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Current Applied Physics 11 (2011) 1144e1148

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Current Applied Physics

journal homepage: www.elsevier .com/locate/cap

The effect of mesoscopic shape on thermal properties of multi-walled carbonnanotube mats

Young Jin Heo a, Chang Hun Yun b, Woo Nyon Kim c, Heon Sang Lee a,*

aDepartment of Chemical Engineering, Dong-A University, Hadan 840, Saha-Gu, Busan 604-714, Republic of Koreab LG Chem. Ltd., Technology Center, Jang-Dong 84, Yusung-Gu, Daejeon 305-343, Republic of KoreacDepartment of Chemical and Biological Engineering, Korea University, Anam-dong, Seoul 136-701, Republic of Korea

a r t i c l e i n f o

Article history:Received 7 November 2010Received in revised form13 February 2011Accepted 14 February 2011Available online 23 February 2011

Keywords:Multi-walled carbon nanotubesThermal propertiesMesoscopic shapeStatic bending persistence lengthStatic bend pointThermal expansivity

* Corresponding author. Tel./fax: þ82 51 200 7728.E-mail address: heonlee@dau.ac.kr (H.S. Lee).

1567-1739/$ e see front matter � 2011 Elsevier B.V.doi:10.1016/j.cap.2011.02.007

a b s t r a c t

We highlight the effect that mesoscopic shape of individual multi-walled carbon nanotubes (MWCNTs)has on their collective thermal properties when they are lumped together into MWCNT mats. Thethermal properties depend both on the mesoscopic shape of the MWCNTs and on the structure of themat. The mesoscopic shape is represented by static bending persistence length (lsp) and the mat structureis represented by network length (le). It is demonstrated that various thermal properties depend on lsp.The variable thermal properties are linear thermal expansivity, thermal diffusivity, specific heat capacity,and thermal conductivity. In the case of n* > 1, the MWCNT mats contract with increasing temperature.On the contrary, in the case of n* < 1, the mats expand with increasing temperature. The apparentthermal conductivity increases with increasing lsp.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Thermally contracting materials are of special interest becausemost materials tend to expand by increasing temperature. Lowdimensional materials such as single-walled carbon nanotubes(SWCNTs) and graphens are known to show negative linearthermal expansivity (a) at moderate temperatures and to showpositive linear thermal expansivity at high temperatures [1e5]. Thisunusual behavior at moderate temperatures has been explained bythe competition between internal energy and entropy [3]. Thenegative linear thermal expansivity of SWCNTs has been reportedto be small values of a z �1.0 � 10�5 w �1.0 � 10�6 K�1 atmoderate temperatures [3,4]. Recently, drastic thermal contractionwas observed for a single multi-walled carbon nanotube (MWCNT)isolated from neighboring MWCNTs using light scattering [6].Overall size of the MWCNT was reduced up to 10% by increasingtemperatures from 278 to 363 K in a solution [6]. 10% size reductioncorresponds to the large negative value in the linear thermalexpansivity, a z �1.0 � 10�2 K�1. This large thermal contraction isascribed to the thermal fluctuation at static bend points along the

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MWCNT axis [6]. The driving force for the thermal fluctuation atstatic bend points is the translational motion of the MWCNTsegments, which corresponds to the Kuhn segment length (twotimes of static bending persistence length) [5,6]. The translationalmotion of each segment has a tendency to move in a randomdirection and against the bending modulus of the MWCNT. There isa different bending modulus value for each possible bendingdirection at the static bend point. The effective bending modulusrelative to the static bend direction is smaller than the otherdirections. Therefore, the ensemble average of bend angle relativeto the MWCNT axis becomes larger by the thermal fluctuation [6].This leads to the reduction of overall size of an MWCNT isolatedfrom neighboring MWCNTs [6].

The purpose of this work is to discover the relationship betweenindividual MWCNT mesoscopic shapes and their thermal proper-ties such as thermal expansion/contraction, thermal diffusivity,heat capacity, and thermal conductivity of MWCNT mats. Onemight assume that thermal and electrical properties depend onMWCNT mesoscopic shape. In order to verify this assumption, weneed amesoscopic shape factor which can characterize various CNTmesoscopic shapes. When external forces are not large enough toproduce significant elastic deformation of MWCNT, static bendingpersistence length represents mesoscopic shape factor whichdescribes the degree of tortuousness of an individual MWCNT. The

Table 1Characteristics of individual MWCNTs and their mats.

