Electronic thermal conductivity and thermopower of armchair graphene nanoribbons

A theoretical investigation of the diffusion contribution to thermopower, S_d, and the electronic thermal conductivity, κ_e, of semiconducting armchair graphene nanoribbons (GNRs) is made for T ⩽ 300 K. Considering the electrons to be scattered by edge roughness, impurities and deformation-potential coupled acoustic phonons and optical phonons, expressions for S_d and κ_e are obtained. Numerical calculations of S_d and κ_e, as functions of temperature and linear carrier density, bring out the relative importance of the contributing scattering mechanisms. A GNR of width 5 nm, supporting an electron density 2 × 10⁸ m⁻¹, is found to exhibit room temperature values of S_d and κ_e as 42 μV/K and 26.5 W/mK, respectively. A decrease in armchair GNR width, is found to enhance S_d and reduce κ_e. The effect of varying the electron density is to increase their magnitude when Fermi energy moves into the second subband. An analysis of thermopower and thermal conductivity data in clean armchair GNR samples will enable better understanding of the electron–phonon interaction.     

A molecular dynamics study of the thermal conductivity of graphene nanoribbons containing dispersed Stone–Thrower–Wales defects

Classical molecular dynamics with the AIREBO potential is used to investigate the thermal conductivity of both zigzag and armchair graphene nanoribbons possessing different densities of Stone–Thrower–Wales (STW) defects. Our results indicate that the presence of the defects can decrease thermal conductivity by more than 50%. The larger the defect density, the lower the conductivity, with the decrease significantly higher in zigzag than in armchair nanoribbons for all defect densities. The effect of STW defects in the temperature range 100–600 K was also determined. Our results showed the same trends in thermal conductivity decreases at all temperatures. However, for higher defect densities there was less variation in thermal conductivity at different temperatures.     

Effect of hydrogenation on graphene thermal transport

We studied thermal conductivity of the three most stable hydrogenated graphene (graphane) conformers by means of non-equilibrium molecular dynamics. We estimated thermal conductivity for pristine graphene with sample length 2.1 (2.4) μm as large as κ = 745.4 ± 0.3 and 819.1 ± 0.3 W m⁻¹ K⁻¹ in the armchair and zigzag directions, respectively, in very good agreement with previous theoretical results based on the Boltzmann transport equation. In the case of the three graphane isomers we observed a dramatic κ reduction by at least one order of magnitude with respect to pristine graphene. We elucidated this reduction in terms of different phonon density of states and mean-free path distribution between graphene and graphane. The deterioration of thermal transport upon hydrogenation in graphene, could be proposed as a way to tune thermal transport in graphene for phononic applications such as thermal diodes.     

Influence of chemisorption on the thermal conductivity of graphene nanoribbons

The thermal conductivity of graphene nanoribbons (GNRs) functionalized by the chemical attachment of methyl and phenyl groups at random positions is calculated using reverse nonequilibrium molecular dynamics. The GNRs exhibit a rapid drop in thermal conductivity with increasing degree of functionalization; a functional group coverage regime of as little as 1.25% of GNR atoms reduces the thermal conductivity by about 50%. The thermal conductivity of nanoribbons with zigzag edges is more sensitive in the degree of functionalization than nanoribbons with armchair edges. The simulation results indicate that the rapid drop in thermal conductivity is a consequence of the higher angular momentum of functional groups, which rotate the unsupported sp³ bonds and thus reduce the phonon mean free paths.     

Tubular graphene nanoribbons with attached manganese oxide nanoparticles for use as electrodes in high-performance supercapacitors

Graphene nanoribbons (GNRs) with tubular shaped thin graphene layers were prepared by partially longitudinal unzipping of vapor-grown carbon nanofibers (VGCFs) using a simple solution-based oxidative process. The GNR sample has a similar layered structure to graphene oxide (GO), which could be readily dispersed in isopropyl alcohol to facilitate electrophoretic deposition (EPD). GO could be converted to graphene after heat treatment at 300 °C. The multilayer GNR electrode pillared with open-ended graphene tubes showed a higher capacitance than graphene flake and pristine VGCF electrodes, primarily due to the significantly increased surface area accessible to electrolyte ions. A GNR electrode with attached MnO₂ nanoparticles was prepared by EPD method in the presence of hydrated manganese nitrate. The specific capacitance of GNR electrode with attached MnO₂ could reach 266 F g⁻¹, much higher than that of GNR electrode (88 F g⁻¹) at a discharge current of 1 A g⁻¹. The hydrophilic MnO₂ nanoparticles attached to GNRs could act as a redox center and nanospacer to allow the storage of extra capacitance.     

