Dynamic percolation of carbon nanotubes in liquid medium

Marcio D. Lima,*ab Monica J. Andrade,ab Viera Skakalova,b Carlos P. Bergmanna and Siegmar Rothb

Received 9th July 2007, Accepted 20th September 2007

First published as an Advance Article on the web 3rd October 2007

DOI: 10.1039/b710417k

In this article we have measured the electrical behaviour of carbon nanotubes (CNTs) suspended

in electrically insulating liquid. The concentration dependence of conductivity shows a percolation

behaviour similar to that observed in electrical composites with an insulating matrix. The value of

the critical percolation concentration is strongly determined by the aspect ratio of the fillers

forming the network through dynamic percolation. We characterized several single- and multi-

wall carbon nanotube materials by the newly proposed method and received a good correlation

with the results obtained by methods commonly used for CNT characterization (Raman

spectroscopy, transmission electron microscopy and electrical conductivity of free standing

papers). As a comparison, fine graphite material has also been evaluated. The electrical properties

of the suspensions can be used as a method for CNT characterization. This method can yield

important information for CNT producers and for the selection of electrically conducting

structures for composites applications.

Introduction

Carbon nanotubes (CNTs) have unique physical and chemical

properties, yielding more than 24000 publications in the last

16 years.1 Their high electrical conductivity, good chemical

stability combined with huge aspect ratio (.1000) make

carbon nanotubes particularly suitable for use as fillers for

electrical composites and as ideal materials for transparent

conductive coatings. For these applications, CNTs have to

form 2- or 3-dimensional percolating networks. Thanks to

their extremely high aspect ratio, CNTs may reach the

percolation threshold at concentrations two orders of magni-

tude lower than those of networks formed from other sp2

carbon forms.2

However, the optimum performance of the percolating

networks may be limited by defects in the CNT structure as

well as by impurities (amorphous carbon, onions, catalyst

particles, etc.) often present in the source material. In order to

use CNTs for particular applications, it is therefore extremely

important to characterize the CNT material.

A large number of characterization techniques are com-

monly used: electron microscopic techniques (HRTEM, SEM,

and AFM), thermogravimetric analysis (TGA), IR-optical

and Raman spectroscopy, specific surface area, and electrical

conductivity of free standing papers and pellets. However, the

evaluation of the CNT purity remains a challenging task.

HRTEM was the first technique used for characterizing

nanotubes. However, the major problem of this technique is

the small scale of the sample, usually of the order of 10212–

10213g,3 providing only very local information. The same

problem is faced whenever SEM or AFM are used.

TGA allows the measurement of the precise total amount of

carbon in the sample. This makes it suitable for identifying the

concentration of residual catalysts. However, it is not good

for distinguishing between the different forms of carbon—

amorphous carbon, graphite or CNTs. Each carbon structure

burns at slightly different temperatures,4 but the temperature

can be affected by the density and surface area of the material,

as well as by the presence of metals and by the heating rate.5

Near-infrared (NIR) spectroscopy has been established as

an important tool for estimating the content of single-walled

CNTs (SWCNTs) in the sample3,6 and their diameter distribu-

tion. The interband electronic transitions produce prominent

features in the NIR spectral ranges that, while typical for

SWCNTs, are not present in the absorption spectra of

other carbonaceous structures, such as multiwalled CNTs

(MWCNTs), for example.

Raman spectroscopy is used as the major technique for

characterizing CNTs. The resonance nature of the Raman

effect in SWCNTs enables the selective determination of

the diameters of the tubes present in the sample, when the

excitation photon energy is tuned over a wide range. On the

other hand, the resonance enhancement of the signal coming

from SWCNTs makes it impossible to determine the amount

of SWCNTs in a mixture with other carbonaceous structures.

