A Meta-Analysis of Conductive and Strong Carbon Nanotube Materials

Abstract

A study of 1304 data points collated over 266 papers statistically evaluates the relationships between carbon nanotube (CNT) material characteristics, including: electrical, mechanical, and thermal properties; ampacity; density; purity; microstructure alignment; molecular dimensions and graphitic perfection; and doping. Compared to conductive polymers and graphitic intercalation compounds, which have exceeded the electrical conductivity of copper, CNT materials are currently one-sixth of copper's conductivity, mechanically on-par with synthetic or carbon fibers, and exceed all the other materials in terms of a multifunctional metric. Doped, aligned few-wall CNTs (FWCNTs) are the most superior CNT category; from this, the acid-spun fiber subset are the most conductive, and the subset of fibers directly spun from floating catalyst chemical vapor deposition are strongest on a weight basis. The thermal conductivity of multiwall CNT material rivals that of FWCNT materials. Ampacity follows a diameter-dependent power-law from nanometer to millimeter scales. Undoped, aligned FWCNT material reaches the intrinsic conductivity of CNT bundles and single-crystal graphite, illustrating an intrinsic limit requiring doping for copper-level conductivities. Comparing an assembly of CNTs (forming mesoscopic bundles, then macroscopic material) to an assembly of graphene (forming single-crystal graphite crystallites, then carbon fiber), the ≈1 µm room-temperature, phonon-limited mean-free-path shared between graphene, metallic CNTs, and activated semiconducting CNTs is highlighted, deemphasizing all metallic helicities for CNT power transmission applications.

Keywords: carbon nanotubes; conductive polymers; graphitic intercalation compounds; meta-analysis.

Figure 1

The various advanced carbon conductors that compete with traditional metallic conductors. Top row: A–C) Iodine‐doped polyacetylene as shown with a model (A), SEM images (B), and visual photographs (C) showing their shiny nature. Left SEM image in (B): Reproduced with permission.^{[ 85 ]} Copyright 1998, Elsevier. Right SEM image in (B): Reproduced with permission.^{[ 86 ]} Copyright 1998, American Association for the Advancement of Science (AAAS). Left photograph in (C): Reproduced under the terms of the CC‐BY Creative Commons Attribution 3.0 Unported license (https://creativecommons.org/licenses/by/3.0).^{[ 87 ]} Copyright 2013, IOP Publishing Ltd. Right photograph in (C): Reproduced with permission.^{[ 88 ]} Copyright 2010, RSC. Middle row: D–F) Graphitic intercalation compounds as shown with a model (D), SEM images (E) of graphitized carbon fiber before doping, and visual photographs (F) showing the color change. Photos in (E): Reproduced with permission.^{[ 89 ]} Copyright 1982, IOP Publishing. Left photos in (F): Reproduced with permission.^{[ 90 ]} Copyright 2019, American Chemical Society. Right photo in (F): Reproduced with permission.^{[ 50 ]} Copyright 2012, Elsevier. Bottom row: G–I) Doped SWCNT bundles as shown with a model (G), SEM images (H), and visual photographs (I). H,I) Photos in (H) and (I): Reproduced with permission. Copyright Dr. Thurid Gspann.

Figure 2

Transport characteristics of individual CNTs and graphene. a) Mean‐free‐path (L _m) versus temperature (T) for a metallic SWCNT (open circles) and activated semiconducting SWCNTs (closed circles). Dotted straight line indicates T ⁻¹ dependence, the expected behavior for electron–phonon scattering. Reproduced with permission.^{[ 103 ]} Copyright 2007, American Physical Society. b) Graphene has a similar room‐temperature mean‐free‐path as the SWCNTs, which also increases dramatically at colder temperatures. Reproduced with permission.^{[ 122 ]} Copyright 2013, AAAS. c) Compilation of studies showing resistance versus length of long individual SWCNTs, to include activated semiconducting SWCNTs. Resistance per length falls on a master curve at ≈6 kΩ µm⁻¹. Reproduced with permission.^{[ 69 ]} Copyright 2009, Wiley‐VCH. d,e) Density of states of a semiconducting (10,0) SWCNT (d) and a metallic (9,0) SWCNT (e). ϒ ₀ is the nearest neighbor overlap integral; dotted lines are the density of states of graphene. d,e) Reproduced with permission.^{[ 123 ]} Copyright 1992, The American Institute of Physics.

Figure 3

a,b) From data surveyed across the experimental literature: a) electrical conductivities and b) tensile strengths of CNTs, other carbon‐based conductors, and benchmark materials. Filled‐in shapes denote doped materials, as well as the right‐most box plot in each subcategory. Unfilled shapes and the left‐most box plots in each subcategory represent undoped materials. Green lines indicate benchmarks. Key: ) unaligned MWCNT materials; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials; ) conductive polymers; ) graphitic intercalation compounds; ) carbon fiber and graphite. M, F, B indicate individual MWCNTs, FWCNTs, and CNT bundles respectively. For the production method subcategories: AS‐CNT (derived from CNT forest arrays); UF/AF‐CNT (unaligned/aligned CNT film by filtering CNTs suspended in a fluid); DS‐CNT (aligned CNT materials directly extracted from FC‐CVD reactors); SS‐CNT (aligned CNT materials by extruding CNT solutions or suspensions into a coagulant).

