Thermal Transport Measurements of Individual Multiwalled Nanotubes
Open accessAbstract
The thermal conductivity and thermoelectric power of a single carbon nanotube were measured using a microfabricated suspended device. The observed thermal conductivity is more than 3000 W/K m at room temperature, which is 2 orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples. The temperature dependence of the thermal conductivity of nanotubes exhibits a peak at 320 K due to the onset of umklapp phonon scattering. The measured thermoelectric power shows linear temperature dependence with a value of 80 microV/K at room temperature.
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TL;DR
The authors measured thermal transport of an individual multiwalled carbon nanotube using a microfabricated suspended device, finding room-temperature thermal conductivity above 3000 W/m K and thermoelectric power of 80 µV/K. The thermal conductivity peaks at 320 K due to the onset of Umklapp phonon scattering.
Key findings
- For a single MWNT of diameter 14 nm and bridging length 2.5 µm, the measured thermal conductance reaches a maximum of approximately 1.6 × 10⁻⁷ W/K near room temperature, and the derived thermal conductivity is more than 3000 W/m K at room temperature.
- This room-temperature thermal conductivity is two orders of magnitude higher than the previous bulk mat estimate of 20 W/m K, an order of magnitude higher than an aligned SWNT sample value of 250 W/m K, and comparable to a theoretical expectation of 6000 W/m K.
- The thermal conductivity increases with temperature, following a power law with exponent 2.50 for 8 K < T < 50 K, then approximately T² for 50 K < T < 150 K, and peaks at 320 K before decreasing rapidly; the crossover gives an estimated interlayer Debye temperature Θ⊥ = 50 K.
- The thermoelectric power shows linear temperature dependence with a room-temperature value of 80 µV/K, and its positive sign indicates hole-like majority carriers.
Methods
- Suspended devices were fabricated on a silicon nitride/silicon oxide/silicon multilayer, with two 10 µm × 10 µm silicon nitride membrane islands suspended by silicon nitride beams; Pt thin-film resistors on each island served as both heaters and thermometers.
- A single MWNT was placed to bridge the two suspended islands by mechanical manipulation. Joule heating in one resistor created a temperature gradient, and the resulting temperature changes of both islands were measured from resistance changes versus applied power.
- Thermal conductance was extracted using a simple heat-transfer model, and thermal conductivity was estimated assuming a solid isotropic material and neglecting junction thermal conductance. Thermoelectric power was obtained from the slope of thermoelectric voltage versus Joule heating power.
Limitations
- Stated: the reported thermal conductivity is a lower bound because the authors neglect junction thermal conductance and assume a solid isotropic material to correct geometric factors; they note that further study is needed to analyze the contribution of individual MWNT layers.
- Stated: below 8 K, both resistors saturate due to impurity scattering and cannot be used as temperature sensors; the diameter measurement has a resolution limit of 2 nm, which is the major uncertainty in κ.
- Stated/evident: the TEP measurement may be affected by gas adsorption and oxygen doping because the MWNTs were exposed to air; the results are from a single MWNT, so generalization to other nanotubes or ensembles is not established in the text.
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- Findingcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The thermal conductance of the junction between a self-heated MWNT and a metal electrode at room temperature is ∼0.5 W/m K per unit length per unit temperature difference.
“From our separate study of scanning thermal microscopy on a self heated MWNT[18], we have estimated the thermal conductance of the junction at room temperature; the heat flow rate from a unit length of the tube to metal electrode at a given unit junction temperature difference was found to be ∼ 0.5 W/m K.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [18]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
In the intermediate temperature range (50 K < T < 150 K), the thermal conductivity of the MWNT increases almost quadratically in T.
“In the intermediate temperature range (50 K < T < 150 K), κ ( T ) increases almost quadratically in T (i.e., κ ( T ) ∼ T 2 ).”
Quote in the paperSubstantial claim - Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
Beyond the peak at 320 K, the thermal conductivity of the MWNT decreases rapidly.
“Beyond this peak, κ ( T ) decreases rapidly.”
Quote in the paperNot a substantial claim - Findingreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The temperature dependence of the thermal conductivity of an individual MWNT exhibits a peak at 320 K.