The characterization of CNTs in bulk form (free standing

papers or pellets) by conventional measurements of electrical

conductivity is costly in terms of the time consumed for sample

preparation and of the amount of material used. Moreover,

as the density of bulk samples may vary (packing of the

particles and residues of surfactant), the measured values of

conductivity often differ from sample to sample for the same

CNT material.

To conclude, none of the currently used techniques provides

satisfying information on the characteristics of the CNT

material, especially with respect to applications that require

the formation of a percolation network of nanotubes.

The new method that we propose for characterization of

CNTs overcomes many of the limitations/problems mentioned

aFederal University of Rio Grande do Sul, Porto Alegre, Brazil.E-mail: marciodiaslima@yahoo.com.brbMax Planck Institute for Solid State Research, Stuttgart, Germany

PAPER www.rsc.org/materials | Journal of Materials Chemistry

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above. It is based on electrical conductivity measurements of

CNTs suspended in an electrically insulating liquid (chloro-

form was used in this study) with nanotubes forming a

‘‘dynamic’’ percolating network. It is a fast, simple and

inexpensive measurement, using small amounts of material. It

also allows the determination of the value of the percolation

threshold concentration, by way of systematically tuning the

amount of CNTs in the liquid. Since its value depends on the

average aspect ratio of the conductive particles in the sample

and the presence of impurities in the sample decreases the

average aspect ratio of the system, the percolation threshold

concentration also reflects the amount of impurities in the

CNT material.

Herein we describe how this new technique was used for

evaluating the quality of several CNT materials with respect to

percolation network applications.

Experimental

Electrical conductivity in liquid measurements

Electrical measurements in a 2-probe configuration (distance

between the electrodes was 3 mm and 1 6 15 6 5 mm were the

dimensions of each immersed electrode) and ultrasonication

were performed in a cell schematically shown in Fig. 1. DC

current between 1.5 and 10 V was applied between the

electrodes (0.104 and 6.934 V cm21, respectively). For

comparison, we also performed measurements in a four-probe

configuration. Chloroform (dielectric constant = 4.8069) was

used as the liquid medium for the CNT suspensions. The

electrical conductivity was calculated by using the relation

s = I 6 L/(V 6 A) (1)

where s is the electrical conductivity, I is the electrical current

measured between the electrodes, V is the voltage applied

between the electrodes and A is the area of the electrodes

immersed in the liquid.

In order to avoid heating the CNT suspension, the

sonication and electrical experiments were done under immer-

sion in a water-ice bath. This preserves a stable temperature

during the measurements and also ensures better dispersion.

The ultrasonicator used was a UP100H Dr. Hielscher, with a

titanium probe of a diameter of 2.5 mm, output power of

100 W and a working frequency of 30 kHz.

Materials

CNT samples prepared through different techniques were

analysed: arc-discharge (AD) SWCNTs, produced using a

Ni–Y catalyst without any purification; purified HipCo

SWCNTs from Carbon Nanotechnology Inc.; and three

different samples from CVD MWCNTs that were called

MWCNT I, MWCNT I-short (shortened MWCNT I) and

MWCNT II. As a comparison, a sample of fine graphite

powder from Merck was also analysed. Suspensions with

carbon material concentrations ranging from 0.01 to

5 mg mL21 were prepared. At higher concentrations of carbon

material the viscosity of the suspensions increases, reducing

heat dissipation by convection, which leads to local evapora-

tion of the solvent and loss of sonication energy. At

concentrations above 1 mg mL21, the dispersion becomes less

homogeneous.

The measured value of electrical conductivity of pure

chloroform (Merck, analytical grade) was 1–3 6 1028 S cm21.

After removal of CNTs from the chloroform suspension by

centrifugation (2000 g for half an hour), the value of electrical

conductivity for the chloroform was found not to have

changed.

Characterization of the materials

Free standing papers made of CNT materials were also

prepared for electrical conductivity measurements in a 4-probe

configuration (Keithley Instruments). The microstructure

of the samples was evaluated using a Philips CM 200

Transmission Electron Microscope (TEM). Raman spectro-

scopy measurements were done with a 206 objective lens with

a 632.8 nm laser line and a laser power of about 4 mW (Jobin

Yvon-LabRam spectrometer).

