On the linear dependence of a carbon nanofiber thermal conductivity on wall thickness
Alexandros Askounis,1,2,*Yutaka Yamada,3 Tatsuya Ikuta,1,5 Koji Takahashi,1,4,5 Yasuyuki Takata,1,2,4 and Khellil Sefiane6,7
1International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 819-0395, Japan
2Department of Mechanical Engineering, Thermofluid Physics Laboratory, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
3Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
4Japan Science and Technology Agency (JST), CREST, Kyushu University, Fukuoka 819-0395, Japan
5Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyushu University, Fukuoka 819-0395, Japan
6Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King’s Buildings, Robert Stevenson Road, Edinburgh EH9 3FB, UK
7Tianjin Key Lab of Refrigeration Technology, Tianjin University of Commerce, Tianjin City, 300134, PR China
Abstract
Thermal transport in carbon nanofibers(CNFs) was thoroughly investigated. In particular, individual CNFs were suspended on a T-type heat nanosensor and their thermal conductivity was measured over a range of temperatures. Unexpectedly, thermal conductivity was found to be dependent on CNF wall thickness and ranging between ca.28 and 43 W/m∙K. Further investigation of the CNF walls with high resolution electron microscopy allowed us to propose a tentative description of how wall structure affectsphonon heat transport inside CNFs.The lower thermal conductivities, compared to other CNTs, was attributed to unique CNF wall structure. Additionally, wall thickness is related to the conducting lattice length of each constituent graphene cone and comparable to the Umklapp length. Hence, as the wall thickness and thus lattice length increase there is a higher probability for phonon scattering to the next layer.
Carbon nanotubes (CNTs) is a low dimensional nanomaterial with unique properties and have attracted considerable scientific attention ever since their discovery by Iijima in 1991.1CNTs consist of a single (SWNT) or multiple (MWNT) graphene sheets rolled up into a cylinder. In particular, their thermal conductivity was predicted to be exceptionally high, up to 6000 W/m∙K.2-5 Experimentally, their thermal conductivity was measured to be of the same order of magnitude, although a bit smaller up to 3000W/m∙K,and inversely proportional to their diameter.6-9 Their exceptional thermal behavior combined with their low dimensions, should pave the way for the use of CNTs in nanodevices thermal management applications.10
Carbon nanofibers (CNFs) are, essentially, a “modified” MWNT which consists of a series of graphene sheets rolled up into cones and stacked one inside the other. CNF thermal conductivity was reported to be considerably lower than conventional CNTs,11,12 resembling that of larger carbon fibers.13,14This difference has been attributed to defects in the wall structure, without providing sufficient evidence.11 Elsewhere, phonon thermal transport, the main way of heat conduction, in CNFs was predicted to be ballistic along the tube axis.12,15However, in a different work,phonon transport was reported to be ballistic only inside each individual cone and diffusive across the CNF length.16
Evidently, the exact heat transport mechanism in CNFs remains elusive,albeit their potentialin applications such as thermoelectrics or nanoscale thermal management.10In this Letter, we attempt to shed light on the heat transport within CNFs. To that end, we fabricated a T-type heat nano-sensor and measured the thermal conductivity of a number ofsingle, hollow CNFs with varying wall thickness. Unexpectedly and contrary to other CNTs, the thermal conductivity of CNFs was found to be dependent on CNF wall thickness. We propose a tentative description of the underpinning physics, based on how the unique wall structure affects the phonon heat conduction.
FIG. 1. TEM micrographs of three CNTs used in this study with increasing wall thickness from left to right. The lines show the inclination angle of the graphite walls.
Hollow CNFs were acquired from US Nanomaterials (Houston, TX, USA) and were dispersed in ethanol by ultrasonication. A drop of the solution was deposited on a transmission electron microscopy (TEM) copper microgrid (Ouken Shoji Inc., Japan) and left to dry overnight. Individual CNFs were assessed and chosen according to their structure, wall thickness and length using a JEM-3200FSK TEM (JEOL Ltd., Japan) operating at an accelerating voltage of 300kV. After characterization, each CNT was attached to the ultra-sharp metallic tip of a micromanipulator Versa 3D SEM (FEI Co., Hillsboro, OR, USA) using local focused electron beam irradiation. Using the same SEM,each CNFwas, subsequently, attached to a T-type heat nanosensor first on the heat sensing nanofilm (NS) and then on the heat sink (HS). An SEM micrograph of a sample attached sensor is shown in FIG. 2.The T-type heat nanosensors were fabricated using typical electromechanical systems (MEMS) techniques according to the procedure described elsewhere8,17. In short, they consisted of a suspended platinum nanofilm on a multilayered film of electron beam resist/silicon oxide/ silicon. Typical NS dimensions were ca. 40 μm in thickness, 500 nm in width and 9.5 μm in length.Amorphous carbon was deposited on each CNF end, via local focused electron beam irradiation to strengthen the CNF-substrate bond and simultaneously minimise the junctioncontact thermal resistance.8,9,18
FIG. 2 SEM micrograph of a T-type heat nanosensor with an attached CNF.
