Thermal conductivity of carbon nanofiber mats

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Thermal conductivity of carbon nanofiber mats Nayandeep K. Mahanta a, Alexis R. Abramson a,*, Max L. Lake b, David J. Burton b, John C. Chang c, Helen K. Mayer c, Jessica L. Ravine d a

Department of Mechanical and Aerospace Engineering, 10900 Euclid Avenue, Case Western Reserve University, Cleveland, OH 44106-7222, USA b Applied Sciences, Inc., 141 West Xenia Avenue, Cedarville, OH 45314, USA c GrafTech International Limited, 12900 Snow Road, Parma, OH 44130, USA d National Composite Center, 2000 Composite Drive, Kettering, OH 45420, USA

A R T I C L E I N F O

A B S T R A C T

Article history:

The anisotropic thermal conductivity of novel vapor grown carbon nanofiber (VGCNF)

Received 5 October 2009

based paper-like mats was measured for increasing volume fraction and at different stages

Accepted 4 August 2010

of heat-treatment. These nanofiber mats were prepared to exhibit high in-plane and low

Available online 10 August 2010

through-plane thermal conductivities with the goal of assessing their potential as 2-D heat spreaders. The in-plane thermal conductivity of the mats varied from 12 W/m-K to 157 W/ m-K for volume fractions of 0.067 and 0.462, respectively, while the corresponding throughplane thermal conductivities were measured to be 0.428 W/m-K and 0.711 W/m-K. Heat treatment to temperatures above 3000 C increased the through-plane thermal conductivity of the mats by an order of magnitude. However, the in-plane thermal conductivity, at best, was only seen to double. A model is proposed to describe the arrangement of nanofibers in the mats, and analytical expressions were used to estimate the thermal conductivity of an individual nanofiber using experimental results. Thermal conductivities of approximately 1400 W/m-K and 1600 W/m-K were calculated for individual VGCNFs heat treated to temperatures of around 1100 C and above 3000 C, respectively.  2010 Elsevier Ltd. All rights reserved.

1.

Introduction

With ever increasing processing speeds of modern microelectronic chips, the problem of efficient heat dissipation has become a critical concern for the semiconductor industry. Traditional thermal management materials, which include metals or ceramics dispersed in polymer matrices, are reaching their performance limits in terms of their ability to eliminate ‘‘hot-spots.’’ This, coupled with the need to provide increasing user comfort, calls for the development of next generation thermal management materials. Recently, carbon nanostructures have been proposed as potential filler materials in thermal management solutions for consumer electronics of the future. Consequently, thermal transport properties

of carbon nanotube composites have been the subject of much attention due to the extremely high thermal conductivity reported for single-walled (6600 W/m-K) [1] and multiwalled nanotubes (3000 W/m-K) [2]. However, the presence of considerable thermal resistances at the interfaces between adjacent nanotubes (and proposed matrix materials) has limited researchers from demonstrating high thermal conductivities of composites containing carbon nanotubes as fillers [3–6]. Compared to carbon nanotubes, there have been many fewer reports that have investigated the potential for using carbon nanofibers for a similar purpose (albeit carbon microfibers, with diameters greater than 500 nm, have been extensively studied to assess their thermal properties). Nonetheless, prior work on other aspects of vapor grown carbon

* Corresponding author: Fax: +1 216 368 6445. E-mail address: [email protected] (A.R. Abramson). 0008-6223/$ - see front matter  2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2010.08.005

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nanofibers (VGCNFs) and their composites [7–12] suggest that VGCNFs are much cheaper and easier to synthesize than nanotubes even if their individual thermal, electrical and mechanical properties are not ostensibly as impressive. However, nanofibers can be heat treated to improve their transport properties using a graphitization procedure which results in a considerable increase in density and a structural reorientation of the graphitic planes that favor axial transport characteristics. Consequently, VGCNFs transform from bamboo (tapered MWCNTs) to an ordered stacked-cone structure [13,14], and their thermal conductivity approaches the value for the basal plane of pyrolytic graphite (1950 W/m-K) [15]. While the interfacial thermal resistance between fibers and/ or the matrix may still be large and comparable to nanotube-nanotube or nanotube-matrix resistances, the structures themselves are long (i.e. exhibit a high aspect ratio) and may be simply processed to form a well-aligned mat of nanofibers, thereby leading to fewer interfaces and relatively high effective thermal conductivities. Therefore, macroscopic materials comprised of carbon nanofibers have the potential to provide a cost effective thermal management solution for next generation electronic devices. The present work is focused on measuring the thermal conductivity of mats of VGCNFs complemented by a theoretical analysis of the observed behavior of these materials with an aim to assess their viability for thermal management applications.