Results and discussion

Structure features of the carbonaceous materials

The TEM images of the carbon samples studied in this

work are presented in Fig. 2. Fig. 2A shows a structureless

agglomeration of graphitic particles over the carbon grid

membrane. All MWCNT samples (Fig. 2B, C and D) look

very similar, even though, as demonstrated later by the results

obtained from our new method, they exhibit quite different

electrical properties of percolating networks. The average

diameter for MWCNT I and MWCNT I-short is about

5–10 nm, while for MWCNT II it is between 10–20 nm, as

measured by TEM. The MWCNT II also have a ‘‘bamboo

structure’’ more pronounced than that of the MWCNT I. This

structure is caused by a conical angle along the tubes.7 An

appreciation of the purity and diameter of SWCNT materials

can be made by comparing the images of HipCo SWCNTs

and AD SWCNTs, respectively (Fig. 2E and F). As can be

observed, the AD SWCNTs contain a larger amount of metal

catalyst impurities than the HipCo material. Both have a

carbon nanotube diameter of 1–2 nm.Fig. 1 Apparatus used for the electrical measurements.

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Fig. 3 shows Raman spectra of CNTs and graphite. All the

spectra are normalized to the D* mode at about 2600 cm21,

which does not depend on defect concentration.8

Raman spectra of the two SWCNT samples are shown in

Fig 3A. From comparison of the radial breathing modes

(RBM) at low frequencies it follows that AD SWCNTs have a

diameter distribution around 1.5 nm, while HipCo SWCNTs

have a broader distribution centred on 1.2 nm. The Diamond

(or ‘‘defect’’) mode (D) at about 1302 cm21, induced by sp3

electronic states (considered as defects in the planar sp2

graphitic structure), indicates that HiPco SWCNTs contain

less structural defects than the AD SWCNTs material, since

the intensity of this mode in the latter is almost double that of

the former. In the case of SWCNTs, the strong signal of the

graphene tangential mode (G) at about 1580 cm21 is strongly

affected by the resonance effect, which impairs the reliability of

the G/D ratio; some reports, therefore, use D/D* instead.8 The

D/D* ratios of SWCNTs are listed in Table 1.

The Raman spectra of graphite and MWCNTs (Fig. 3B)

differ from the spectra of SWCNTs mainly by the absence of

the RBM feature. Since the resonance effect in MWCNTs is

small, structural disorder is well characterized by the ratio of

the G to D modes’ intensities. The values of this ratio are

summarized in Table 1 and demonstrate that the graphite

Fig. 2 TEM pictures of the several carbon samples analysed in this study: (A) graphite, (B) MWCNT I-short, (C) MWCNT II, (D) MWCNT I,

(E) HipCo SWCNT, (F) AD SWCNT. Scale bar for A: 500 nm; for B to F: 50 nm.

Fig. 3 Raman spectra of carbon samples analysed with a laser line of 632.8 nm.

Table 1 G/D ratios of graphite and MWCNTs materials and D/D* of SWCNTs after normalization of the D* mode8

HiPCo SWCNT AD SWCNT Graphite MWCNT I MWCNT I-short MWCNT II

G/D ratio 19 3 2.5 0.6 0.59 0.57D/D* ratio 0.43 0.54 — — — —

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studied in the work has far fewer sp3 defects than MWCNTs.

Slightly more defects are present in MWCNT I-short than in

MWCNT I (longer tubes), but MWCNT II exhibits the

most disordered structure. This coincides with the observa-

tions from the TEM images (Fig. 2). The more pronounced

‘‘bamboo-like’’ structure in MWCNT II could be considered

as reflecting defects in its structure.