MWCNT1 MWCNT2 MWCNT3 MWCNT4

Average outer diameter (nm) 9.5 21 27 50IG/ID 0.74 1.08 2.04 9.66Static bending persistence

length, lsp (nm)70 271 800 >3000

ra (g/cm3)a 0.282 0.278 0.145 0.126le (nm)a 258 709 1285 2599n*a 1.84 1.31 0.80 0.13

a Values for MWCNT mats.

Y.J. Heo et al. / Current Applied Physics 11 (2011) 1144e1148 1145

bending ratio (Db) is defined as the ratio of themean square end-to-end distance (hR2i) and the square contour length (L2) [6e8].

Dbh

DR2E

L2(1)

Eq. (2) gives the relationship between themesoscopic shape andthe overall size [6e8].DR2E

¼ 2lspLþ 2l2sp�e�L=lsp � 1

�(2)

where lsp is the static bending persistence length (maximumstraight length that is not bent by a permanent structural defor-mation), and L is contour length along the tube axis. When L>> lsp,the rigid random-coil limit applies, hR2i ¼ 2lspL. When L < lsp, therigid rod limit applies, hR2i ¼ L2. lsp represents the mesoscopicshape factor of MWCNTs. With decreasing lsp, the MWCNT looksmore tortuous. Here, it is noted that the mesoscopic shape of an

Fig. 1. SEM images of as synthesized or as-received MWCNTs (a) MWCNT1, scale bar 50scale bar 10 mm.

MWCNT is mainly determined by static bending rather than elasticbending [6,7].

We have demonstrated that the electrical percolation ofMWCNT film depends on the mesoscopic shape factor, representedby lsp, of the CNTs of which it is comprised [8]. In this paper weshowed that the linear thermal expansivity, heat capacity, andthermal conductivity depend strongly on lsp for MWCNTs. Particu-larly, we demonstrated that the sign of thermal expansion (positiveversus negative) is changed by the ratio between network length(le) and lsp in MWCNT mats. We also observed that thermalconductivity linearly depends on the ratio between le and lsp.

2. Experiment details

We obtained four groups of MWCNTs from various sourceswhich were designated as MWCNT1, MWCNT2, MWCNT3, andMWCNT4. MWCNT1 was supplied from a commercial source,Nanocyl, Belgium; MWCNT2 was synthesized in our laboratory asdescribed in [6], MWCNT3 was synthesized at 1073 K using theprocedure described in [6], MWCNT4 was from commercial source,NCT, Japan. In order to fabricate the MWCNT mats, the followingprocedure was applied to each group. 0.1 g of MWCNTs was placedinto a cylindrical moldwith 12mmdiameter and 30mmdepth, andcompressed with 1 ton of pressure for 10 min. The resulting mat ofMWCNTs dried in a vacuum oven at 110 �C for 24 h. The bulkdensity of the mat was evaluated by measuring the weight ofMWCNT Mat. The density of graphene layer was evaluated to be2.2 g cm�3 according to the literature data [7].

The bucky papers were fabricated by following procedure.200 mg of MWCNTs and 20 ml of ethanol were placed intoa zirconia pot (300 ml) and ball-mill at 400 rpm for 2 h, where 28

0 nm (b) MWCNT2, scale bar 500 nm (c) MWCNT3, scale bar 2.5 mm (d) MWCNT4,

Fig. 2. Dimensional changes of MWCNT mats with increasing temperature.Fig. 4. Linear thermal expansivity of various MWCNT mats with respect to number ofstatic bend points (n*) within the network length (le).

Y.J. Heo et al. / Current Applied Physics 11 (2011) 1144e11481146

zirconia balls with diameter of 5 mm were used. The ball-milledMWCNTs were filtered using a filter paper (Millipore, 0.45 mm ofporesize, diameter of 47 mm) and then dryed in oven at 373 K for12 h. In order to fabricate the MWCNT bucky paper, the followingprocedure was applied to each group of MWCNTs. 6 mg of ball-milled MWCNT was dissolved in 30 ml DMF and then the solutionwas sonicated for 2 h at 323 K using bath type sonicator operatingat 40 kHz frequency. And then the solutionwas centrifuged (exceptMWCNT4 solution) under 3000 rpm for 30min. 6ml of supernatantwas diluted by 24ml of DMF. The diluted solutionwas filtered usinga filter paper (Millipore, 5 mm of poresize, diameter of 47 mm) andthen sample was dryed in vacuum oven at 373 K for 24 h.