2.

Materials and methods

The VGCNFs studied in this work, termed as PR-25 nanofibers, were synthesized by Applied Sciences, Inc. (Cedarville, OH). They belong to the Pyrograf – III family of nanofibers and have diameters that vary from 50 nm to 150 nm and lengths that range between 50 lm and 150 lm. The carbon nanofibers were produced using the floating catalyst method [16]. In this technique, a metal catalyst, such as iron, is introduced into a flowing hydrocarbon gas stream, such as methane, which is heated to approximately 1100 C. The nucleation rate can be markedly enhanced through addition of a small quantity of sulfur, which apparently forms an iron sulfide eutectic, and enables liquid phase diffusion of carbon through the catalyst [17]. As free carbon condenses on the front surface of the metal particle, carbon forms a graphite lattice structure which grows from the back face of the metal particle, and is termed the catalytic core. A typical structure comprises graphene layers which are at an angle of around 25–27 from the axis of the nanofiber. This configuration consists of stacked conical sections, and is commonly referred to as a ‘‘stacked-cup’’ structure. Conditions are maintained so that no additional carbon condenses on the hollow tube, and the fiber is extracted with very little or no disordered carbon on the surface. This structure is typical of the PR-25 nanofibers studied in this work. In contrast, if the nanofibers dwell in the reactor sufficiently long to enable further carbon deposition, a disordered or turbostratic layer of graphite forms on the surface, resulting in the formation of previously reported [13], commercial Pyrograf – III nanofibers, namely PR-19 and PR-24. When the carbon nanofibers are subjected to heat treatment at 3000 C, the CNF appears

to be predominantly composed of nested conic sections of graphene having a hollow core and exhibit a high index of graphitization with a d002 spacing of 0.3354 nm as previously determined by X-ray diffraction [18,19]. At the National Composite Center (Kettering, OH), the nanofibers were then made into ‘‘mat-like’’ materials. This was accomplished by dispersing the carbon nanofiber in a proprietary solvent and filtering the solution. No binder or processing additives were included; the carbon nanofiber mats were held together only by the mechanical interlocking and Van der Waals forces of the nanofibers. The mats studied were of four different overall densities: 0.106 g/cm3, 0.186 g/ cm3, 0.437 g/cm3 and 0.739 g/cm3 corresponding to volume fractions of 0.067, 0.116, 0.273 and 0.462, respectively. Mats with this density range were produced by customizing the formulation of the carbon nanofiber paper by varying raw material constituent properties such as carbon nanofiber density and length. Specifically, four bulk densities of Applied Sciences’ PR-25 carbon nanofiber were considered to tailor the density of the mats: 0.67 lb/ft3, 2 lb/ft3, 10 lb/ft3 and 18 lb/ft3. The lower bulk density options (0.67 and 2 lb/ft3) offer longer fiber length, enhancing the handleability of the resulting mat and potentially enhancing conductivity by minimizing fiberto-fiber interfaces. As a result of the milling process employed to increase the bulk density, the 10 and 18 lb/ft3 PR-25 are too short to form a mat as the sole constituent (insufficient fiber interlocking), and must be mixed as a filler with a longer fiber. Leveraging these attributes, NCC employed design of experiment techniques to tailor a range of mat densities for this study. The volume fraction was calculated as a ratio of the density of the mat (determined from the measured weight and volume of the specimens) to the density of an individual nanofiber. The intrinsic density of the individual nanofibers was measured by Applied Sciences, Inc. to be 1.6 g/cm3 for both ungraphitized (heat treated to around 1500 C) and graphitized (heat treated to over 3000 C) nanofibers, which is slightly less than the density of pyrolytic graphite fibers [20,21] and the density of single-crystal graphite [20] due to the presence of a hollow core. Measurement of mass and volume of the various mats was used to determine their effective densities. Fig. 1a and b show the SEM images of the surface of an ungraphitized mat with a density of 0.106 g/cm3 while Fig. 1c and d show an ungraphitized sample with a density of 0.739 g/cm3. As illustrated, the nanofibers in the higher density samples are much shorter than the ones in the lower density samples. Shorter lengths were required to obtain a better packing of the nanofibers. In addition, the SEM images provide important information regarding the arrangement of nanofibers in these materials; almost all of the nanofibers seem to be arranged parallel to the surface plane, and very rarely does the cross-section of a nanofiber appear in the image, indicating that the fraction of nanofibers spanning through the thickness of these materials is likely to be extremely small. Such an arrangement was anticipated due to the processing conditions imposed. It is important to note that there were regions in the mats with a non-uniform distribution of nanofibers within the horizontal plane, as shown in Fig. 1b. However, multiple SEM images taken from different areas of a single mat indicated that overall, the nanofibers

