Centimeter-Long Weavable Fibers of Carbon Nanotubes 1 with Giant Thermoelectric Power Factor 2

nanotubes to such as ﬂexibility and light weight. However, the large power factor of individual carbon nanotubes in macroscopic assemblies has been challenging, primarily due to poor sample morphology and a lack of proper Fermi energy tuning. Here, we report an unprecedentedly high value of power factor (14 ± 5 mWm − 1 K − 2 ) for centimeter-long weavable ﬁbers of aligned carbon nanotubes with ultrahigh electrical and thermal conductivity. Our theoretical simulations show that the observed giant power fac- tor originates from the one-dimensional quantum conﬁnement of charge carriers, appearing when the Fermi energy is near a van Hove singularity in the electronic density of states. We fabricated a textile thermoelectric generator based on these carbon nanotube ﬁbers, which demonstrated high thermoelectric performance, weavablity, and scalability. The giant power factor we observed make these ﬁbers strong candidates for the emerging ﬁeld of thermoelec- tric active cooling, which requires a large thermoelectric power factor and a large thermal conductivity at the same time.

Introduction 31 Thermoelectric (TE) materials convert heat into electricity and vice versa, offering great potential 32 for waste heat recovery and solid-state cooling 1 . TE materials are usually evaluated by the ZT fac-33 tor, defined as ZT = (S 2 σT )/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, 34 κ is the thermal conductivity, and T is the temperature. While previous studies on thermoelectric 35 materials have primarily focused on reducing κ to improve ZT , enhancing the power factor (P F ), 36 defined as P F = S 2 σ, is more important for certain applications. For examples, for the energy 37 harvesting application, large P F is crucial for maximizing the output power density when the heat 38 source is unlimited (such as solar heat and industrial waste heat) 2-4 . Furthermore, P F must be 39 large for so-called active cooling 5, 6 , in which the Peltier effect is leveraged to enhance the heat 40 flow rates from the hot side to the cold side. This active cooling mode is promising for electronics 41 thermal management applications, and is distinct from the more traditional refrigeration opera-42 tional mode in which heat is pumped from the cold side to the hot side via the Peltier effect 5, 6 . 43 The maximum hot-side heat flow rate in active cooling is proportional to the effective thermal con-44 ductivity κ eff , defined as 5 κ eff = κ + P F ·T 2 H 2∆T , where T H is the hot-side temperature and ∆T is the 45 temperature difference between the two sides, suggesting that the active cooling requires large κ 46 together with large P F , instead of high ZT . 47 In addition to the basic TE properties, practical applications require other considerations, 48 such as toxicity, flexibility, and scalability 7, 8 . Conventional inorganic TE materials such as Bi 2 Te 3 49 and their alloys have shown high performance, e.g., ZT ∼ 1.2 and P F ∼ 4.5 mWm −1 K −2 at 50 3 room temperature 9 . However, their toxicity, scarcity, and rigidity prevent their wide use. On the 51 other hand, organic materials are safe, flexible, and inexpensive, but they have exhibited small P F 52 values 7 . These issues have resulted in a search for organic-like materials with inorganic-like TE 53 performance. 54 Low-dimensional materials are believed to hold the key to achieving this goal. Recent  holds for a mixture of semiconducting and metallic SWCNTs, and a theoretical study predicts a 76 P F higher than 100 mWm −1 K −2 23 . However, experimentally measured P F for CNT assemblies 77 has remained small 8 , presumably due to low σ originating from poor sample morphology.

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Here, we studied the TE properties of centimeter-long weavable CNT fibers. These neat CNT 79 fibers simultaneously possess a high degree of CNT alignment, a high density, a high CNT aspect 80 ratio (length/diameter), and a low level of impurities 16 , leading to ultrahigh electrical conductivity, 81 σ >10 MSm −1 15 . We tuned E F to the vicinity of a 1D VHS through chemical treatment to 82 maximize S, obtaining P F as high as 14±5 mWm −1 K −2 . This is the highest P F value achieved 83 for any CNT system and is comparable to the highest values reported for 2D materials and of bulk 84 materials 10,11 . We developed a theoretical model to explain this high P F value and validated it 85 with finer E F tuning using electrolyte gating. Finally, we demonstrated weavablity and scalability 86 by fabricating a textile TE generator based on these CNT fibers, which produced enough power to 87 turn on a light-emitting diode (LED).  Table S1). The as-produced CNT fibers were heavily p-95 doped with residual acid during the solution spinning process 16 , and exhibited σ of 11±2 MSm −1 .

