The DOI matches its Crossref record; 20 of the 21 references it cites were found in a registry or an index; none of the 28 sources its claims cite is checked for support yet.
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.
Model-written summary. Check it against the paper before relying on it.
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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.
hedgedSingle 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.
- Not matched
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
“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.
- 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.
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
“Beyond this peak, κ ( T ) decreases rapidly.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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.
- 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.
- 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.”
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.
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.
- 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.
- 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.
- 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.
- 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.”
plainSingle 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.
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 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.
- 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.
- 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.
- 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. 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”
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A practical dimensionless equation for the thermal conductivity of carbon nanotubes and CNT arrays
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Integration of CNTs thin film for sensing and actuating micro structures
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Carbon Nanotube Bolometer: Transport Properties and Noise Characteristics
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“3 g cm –3 , the thermal conductivity of CNT k = 3000 W/(K m) [12], and the average power density absorbed by magnetic grains p = 62 kW/cm 3”
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A Hierarchical Modeling Approach of Thermal Vias Using CNT-based Composites
Hertwig, J., Neubert, H., & Lienig, J. (2012) · Springer eBooks · doi:10.1007/978-3-642-28522-6_30 · Cited by 1
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Structure – Property Relationships for Nanofluids
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Phonon-phonon interactions and phonon damping for the curvature modes in carbon nanotubes
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Thermal conductance in a two-slit quantum waveguide
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Sonochemical Grafting of Poly(vinyl alcohol) onto Multiwall Carbon Nanotubes in Water
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Impact of Mass and Bond Energy Difference and Interface Defects on Thermal Boundary Conductance
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Thermal and Thermoelectric Properties of Nanomaterials
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Cross-Linked Carbon Nanotube Heat Spreader
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Syntheses and Processing of CPs
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Brief, General Overview of Applications
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Structural Aspects and Morphology of CPs
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Electrochemomechanical, Chemomechanical, and Related Devices
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Displays, Including Light-Emitting Diodes (LEDs) and Conductive Films
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Miscellaneous CNT Applications
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CNT Applications in Specialized Materials
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Electronic Structure and Conduction Models of Graphene
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Physical, Mechanical, and Thermal Properties of CNTs
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Synthesis and Chemical Modification of Graphene
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Thermal Interface Resistance Between Silicon and Single Wall Carbon Nanotubes
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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
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