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Fig. 1 – SEM images of mats with different overall densities. (a and b) 0.106 g/cm3 and (c and d) 0.681 g/cm3. The nanofibers were deliberately shortened in length to achieve better packing fractions for the higher density samples. The SEM images indicate that majority of the nanofibers are dispersed within a plane with an extremely small fraction of them spanning across the thickness of the samples.

were more randomly distributed along individual planes parallel to the surface. The planar arrangement of the nanofibers is confirmed by the SEM image of a cross-section of the mats shown in Fig. 2. This image illustrates that the mats consist of stacks of various aligned sub-layers with only a small fraction of the nanof-

Fig. 2 – SEM image of the cross-section of a nanofiber mat. Nanofibers seen horizontal are arranged along planes parallel to the surface of the mats and the ones seen vertical are aligned in the through-thickness direction.

ibers oriented vertically through the thickness. This particular feature of the anisotropy is reflected in the analytical model described later in the text. Following thermal conductivity measurements at Case Western Reserve University, these mats were heat treated by GrafTech International to temperatures in excess of 3000 C for graphitization. After the graphitization process, thermal conductivity of these materials was again measured. Thermal characterization of the mats involved measurement of the in-plane and through-plane thermal conductivities of the experimental materials. The in-plane thermal conductivity was measured using a dual-mode heat flow meter technique [22]. In this method, the steady-state temperature distribution of the heated sample (placed inside a vacuum chamber) is compared with that predicted by an analytical solution that considers both radiative and conductive transport. The typical experimental configuration involved a thin specimen (5 mm · 50 mm, width · length) in line with and contacting a similar sized piece of copper (Alloy 110 ASTM B-152, thermal conductivity of 388 W/m-K). Two strip heaters were placed above and below the copper strip at one end and the entire assembly was suspended using clamps mounted on two end supports. The stainless steel base of the vacuum chamber was in thermal contact with the end support clamping the sample and served as the heat sink. Temperature data was obtained from eight thermocouples: two on the copper reference, four on the sample, one for measuring the temperature of the heat sink and one for measuring the ambient temperature. A schematic of the experimental arrangement can be seen in Fig. 3. The best-fit

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Fig. 3 – Schematic of the experimental setup for the dualmode heat flow meter technique. The thermocouple used for measuring the ambient temperature is not shown in the schematic [22].

(maximum coefficient-of-determination) between the experimental and analytical temperature profiles gives the thermal conductivity of the sample. The method was validated with a wide variety of materials with thermal conductivities spanning over four orders of magnitude with the results being presented in Table 1. More details on the system modeling and data analysis involved in the dual-mode heat flow meter technique can be found in Ref. [22]. Fig. 4 shows a schematic of the experimental setup for measuring the through-plane thermal conductivity using the dynamic plane source method [24]. In this technique a very thin strip heater (100 lm · 15 mm · 45 mm, H · W · L) is placed between two identical pieces of the sample to be tested. The length and width of the test specimens are identical to the heater. The test specimens and the heater are then sandwiched between two HDPE blocks of the same length and width. The height of the HDPE blocks is much more than the sample and heater to ensure a semi-infinite configuration. The heater is connected to a Keithley Instrument 2400 Sourcemeter that provides a constant current and monitors the voltage drop across the two terminals. The temperature rise of the heater increases the resistance leading to a voltage rise, which is a function of the thermal properties of the unknown sample and the HDPE supporting blocks. This experimental transient voltage profile is then compared with that predicted by an analytical expression [24]. The sample thermal conductivity used for obtaining the analytical voltage profile is varied until a best-fit with the experimental profile is obtained,

Fig. 4 – Schematic of the experimental setup for the dynamic plane source technique. The transient voltage response of the heater – temperature sensor is recorded to calculate the thermal conductivity of the unknown sample.

which is then the thermal conductivity of the sample. The method was validated using materials of known thermal conductivities, the results of which are presented in Table 2.