“The temperature dependence of the thermal conductivity of nanotubes exhibits a peak at 320 K due to the onset of Umklapp phonon scattering.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
“Above this temperature range, κ ( T ) deviates from quadratic temperature dependence and has a peak at 320 K.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
“The temperature dependence of the thermal conductivity shows a peak at 320 K due to the onset of Umklapp phonon scattering.”
Quote in the paperSubstantial claim - Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
At low temperatures (8 K < T < 50 K), the thermal conductivity of the MWNT increases following a power law with an exponent 2.50.
“At low temperatures, 8 K < T < 50 K, κ ( T ) increases following a power law with an exponent 2.50.”
Quote in the paperSubstantial claim
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The observed thermal conductivity of an individual multiwalled nanotube is more than 3000 W/m K at room temperature.
“The observed thermal conductivity is more than 3000 W/K m at room temperature, which is two orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
“First, the room temperature value of κ ( T ) is over 3000 W/m K [20], whereas the previous 'bulk' measurement on a MWNT mat using the 3w method estimates only 20 W/m K [4].”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
“The observed thermal conductivity of a MWNT is more than 3000 W/m K at room temperature and the phonon mean free path is ∼ 500nm.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The thermoelectric power of an individual MWNT is 80 μV/K at room temperature.
“with a value of 80 µ V/K at room temperature.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
“with room temperature value 80 µ V/K.”
Quote in the paperSubstantial claim - Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The thermal conductance of a single MWNT with a diameter of 14 nm and a bridging segment length of 2.5 μm was measured.
“Fig.3 displays measured thermal conductance of a single MWNT with a diameter 14 nm and the length of the bridging segment 2.5 µ m.”
Quote in the paperSubstantial claim - Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The measured thermoelectric power of an individual MWNT shows linear temperature dependence.
“The measured thermoelectric power shows linear temperature dependence with a value of 80 µ V/K at room temperature.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
“The observed temperature dependent TEP of MWNTs (Fig.4) shows a linear T dependence, with room temperature value 80 µ V/K.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
“The thermoelectric power shows an expected linear T dependence, which was absent previous bulk measurements.”
Quote in the paperSubstantial claim - Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
- Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
Above 150 K, the thermal conductivity of the MWNT deviates from quadratic temperature dependence.
“Above this temperature range, κ ( T ) deviates from quadratic temperature dependence and has a peak at 320 K.”
Quote in the paperSubstantial claim - Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The thermal conductivity and thermoelectric power of a single carbon nanotube were measured using a microfabricated suspended device.
“The thermal conductivity and thermoelectric power of a single carbon nanotube were measured using a microfabricated suspended device.”
Quote in the paperSubstantial claim - Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The thermal properties of carbon nanotubes had not been measured at a mesoscopic scale prior to this study.
“Unlike electrical and mechanical properties, which have been studied at a single nanotube level [2], the thermal properties of carbon nanotubes have not been measured at a mesoscopic scale.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Premisereasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
In thermal transport measurements of carbon nanotube mats, it is difficult to extract absolute values for thermal conductivity and TEP due to numerous tube-tube junctions.
“More importantly, in thermal transport measurements such as thermal conductivity and TEP, it is difficult to extract absolute values for these quantities due to the presence of numerous tube-tube junctions.”
Quote in the paperSubstantial claim - Premisenone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
Bulk measurements of carbon nanotube mats yield an ensemble average over the different tubes in a sample.
“One problem is that these measurements yield an ensemble average over the different tubes in a sample.”
Quote in the paperSubstantial claim - Study design and conductreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The Pt thin film resistor on each suspended island serves as a thermometer to measure the temperature of the island.
“Since the resistance of the Pt resistor changes with temperature (Fig.1(b)), they also serve as a thermometer to measure the temperature of each island [15].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [15]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The large difference between single-tube and bulk thermal conductivity measurements suggests that numerous highly resistive thermal junctions between tubes largely dominate thermal transport in mat samples.
“This large difference between singletube and 'bulk' measurements suggests that numerous highly resistive thermal junctions between the tubes largely dominate the thermal transport in mat samples.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The intrinsic thermal conductance of the tube is the major part of the measured thermal conductance.
“Since the total measured thermal conductance is 1.6 × 10 -7 W/K, this suggests that the intrinsic thermal conductance of the tube is the major part of measured thermal conductance.”
Quote in the paperNot a substantial claim - Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The specific heat, thermal conductivity and thermoelectric power of millimeter-sized mats of carbon nanotubes have been measured by several groups.
