs was shown to have a direct effect on their dispersion and, thereby, on rheological, dc-conductivity, radio frequency, and microwave response properties of the composite. In particular, it was possible to achieve the same microwave shielding effectiveness as with composites doped with other nanocarbons, but here with a much smaller concentration of fillers [R. Kotsilkova et al, Composites Sci. Technol. 106 (2015) 85].


Effects of an electric field on monolayer chevron-type graphene nanoribbons has been explored. The band structure of these ribbons, referred to as jagged graphene nanoribbons, has been calculated for applied fields up to 1V/nm. According to the tight-binding model used, band gap opening (or closing) takes place for some types of jagged graphene nanoribbons in the external electric field aligned with the atomic planeand perpendicular to the longitudinal axis of the structure. Tunability of the band gap up to 0.6 eV is attainable for narrow ribbons. For jagged ribbons with zigzag and armchair edges, regions of linear and quadratic dependence of the band gap on the external electric field have been found that may be useful for devices requiring controllable modulation of the band gap [V.A. Saroka et al, J. Phys.: Condens. Matter 27 (2015) 145305]

electrical conductivity at 100 Hz

Thermostable composite materials based on phosphate binders combine many interesting physical and chemical properties. When loaded with a small fraction of carbon MWNTs, their electrical conductivity increases by several order of magnitudes. Depending on whether the binder is a liquid aluminum phosphate (AP) or a solid magnesium phosphate (MP), percolation is achieved with 1.56 or 0.81 wt%, respectively (the figure shows the variation of the conductivity of both composites measured at 100 Hz). Electromagnetic measurements across 2-mm thick samples indicate that both phosphate-based composites loaded with 2 wt% MWNT block the transmission of GHz radiations [N. Apanasevich et al, Ceramics International 41 (2015) 12147].

graphene/PMMA multilayer

Graphene produced by CVD is an interesting RF shielding material because its DC conductivity is close to the intrinsic admittance of air, ε0c. Indeed, maximum absorption of electromagnetic radiations by a thin conducting sheet occurs when its conductivity in unit of ε0cmatches the sum of the refractive indices of the media that line the sheet on both sides. This condition can be achieved by stacking a few layers of graphene. Artificial metamaterials consisting of a few graphene planes alternating with thin PMMA spacers are excellent shielding devices because there is no perturbation of the transport properties of the individual planes induced by proximity effect [K. Batrakov et al, Scientific Reports 4 (2014) 7191].


Bilayer of graphene with interconnected holes

For some applications, the fact that graphene has a zero band gap is a drawback. There are many ways to introduce a band gap, at least conceptually. One of them would be to perforate holes in a bi-layer of graphene and let the dangling bonds along the edges of the holes to reconstruct trough interconnection links between the layers. In so doing, a sort of mesh of flattened nanotubes is obtained whose electronic structure has been explored theoretically [L.A. Chernozatonskii et al, JETP Letters 99 (2014) 309].


Cars image opf a MWNT

CARS (coherent anti-Stokes Raman scattering: four-photon nonlinear process that can resonantly probe Raman-active vibrations and is mainly used for chemical mapping at sub-micrometer scale) image of a multi-walled carbon nanotube on glass at the frequency of the D-mode (1310 cm-1). The image has the same intensity along the nanotube, which indicates a uniform density of defects [G. Dovbeshko et al, Nanoscale Res. Lett. 9 (2014) 263].


Hardness and Young modulus of an epoxy composite

Mechanical properties of an epoxy composite containing 1 wt% micro-sized exfoliated graphite. The apparent hardness (o) and Young modulus (Δ) were determined by nano-indentation through a series of 48 load-displacement measurements distributed along four lines on the surface of the sample [P. Kuzhir et al, J. Appl. Phys. 114 (2013) 164304].


Carbon black in epoxy

Temperature dependence of dc electrical conductivity of epoxy composites filled with carbon black of high and low surface area (CBH and CBL, respectively) below the percolation threshold. In the temperature interval considered, 350K to 450K, the curves follow the Arrhenius law [J. Macutkevic et al, J. Nanosci. Nanotechn. 13 (2013) 5434].