3.

Results and discussion

Fig. 5 shows a plot of the experimentally determined thermal conductivity of both the ungraphitized and graphitized mats as a function of the volume fraction of nanofibers. Each data point in the figure is an average of five measurements taken on the different samples. Overall, the in-plane thermal conductivity values were seen to be orders of magnitude higher than previously reported values for VGCNF-epoxy composites [25,26]. Such a discrepancy is believed to be primarily due to the free-standing network of nanofibers in the absence of a solid matrix material, which leads to direct contact between adjacent nanofibers resulting in enhanced thermal conduc-

Table 1 – Thermal conductivity of standard materials obtained using the dual-mode heat flow meter setup. The samples marked with an asterisk are natural graphite samples obtained from Graftech International Limited. Material

Thermal conductivity (W/m-K) Measured (mean ± SD)



Cirlex FEP Teflon Aluminum (1100–H19 Foil) Brass (230 Brass OSO15) HT-1210* HT-710* SS-600* SS-1500* i

0.16 ± 0.01 0.17 ± 0.02 214 ± 15 170 ± 11 106 ± 5 216 ± 8 560 ± 34 1522 ± 74

Percentage error (%)

Literature 0.17i 0.20ii 218iii 159iv 108 [23] 217 [23] 585 [23] 1536 [23]

5.88 15.0 1.84 6.92 1.85 0.46 4.27 0.91

Fralock – A Division of Lockwood Industries, Inc., Cirlex technical data sheet. McMaster-Carr Document No. 8545KAC, More about high-performance plastics. iii Properties and selection: nonferrous alloys and special-purpose materials, Metals Handbook, Vol. 2 10th ed., ASM International, 1990. iv J. R. Davis, Copper and copper alloys, Davis and Associates, ASM Specialty Handbook, ASM International, 2001. ii

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Table 2 – Thermal conductivity of standard materials obtained using the dynamic plane source technique. The samples marked with an asterisk are natural graphite samples obtained from Graftech International Limited. Material

Cirlex Quartz pure glass Stainless steel (type 316) eGraf 1210* SS500 (934)* SS500 (935)*

Thermal conductivity (W/m-K) Measured

Literature

0.18 1.46 16.6 6.17 3.31 2.01

0.17i 1.48v 16.2vi 6.24vii 3.27vii 2.00vii

Percentage error (%)

5.88 1.35 2.47 1.12 1.22 0.5

i

Fralock – A Division of Lockwood Industries, Inc., Cirlex technical data sheet. McMaster-Carr Document No. 8577KAC, More about glass, ceramics and carbon. vi McMaster-Carr Document No. 8984KAC, More about stainless steel alloys. vii Private communication with Graftech International Limited v

Fig. 5 – Thermal conductivity of mats as a function of the volume fraction of nanofibers. Both in-plane and throughplane thermal conductivities increase with graphitization.

tivity. In addition, it is interesting to note that the thermal conductivity obtained for the mats ranged from a third to half of the thermal conductivity of VGCF-epoxy composites with similar loadings of carbon fibers [27]. This was expected because the conventional carbon fibers can be grown much longer than PR-25 nanofibers resulting in fewer interfaces and higher thermal conductivities. Thus, it establishes the fact that composites and/or mats made from VGCFs represent the upper limit of thermal conductivity achievable with these nanofibers [28]. To analyze the behavior demonstrated in the figure, composite theory may be applied since the mats can be considered as composites of nanofibers and air (filling the pores); a valid approach in the absence of a matrix material. Fig. 5 shows that the thermal conductivity of the mats increases with an increasing volume fraction of nanofibers for both the in-plane and through-thickness measurements. As confirmed by numerous theoretical and experimental studies on composites available in the literature [26,29–32], an increasing volume fraction of nanofibers (i.e. an overall density enhancement in the mats) should result in an increase in thermal conductivity, as shown in Fig. 5. Moreover, the order of magnitude discrepancy between the in-plane and through-thickness conductivities as illustrated was antici-