Electrical conductivity in an electrically insulating liquid

When nanotubes are dispersed in an electrically insulating

matrix, they are capable of conducting electrical current. At a

critical concentration, percolation of the conductive particles

is reached.9 In solid composites or coatings, the CNTs form

a pathway between the electrodes in an electrical circuit.

According to other reports,10,11 CNTs can also create such

percolating networks and conduct electrical current in a liquid

medium. In this case, the connections between the suspended

tubes are dynamic (Brownian motion and, eventually, liquid

agitation).

The electrical conductivity of CNTs in suspensions was

measured under ultrasonication (Fig. 4a), as well as in the

static state (without ultrasonication), once the electrical

current stabilized (Fig. 4b). At higher concentrations of

CNTs (above the percolation threshold), the conductivity of

the suspensions is approximately the same in both cases,

namely with or without ultrasonication. However, at lower

concentrations (below the percolation threshold), there is a

clear difference in the shapes of the conductivity curves.

Fig. 4a clearly shows that MWCNT I, MWCNT I-short and

HipCo SWCNT have lower percolation thresholds. They

are one order of magnitude lower than those for AD SWCNTs

and MWCNTs II, presumably due to their higher purity and

higher aspect ratio. As also expected, a shift of the percolation

threshold to lower values for the longer tubes MWCNT I

with a higher aspect ratio compared to MWCNT I-short

is observed.

When ultrasonication was applied during the measurements

(Fig. 4a), the electrical conductivity showed a shift in the

percolation point to higher concentrations, relative to the

static situation (Fig. 4b). We assume that this is due to

the induced dipole moment, which tends to align the elongated

CNTs in the direction of the electrical field.12–17 This is clearly

demonstrated in Fig. 5, where some filamentous structures

formed between two copper electrodes. When aligned in

parallel to the electric field, fewer nanotubes are necessary to

form a percolation pathway between the electrodes than in the

case of a random orientation when ultrasound is applied.

Similar behaviour of increasing the electrical conductivity with

a certain alignment was also observed for partially oriented

solid composites by Fischer et al.18

However, under ultrasound agitation, the configuration of

CNTs in suspension corresponds to that in solid composites,

the CNTs are mixed randomly and no ‘‘alignment effect’’ takes

place. The percolation threshold found for the dynamic

network should therefore reflect a value similar to that in

solid composites with the same concentration of randomly

dispersed CNTs.19 It is important to note that the lower

percolation points in both cases also have a contribution

from the dipole momentum and ionic conductivity of the

particles moving.

The suspension of graphite particles with the highest used

concentration does not exhibit any measurable value of

electrical conductivity. This reflects the fact that the aspect

Fig. 4 Electrical conductivity of the carbon suspensions in chloro-

form at 1.5 V DC: (A) during sonication and (B) after stopping

sonication and stabilization of the electrical current.

Fig. 5 Filamentous structures forming between the electrodes (dis-

tance between the electrodes is 10 mm) during electrical measurements

without ultrasound sonication. HipCo SWCNT material in a

concentration of 0.025 mg mL21 and a voltage of 1.5 V. The pictures

were taken at 0 min (A), 2 min (B) and 10 min (C) after current

application.

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ratio of graphite particles is many orders of magnitude lower

than the aspect ratio of carbon nanotubes.

Fig. 5 presents a sequence of image captions of two

electrodes immersed in a suspension with 0.025 mg mL21 of

HipCo SWCNTs, after 0 min (A), 2 min (B), and 10 min (C) of

applying a voltage of 1.5 V between the electrodes. It clearly

demonstrates the development of the aligned percolating

pathway. Over the application period of the field, the CNTs

tend to form fibrous structures, while some areas of the

suspension become more diluted.