Grain boundary 5766

Grain boundaries are constitutional elements of graphene grown by CVD on a Cu foil. Atomic models like the one shown here allow us to investigate the properties of grain boundaries in graphene and help us to understand experimental data, such as STM images and scanning tunneling spectra of these structures [Ph. Lambin et al, in "Nanomeeting 2013" (World Scientific, Singapore, 2013) 203].


Permittivity of epoxy

Temperature dependence of the imaginary part of the dielectric permittivity of an epoxy resin filled with multiwall carbon nanotubes. Heating and cooling measurements at frequency of 129 Hz are shown. The percolation threshold is estimated to be 1.5 wt% MWCNT in this nanocomposite system [J. Macutkevic et al, J. Nanophotonics 7 (2013) 073593; D. Bychanok et al, J. Appl. Phys. 113 (2013) 124103].

Bilayer grpahene with an oval hole

Bilayer graphene in the AB stacking with an elongated reconstructed hole. The layers are interconnected by setting up bonds between the edge atoms. In this particular example, 28 atoms have been removed in each layer, leaving 14 edge atoms. Interconnecting these atoms leads to 4 hexagons, 8 heptagons and 2 octagons around the hole. The structure was made periodic by repetition of a pxp supercell constructed on the lattice vectors of the unperturbed bilayer (p = 4, 5 ...) and was optimized. The electronic band structure of the superlattice was computed with DFT using the SIESTA package. This particular structure is a semiconductor whose band gap decreases with increasing p. Other structures of perforated bilayer graphenes have been constructed with either AA, AB or moiré arrangements of the lattices. A rich variety of electronic properties have been predicted [D.G. Kvashnin et al, Nano Res. 8 (2015) 1250; L.A. Chernozatonskii et al, Phys. Chem. Chem. Phys. 18 (2016) 27432].


How the electrical conductivity of graphene is affected by the presence of defects (impurities, grain boundaries ...) has been addressed by wave-packet dynamics. The calculations were based either on the full time-dependent Schroedinger equation on an atomic lattice [G. Mark et al, in "Fundamental and Applied NanoElectroMagnetics", edit. A. Maffucci and S. Maksimenko (Springer, Amsterdam, 2016), 89] or on the time-dependent Dirac equation in a continueous-medium approach [K. Rakhimov et al, Appl. Sci. 6 (2016) 256]. The figure is a snapshot of an electronic Gaussian wavefront moving upwards in graphene with the Fermi velocity. At the moment of the snapshot, the center of the wavepacket has arrived at coordinate y = 0. Its propagation is perturbed by nitrogen impurities randomly distributed in the horizontal band extending between y = -20 nm and y = +20 nm in otherwise perfect graphene. The atomic concentration of N is 0.4%. The color scale is proportional to the power 1/4 of the probability density obtained by solving the time-dependent Dirac equation for massless fermions.

fragment of graphene used for I-V curve calculations

The electron work function for graphene fragments with pure edges and those functionalized by hydrogen atoms was calculated using DFT. The results obtained were used to evaluate the current-voltage characteristics of a vertically aligned rectangular graphene sheet. The calculated values of the electrostatic potential spatial distribution in the vicinity of the graphene layer indicates a highly inhomogeneous distribution of the electric field amplification factor along its external edge, so that the maximum amplification occurs near the vertices of the layer [G.S. Bocharov et al, J. Vac. Sci. Technol. B 33 (2015) 041801].

SEM picture of carbon foam

Reticulated carbon foams have been synthesized using polyurethane foams as templates. The image is a SEM picture of a carbon foam prepared with polyurethane foam having an average cell diameter of 0.32 mm. Combining lightness (55 mg/cm³ for the sample of the picture) and good electrical conductivity (44 S/m for the sample of the picture), carbon foams are promising 'green' materials for electromagnetic applications. The measured shielding effectiveness of a 1.7-mm thick sample reaches 18.5 dB at 30 GHz [D. Bychanok et al, Phys. Scripta 90 (2015) 094019]. Similar results were obtained with tannin-based carbon foams of various densities that were analyzed by broadband dielectric spectroscopy and microwave S-matrix measurements [M. Letellier et al, IEEE Transaction on Electromagnetic Compatibility 57 (2015) 989; M. Lettelier et al, Ferroelectrics 479 (2015) 119].