“The specific heat, thermal conductivity and thermoelectric power (TEP) of millimeter-sized mats of carbon nanotubes have been measured by several groups [3-13].”
Quote in the paperSubstantial claim0 of 10 sources checked- cites [3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Study design and conductcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The thermal conductance of the single MWNT was measured in the temperature range 8-370 K.
“The thermal conductance was measured in a temperature range 8-370 K [17].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The thermal properties of carbon nanotubes play a critical role in controlling the performance and stability of nanotube devices.
“The thermal properties of carbon nanotubes are of fundamental interest and also play a critical role in controlling the performance and stability of nanotube devices [1].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The thermal conductivity reported in the paper is a lower bound of the intrinsic axial thermal conductivity of a MWNT.
“This simplification implies that the thermal conductivity reported in this letter is a lower bound of the intrinsic axial thermal conductivity of a MWNT.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The thermal conductivity estimate assumes a solid isotropic material to correct geometric factors.
- The authors state this as an assumption: The thermal conductivity estimate neglects the junction thermal conductance.
- Premisenone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
Tube-tube junctions are the dominant barriers to thermal transport in a mat of nanotubes.
“These junctions are in fact the dominant barriers to thermal transport in a mat of nanotubes.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The junction thermal conductance for the measured MWNT at room temperature is ∼5 × 10^-7 W/K.
“Considering the contact length of the MWNT to the electrodes on the islands is ∼ 1 µ m, the junction thermal conductance is ∼ 5 × 10 -7 W/Kat room temperature.”
Quote in the paperSubstantial claim - Study design and conductnone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The measured thermal conductance includes the thermal conductance of the junction between the MWNT and the suspended islands in addition to the intrinsic thermal conductance of the MWNT itself.
“The measured thermal conductance includes the thermal conductance of the junction between the MWNT and the suspended islands in addition to the intrinsic thermal conductance of the MWNT itself.”
Quote in the paperSubstantial claim - Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The observed thermal conductivity of an individual MWNT is comparable to theoretical expectations.
“The observed thermal conductivity of MWNT is two orders of magnitude higher than the value found in previous 'bulk' measurements and is comparable to the theoretical expectations.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
“but comparable to the recent theoretical expectation, 6000 W/m K [21].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [21] S. Berber, Y. K. Kwon, and D. Tomanek, Phys. Rev. Lett. 84 , 4613 (2000).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
- Interpretationown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The observed room-temperature thermal conductivity of an individual MWNT is two orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples.
“The observed thermal conductivity is more than 3000 W/K m at room temperature, which is two orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1 · plain
“The observed thermal conductivity of MWNT is two orders of magnitude higher than the value found in previous 'bulk' measurements and is comparable to the theoretical expectations.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1 · plain
- Study design and conductnone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The microfabricated suspended device hybridized with MWNTs probes thermal transport free from a substrate contact.
“We have developed a microfabricated suspended device hybridized with multiwalled nanotubes (MWNTs) to probe thermal transport free from a substrate contact.”
Quote in the paperSubstantial claim - Study design and conductnone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2
The mechanical manipulation approach routinely produces a nanotube device that can be used to measure the thermal conductivity and TEP of the bridging nanotube segment.
“This approach routinely produces a nanotube device that can be used to measure the thermal conductivity and TEP of the bridging nanotube segment.”
Quote in the paperSubstantial claim - Interpretationown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The room-temperature thermal conductivity of an individual MWNT is an order of magnitude higher than that of an aligned SWNT sample (250 W/m K).
“Note that our observed value is also an order of magnitude higher than that of aligned SWNT sample (250 W/m K) [7] but comparable to the recent theoretical expectation, 6000 W/m K [21].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationnone given§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
The peak in thermal conductivity at 320 K is due to the onset of Umklapp phonon scattering.
“due to the onset of Umklapp phonon scattering.”
- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
“due to the onset of Umklapp phonon scattering.”
Quote in the paperSubstantial claim - Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
- Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The estimated Θ⊥ = 50 K is comparable to the value obtained from a specific heat measurement of MWNT.
“This value is comparable to the value obtained by a measurement of specific heat of MWNT [4].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
A mesoscopic measurement of a single tube is necessary to properly probe the intrinsic TEP of nanotubes.
