Thermal Conductivity of Individual Carbon Nanofibers

CARBON 62 (2013) 493– 500

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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 resolution scanning electron microscope. The results show a significant increase in the thermal 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 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 1 h ¼ Q R 1 ð1 þ g1Þ 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. CNF samples ðDRe3x;RMS=DQRMSÞNo Sample and the sample thermal resistance can be found via Eqs. (6), The two sample groups examined in this study are: (1) CNF (7), and (8), as samples grown using thermal CVD, and (2) CNF samples 1 3 grown using thermal CVD, which are then thermally an- R ¼ R 1 ð9Þ th;S 4 th;P 4ð1 /Þ nealed at 2800 °C for 20 h. The as-grown CNFs were procured from US Nanomaterials Research (US4450) and are referred to The thermal conductivity of the sample can then be deter- as ‘‘non-heat-treated’’ samples. The thermally annealed or = mined from kS ¼ LS Rth;sAS, where the cross-sectional area is ‘‘heat-treated’’ samples were obtained from US Nanomateri- A ¼ pðr2 r2Þ. Many studies have shown CNFs to have hollow S o i als Research, Inc. (Serial number US4460). cores, like tubes [5,15–17], with inner diameters shown to be SEM micrographs of the samples (Fig. 1) reveal large in the range from 2 to 50 nm [17]. In the present study, the in- amounts of amorphous carbon throughout the heat-treated ner radius, ri, is taken to be much smaller than the outer ra- batch when compared with the non-heat-treated batch. SEM dius, r , such that r2=r2 1. The effective cross-sectional o i o micrographs of individual CNFs also show the presence of area of the sample can therefore be approximated as amorphous carbon attached to the surfaces. In addition the A ¼ pr2 S o . comparison of the heat-treated and non-heat-treated sample

Fig. 3 – SEM micrographs of heat-treated sample experiments. Each image shows the probe wire above the manipulator tip with the CNF connecting the probe wire to the manipulator. The samples representing the heat-treated group have measured thermal conductivities of (A) 378 ± 48 W/m-K, (B) 434 ± 38 W/m-K, (C) 16.2 ± 2.5 W/m-K, (D) 241 ± 19 W/m-K, (E) 78 ± 7 W/m-K, and (F) 123 ± 14 W/m-K. The values are not corrected for thermal contact resistance. CARBON 62 (2013) 493– 500 497

images indicate that the heat treatment process promotes fu- Table 1 – Non-heat-treated sample dimensions and thermal sion of adjacent CNFs. conductivities.

3.1. Raman spectroscopy Experiment Length Average Thermal number (lm) diameter (nm) conductivity (W/m-K) Raman spectroscopy is used to examine the improvement in graphitization and reduction of defects in the heat-treated 1 13.5 ± 0.3 489 ± 39 9.7 ± 1.6 samples when compared to the non-heat-treated samples. 3 10.7 ± 0.3 446 ± 11 2.5 ± 0.3 4 12.7 ± 0.1 390 ± 23 2.5 ± 0.3 The excitation wavelength used for this assessment was 5 3.59 ± 0.06 292 ± 27 2.2 ± 0.4 785 nm. The analysis of the sample quality is made by observ- 6 19.9 ± 0.2 273 ± 20 7.2 ± 1.0 1 ing the ratio of the D band peak intensity (1330 cm ) and 23 6.94 ± 0.06 151 ± 11 3.1 ± 0.4 the G-band peak intensity (1875 cm1). The D band is associated with the loss of symmetry of atoms at the graphene sheet boundaries, which appears in the form of defects and carbonaceous impurities [18]. The G band is associated with the sp2 bonding in carbon systems, and indicates the degree 4. Results and discussion of graphitization in the sample [19]. Thus, a lower D/G ratio 4.1. Thermal conductivity measurements of band intensity indicates that the sample batch has fewer defects and a higher degree of graphite crystallinity. Since To determine the effect that heat treatment has on CNF ther- there are currently no standards for D/G ratio for CNFs by mal conductivity, 15 heat-treated CNFs (Fig. 3) and 6 on non- which to judge the quality of the batches, only a qualitative heat-treated CNFs (Fig. 4) were tested in the present study. comparative study of the CNF batches can be conducted. It The heat-treated batch produced a mean thermal conduc- should also be noted that the band peaks are a result of an tivity of 160 ± 139 versus 4.5 ± 3.1 W/m-K for the non-heat- average of all of the samples in the area excited by the laser treated samples. The large standard deviations associated and not of individual samples. with the average values reﬂect the large variation in individ- Fig. 2A and B compare the Raman intensity of the heat- ual sample thermal conductivity, not uncertainty in the mea- treated and non-heat-treated sample batches. The Raman surements. The values of length, diameter, and thermal intensities are normalized with respect to the D-peak. Fig. 2 conductivity are listed in Tables 1 and 2 for the non-heat- shows evidence of signiﬁcant defect healing and improved treated and heat-treated samples, respectively. graphitization.

