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Thermal Conductivity of Individual Carbon Nanofibers

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Thermal Conductivity of Individual Carbon Nanofibers CARBON 62 (2013) 493– 500 Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/carbon Thermal conductivity of individual carbon nanofibers Eric Mayhew, Vikas Prakash * Department of Mechanical Engineering, Case Western Reserve University, 2123 Martin Luther King Jr. Drive, Glennan Building, Cleveland, OH 44106, USA ARTICLE INFO ABSTRACT Article history: In the present paper, we present results of thermal conductivity measurements in commer- Received 8 November 2012 cially-available, chemical vapor deposition grown, heat-treated and non-heat-treated indi- Accepted 17 June 2013 vidual carbon nanofibers (CNFs). The thermal conductivity measurements are made using Available online 24 June 2013 the T-type probe experimental configuration using a Wollaston wire probe inside a high res- olution scanning electron microscope. The results show a significant increase in the ther- mal conductivity of CNFs that are annealed at 2800 °C for 20 h when compared with the non-heat-treated CNF samples. When adjusted for thermal contact resistance, the highest measured thermal conductivity is 449 ± 39 W/m-K. The average thermal conductivity of the heat-treated samples is 163 W/m-K, while the average thermal conductivity of the non- heat-treated samples is 4.6 W/m-K. The results demonstrate the importance of the quality of the CNFs, in particular their heat treatment (high temperature annealing), in controlling their thermal conductivity for thermal management applications. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction the heat-treated CFs suggest the potential use of CFs and per- haps CNFs as thermal interface materials [3,4,8]. Although a relatively large body of literature exists for ther- Most CFs and CNFs are synthesized in any one of the fol- mal conductivity measurements in large diameter carbon fi- lowing three ways: (1) carbonization of spun polyacrylonitrile bers (CFs) [1–6], only a few measurements of thermal (PAN-based fibers), (2) carbonization of spun petroleum pitch conductivity have been reported in individual carbon nanofi- (pitch-based fibers), and (3) carbon chemical vapor deposition bers (CNFs) [7]. The individual CFs for which thermal conduc- (CVD), usually using methane or benzene [1]. The simplicity tivity measurements are available in the literature have outer of the CVD process suggests that the production of vapor diameters ranging from 4 to 71.4 lm [1,2], and their room grown CFs and CNFs can be much less expensive than for temperature thermal conductivities range from 12 to their PAN-based and pitch-based counterparts [8]. The oppor- 1950 W/m-K [1–6]. This relatively large variation in the mea- tunity for wide-spread use of CVD grown CNFs along with sured thermal conductivity of CFs can be attributed to the dif- their potential for dramatic improvement in thermal conduc- ferences in sample diameter, synthesis method employed, tivity by heat treatment provide the motivation for the pres- resultant defect structure, and heat treatment [1,2,7]. Here- ent study. mans and Beetz [2] were the first to show that heat-treatment While a number of thermal conductivity measurements of CFs (at 3000 °C) significantly improved their room tempera- have been made on heat-treated and non-heat-treated CFs, ture thermal conductivity. The high thermal conductivity of to the best of authors’ knowledge only one previous study * Corresponding author: Fax: +1 216 368 6440. E-mail address: [email protected] (V. Prakash). 0008-6223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.06.048 494 CARBON 62 (2013) 493– 500 has analyzed thermal conductivity of individual CNFs [7]; the transport in individual nanostructures, including CFs and CNFs used in the study had a diameter of approximately multi-walled carbon nanotubes [3,4,9,13]. In the present study 152 nm and a room temperature thermal conductivity of thermal conductivity of both heat-treated and non-heat- 13 W/m-K. Moreover, the CNF samples analyzed in [7] were treated CNF specimens is determined using the 3x, Wollaston as received, and thus non-heat treated. The dramatic increase wire, T-type probe method. in thermal conductivity of CFs after the high temperature annealing step suggests that CNFs may also show improve- 2. Experimental methods ment in thermal conductivity with annealing heat treatment. Heat treatment of CFs, CNFs, and multiwall carbon nanotubes 2.1. Three omega analysis (MWCNTs) at temperatures up to 3000 °C has been shown to remove defects and impurities, such as left over metal cata- In the present study, thermal conductivity measurements are lysts, as well