Figure 4

Conductivity and strength relationships in CNT materials and benchmarks across the literature surveyed. a) Tensile strength versus Young's modulus and conductivity versus tensile strength. b) Depiction of the multifunctional metric (conductivity multiplied by tensile strength), partitioned by CNT categories. c) Dependence of conductivity and strength on fiber diameter. Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials; ) conductive polymers; )graphitic intercalation compounds; ) carbon fiber and graphite. M, F, B indicate individual MWCNTs, FWCNTs, and CNT bundles respectively. “x” indicated annotated benchmarks. Only in (b) do filled in shapes indicate doped materials. Ellipses help identify trends and are adjusted to cover 90% of the points. For the production method subcategories: AS‐CNT (derived from CNT forest arrays); UF/AF‐CNT (unaligned/aligned CNT film by filtering CNTs suspended in a fluid); DS‐CNT (aligned CNT materials directly extracted from FC‐CVD reactors); SS‐CNT (aligned CNT materials by extruding CNT solutions or suspensions into a coagulant).

Figure 5

a) Thermal conductivity of CNT categories and benchmarks. b) Thermal conductivity versus electrical conductivity. Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials; ) carbon fiber, diamond, and graphite. M, F, B indicate individual MWCNTs, FWCNTs, and CNT bundles respectively. Only in (a) do filled in shapes indicate doped materials, as does the right‐most box plots in each subcategory. Ellipses help identify trends and are adjusted to cover 90% of the points. For the production method subcategories: AS‐CNT (derived from CNT forest arrays); UF/AF‐CNT (unaligned/aligned CNT film by filtering CNTs suspended in a fluid); DS‐CNT (aligned CNT materials directly extracted from FC‐CVD reactors); SS‐CNT (aligned CNT materials by extruding CNT solutions or suspensions into a coagulant).

Figure 6

Ampacity relationships, open symbols indicate vacuum measurements and filled symbols indicate measurement in air, for all graphs. a) Ampacity of CNT materials surveyed across the literature, along with metals and other carbon‐based conductors. Blue circles are suspended samples, while red diamonds are samples measured on various substrates. b) An example of current density versus resistivity curve. c) Log−log plot of ampacity versus conductivity for all material classes. d) Ampacity versus diameter master curve for all materials studied here including metals, metalized CNTs, pure CNTs, and other carbons. Samples that did not fail or whose diameters cannot be confidently determined are shown with square symbols. e) Ampacity versus diameter plot for CNT materials only classified based on presence or absence of substrates. The ellipses in this figure (only) represent a 95% confidence region of the linear fits from which the power‐law exponents can be obtained.

Figure 7

Density and density normalized characteristics for CNTs and benchmarks. a) Theoretical density of an individual CNT, as a function of diameter and wall number. Reproduced with permission.^{[ 266 ]} Copyright 2010, Elsevier. Alongside is the density of various CNT textiles. b) Conductivity and tensile strength as a function of density; c) specific conductivity and specific strength as a function of density. Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials; ) conductive polymers; ) graphitic intercalation compounds; ) carbon fiber and graphite. M, F, B indicate individual MWCNTs, FWCNTs, and CNT bundles respectively. “x” indicated annotated benchmarks. Only in (a) do filled in shapes indicate doped materials. Ellipses help identify trends and are adjusted to cover 90% of the points. For the production method subcategories: AS‐CNT (derived from CNT forest arrays); UF/AF‐CNT (unaligned/aligned CNT film by filtering CNTs suspended in a fluid); DS‐CNT (aligned CNT materials directly extracted from FC‐CVD reactors); SS‐CNT (aligned CNT materials by extruding CNT solutions or suspensions into a coagulant).

Figure 8

a–c) Material properties versus different microstructure alignment/anisotropy metrics across the literature: a) FWHM of the intensity variation measured in the azimuthal circle of a Bragg peak in X‐ray diffraction; b) Raman spectroscopy's G peak anisotropy; and c) electrical anisotropy. Key: ) aligned MWCNT materials; ) aligned FWCNT materials; ) conductive polymers; ) graphitic intercalation compounds. Ellipses help identify trends and are adjusted to cover 90% of the points.

Figure 9

a–c) Conductivity and strength metrics versus Raman spectroscopy G:D ratio (a), Raman spectroscopy G:D ratio × λ⁴ (b), and CNT diameter (c). Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials. M and F indicate individual MWCNTs and FWCNTs and B indicates individual bundles. Ellipses help identify trends and are adjusted to cover 90% of the points.

Figure 10

Surveyed across the experimental literature, effects of doping on CNT material. a) Post‐doped conductivity versus host conductivity for the four CNT categories. b) Post‐doped conductivities for the four CNT categories as a function of categorical dopant intentionally applied as a post‐process. Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT material; ) conductive polymers; ) graphitic intercalation compounds. Ellipses help identify trends and are adjusted to cover 90% of the points.

Figure 11

a–c) Resistance versus temperature traces for specific studies for intrinsic, individual elements (a),^{[ 79} , ¹⁰³ , ¹⁴² , ^{154 ]} carbon‐based materials with high order and microstructure alignment (b),^{[ 15} , ⁷⁹ , ³⁷⁸ , ^{381 ]} and carbon‐based materials with low order and no microstructure alignment (c).^{[ 172} , ³⁰⁹ , ^{379 ]} d) Plot of conductivity versus ratio of resistance at 300 K divided by resistance at 10 K. e,f) Plots showing incremental conductivity and strength improvement over the years since the early 2000s. Key: ) unaligned MWCNT material; ) aligned MWCNT materials; ) unaligned FWCNT materials; ) aligned FWCNT materials. ) conductive polymers; ) graphitic intercalation compounds; ) carbon fiber and graphite. The ellipses help identify trends and are adjusted to cover 90% of the points.