The nanofilm sensor (NS in FIG. 2)was supplied by a constant current, which allowed the measurement of the volumetric heat generation rate, ,defined as, where is the current, the voltage,and the width and thickness of the NS respectively. The nanosensor actssimultaneously as a heater and a thermometer.Prior to CNF attachment, NS was calibrated in order to obtain its electrical resistance, , and the resistance-temperature coefficient, both acquired at 0oC, which lead to the volumetric average temperature rise defined as . Deriving the dimensions of the CNF and nanofilm from the SEM and TEM micrographs, we may thus calculate the thermal conductivity of each CNF as:8
(1),
where is the CNT cross-sectional area, is the CNFlength between NS and HS,the total NS length with andthe NS lengths at either side of the CNT junction (as shown inFIG. 2) and the NS thermal conductivity (measured prior to CNT attachment). We should note at this point that extra care was taken to minimize the thermal resistance by depositing an extra conduction layer of amorphous carbon on each CNF junction.8,9,18 Thus, the thermal contact resistance between the CNF and both the NS and HS were neglected, as they are expected to be considerably smaller than the intrinsic CNF resistance.18,19Nonetheless, the intrinsic thermal conductivity of each CNF should be equal or higher than the one reported here.
FIG. 3CNF thermal conductivity as a function of (a)temperature and (b) wall thickness at room temperature.
The thermal conductivity,,of the CNF is presented in FIG. 3 as a function of temperature and wall thickness in panel (a) and (b) respectively. FIG. 3(a) shows the for three individual CNFs with varying wall thickness. Wall thickness was determined via high-resolution TEM, details are given in Table 1. It is readily apparent that reported herein is considerably lower that MWNTs,8,9 although in accordance with the literature for CNFs.11,12,15 In a previous work, this difference was attributed to low phonon mean free path due to defect scattering, without providing sufficient evidence.11Moreover, was found to be linearly dependent on wall thickness, summarized in FIG. 3 (b) at room temperature, contrary to MWNTs.21In what follows, we shall attempt to address both of these issues by considering the underlying heat conduction physics.
Table 1. Geometrical characteristics of measured CNFs.
CNF / Inner diameter, (nm) / Outer diameter, (nm) / Wall thickness, (nm) / Cone length, (nm)Small / 45 / 83 / 38 / 284
Medium / 92 / 168 / 76 / 567
Large / 112 / 230 / 118 / 880
Heat transfer via radiation and convection are both negligible in our experiments as they are conducted under the high vacuum conditions of the SEM chamber and the temperature change is moderate.8,18 Therefore, heat transfer in CNFs occurs primarilyvia phonon conduction. As a result, heat conduction is limited either by phonon-phonon or defects and boundary scattering.In a previous work, a similar was reported for a CNF and was attributed to defects.11In fact, the values reported herein are higher by an order of magnitude than the 2 W/m∙K c-axis thermal conductivity of graphite22,23 and lower by two orders of magnitude of CNTs.8,24 Hence, we should consider the wall structure of the CNFs, which resemble graphite, and has been connected to the wall structure.16,25 A high-resolution TEM micrograph of a CNF wall and the corresponding heat conduction mechanism are presented in FIG. 4. Essentially, the measured tubularis a combination of the basal (or planar),, and the c-axis (or radial),, graphite thermal conductivities related as :. Therefore, the thermal conductivity we measured is lower than the planar or graphene cone thermal conductivity. The lower, compared to MWNTs, may be attributed to phonon transport similar to few-layer graphene and graphite8,9,25-27. We would also like to note, that the higher values reported for CNFs in Ref. 16 are attributable to the heat treatment at high temperature which forms an extra graphitic layer which allows phonon conduction via a lattice and overcoming the interlayer spacing heat conduction barrier.
FIG. 4. Thermal conduction mechanism in a CNF.
Let us now focus our attention on theunexpected dependenceof on CNF wall thickness. A similar dependence on CNF diameter/wall thickness has been reported but not explained previously.16 The heat conduction mechanism in a single graphene layer is essentially 2D. Rolling the graphene layer into a “conventional” CNT results in a transition from 2D to 1D heat conduction mechanism due to the symmetry of the CNT.26In the case of our CNFs the 2D heat conduction re-emerges, as summarized in FIG. 4, aseach constituent graphene layer can be seen to be at an angle, to the tubular axis. Simple geometrical considerations, allow us toestimate each graphene cone/layer length,,using the relation, where is wall thickness.for each CNF studied herein ispresented in table 1 and varies nm. These values are comparable toUmklapp phonon-phonon scattering length () estimated by Kim et al. to be ~500 nm at 320 K.9 In this context is essentially a threshold until which the thermal conductivity is latticelength dependent.16,28,29Therefore, in our case, phonon conduction is ballistic or semi-ballistic and therefore is lattice length dependent, hence explaining why increasing and hence results in higher . Nonetheless, a computer simulation study is underway to further elucidate this argument, due to the high difficulty of experimentally measuring and quantifying and.
In summary, wemeasured the thermal conductivity of individual carbon nanofibers with varying diameters in an attempt to fully understanding the thermal transport within them, a mechanism which still remains elusive. The thermal conductivity of all samples was found to be considerably lower than other types of carbon nanotubes, due to the nature of the CNF wall and the heat propagation mechanism. Moreover, an unexpected dependence of thermal conductivity on wall thickness was unveiled, owing to ballistic phonon transport inside each individual constituent CNFs layer, making thermal conductivity lattice length dependent. Combining phonon transport theory with geometrical arguments we provided a tentative description of the heat transport mechanism, unique to this type of carbon nanomaterial.
Acknowledgements
This work was financially supported in part by the Core Research for Evolutional Science and Technology project of Japan Science and Technology Agency (JST-CREST) and with a Postdoctoral Fellowship for North American and European Researchers from the Japanese Society for the Promotion of Science (JSPS). We also acknowledge the research laboratory for High Voltage Electron Microscopy at Kyushu University for the TEM facilities.
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Alexandros Askounis
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