The kinetics of the formation of the percolating networks in

a liquid under various conditions was also studied. In Fig. 6

the conductivity of suspensions without ultrasonication, for

different concentrations of HipCo SWCNT, is presented as a

function of the time, at a constant voltage of 1.5 V. In the case

of the most concentrated suspension of HipCo SWCNTs

(0.5 mg mL21), the conductivity is time independent within the

limits of our measurements. At concentrations well above the

percolation threshold, saturation is reached within several

seconds. At a concentration close to the percolation threshold

(0.025 mg mL21), conductivity increases slowly and saturates

in about 10 min. At concentrations close to the percolation

point the percolation is only possible through the alignment of

the CNTs. Therefore, without sonication, the alignment of the

CNTs controls the electrical conductivity by percolation in

these concentrations. Fig. 7 shows the time dependence of

electrical conductivity for two suspensions with CNT con-

centrations of 0.025 and 0.5 mg mL21, measured at three

different voltages: 1.5, 5 and 7 V. The kinetics of formation of

percolating networks at lower concentration is quite dependent

on the applied voltage. On the other hand, the more

concentrated suspension shows a fast saturation of the current

at all voltages. Surprisingly, a slow decrease of conductivity

over time is observed; this effect is more pronounced at higher

voltages. Apparently, at higher concentrations and under

sufficiently powerful electrical fields, the nanotubes form a

percolation pathway quite rapidly, but then they start to

slowly move toward the electrodes due to electrophoretic

forces,20 thus diluting the area between the electrodes.

Assuming a random orientation of CNTs in an insulating

matrix (Fig. 4b), classical percolation theory predicts21 that,

above the percolation threshold, the conductivity of the

composite should be:

s 3 (V 2 Vc)b (2)

where s is the electrical conductivity of the composite, V is

the volume fraction of the conducting filler phase, Vc is

the critical volume for the percolation threshold and b

is a critical exponent that indicates the dimensionality of the

network.19 The theoretical value of b for a 3D network would

be 1.94.

For concentrations lower than approximately 1 mg mL21,

the suspensions follow eqn (1), as shown in Fig. 8 for HipCo

SWCNTs. There is a linear correlation between the reduced

volume and the conductivity. The calculated b was estimated

Fig. 6 Time dependence of the electrical conductivity of HipCo

SWCNT suspensions in chloroform for several concentrations

(mg mL21) of nanotubes without ultrasonication. All measurements

were made at 1.5 V.

Fig. 7 Time dependence of the electrical conductivity of HipCo

suspensions in chloroform without ultrasonication under different

voltages and concentrations.

Fig. 8 Conductivity versus reduced volume for HipCo SWCNTs.

Below 1 mg mL of carbon nanotubes (reduced volume = 3.7) the

conductivity follows a linear correlation. The CNT concentration

(mg mL21) is indicated for each point.

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to be 1.82, which is quite close to the theoretical value for a

3D network.

The value of the critical volume can be calculated by:

1{ exp {VexV

SVeT

� �~Vc (3)

V is the excluded volume of each filler ‘‘particle’’, in this case,

of the carbon nanotubes. Vex represent the total excluded

volume. For randomly oriented infinitely thin cylinders it gives

a value of 1.4, and for spheres, 2.8.2 For the calculation of the

critical volume of real cylindrical particles, these values should

be considered as the lowest and highest limits. The excluded

volume (Ve) can be calculated by:

Ve~4p

3W 3z2pW 2Lz

p

2WL2 (4)

where W is the diameter and L is the length of the nanotubes.

From eqn (3) and (4), it is possible to demonstrate that the

percolation threshold volume fraction is inversely proportional

to the aspect ratio. Longer CNTs will present a percolation

threshold volume lower than for shorter nanotubes, for same

diameter materials. In this way, it is possible to estimate the

aspect ratio of the filler material.

However, the random orientation of the nanotubes in the

suspension could only be assured under ultrasound sonication.

In this case, the suspension’s behaviour could be similar to that

of solid composites with random orientation of CNTs, with a

defined percolation threshold.