Synthesis of high-density arrays of graphene nanoribbons by anisotropic metal-assisted etching

We demonstrate the synthesis of highly aligned dense arrays of graphene nanoribbons (GNRs) based on metal-assisted etching of chemical vapor deposition-grown single-layer graphene. In order to obtain GNR arrays, controlling the direction of the etching becomes an important task. Crystalline surfaces of r- and a-planes of sapphire (α-Al₂O₃) were found to induce anisotropic etching of the graphene along their specific crystallographic directions. In contrast, anisotropic surface of ST-cut quartz induced few etching lines. We found that the graphene etching is strongly dependent on the metal species; the order of the catalytic activity of metal nanoparticles is Ni > Fe > > Cu. Etching temperature and H₂ concentration also strongly influenced the density and quality of the etching lines. Our anisotropic graphene etching is expected to offer a new route toward the synthesis of high density GNR array in large area without relying on any lithographic techniques for future electronic devices.     

On the prediction of graphene’s elastic properties with reactive empirical bond order potentials

The elastic properties of graphene as described by the reactive empirical bond order potential are studied through uniaxial tensile tests calculations at both zero temperature, with a conjugate gradient approach, and room temperature, with molecular dynamics simulations. A perfect linear elastic behavior is observed at 0 K up to ≈0.1% strain. The Young’s modulus and Poisson’s ratio obtained with this potential are of ≈730 GPa and 0.39, respectively, with little chirality effects. These values differ significantly from former estimations, much closer to experimental values. We show that these former values have certainly been obtained by neglecting the effect of atomic relaxation, leading to a severe inaccuracy. At larger strains, an extended apparent linear domain is observed in the stress–strain curves, which is relevant to Young’s modulus calculations at finite temperature. Our molecular dynamics simulations at 300 K have allowed obtaining the following, chirality dependent, apparent Young’s moduli, 860 and 761 GPa, and Poisson’s ratios, 0.12 and 0.23, for armchair and zigzag loadings, respectively.     

Structure-mediated thermal transport of monolayer graphene allotropes nanoribbons

We report the study of the thermal transport management of monolayer graphene allotrope nanoribbons (size ∼20 × 4 nm²) by the modulation of their structures via molecular dynamics simulations. The thermal conductivity of graphyne (GY)-like geometries is observed to decrease monotonously with increasing number of acetylenic linkages between adjacent hexagons. Strikingly, by incorporating those GY or GY-like structures, the thermal performance of graphene can be effectively engineered. The resulting hetero-junctions possess a sharp local temperature jump at the interface, and show a much lower effective thermal conductivity due to the enhanced phonon–phonon scattering. More importantly, by controlling the percentage, type and distribution pattern of the GY or GY-like structures, the hetero-junctions are found to exhibit tunable thermal transport properties (including the effective thermal conductivity, interfacial thermal resistance and rectification). This study provides a heuristic guideline to manipulate the thermal properties of 2D carbon networks, ideal for application in thermoelectric devices with strongly suppressed thermal conductivity.     

Heat transport across the metal–diamond interface

Thermal conductivity of the aluminium–diamond (Al–diamond) composites, prepared by the gas pressure infiltration method, is measured by steady state technique. A detailed theoretical investigation on the heat conduction mechanism across the Al–diamond interface is presented. It was confirmed that both electrons and phonons actively take part in the flow of heat at the interface. In the Al side, electrons of Al couple with the phonons and carry the heat up to the interface. This electron–phonon pair which predominantly carries heat in the Al, breaks down at the Al–diamond interface. The coupling between phonons of both Al and diamond takes place at the interface which eventually leads the heat conduction across the interface to the diamond. The phonon–phonon coupling across the interface is discussed by scattering mediated acoustic mismatch model (SMAMM). It is shown that for Al–diamond composite, the implementation of the SMAMM yields an interface thermal resistance (ITR) value of 4.44 × 10^− 9 m²K/W, which is in fairly good agreement with values derived from experimental thermal conductivity values of this composite implemented in the Hasselman–Johnson (HJ) mean field scheme.     