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Doping an as-produced CNT fiber with iodine monochloride (ICl) increased the value of σ to 97 16±3 MSm −1 through further p-type doping, while annealing them at a temperature of 350 • C 98 (500 • C) decreased σ to 5.6±1.1 MSm −1 (2.7±0.5 MSm −1 ) through dedoping. 99 We measured the σ and S of these CNT fibers at room temperature under vacuum using the carrier type was p-type in these samples. Figure 1c shows a monotonic decrease of S with 103 increasing σ, resulting in a decrease of P F with σ ( Figure 1d). The highest S was obtained for the 104 CNT fiber annealed at 500 • C, and the measurements were repeated for three samples to ensure 105 reproducibility. The average S of the three samples (all annealed at 500 • C) was 68.0±0.3 µVK −1 , 106 corresponding to an average (maximum) P F of 12±2 mWm −1 K −2 (14±5 mWm −1 K −2 ).

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This maximum P F value, 14±5 mWm −1 K −2 , is the highest value ever achieved for any 108 6 CNT sample. Figure 1e summarizes the room-temperature P F values reported for different CNT 109 systems with σ. The highest P F among CNT systems has been ∼3 mWm −1 K −2 , achieved for 110 an unsorted benzyl viologen doped CNT web 24 and CNT-filled polymer nanocomposites 25 . Fur-111 thermore, our value is over three times larger than that of Bi 2 Te 3 , the commercially used inor-112 ganic p-type TE material (∼4.5 mWm −1 K −2 ) 9 , and is comparable to the highest P F achieved at 113 room temperature by 2D materials: monolayer graphene (36.6 mWm −1 K −2 ) 10 Table S4).

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Theoretical model to explain E F dependence of TE properties. To provide insight into the 125 mechanism that led to the high P F in our CNT fibers, we developed a theoretical model and per-126 formed simulations. We chose four representative SWCNTs with appropriate diameters to describe 127 the DWCNT fibers: an inner-wall semiconducting SWCNT (S1), an inner-wall metallic SWCNT  Table S2. We first calculated the DOS (Figure 2d), S, electrical conductance G, 130 and P F ≡ GS 2 for each individual SWCNT. Next, we modeled a DWCNT as consisting of two 131 individual SWCNTs corresponding to the inner and outer nanotubes, while adopting circuit mod-132 els 23, 27, 28 to approximate our DWCNT fiber. We obtained the combined conductance G p (G s ) and when the E F is inside the bandgap. Moreover, maximum |S| appears when E F is in the vicinity 141 of the first VHS of S2, not when E F is near the CNP (Figure 2b). This is because the peak of 142 |S| near the CNP, expected for S1 or S2 alone, is suppressed in our combined system due to     Figure S1a).

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The average outer wall diameter was 1.8 ± 0.2 nm, the average inner wall diameter was 0.9 ± 259 0.1 nm, and the average number of walls was 1.9. The viscosity-averaged aspect ratio of the   Figure S4. The resistance of the entire TEG was ∼300 Ω. The cold side was 295 at room temperature, and the hot side was placed on the hotplates. using a vacuum and low-temperature probe station (Grail 10, Nagase Techno Co.). The con-304 ductivity was calculated from the measured resistance of the fiber. The Seebeck coefficient was 305 measured in the same manner as that described in Ref. 29 .

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The CNT fiber was transferred onto a glass slide with pre-deposited gold electrodes (thickness 308 ∼100 nm). A heater, thermocouples and gold wires were fixed on the fiber as described above.

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To ensure that no chemical reaction occurs between silver and ionic liquid, insulating sealant  shows the output voltage and power when the temperature difference was 62.5 K. Figure 2d 339 plots the maximum power, which was obtained when the load resistor value was the same as 340 the TEG resistance (∼300 ).