“Again, we believe that the numerous unknown tubetube junctions in the 'mat' sample may produce these differences, and that a mesoscopic measurement of a single tube is necessary to properly probe the intrinsic TEP of nanotubes.”
Quote in the paperSubstantial claim - Interpretationown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The estimated static scattering length of ∼500 nm is comparable to the length of the measured MWNT (2.5 μm).
“Note that this value is an order of magnitude higher than previous estimations from 'bulk' measurements [7] and is comparable to the length of the measured MWNT (2.5 µ m).”
Quote in the paperSubstantial claim - Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The estimated static scattering length of ∼500 nm is an order of magnitude higher than previous estimations from bulk measurements.
“Note that this value is an order of magnitude higher than previous estimations from 'bulk' measurements [7] and is comparable to the length of the measured MWNT (2.5 µ m).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The differences between single-tube and bulk TEP measurements may be produced by numerous unknown tube-tube junctions in the mat sample.
“Again, we believe that the numerous unknown tubetube junctions in the 'mat' sample may produce these differences, and that a mesoscopic measurement of a single tube is necessary to properly probe the intrinsic TEP of nanotubes.”
Quote in the paperSubstantial claim - Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The observed linear temperature dependence of TEP is expected from a theory for metallic and doped semiconducting nanotubes.
“The linear T dependence is expected from a theory for metallic and doped semiconducting nanotubes [9,13], and the positive sign indicates hole-like major carrier [25].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [13]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
At the peak of κ(T) at 320 K, the static scattering length l_st is estimated to be ∼500 nm for the MWNT.
“At the peak value of κ ( T ), where l st ∼ l um ( T = 320 K), we can estimate the T -independent l st ∼ 500 nm for the MWNT.”
Quote in the paperSubstantial claim - Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
For MWNTs below the Debye temperature of the interlayer phonon mode, κ(T) has a slight three-dimensional nature and scales as T^2.5, as observed in graphite single crystals.
“For MWNTs, below the Debye temperature of interlayer phonon mode, Θ ⊥ , κ ( T ) has slight three dimensional nature, and κ ( T ) ∼ T 2 . 5 as observed in graphite single crystals [23].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [23] B. T. Kelly, Physics of Graphite (Applied Science Publishers, London, 1981).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The Debye temperature of the interlayer phonon mode for the MWNT is estimated to be 50 K.
“From this cross over behavior of κ ( T ), we estimate Θ ⊥ = 50 K.”
Quote in the paperSubstantial claim - Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The observed TEP of an individual MWNT is markedly different from previous bulk measurements, which exhibited somewhat smaller TEP and deviations from a linear T dependence.
“It is worth noting that this observed TEP is markedly different from the previous 'bulk' measurement that exhibited somewhat smaller TEP and deviations from a linear T dependence [8].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [8]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationcitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3
The positive sign of the TEP indicates hole-like major carriers.
“The linear T dependence is expected from a theory for metallic and doped semiconducting nanotubes [9,13], and the positive sign indicates hole-like major carrier [25].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [25]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- May combine two claims. 5
- Classified as probably not a substantial claim. 2
May combine two claims.
Findingown data§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 2The thermal conductance of the single MWNT increases by several orders of magnitude as temperature is raised, reaching a maximum of approximately 1.6 × 10^-7 W/K near room temperature before decreasing at higher temperatures.
“It increases by several orders of magnitude as the temperature is raised, reaching a maximum of approximately 1.6 × 10 -7 W/K near room temperature before decreasing again at higher temperatures.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3The phonon thermal conductivity can be written as κ = ∑_p C_p v_p l_p, where C_p, v_p, and l_p are the specific heat capacity, phonon group velocity, and mean free path of phonon mode p.
“In a simple model [22], the phonon thermal conductivity can be written as: κ = ∑ p C p v p l p , where C p , v p , and l p is the specific heat capacity, phonon group velocity, and the mean free path of phonon mode p .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [22]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3The nearly ballistic phonon transport behavior was not seen in bulk experiments, possibly due to additional extrinsic phonon scattering mechanisms such as tube-tube interactions.
“This remarkable behavior was not seen in the bulk experiments, possibly due to additional extrinsic phonon scattering mechanisms such as tube-tube interactions.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3At low temperatures, Umklapp scattering freezes out, so the phonon mean free path equals the static scattering length and κ(T) follows the temperature dependence of the specific heat.