Ultra-low-edge-defect graphene nanoribbons patterned by neutral beam

Top-down process, comprising lithography and plasma etching is widely used in very-large-scale integration due to its scalability, has the greatest potential to fabricate graphene nanoribbon based nanoelectronic devices for large-scale intergraded circuits. However, conventional plasma etching inevitably introduces plenty of damage or defects to the etched materials, which drastically degrades the performance of nano materials. In this study, extremely low-damage neutral beam etching (NBE) is applied to fabricate ultra-low-defect graphene nanoribbon array (GNR). The ultra-low-edge-defect GNRs are fabricated by E-beam lithography followed by oxygen NBE from large-scale chemical-vapor-deposition-grown graphene. AFM images clearly shows the GNRs patterned by NBE and E-beam lithography, and Raman spectroscopy exhibits extremely low I_D/I_G of GNRs, which indicate that high-quality GNRs can be successfully fabricated by neutral beam. We also demonstrated bottom-gated field-effect transistor with the high-quality GNR and observed a high carrier mobility (>200 cm² V⁻¹ s⁻¹) at room temperature.     

High thermal conductivity in pressureless densified SiC ceramics with ultra-low contents of additives derived from novel boron–carbon sources

In order to attain high thermal conductivity, SiC was doped with ultra-low amounts of B and C as sintering additives using boric acid together with d-fructose as boron–carbon sources. The contents of in situ generated B and C were both tailored as low as 0.4 wt.%, which can significantly reduce the impurities induced phonon scattering effect. The SiC ceramics were pressureless densified at 2150 °C for 1 h, and some samples experienced subsequent annealing at 1950 °C for 4 h. High thermal conductivities of 180.94 W/(m K) for the as-sintered SiC ceramics and 192.17 W/(m K) for the annealed specimens at room temperature were achieved. The reasons for the high thermal conductivity in the polycrystalline SiC ceramics were specified, based on the close correlation with microstructure.     

High and anisotropic thermal conductivity of body-centered tetragonal C4 calculated using molecular dynamics

The thermal properties of body-centered tetragonal C₄ (bct-C₄), a new allotrope of carbon, were investigated using molecular dynamics (MD) simulations. The calculations gave a high and anisotropic thermal conductivity that is the first of its kind. The cross-plane thermal conductivity is 1209 W/(m K) at room temperature, which is even higher than that of diamond. The thermal conductivity decreases as the temperature increases from 80 to 400 K. The density of states of bct-C₄ was analyzed, which has a prominent peak at 36 THz. The relaxation times were calculated by fitting a heat flux autocorrelation function. The results showed that the acoustic phonons play the dominant role in the heat conduction, with a contribution of more than 99%. The relaxation times decrease with increasing temperature, as does the contribution of the acoustic phonons. Finally, the thermal conductivity based on lattice dynamics agreed well with that from the MD method, with which the group velocity and mean free path were deduced. This outstanding thermal property makes bct-C₄ a promising substitute for diamond, especially as thermal interface materials in microelectronic packaging.     

Measuring the thermal conductivity of residue-free suspended graphene bridge using null point scanning thermal microscopy

Despite the importance of the accurate measurement of the thermal conductivity of graphene, deviations in previous data are still quite large due to the low signal-to-noise ratio in the measurement of graphene temperature, the uncertainties in the measurement of the heat dissipation, and the influence of the polymeric residues. Herein, we improve signal-to-noise ratio by using null point scanning thermal microscopy, which profiles temperature quantitatively with nanoscale spatial resolution (∼50 nm), independently of both the heat flux through the air and the variation of the sample surface properties. Also, we control and monitor the heat generation rate accurately by heating the suspended graphene bridge electrically. Furthermore, we prevent the disturbance of the thermal conductivity caused by the polymeric residues by using polydimethylsiloxane stamping method, which leaves much less residue than using polymethylmethacrylate. The thermal conductivity values of graphene, whose length and width are 3.6 and 5.52 μm, respectively, were measured as 2430 ± 190, 2150 ± 170, and 2100 ± 160 W/mK at the peak temperatures of 335, 361, and 366 K, respectively, with much smaller error range compared to the previously reported values. The measured values exceed the highest value (∼2000 W/mK at room temperature) obtained for graphite.     