From Fig. 4a it is possible to calculate the percolation

threshold of some carbon materials by fitting with eqn (2),

assuming a density of 1.2 g cm23.22 Table 2 presents the

estimated critical percolation thresholds for HipCo SWCNTs,

MWCNT I and MWCNT I-short. The aspect ratios calculated

from eqn (3) and (4) are also shown. However, the dynamic

movement of the particles should yield to a lower percolation

threshold (dipole momentum plus ionic conductivity); this

effect, therefore, needs to be more deeply studied.

When the values of Vex predicted by the percolation theory

for cylinders (1.4) are used, the calculated aspect ratios

obtained are higher by a factor of 6–7 than those observed

by microscopy. Using a Vex of 0.3 in eqn (3) and (4) it is

possible to obtain better agreement between the observed

ratios. The explanation for this much reduced total exclude

volume could be a very high local anisotropy in the filler

orientation,23 caused by the ultrasonication.

The percolation thresholds measured by our novel method

are one order of magnitude lower than the typical percolation

threshold values obtained for CNTs in isolating matrix

composites, usually around 0.1–0.4 wt%.24 However, using

special techniques, such as in-situ polymerization, McLachlan

et al. achieved a very low percolation threshold of 0.05 wt%25

for HipCo tubes. This value is similar to that found here for

the HipCo samples under ultrasonic agitation (0.02–0.03 wt%).

The advantages of the proposed method are most clearly

demonstrated by the results of electrical conductivity measure-

ments for various MWCNT suspensions. To achieve a con-

ductivity of 1 6 1025 S cm21, the amount of MWCNT II

material required is six times higher than that for MWCNT I

material for a given volume of suspension.

Fig. 9 shows the electrical conductivity of free standing

papers from CNT materials, measured by the four-probe

method, compared with the conductivities of the same carbon

materials, measured in a liquid medium in the dynamic

mode at 1.5 V DC for a concentration around 5 mg mL21.

Due to the differing porosity of the free standing papers,

the electrical conductivities of the papers were normalized

to their density. The results for the electrical conductivities

of free standing papers are similar to the values obtained for

the suspensions with the highest concentration. The main

difference between the two measurements was found for the

AD SWCNT material. This is due to the fact that the AD

SWCNT sample in liquid did not reach the saturation point

at the highest concentration (5 mg mL21) in chloroform

(Fig. 4a), so that an appropriate conductivity value was not

available. The normalized conductivities of the free standing

papers of AD SWCNT and MWCNT II materials are quite

similar, 30–40 S cm2 g21, while MWCNT I and MWCNT

I-short materials show normalized conductivities about

60–75 S cm2 g21. These results are in accordance with the

conductivity measurements in suspension. The electrical

conductivity measured for HipCo SWCNT material is five

times higher than that for MWCNT I material, although in the

Table 2 Observed and calculated aspect ratios for various carbon materials

Material Observed critical volume (%) Aspect ratio provided by producers (average) Calculated aspect ratio for Vex = 1.4

HipCo SWCNT 0.02 550 3700MWCNT I 0.01–0.2 750 4500MWCNT I-short 0.03–0.04 370 2000

Fig. 9 Electrical conductivity of free standing papers produced

from different carbon materials, compared with the same materials’

conductivities in liquid medium in the dynamic mode, at the highest

concentration measured (around 5 mg mL21).

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suspensions with ultrasonication, the HipCo SWCNT material

exhibits a conductivity only two times higher than that of the

MWCNT I material. This discrepancy could be explained by

the fact that in composites (with a liquid or solid matrix),

the conductivity for smaller concentrations of nanotubes is

dominated by the electrical resistance of the contacts between

the nanotubes. On the other hand, for higher concentrations of

nanotubes, the intrinsic resistance of the nanotubes starts

to play the dominant role. SWCNTs have a higher specific

conductivity than MWCNTs. Usually only the external shell

of the MWCNT participates in electrical conduction.26 Free

standing papers can be seen as extremely concentrated

composites. In their case, the intrinsic electrical conductivity

of the tubes plays the dominant role.