“At low temperatures, the Umklapp scattering freezes out, l = l st , and thus κ ( T ) simply follows the temperature dependence of C p 's.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3The phonon mean free path consists of two contributions: l^-1 = l^-1_st + l^-1_um, where l_st and l_um are static and Umklapp scattering lengths.
“The phonon mean free path consists of two contributions: l -1 = l -1 st + l -1 um where l st and l um are static and Umklapp scattering length, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3Below room temperature, where phonon-phonon Umklapp scattering is minimal, phonons have only a few scattering events between the thermal reservoirs and phonon transport is nearly ballistic.
“Thus below room temperature where the phonon-phonon Umklapp scattering is minimal, phonons have only a few scattering events between the thermal reservoirs, and the phonon transport is 'nearly' ballistic.”
Quote in the paperSubstantial claimMay combine two claims.
Premisecitation§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3As T exceeds the Debye temperature of the interlayer phonon mode, the interlayer phonon modes are fully occupied and κ(T) scales as T^2, indicating two-dimensional thermal conduction in a MWNT.
“As T > Θ ⊥ , the interlayer phonon modes are fully occupied, and κ ( T ) ∼ T 2 , indicative of the two dimensional nature of thermal conduction in a MWNT [24].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [24]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
The authors state this as an assumption.
The thermal conductivity estimate assumes a solid isotropic material to correct geometric factors.
“In the following, however, we simply estimate the thermal conductivity neglecting the junction thermal conductance and assuming a solid isotropic material to correct geometric factors.”
The authors state this as an assumption.
The thermal conductivity estimate neglects the junction thermal conductance.
“In the following, however, we simply estimate the thermal conductivity neglecting the junction thermal conductance and assuming a solid isotropic material to correct geometric factors.”
The authors state this as an assumption.
The MWNTs used in the experiments were exposed to air and presumably doped with oxygen.
“The MWNTs used in our experiments were exposed in air and presumably doped with oxygen.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Suspending legs have two stated lengths
MinorThe device description says the suspending beams are 200 μm long, while the caption for the same device says its legs are 250 μm long.
“two 10 µ m × 10 µ m adjacent silicon nitride membrane (0.5 µ m thick) islands suspended with 200 µ m long silicon nitride beams.”
“Two independent islands are suspended by three sets of 250 µ m long silicon nitride legs”
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Role of thermal boundary resistance on the heat flow in carbon-nanotube composites
Shenogin, S. V., Xue, L., Ozisik, R., Keblinski, P., & Cahill, D. G. (2004) · Journal of Applied Physics · doi:10.1063/1.1736328 · Cited by 520 · see citing works
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Breakdown of Fourier’s Law in Nanotube Thermal Conductors
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Self-citationElectrical Properties of Carbon Nanotube Based Fibers and Their Future Use in Electrical Wiring
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Carbon nanotubes-properties and applications: a review
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UNUSUAL PROPERTIES AND STRUCTURE OF CARBON NANOTUBES
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Thermal conductivity of multiwalled carbon nanotubes
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- Authors
- Kim, P., Shi, L., Majumdar, A., & McEuen, P. L.
- Affiliations
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2001-10-31
- Volume
- 87
- Issue
- 21
- Pages
- 215502-215502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2170116274
- Semantic Scholar
- 6afd3f2f6be3f5b0608297a41e67c4510a4ede69
- Cited by
- 3,378
- References
- 21
- Citations by year
- 2026: 58 · 2025: 83 · 2024: 80 · 2023: 114 · 2022: 138 · 2021: 167 · 2020: 142 · 2019: 182 · 2018: 218 · 2017: 168 · 2016: 177 · 2015: 174 · 2014: 172 · 2013: 205 · 2012: 209
- FWCI
- 30.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Technische Universität Dortmund Eldorado (Technische Universität Dortmund) (submittedVersion)
- arXiv (Cornell University)
- Technische Universität Dortmund Eldorado (Technische Universität Dortmund)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Materials Science › Materials Chemistry › Carbon Nanotubes in Composites
- Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
- Keywords
- carbon nanotubes, multi-walled carbon nanotubes, thermal conductivity, thermoelectric power, temperature dependence, phonon transport
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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