Fig. 4 – SEM micrographs of non-heat-treated sample experiments. Each image shows the probe wire above the manipulator tip with the CNF connecting the probe wire to the manipulator. The samples representing the non-heat-treated group have measured thermal conductivities of (A) 9.7 ± 1.6 W/m-K, (B) 2.5 ± 0.3 W/m-K, and (C) 3.1 ± 0.4 W/m-K. The values are not corrected for thermal contact resistance. 498 CARBON 62 (2013) 493– 500

4.2. Thermal contact resistance Table 2 – Heat-treated sample dimensions and thermal conductivities. Bifano et al. [9] demonstrated the importance of improving Experiment Length Average Thermal the thermal contacts for the Wollaston wire, T-type probe number (lm) diameter conductivity experiments. To decrease the thermal contact resistance (nm) (W/m-K) (TCR), samples are attached to the Wollaston wire by appli- 8 9.28 ± 0.03 339 ± 70 24.5 ± 9.8 cation of platinum electron beam induced deposition (EBID) 9 492 ± 2 536 ± 96 196 ± 67 inside of the SEM. The TCR for multi-wall carbon nanotubes 10 100.4 ± 0.3 412 ± 30 134 ± 19 (MWCNT) tested using the Wollaston wire, T-type probe 11 16.7 ± 0.4 226 ± 21 117 ± 22 method was calculated by utilizing an anisotropic diffusive 12 102.5 ± 0.4 369 ± 15 66.8 ± 5.6 13 53.9 ± 0.2 187 ± 24 382 ± 97 mismatch model including the ﬁn resistance due to the 14 50.5 ± 0.3 206 ± 13 378 ± 49 platinum EBID [9]. The calculated thermal contact resis- 15 32.8 ± 0.2 235 ± 6 139 ± 8 tance, when subtracted from the total thermal resistance, 16 26.1 ± 0.1 171 ± 8 434 ± 38 resulted in approximately a 5% increase in the thermal con- 17 7.85 ± 0.08 200 ± 15 16.2 ± 2.5 ductivity of the MWCNT samples [9]. By modeling the CNFs 18 31.4 ± 0.2 199 ± 8 241 ± 19 in the same way, as graphitic planes, a similar analysis can 19 10.3 ± 0.1 112 ± 5 77.8 ± 7.3 20 204.8 ± 0.1 228 ± 40 48.5 ± 16.6 be conducted. The total thermal contact resistance for the 21 30.0 ± 0.2 244 ± 14 123 ± 14 CNF-wire contact and the CNF-manipulator contact can be 22 28.2 ± 0.2 218 ± 36 24.4 ± 7.9 written as

2 qffiffiffiffiffiffiffiffi RTCR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10Þ hP hPkSAS tanh LC k A A Welch’s T-test for unequal sample size and unequal var- S S iance produced a p-value of 0.0007, indicating that the heat The heat transfer coefficient is h ¼ 1=Rb, where Rb is the treatment of the samples produced statistically significant boundary resistance. Bifano et al. [9] estimated boundary 9 2 differences in thermal conductivity. resistance values of Rb ¼ 5:79 10 K-m =W for a pure plati- 9 2 The largest value of thermal conductivity is 434 ± 38 W/m- num EBID and Rb ¼ 5:18 10 K-m =W for an amorphous

K, measured on a sample having an average diameter of carbon EBID. The ﬁn perimeter is P ¼ pDo=2 þ b, where Do is 171 nm and a length of 26.1 lm. Even the maximum value the sample outer diameter, and b is the contact width, esti- for these samples is much lower than highest reported value mated from the elastic properties of the sample and wire for a vapor grown carbon ﬁber of 1950 W/m-K [1]. Fig. 5 plots [9,20]. The sample-wire contact length, LC, is measured inside the thermal conductivities versus the sample diameters. the SEM.