Thermal chemical vapor deposition grown graphene heat spreader for thermal management of hot spots

Graphene of different layer numbers was fabricated using thermal chemical vapor deposition (TCVD), and it was demonstrated as a heat spreader in electronic packaging. Platinum thermal evaluation chips were used to evaluate the thermal performance of the graphene heat spreaders. The temperature of a hot spot driven at a heat flux of up to 430 W cm⁻² was decreased from 121 °C to 108 °C (ΔT ≈ 13 °C) with the insertion of the monolayer graphene heat spreader, compared with the multilayer (n = 6–10) ones’ temperature drop of ∼8 °C. Various parameters affecting the thermal performance of graphene heat spreaders were discussed, e.g. layer numbers of graphene, phonon scattering, thermal boundary resistance. We demonstrate the potentials of using a complementary metal oxide semiconductor compatible TCVD process to utilize graphene as a heat spreader for heat dissipation purposes.     

Numerical experiments on phonon properties of isotope and vacancy-type disordered graphene

We have studied phonon properties of graphene theoretically with different concentrations of ¹³C isotope and vacancy-type defects. The forced vibrational method, which is based on the mechanical resonance to extract the pure vibrational eigenmodes by numerical simulation, has been employed to compute the phonon density of states (PDOSs) and mode pattern of isotope-disordered graphene as well as a combined isotope and vacancy-type defective graphene structure. We observe a linear reduction of the E_2g mode frequencies with an increase in ¹³C concentration due to the reduced mass variation of the isotope mixture. We find a downshift of the E_2g mode of 65 cm^− 1, which is a very good agreement with the experimental results, and the phonon frequencies described by the simple harmonic oscillator model. The vacancy-type defects break down the phonon degeneracy at the Г point of the LO and TO modes, distort and shift down the phonon density of states significantly. The PDOS peaks for the combined isotope and vacancy-type defects show the remarkable increase in the low-frequency region induced by their defect formations. Due to phonon scattering by ¹³C isotope or vacancies, some graphene phonon wave functions become localized in the real space. Our numerical experiments reveal that the lattice vibrations in the defective graphene show the remarkably different properties such as spatial localization of lattice vibrations due to their random structures from those in the perfect graphene. The calculated typical mode patterns for in-plane K point optical phonon modes indicate that the features of strongly localized state depend on the defect density, and the phonon is localized strongly within a region of several nanometers in the random percolation network structures. In particular, for in-plane K point optical phonon modes, a typical localization length is on the order of ≈ 7 nm for isotope impurities, ≈ 5 nm for vacancy-type defects and ≈ 6 nm for mixed-type defects at high defect concentrations of 30%. Our findings can be useful for the interpretation of experiments on infrared, Raman, and neutron-diffraction spectra of defective graphene, as well as in the study of a wide variety of other physical properties such as thermal conductivity, specific heat capacity, and electron–phonon interaction.     

Heat conduction mechanisms in hot pressed ZrB2 and ZrB2–SiC composites

Thermal diffusivity and conductivity of hot pressed ZrB₂ with different amounts of B₄C (0–5 wt%) and ZrB₂–SiC composites (10–30 vol% SiC) were investigated experimentally over a wide range of temperature (25–1500 °C). Both thermal diffusivity and thermal conductivity were found to decrease with increase in temperature for all the hot pressed ZrB₂ and ZrB₂–SiC composites. At around 200 °C, thermal conductivity of ZrB₂–SiC composites was found to be composition independent. Thermal conductivity of ZrB₂–SiC composites was also correlated with theoretical predictions of the Maxwell–Eucken relation. The dominated mechanisms of heat transport for all hot pressed ZrB₂ and ZrB₂–SiC composites at room temperature were confirmed by Wiedemann–Franz analysis by using measured electrical conductivity of these materials at room temperature. It was found that electronic thermal conductivity dominated for all monolithic ZrB₂ whereas the phonon contribution to thermal conductivity increased with SiC contents for ZrB₂–SiC composites.     