as increase the crystallinity of the graphite made in individual CNFs using a Wollaston wire T-type probe planes [9–12]. More continuous graphene planes as well as re- inside a scanning electron microscope (SEM) [9,13]. The Woll- moval of defects increases the phonon mean free path, and aston wire is Joule heated using an alternating current, and consequently the thermal conductivity of the annealed sam- the third harmonic voltage across the wire is measured. The ples [9]. In the present study we focus on the extent to which thermal resistance and thermal conductivity of the specimen heat treatment improves the thermal conductivity in CVD are deduced from an analytic model that relates the third har- grown CNFs. monic voltage, the drop in average temperature of the wire Many studies have explored thermal properties of test when the sample is attached, and the thermal conductivity specimens by measuring the third harmonic voltage in a 3x of the sample [3,4,9,13]. experimental set-up as the sample is Joule heated with an The configuration, technique, and analysis used in this study alternating current [9,13,14]. The ‘‘T-type probe’’ is one meth- for making the thermal conductivity measurements of CNFs are od that can employ third harmonic voltage detection to make described in detail by Bifano et al. [9]. The platinum probe thermal conductivity measurements. For the T-type probe wire is heated by an alternating current IðtÞ¼I sin xt ¼ pffiffiffi 1x method, a suspended wire of known electrical resistivity I1x;RMS 2 sin xt,whereI1x is the current amplitude, and I1x;RMS and temperature coefficient of resistance is Joule heated by is the RMS current. The Joule heating in the wire is given by a current source until it reaches a steady-state. A sample is 2 2 QðtÞ¼I ðtÞReo ¼ I Reoð1 À cos 2xtÞ; ð1Þ attached, and the reduction in the spatially averaged temper- 1x;RMS ature of the probe wire is measured via the change in voltage. where Reo is the electrical resistance of the probe wire at zero The sample thermal conductivity is determined from the current. The spatially averaged temperature of the wire above average temperature drop and the sample geometry. The the ambient temperature, hðtÞ, is directly proportional to the method has been used to great effect in studying thermal Joule heating by the thermal transfer function Zo such that Fig. 1 – SEM images of CNF batches from which individual samples are selected. (A) and (B) are representative of US Nanomaterials Research heat-treated batch US 4460). (C) and (D) are representative of US 4450. CARBON 62 (2013) 493– 500 495 hðtÞ¼ZoQðtÞ: ð2Þ where x is the position marked from the midpoint of the wire, k is the thermal conductivity of the wire, A is the cross- The electrical resistance of the probe wire changes accord- P P sectional area of the wire, and LP is the length of the wire. ing to ReðtÞ¼Reo½1 þ ahðtÞ, where a is the temperature coeffi- Heat loss due to convention and radiation can be neglected cient of resistance of the wire. The RMS Joule heating is 2 [9] because the experiments are conducted in vacuum in a defined to be Q I Reo. When the wire is Joule heated, RMS 1x;RMS high resolution SEM and involve only small temperature rises. the third harmonic voltage across the wire is given by Using constant ambient temperature boundary conditions at 1 the ends of the wire and a heat flux out of the wire where the V3x;RMS ¼ aZoI1x;RMSQRMSReo: ð3Þ 2 sample is attached, the spatially averaged temperature is Defining the third harmonic RMS electrical resistance as given as Re3x;RMS V3x;RMS=I1x;RMS, the third harmonic resistance is 1 3 À1 h ¼ Q R 1 À ð1 þ gÀ1Þ ¼ Q Z ; ð6Þ found to be directly proportional to the RMS Joule heating by 12 RMS th;P 4 RMS o 1 R ; ¼ aR Z Q : ð4Þ where the thermal resistance of the probe and sample are gi- e3x RMS 2 eo o RMS ven by Rth;P ¼ LP=kPAP and Rth;S ¼ LS=kSAS; respectively. The ra- The thermal transfer function is determined experimen- tio of thermal resistances, g, is defined by g Rth;P=4Rth;S. tally by measuring the slope of Re3x;RMS versus QRMS . 2.3. Experimental procedure 2.2. Theoretical considerations: thermal transfer function When no sample is attached, i.e. g ¼ 0, the thermal resistance of the probe wire is deduced using Eqs. (4) and (6) to be The steady state response of the probe wire is modeled in one dimension by 24 DRe3x;RMS Rth;P ¼ ð7Þ aReo DQRMS d2h Q k ¼ RMS ; ð Þ P 2 5 The ratio of the slopes is then defined as dx APLP Fig. 2 – Raman intensity versus wavenumber (785-nm excitation wavelength) of (A) non-heat-treated sample batch US4450 and (B) heat-treated sample batch US4460. Raman intensity is normalized by the D peak. 496 CARBON 62 (2013) 493– 500 ðDRe3x;RMS=DQRMSÞWith Sample / ð8Þ 3.
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