Average diameters of MWCNTs were measured by transmissionelectron microscopy (TEM, JEOL JEM-3011, 300 kV). The morphologyand microscopic structure of individual MWCNTs from the mat orthe bucky paper were characterized by scanning electron micros-copy (SEM, Hitach S-4700). Ramanmeasurement (Horiba Jobin-YvonHR-800 UV) was done to evaluate IG/ID. lsp was evaluated using thesame procedure reported in reference [7]. The characteristics ofMWCNTs and MWCNT mats are listed in Table 1. Linear thermalexpansivities (a) of MWCNT mats were measured using a thermo-mechanical analyzer (TMA2940, TA instrument, USA) with a heating

Fig. 3. Illustrations using a

rate of 5 �C/min under nitrogen atmosphere. The thermal diffusivityof the MWCNT mats was measured at room temperature (135 K)using laser flash method (LFA447, NETZSCH, Germany). The specificheat capacity of the MWCNTmats was measured using a differentialscanning calorimeter.

3. Results and discussion

The static bending persistence lengths (lsp) of MWCNT1,MWCNT2, MWCNT3, and MWCNT4 were 70 nm, 271 nm, 800 nm,and >3 mm, respectively. lsp is a key measurand for describing themesoscopic shape of MWCNTs. At first glance, the SEM images inFig. 1(a)e(d) appear similar. Noting that the magnitude of the scalebars in the images are very different, it becomes apparent that themesoscopic shape of the MWCNTs become more tortuous as lspbecomes shorter as seen in Fig.1(a)e(d). This is themanifestation ofthe scaling concept [9] in static conformation of MWCNTs [6e8].

Fig. 2 shows a comparison of the linear thermal expansivity ofMWCNT mats made from the four different MWCNT sources. Themats made of MWCNT1 and MWCNT2 contract with increasingtemperature, while mats made of MWCNT3 and MWCNT4 expandwith increasing temperature. So the sign of linear thermal

simple lattice model.

Fig. 5. Thermal diffusivity of various MWCNT mats.

Fig. 7. Thermal conductivity of MWCNT: (a) Out-of-plane conductivity of MWCNTmats; (b) In-plane conductivity of MWCNT bucky papers.

Y.J. Heo et al. / Current Applied Physics 11 (2011) 1144e1148 1147

expansivity is negative for MWCNT1 and MWCNT2, while positivefor MWCNT3 and MWCNT4.

The sign of linear thermal expansivitymay be determined by thecompetition between thermal fluctuation and mechanical inter-locking. An MWCNT with static bend points tends to contract bythermal fluctuation [7] at moderate temperatures, when it is iso-lated from neighboringMWCNTs. InMWCNTmats or networks, themechanical interlocking by neighboringMWCNTs tends to suppressthe thermal fluctuations of individual MWCNTs. According to thedefinition of lsp, the number of static bend pointswithin an arbitrarylength can be estimated using the ratio between the contour lengthand 2lsp. Therefore, the number of static bend points (n*) withina network length (le) can be defined as follows,

n*hle2lsp

(3)

When n* >> 1, there are many static bend points within le asseen in Fig. 3. In this limit, thermal fluctuation at the static bend

Fig. 6. Network length with respect to static bending persistence length.

points may lead to the thermal contraction. When n* << 1, thereis no static bend point within le as seen in Fig. 3. In this limit,thermal fluctuation may be suppressed by the mechanicalconstraint. Without the effects of thermal fluctuation, threedimensional solids are normally expected to expand withincreasing temperature. To describe the competition between thethermal fluctuation and the mechanical constraint quantitatively,we need to know lsp and le. It is very difficult to obtain an exactvalue of le, because the MWCNTs are entangled with each otherwithin the mats. We can approximate le from the bulk density ofthe mats. As expected, the bulk density decreases as le becomeslonger. Assuming the mat is made of a rectangular lattice, as seenin Fig. 3, the bulk density (ra) of the MWCNT mat can be obtainedas following,

ra ¼"2�1leþ 1

�2pr�r2o � r2i

�#(4)

where le is network length, r is density of the MWCNT graphenlayers, ro and ri are outer and inner diameters of a single MWCNT,respectively. By rearrangement of Eq. (4), le of an MWCNT mat canbe obtained using Eq. (5) when we have a measured value of ra.

Y.J. Heo et al. / Current Applied Physics 11 (2011) 1144e11481148

l ¼"

ra� �!1=2

�1

#�1

(5)

e2rp r2o � r2i

Although Eq. (5) is an approximation, it has physical significanceas discussed in the next section.