Conclusions

The pattern of changes over time in the electrical conductivity

of several CNT materials suspended in chloroform has been

investigated, using applied electric fields at different concen-

trations and voltages.

It was observed that the electrical conductivity of CNT

suspensions in an insulating liquid is dependent on the CNT

concentration, their aspect ratio, the type of CNTs used,

the applied electric field and the randomicity of the CNT

distribution in the liquid medium. When the liquid is not

disturbed, the nanotubes are aligned by the electric field and a

very low percolation threshold is achieved. However, when the

suspension is submitted to ultrasonication, the percolation

threshold value is closer to that for composites of randomly

dispersed CNTs in an insulating solid matrix with a strong

dependence on the average aspect ratio of the samples, while

the electrical conductivity of the suspensions follows a power

law, as predicted by classical percolation theory.

However, the values of the percolation threshold for

suspensions were found to be smaller than most reports about

solid composites with randomly aligned CNTs. A possible

explanation for this is that, under dynamic conditions,

the probability for the constantly moving nanotubes in the

suspension to form a percolation network is higher than under

static conditions.

A clear correlation was also found between the conduc-

tivities measured for suspensions of CNTs in an insulating

liquid, after reaching the percolation point, compared to those

of free standing papers. Thus, the new measurement method

presented herein promises to be a fast and inexpensive

technique for CNT characterization. The authors believe that

this method will be particularly useful for the selection of

carbon nanotube materials to be used for the preparation

of electrically conductive composites, as well as for quality

control in CNT synthesis processes. This same procedure

should also be applicable for any other conductive particles.

Acknowledgements

M.J.A. and M.D.L. are grateful for CNPq/DAAD grants. We

thank Peter van Aken and Marion Kelch for help in operating

the TEM, and Max Planck Institute for Metals Research

for providing access to the TEM. We also are grateful for

the assistance of Mr Kalman Blum for contributions in text

corrections.

References

1 Web of science search engine using the words ‘‘carbon nanotube*’’(www.isiknowledge.com).

2 A. Celzard, E. McRae, C. Deleuze, M. Dufort, G. Furdin and J. F.Mareche, Critical concentration in percolating systems containinga high-aspect-ratio filler, Phys. Rev. B, 1996, 53, 6209–6214.

3 M. E. Itkis, D. E. Perea, S. Niyogi, S. M. Rickard, M. A. Hamon,H. Hu, B. Zhao and R. C. Haddon, Purity Evaluation ofAs-Prepared Single-Walled Carbon Nanotube Soot by Use ofSolution-Phase Near-IR Spectroscopy,, Nano Lett., 2003, 3(3),309–314.

4 M. Zhang, M. Yudasaka, A. Koshio and S. Iijima,Thermogravimetric analysis of single-wall carbon nanotubesultrasonicated in monochlorobenzene, Chem. Phys. Lett., 2002,364, 420–426.

5 S. Arepalli, P. Nikolaev, O. Gorelik, V. G. Nadjiev, W. Holmes,B. Files and L. Yowell, Protocol for the characterization of single-wall carbon nanotube material quality, Carbon, 2004, 42,1783–1791.

6 M. E. Itkis, D. E. Perea, R. Jung, S. Niyogi and R. C. Haddon,Comparison of analytical techniques for purity evaluation ofsingle-walled carbon nanotubes, J. Am. Chem. Soc., 2005, 127,3439–3448.

7 Y. D. Li, J. L. Chen, Y. M. Ma, J. B. Zhao, Y. N. Qin andL. Chang, Formation of bamboo-like nanocarbon and evidence forthe quasi-liquid state of nanosized metal particles at moderatetemperatures, Chem. Commun., 1999, 1141–1142.

8 J. Mautzsch, S. Reich, C. Thomsen, S. Webster, R. Czerw,D. L. Carroll, S. M. C. Vieira, P. R. Birkett and C. A. Rego,Raman characterization of boron-doped multiwalled carbonnanotubes, Appl. Phys. Lett., 2002, 81, 2647–2649.