Band structure of gr-BN bilayer

DFT calculations have shown that the electronic properties of hybrid structures composed of a graphene layer deposited on a boron nitride monolayer change significantly upon hydrogenation of the bilayer. H atoms adsorbed directly on B atoms of the BN layer open a band gap in the band structure. The value of the band gap depends on the angular orientation of the graphene lattice compared to the BN lattice [D.G. Kvashnin et al, Phys. Chem. Chem. Phys. 17 (2015), 4354].

Equivalent randon RDC circuit

The dielectric properties of a composite system can be reproduced by an electrical circuit composed of a random distribution of resistors (represented in red in the figure), capacitors (in blue) and diodes (in green) with electrical contacts (in gray) allowing percolation pathes through the diodes and capacitors. Using Kirchhoff's laws, it is possible to calculate the impedance of such a network and to transform it to an equivalent dielectric permittivity whose frequency dependence mimics the one of the composite [A. Plyushch et al, Phys. Stat. Solidi (a) 211 (2014) 2580; D.S. Bychanok et al, Appl. Phys. Lett. 103 (2013) 243104].


Transformation of a graphene bilayer into 2D diamond

An hexagonal-shaped hydrogenated graphene bilayer with AAAA stacking can transform spontaneously into a two-layered sp3 hybridized diamond-like structure, and this in a large temperature interval. According to DFT calculations, this transformation remains possible for multilayers composed of up to 25 graphene planes [A.G. Kvashnin et al, Nano Lett. 14 (2014) 676].


Wavepacket on a grain boundary

An electron wavepacket is injected in a graphene sheet from a simulated STM tip situated above a C atom 2.5 nm away from a grain boundary line on the right-hand side grain. After injection, the wavepacket begins to spread along the surface. When it hits the grain boundary, part of the wavepacket is reflected back into the right-hand side grain, the rest being transmitted into the left-hand side grain. The figure is a colored representation of the electron probability density on the graphene sheet at the Fermi energy, using different normalization below the STM tip inside and outside a circle of 1.5 nm radius. There is a strong localization of electrons around a four membered carbon ring located in the grain boundary (red circle). The size of the presentation window is 7.68 nm in both vertical and horizontal directions [P. Vancsó et al, Appl. Surf. Sci. 291 (2014) 58].


Real part of epsilon for carbon black composite

The real part of the dielectric permittivity of an epoxy resin loaded with 2 wt% of conductive carbon blacks with high surface area (770 m2/g according to BET) measured at several frequencies is plotted against absolute temperature. For this type of composite, the percolation threshold is 1 wt%. [J. Macutkevic et al, J. Appl. Phys. 114 (2013) 033707].


Phosphate composite

SEM image of a phosphate ceramic loaded with 1.5 wt% multiwall carbon nanotubes. The matrix consists of aluminum-phosphate binder and filler containing corundum and aluminum nitride. This composite is almost opaque to microwave radiations in the Ka band (5% transmission at 30 GHz for a thickness of 2mm) [M.A. Kanygin et al, J. Appl. Phys. 113 (2013) 144315].


THz peak

The optical absorbance of a film containing bundles of single-walled carbon nanotubes has a broad peak in the THz region, whose position depends on the length of the tubes and on the diameter of the bundles. The samples H1, H2 and H3 for which spectra are shown herewith have a mean length of 0.74, 0.24 and 0.18 µm, respectively. The observed redshift of the THz peak with increasing length validates the hypothesis that this peak is an antenna resonance [M.V. Shuba et al, J. Nanophotonics 6 (2012) 061707].



Average values of the transmittance, absorbance and reflectance of 2 mm thick samples of carbon foam vs bulk density in the microwave Ka band. The foam was prepared from commercial tannin and furfuryl alcohol [P.P. Kuzhir et al, J. Nanophotonics 6 (2012) 061715].

AFM image of bundles of single-wall carbon nanotubes produced by the HiPCO process after application of a low-temperature cutting treatment of 30 hour duration. The method involves intensive ultrasonication in a mixture of sulfuric and nitric acids. It is nondestructive with a yield close to 100%. The average tube length is 180 nm, while the average diameter of the bundles is reduced to 2-4 nm [M.V. Shuba et al, Nanotechn. 23 (2012) 495714].

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