In Fig. 4, the linear thermal expansivities (a) of various MWCNTmats at 343 K are plotted with respect to n*. For the case of n* > 1(mats made of MWCNT1 and MWCNT2), thermal contraction isobserved as shown in Fig. 4. For the case of n* < 1 (mats made ofMWCNT3 and MWCNT4), thermal expansion is observed as shownin Fig. 4. This result is consistent with the prediction by the simplelattice model depicted in Fig. 3. a for MWCNT1 and MWCNT2 are�1.32�10�3 K�1 and�1.01�10�5 K�1, respectively. a for MWCNT3andMWCNT4 are 6.78� 10�5 K�1 and 2.52�10�5 K�1, respectively.It is worth noting that the negative value of linear thermalexpansivity for MWCNT1 is much larger than those for an SWCNT[3,4].

Fig. 5 shows the thermal diffusivity of MWCNT mats. Followingthat thermal diffusivity is expressed as l ¼ k=Cpra, we measuredapparent specific heat capacity of each MWCNT mat. Apparentspecific heat capacities at 298 K were 0.927, 0.556, 0.445, and0.509 Jg-1k�1 for the MWCNT1-, MWCNT2-, MWCNT3-, andMWCNT4-mats, respectively. Specific heat capacity for a carbonnanotube can be expressed by a standard statistical mechanicsformula [10e12]. Since electron contribution is negligible, phononcontribution is the major factor determining specific heat capacityfor a carbon nanotube [11].

If anMWCNT has static bend points within le, additional degreesof freedom needs to be taken into account due to thermal fluctu-ation at the static bend points for the estimation of apparentspecific heat capacity of MWCNT mat. We expected apparentspecific heat capacity of mats made of MWCNT1 and MWCNT2 tobe larger than those of MWCNT3 and MWCNT4 due to thermalfluctuation, as described in the discussion of Fig. 4.

The results for apparent specific heat capacity were consistentwith the expected results for thermal expansion. The thermalconductivity of each MWCNT mat was evaluated from themeasured values of thermal diffusivity, apparent specific heatcapacity, and density at 298 K.

Thermal conductivity of MWCNT mat may depend on thevarious geometric properties of MWCNT such as diameter, networklength, total length, static bending persistence length, and others.These variables are conceptually independent from each other.However, static bending persistence is increased with the increaseof diameter in Table 1. Also, the network length is almost linearlyincreased with the increase of static bending persistence length,which is plotted in Fig. 6. The apparent thermal conductivity ofMWCNT mats to out-of-plane direction is presented in Fig. 7(a).Length-wise thermal conductivity of individual MWCNT is knownto increase with decreasing the diameter [13,14]. The thermalconductivity to out-of-plane direction is increased with theincrease of diameter in Fig. 7(a). This result may indicate that thethermal conduction to out-of-plane was mainly ascribed to contactthermal resistance rather than the length-wise thermal conduc-tivity of individual MWCNT [14,15]. The values of thermalconductivity in Fig. 7(a) are about 0.12e0.20 Wm�1K�1 which issimilar to the literature value [15] in which the low thermalconductivity of MWCNT mat was attributed to the large contact

thermal resistance between individual MWCNT. The large thermalresistance may be observed at the static bending point as well asthe contact point between individual MWCNT. The number ofcontact points is increased with decreasing the network length (le)as illustrated in Fig. 3. Also, the number of static bending points isincreased with decreasing the static bending persistence length(lsp). Therefore, we expect the thermal conductivity of MWCNTmatincreases with increasing lsp and le, which is consistence with theexperimental observation in Fig. 7(a). In order to measure thethermal conductivity to in-plane direction we fabricated buckypapers, since MWCNTmats are too short tomeasure it. The thermalconductivity to in-plane direction is also expected to increase withincreasing lsp, which is consistence with experimental data inFig. 7(b). This result suggests that the apparent thermal conduc-tivity of an MWCNT depends on it’s mesoscopic shape factor, rep-resented by lsp.

4. Conclusion

We explored the effect that mesoscopic shape of individualmulti-walled carbon nanotubes (MWCNTs) has on their collectivethermal properties when they are lumped together into MWCNTmats. The thermal properties depend both on the mesoscopicshape of the MWCNTs and on the structure of the mat. The meso-scopic shape is represented by static bending persistence length(lsp) and themat structure is represented by network length (le). Wedemonstrated that various thermal properties depend on lsp. Thevariable thermal properties are linear thermal expansivity, thermaldiffusivity, specific heat capacity, and thermal conductivity. In thecase of n* > 1, the MWCNT mats contract with increasingtemperature. On the contrary, in the case of n*< 1, themats expandwith increasing temperature. The apparent thermal conductivityincreases with increasing lsp.

Acknowledgment

This study was supported by research fund from Dong-AUniversity.

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