Fig. 5 – Thermal conductivity measurements of heat-treated and non-heat-treated samples plotted against sample length. The values are not adjusted for thermal contact resistance. CARBON 62 (2013) 493– 500 499

Fig. 6 – Thermal conductivity of heat-treated and non-heat-treated samples adjusted for thermal contact resistance plotted against sample length. The values are adjusted by subtracting the estimated thermal contact resistance from the measured thermal resistance.

The TCR and adjusted thermal conductivity are obtained (AFOSR) grant FA9550-08-1-0372 (Program Manager: Dr. ‘‘Les’’ iteratively because the TCR requires a thermal conductivity Lee), AFOSR MURI FA9550-12-0037 (Program Manager: Dr. for the calculation. For the CNF samples, the TCR accounted Joycelyn Harrison), and NSF Major Research Instrument Grant for an average 1.7% increase in the thermal conductivity. NSF MRI CMMI-0922968. Fig. 6 shows the thermal conductivity adjusted for TCR. The average adjusted thermal conductivities for the heat-treated REFERENCES and non-heat-treated samples are 163 and 4.6 W/m-K, respectively. The highest thermal conductivity adjusted for TCR is 449 ± 39 W/m-K. [1] Heremans J, Rahim I, Dresselhaus MS. Thermal conductivity and Raman spectra carbon fibers. Phys Rev B 5. Summary 1985;32(10):6742–7. [2] Heremans J, Beetz CP. Thermal conductivity and In the present study, thermal conductivity measurements thermopower of vapor-grown graphite fibers. Phys Rev B are made in individual CNFs using a Wollaston wire, T-type 1985;32(4):1981–6. [3] Wang JL, Gu M, Zhang X, Song Y. Thermal conductivity probe method inside of an SEM [9,13]. The results of the measurement of an individual fibre using a T type probe study indicate that significant improvements in thermal method. J Phys D Appl Phys 2009;42(10):105502. conductivity are obtained by heat treatment of CNFs to [4] Wang JL, Gu M, Ma W, Zhang X, Song Y. Temperature 2800 °C for 20 h. The average measured thermal conductivity dependence of the thermal conductivity of individual of the heat-treated batch is 160 W/m-K when compared to pitch-derived carbon fibers. New Carbon Mater 2008;23(3): the much lower average of 4.5 W/m-K for the as-grown 259–63. [5] Piraux L, Nysten B, Haquenne A, Issi JP, Dresselhaus MS, Endo non-heat-treated samples. The highest measured thermal M. The temperature variation of the thermal conductivity of conductivity when adjusted for TCR is 449 ± 39 W/m-K. benzene-derived carbon fibers. Solid State Commun Raman spectroscopy also indicated an improvement in the 1984;50(8):697–700. degree of crystallinity for the heat-treated samples. The [6] Nysten B, Piraux L, Issi JP. Thermal conductivity of pitch- results suggest that the quality and heat-treatment of CNFs derived fibres. J Phys D Appl Phys 1985;18(7):1307–10. are important considerations for potential use in thermal [7] Yu C, Saha S, Zhou J, Shi L, Cassell A, Cruden B, et al. Thermal management applications. contact resistance and thermal conductivity of a carbon nanofiber. J Heat Transfer 2006;128:234–9. [8] Tibbetts GG, Lake M, Strong KL, Rice BP. A review of the Acknowledgements fabrication and properties of vapor-grown carbon nanofibers/ polymer composites. Compos Sci Technol 2007;67(7– 8):1709–18. The authors would like to thank Dr. M.F.P. Bifano for all his [9] Bifano M, Park J, Kaul P, Roy A, Prakash V. Effects of heat assistance in executing the experiments. The authors would treatment and contact resistance on the thermal like to acknowledge the financial support of the Ohio Space conductivity of individual multiwalled carbon nanotubes Grant Consortium. The authors would finally like to acknowl- using a Wollaston wire thermal probe. J Appl Phys edge the support of the Air Force Office of Scientific Research 2012;111(5):054321. 500 CARBON 62 (2013) 493– 500

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