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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.
Overview
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Written from the paper’s full text.
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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Claims the paper makes
18 Sources not found · 13 Own interpretation · 9 Own result · 4 No basis given · 3 Own method · 1 Not checked yet
In the paper
“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.”
What the sources say
- Not matchedcites [18]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“In the intermediate temperature range (50 K < T < 150 K), κ ( T ) increases almost quadratically in T (i.e., κ ( T ) ∼ T 2 ).”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“Beyond this peak, κ ( T ) decreases rapidly.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
plaincorrelationalSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At low temperatures, 8 K < T < 50 K, κ ( T ) increases following a power law with an exponent 2.50.”
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In the paper
“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.”
What the sources say
- Not matchedcites [20]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
plainSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
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In the paper
“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.”
plaincorrelationalSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Above this temperature range, κ ( T ) deviates from quadratic temperature dependence and has a peak at 320 K.”
plainSingle case- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The thermal conductivity and thermoelectric power of a single carbon nanotube were measured using a microfabricated suspended device.”
plainSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
What the sources say
- Not matchedcites [2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
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In the paper
“One problem is that these measurements yield an ensemble average over the different tubes in a sample.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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].”
What the sources say
- Not matchedcites [15]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
hedgedSingle case- Asserted: passes — The authors put it forward as true.
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None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“The specific heat, thermal conductivity and thermoelectric power (TEP) of millimeter-sized mats of carbon nanotubes have been measured by several groups [3-13].”
What the sources say
- Not matchedcites [3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [4]
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- Not matchedcites [8]
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- Not matchedcites [9]
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- Not matchedcites [10]
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- Not matchedcites [11]
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- Not matchedcites [12]
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plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The thermal conductance was measured in a temperature range 8-370 K [17].”
What the sources say
- Not matchedcites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“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].”
What the sources say
- Not matchedcites [1]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This simplification implies that the thermal conductivity reported in this letter is a lower bound of the intrinsic axial thermal conductivity of a MWNT.”
plain- Asserted: passes — The authors put it forward as true.
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- 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.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These junctions are in fact the dominant barriers to thermal transport in a mat of nanotubes.”
boosteddirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
plainSingle case- Asserted: passes — The authors put it forward as true.
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What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
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In the paper
“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].”
What the sources say
- Not matchedcites [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.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 3 · plain
In the paper
“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.”
What the sources say
- Not matchedcites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1 · plain
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We have developed a microfabricated suspended device hybridized with multiwalled nanotubes (MWNTs) to probe thermal transport free from a substrate contact.”
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In the paper
“This approach routinely produces a nanotube device that can be used to measure the thermal conductivity and TEP of the bridging nanotube segment.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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].”
What the sources say
- Not matchedcites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainSingle case- Asserted: passes — The authors put it forward as true.
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- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 4 · plain
In the paper
“This value is comparable to the value obtained by a measurement of specific heat of MWNT [4].”
What the sources say
- Not matchedcites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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).”
plaincorrelationalSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“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).”
What the sources say
- Not matchedcites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainSingle case- Asserted: passes — The authors put it forward as true.
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- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“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].”
What the sources say
- Not matchedcites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [13]
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plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
hedgedSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“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].”
What the sources say
- Not matchedcites [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.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From this cross over behavior of κ ( T ), we estimate Θ ⊥ = 50 K.”
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“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].”
What the sources say
- Not matchedcites [8]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Not matched
In the paper
“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].”
What the sources say
- Not matchedcites [25]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Not matched
- It may state two separate claims as one. 5
- Probably not a substantial claim. 2
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“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 .”
What the sources say
- Not matchedcites [22]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This remarkable behavior was not seen in the bulk experiments, possibly due to additional extrinsic phonon scattering mechanisms such as tube-tube interactions.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At low temperatures, the Umklapp scattering freezes out, l = l st , and thus κ ( T ) simply follows the temperature dependence of C p 's.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“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.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
hedgeddirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“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].”
What the sources say
- Not matchedcites [24]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
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.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
“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.”
§ Thermal Transport Measurements of Individual Multiwalled Nanotubes · p. 1
“Two independent islands are suspended by three sets of 250 µ m long silicon nitride legs”
Citations
Cites
Science of fullerenes and carbon nanotubes
Ebert, L. B. (1997) · Carbon · doi:10.1016/s0008-6223(97)89618-2 · Cited by 4,517
Unusually High Thermal Conductivity of Carbon Nanotubes
Berber, S., Kwon, Y., & Tománek, D. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.4613 · Cited by 3,090
Extreme Oxygen Sensitivity of Electronic Properties of Carbon Nanotubes
Collins, P. G., Bradley, K., Ishigami, M., & Zettl, A. K. (2000) · Science · doi:10.1126/science.287.5459.1801 · Cited by 2,977
Nanotubes as nanoprobes in scanning probe microscopy
Dai, H., Hafner, J. H., Rinzler, A. G., et al. (1996) · Nature · doi:10.1038/384147a0 · Cited by 2,214
Engineering Carbon Nanotubes and Nanotube Circuits Using Electrical Breakdown
Collins, P. G., Arnold, M. S., & Avouris, P. (2001) · Science · doi:10.1126/science.1058782 · Cited by 1,720
Carbon Nanotubes as Molecular Quantum Wires
Dekker, C. (1999) · Physics Today · doi:10.1063/1.882658 · Cited by 1,417
Thermal conductivity of single-walled carbon nanotubes
Hone, J., Whitney, M., Piskoti, C., & Zettl, A. K. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.59.r2514 · Cited by 1,195
Thermal conductivity of carbon nanotubes
Che, J., Çağın, T., & Goddard, W. A. (2000) · Nanotechnology · doi:10.1088/0957-4484/11/2/305 · Cited by 1,139
Measurement of the quantum of thermal conductance
Schwab, K., Henriksen, E. A., Worlock, J. M., & Roukes, M. L. (2000) · Nature · doi:10.1038/35010065 · Cited by 916
Hone, J., Llaguno, M. C., Nemes, N. M., et al. (2000) · Applied Physics Letters · doi:10.1063/1.127079 · Cited by 834
Research works printed but not linked: 2
- M. Osman, 2001, Nanotechnology, 12, 21, 10.1088/0957-4484/12/1/305 · DOI
- B. T. Kelly, 1981, Physics of Graphite
Cited by
Sorted by citations
Superior Thermal Conductivity of Single-Layer Graphene
Balandin, A. A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F., & Lau, C. N. (2008) · Nano Letters · doi:10.1021/nl0731872 · Cited by 13,823
Carbon Nanotubes--the Route Toward Applications
Baughman, R. H., Zakhidov, A. A., & de Heer, W. A. (2002) · Science · doi:10.1126/science.1060928 · Cited by 10,251
Thermal properties of graphene and nanostructured carbon materials
Balandin, A. A. (2011) · Nature Materials · doi:10.1038/nmat3064 · Cited by 6,244
Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites
Coleman, J. N., Khan, U., Blau, W. J., & Gun’ko, Y. K. (2006) · Carbon · doi:10.1016/j.carbon.2006.02.038 · Cited by 4,074
“Ballistic conduction has been observed by a number of groups [27] and thermal conductivities as high as 3000 W/m K have been measured [28].”
Zinc oxide nanostructures: growth, properties and applications
Wang, Z. L. (2004) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/16/25/r01 · Cited by 3,694
Metadata
- 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
About these checks
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.
A language model drew the claims from the paper on 2026-10-20, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-20 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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