pated due to the anisotropic arrangement of nanofibers in the mats, which is apparent in the SEM images of Figs. 1 and 2. As discussed previously, an extremely high fraction of the nanofibers were apparently aligned parallel to the surface planes of the mats, thereby causing the in-plane thermal conductivity to be much higher than the corresponding through-plane values. In addition, the figure shows that graphitized samples demonstrate thermal conductivities approximately 1.5–2 times those exhibited by their ungraphitized counterparts. A plausible explanation for this can be provided in terms of the structural changes exhibited by the samples as a result of the graphitization process and by better understanding how thermal transport proceeds in these materials. By considering the diagrammatic representation of the nanofiber network shown in Fig. 6 and with the knowledge that the radial conductivity of the nanofibers is expected to be at least two orders of magnitude lower than their axial

Fig. 6 – Proposed model for the distribution of nanofibers in the mats. a–a 0 and b–b 0 represent the in-plane directions with c–c 0 representing the through-plane direction. Majority of the nanofibers are dispersed within a plane and oriented along the two mutually perpendicular directions. A very small fraction of the nanofibers are aligned perpendicular to the plane. Half of the fraction of nanofibers within a plane are aligned along each of the two mutually perpendicular directions (a–a 0 and b–b 0 ).

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Table 3 – Variations in thickness and density of the nanofiber mats caused by the graphitization process. Reduction in sample thickness was observed which led to an increase in density. Sample

1 2 3 4

Density (g/cm3)

Thickness (lm) Ungraphitized

Graphitized

Ungraphitized

Graphitized

801 792 225 196

669 556 156 122

0.106 0.186 0.437 0.739

0.154 0.296 0.581 1.034

conductivity [20,33], it is reasonable to assume that the inplane and through-plane thermal conductivities of these materials depend largely on the fraction of nanofibers offering axial conduction paths along these directions. Further, a restructuring of the free-standing network of nanofibers, caused by the thermal expansion and shrinkage following graphitization, is quite conceivable in the absence of a solid matrix to hold the nanofibers in place. In this case, graphitization was seen to cause a reduction in the thickness of the mats, thereby increasing the density of the materials. Table 3 shows the thicknesses and densities of the various samples before and after graphitization. Note that the thickness and density measurements were taken on different specimens cut from the same mat, before and after graphitization. Due to the destructive nature of the in-plane thermal characterization technique, the same exact specimen could not be measured, graphitized and measured again. Nonetheless, multiple thermal conductivity tests from various sections of a single mat consistently demonstrated very little variation (<10%) among the data, providing confidence in the approach implemented. The density of individual nanofibers remained constant and as a result, the graphitized samples had a much better packing of nanofibers as compared to their ungraphitized counterparts. Another highlight of Fig. 5 is the relatively more pronounced improvement in the through-plane thermal conductivity of the graphitized samples. Prior to graphitization, the mats studied for this work were only slightly thicker in comparison with the length of an individual nanofiber, which is evident from the thickness measurements shown in Table 3. Thus, in the limit of the thickness of the samples approaching the length of an individual nanofiber, the phonon transport through the small fraction of nanofibers spanning the thickness is rendered more closely obstacle free, thereby leading to a relatively larger enhancement in through-thickness versus in-plane thermal conductivity.

4. Theoretical analysis and conductivity of individual nanofibers

thermal

The measured in-plane (kIP) and through-plane (kTP) thermal conductivities of the mats can be additionally used to develop a better fundamental understanding of thermal transport in these materials and to, more specifically, determine the apparent thermal conductivity of the individual nanofibers in the system. Using an interaction direct derivative (IDD)

micromechanics scheme, the following equations apply [34,35]: 2 3 kIP x=2 6 7 ¼ 1 þ f 4 1 þ H5 kair eff kaxial =kair  1 2 3 kTP 1x 6 7 ¼ 1 þ f 4 1 þ H5 kair eff kaxial =kair  1