Advanced multifunctional graphene aerogel – Poly (methyl methacrylate) composites: Experiments and modeling

In this work, graphene aerogel (GA)–poly (methyl methacrylate) (PMMA) composites are first developed by backfilling PMMA into the pores of the GAs, providing uniform distribution of multi-layer reduced graphene oxide (m-rGO) sheets in the PMMA matrix. Electrical, mechanical and thermal properties of the as-prepared GA–PMMA composites are investigated by two-probe, microindentation and comparative infrared techniques respectively. As graphene loadings increase from 0.67 to 2.50 vol.%, the composites exhibit significant increases in electrical conductivity (0.160–0.859 S/m), microhardness (303.6–462.5 MPa) and thermal conductivity (0.35–0.70 W/m K) from that of pure PMMA as well as graphene–PMMA composites prepared by traditional dispersion methods. Thermal boundary resistance between graphene and PMMA is estimated to be 1.906 × 10⁻⁸ m² K/W by an off-lattice Monte Carlo algorithm that takes into account the complex morphology, size distribution and dispersion of m-rGO sheets.     

Thermal conductivity of a graphene oxide–carbon nanotube hybrid/epoxy composite

Thermally conductive graphene oxide (GO)–multi-wall carbon nanotube (MWCNT)/epoxy composite materials were fabricated by epoxy wetting. The polar functionality on the GO surface allowed the permeation of the epoxy resin due to a secondary interaction between them, which allowed the fabrication of a composite containing a high concentration of this hybrid filler. The thermal transport properties of the composites were maximized at 50 wt.% of filler due to fixed pore volume fraction in filtrated GO cake. When the total amount of filler was fixed 50 wt.% while changing the amount of MWCNTs, a maximum thermal conductivity was obtained with the addition of about 0.36 wt.% of MWCNTs in the filler. Measured thermal conductivity was higher than the predicted value based on the by Maxwell–Garnett (M–G) approximation and decreased for MWCNT concentrations above 0.4%. The increased thermal conductivity was due to the formation of 3-D heat conduction paths by the addition of MWCNTs. Too high a MWCNT concentration led to increased phonon scattering, which in turn led to decreased thermal conductivity. The measured storage modulus was higher than that of the solvent mixed composite because of the insufficient interface between the large amount of filler and the epoxy.     

Thermophysical properties of carbon fiber reinforced multilayered (PyC–SiC)n matrix composites

Three kinds of carbon fiber reinforced multilayered (PyC–SiC)_n matrix (C/(PyC–SiC)_n) composites (n = 1, 2 and 4) were prepared by means of layer-by-layer deposition of PyC and SiC via chemical vapor infiltration. Thermal expansion behaviors in the temperature range of 800–2500 °C and thermal conductivity from room temperature to 1900 °C of C/(PyC–SiC)_n composites with various microstructures were investigated. The results show that with increasing PyC–SiC sequences number (n), the coefficients of thermal expansion of the composites decrease due to the increase of interfacial delamination, providing room for thermal expansion. The thermal diffusivity and thermal conductivity also decrease with the increase of sequences number, which are attributed to the enhancement of phonon-interface scattering resulted from the increasing number of interfaces. Modified parallel and series models considering the interfacial thermal resistance are proposed to elaborate thermal conductivity of the composites, which is in accordance with the experimental results.     

Determination of chiralities of single-walled carbon nanotubes by neutron powder diffraction technique

The radial distribution function (RDF) of different single-walled carbon nanotubes (SWCNTs) has been calculated showing characteristic patterns. Features related to diameter, chirality and doping in these nanostructures are analyzed. We also investigate the induced chirality of two samples, prepared with the chemical vapor deposition (CVD) method and the high-pressure Co conversion (HIPCo) procedure, respectively, by comparing the experimental RDF signal obtained from the neutron scattering technique with the RDFs of our simulations. We found armchair and zigzag nanotubes in the sample, but we cannot discard the presence of other chiralities. We believe that this is a useful method to study chiralities induced by different methods of production. Data up to Q = 30 Å^− 1 were used in the Fourier transform, giving a high real space resolution of Δr ∼ 0.2 Å.