ð1aÞ

ð1bÞ

where f is the total volume fraction of nanofibers and x is the fraction of nanofibers dispersed within a plane with 1  x fraction of fibers going through the thickness. It is assumed that the fraction of nanofibers contained in a plane and aligned along each of the two mutually perpendicular directions (a–a 0 and b–b 0 axes in Fig. 6) are equal. In other words, the fraction of nanofibers aligned along one of the two ineff plane directions (a–a 0 or b–b 0 axes) is x/2. kaxial is the effective axial thermal conductivity of the nanofibers, and kair is the thermal conductivity of air. Note that the effective axial thermal conductivity of the nanofibers is employed in this analysis to describe true transport characteristics in the in-plane and through-plane directions rather than intrinsic thermal conductivity which would otherwise fail to capture the effects of interfacial thermal resistance between nanofibers. H is a function of the aspect ratio, p, of the nanofibers such that [33,34]: " #  pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 p pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ln p þ p2  1  1 ð2Þ HðpÞ ¼ 2 p 1 p2  1 The typical aspect ratios of the nanofibers used in this work varied from 600 for the higher density mats to 1000 for the lower density ones. Based on multiple experimentally obtained in-plane and through-plane thermal conductivities of the mats, unique values of x and effective conductivity of the nanofibers were calculated from Eqs. (1a) and (1b) using an iterative procedure. As a result, the value of x was calculated to be around 0.99 and 0.98 for the ungraphitized and graphitized mats, respectively. Both values are close to unity, establishing that the nanofibers were predominantly aligned along the in-plane directions as assumed. Effective axial thermal conductivities calculated for the ungraphitized and graphitized nanofibers were 429 ± 22 W/m-K and 589 ± 29 W/ m-K, respectively. Therefore, in addition to the influence of the increasing volume fraction, the large jump in thermal conductivity of approximately 50–100% between the ungraphitized and graphitized mats (Fig. 5) can be attributed to the

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Fig. 7 – Effective thermal conductivities of nanofibers. The effective thermal conductivities obtained by extrapolating the in-plane thermal conductivity of ungraphitized and graphitized mats match the values obtained from the analytical expressions.

increase in the intrinsic axial thermal conductivity of the nanofibers themselves. This behavior is comparable to previously reported data on the thermal conductivity of different types of carbon fibers [15,36]. An alternate route for estimating the effective axial thermal conductivity of a nanofiber is to extrapolate the line corresponding to the in-plane thermal conductivity of the mats in Fig. 7 to a volume fraction of unity, which corresponds to the density of a single nanofiber. Doing so leads to values of approximately 408 W/m-K and 508 W/m-K as the effective thermal conductivities of the ungraphitized and graphitized nanofibers, respectively (Fig. 7). These values compare well with the values obtained analytically (429 ± 22 W/m-K and 589 ± 29 W/m-K, respectively). It is important to note that the extrapolation should be carried out to the point when the fraction of nanofibers aligned along either the a–a 0 or b– b 0 axis (i.e. xf/2) and not the overall volume fraction (i.e. f), reaches unity. This is because the experimental values were obtained by measuring the conductivity along either the a– a 0 or b–b 0 axis, which as explained previously is a result of the axial conduction through xf/2 fraction of nanofibers. The intrinsic thermal conductivity of an individual nanofiber relates to its effective thermal conductivity by considering the presence of Kapitza resistances between nanofibers such that: [33,34] intrnsic

eff

k

¼

k

intrnsic

1 þ 2RK k L

ð3Þ

This equation may be used by assuming a Kapitza resistance (RK) of 8 · 108 m2-K/W for the carbon–carbon interface, which was obtained by using molecular dynamics simulations of a suspension of carbon nanotubes in a hydrocarbon liquid [4]. Using this relation, the intrinsic thermal conductivities of the ungraphitized and graphitized nanofibers were computed to be 1380 W/m-K and 1594 W/m-K, respectively. The latter value is lower than the one previously reported for pyrolytic graphite (Pyrograf – I) fibers (1950 W/m-K) [15], which can be attributed to the orientation of the graphitic

Fig. 8 – TEM image of an individual nanofiber following heat treatment at 3000 C. The nanofibers were seen to retain the hollow core and the stacked-cone arrangement of the graphitic planes even at very high heat treatment temperatures. This is different from the behavior of pyrolytic graphite fibers which undergo reorientation of the graphitic planes parallel to the axis giving them a very high axial thermal conductivity. TEM image courtesy of Dr. Jane Howe from the Oak Ridge National Laboratory.

planes forming the walls of these nanofibers. Unlike the stacked-cone arrangement found in the PR-25 nanofibers, the graphitic planes have a parallel-to-the-axis orientation in conventional Pyrograf – I fibers, which is more favorable for phonon transport along the axis of the fiber, thus leading to a higher thermal conductivity. In addition, the calculated increase in axial thermal conductivity caused by the graphitization of PR-25 nanofibers can be considered to be almost negligible compared to the Pyrograf – I fibers, where graphitization has been known to cause the axial thermal conductivity to increase from 20 W/m-K to 1950 W/m-K. This apparent contradictory behavior of the two types of carbon filaments can be explained on the basis of the differences in their methods of synthesis and by comparing the graphitization indices at successive stages of heat treatment. Based on the data compiled by Lake and Ting [12], Pyrograf – III nanofibers synthesized by the floating catalyst method showed a 64% degree of graphitization prior to any post-production heat treatment process. When compared to Pyrograf – I fibers obtained from the fixed catalyst method, the degrees of graphitization determined for fibers subjected to heat treatment at 2200 C and 2800 C were 23% and 86%, respectively [12]. Thus, the Pyrograf – III nanofibers are seen to demonstrate a very high initial (prior to post-production heat treatment) index of graphitization. In other words, such nanofibers are not expected to show any tendency for reorientation of the graphitic planes parallel to the axis. TEM images of individual nanofibers, taken at different stages of

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heat treatment, confirmed that the stacked-cone morphology was preserved, even after heat treatment at 3000 C (Fig. 8). It should be noted that the percentage graphitization indices listed above are calculated based on the conventional definition which assumes that the d002 spacing is minimum for pure graphite. However, d002 spacings less than that of pure graphite have been recently reported for some form of carbon nanofibers [19]. Nonetheless, for the purpose of this study and since the focus is on the comparison between the PR-25 nanofibers and Pyrograf – I fibers and their response to heat treatment, the conventional definition is believed to be adequate for explaining the differences in the microstructure and hence the thermal conductivity change brought about by the graphitization process.

5.

Conclusion

In conclusion, a new type of Pyrograf – III nanofiber, termed as PR-25 and differing from the conventional PR-19 and PR-24 nanofibers reported previously [12,13], was used to form mats which were then subjected to further heat treatment. Thermal characterization of the mats showed relatively high inplane and low through-plane conductivities, which was consistent with their layered structure, with the highest value reaching approximately 150 W/m-K. While the nanofiber mats characterized for this work may not necessarily be suitable as heat spreader materials, which typically exhibit thermal conductivities greater than 500 W/m-K, understanding thermal transport in these materials will help with their further development. Both in-plane and through-plane thermal conductivities were seen to increase with the increasing volume fraction of nanofibers as well as after graphitization. Graphitization of the mats had a relatively greater influence on the through-plane thermal conductivity which is believed to be explicable on the basis of re-arrangements within the network of nanofibers due to the heat treatment process. The experimentally obtained thermal conductivity data was employed to estimate the intrinsic thermal conductivity of the individual PR-25 nanofibers, and the values computed were within range of results expected based on the data published on Pyrograf – I fibers [15]. The lower thermal conductivity of the nanofibers can be attributed to the conical array of the graphitic planes instead of the usual parallel to the axis orientation as found in Pyrograf – I fibers. Finally, the slight enhancement in thermal conductivity of the individual PR25 nanofibers following graphitization is believed to be, in absence of reorientation of the graphitic planes, caused by the elimination of lattice defects from such graphene planes during the heat treatment process. Contrary to conventional Pyrograf – I fibers, the PR-25 nanofibers demonstrated a very high initial (in their ‘‘as-grown’’ state) index of graphitization and are not prone to any significant, thermally induced, structural re-arrangement.

Acknowledgements The authors offer their sincere gratitude to Martin D. Smalc of GrafTech International Limited for his helpful discussions and Jane Howe of Oak Ridge National Laboratory for her help

with Transmission Electron Microscopy of the PR-25 nanofibers. This paper was prepared with financial support from the State of Ohio. The content reflects the views of the authors and does not purport to reflect the views of the State of Ohio.

R E F E R E N C E S

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