9 J. N. Coleman, S. Curran, A. B. Dalton, A. P. Davey,B. McCarthy, W. Blau and R. C. Barklie, Percolation-dominatedconductivity in a conjugated-polymer-carbon-nanotube composite,Phys. Rev. B, 1998, 58, R7492–R7495.

10 L. Y. Liu, Y. G. Yang and Y. F. Zhang, A study on the electricalconductivity of multi-walled carbon nanotube aqueous solution,Physica E, 2004, 24, 343–348.

11 M. O. Lisunova, N. I. Lebovka, E. V. Melezhyk and Y. P. Boiko,Stability of the aqueous suspensions of nanotubes in the presenceof nonionic surfactant, J. Colloid Interface Sci., 2006, 299,740–746.

12 L. X. Benedict, S. G. Louie and M. L. Cohen, StaticPolarizabilities of Single-Wall Carbon Nanotubes, Phys. Rev. B,1995, 52, 8541–8549.

13 K. Yamamoto, S. AkitA and Y. Nakayama, Orientation andpurification of carbon nanotubes using ac electrophoresis, J. Phys.D: Appl. Phys., 1998, 31, L34–L36.

14 X. Q. Chen, T. Saito, H. Yamada and K. Matsushige, Aligningsingle-wall carbon nanotubes with an alternating-current electricfield, Appl. Phys. Lett., 2001, 78, 3714–3716.

15 M. R. Diehl, S. N. Yaliraki, R. A. Beckmann, M. Barahona andJ. R. Heath, Angew. Chem., 2002, 114, 363.

16 L. A. Nagahara, I. Amlani, J. Lewenstein and R. K. Tsui, Directedplacement of suspended carbon nanotubes for nanometer-scaleassembly, Appl. Phys. Lett., 2002, 80, 3826–3828.

17 R. Krupke, F. Hennrich, H. B. Weber, D. Beckmann, O. Hampe,S. Malik, M. M. Kappes and H. V. Lohneysen, Contacting singlebundles of carbon nanotubes with alternating electric fields, Appl.Phys. A, 2003, 76, 397–400.

18 S. Badaire, V. Pichot, C. Zakri, P. Poulin, P. Launois, J. Vavro,C. Guthy, M. Chen and J. E. Fischer, Correlation of propertieswith preferred orientation in coagulated and stretch-aligned single-wall carbon nanotubes, J. Appl. Phys., 2004, 96, 7509–7513.

19 I. Balberg, N. Bibenbaum and N. Wagner, Percolation Thresholdsin the 3-Dimensional Sticks System, Phys. Rev. Lett., 1984, 52,1465–1468.

20 K. Yamamoto, S. Akita and Y. Nakayama, Orientation of carbonnanotubes using electrophoresis, Jpn. J. Appl. Phys., Part 2, 2006,35(7B), L917–L918.

4852 | J. Mater. Chem., 2007, 17, 4846–4853 This journal is � The Royal Society of Chemistry 2007

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21 J.-M. Benoit, B. Corraze, S. Lefrant, P. Bernier and O. Chauvet,Electric transport properties and percolation in carbon nanotubes/PMMA composites, Mater. Res. Soc. Symp. Proc., 2002, 706,85–90.

22 J. M. Benoit, B. Corraze, S. Lefrant, P. Bernier and O. Chauvet,Electric transport properties and percolation in carbon nanotubes/PMMA composites, Mater. Res. Soc. Symp. Proc., 2001, 706,85–90.

23 I. Balberg, ‘‘Universal’’ percolation-threshold limits in the con-tinuum, Phys. Rev. B, 1985, 31, 6.

24 V. Skakalova, U. Dettlaff-Weglikowska and S. Roth, Electricaland mechanical properties of nanocomposites of single wall carbonnanotubes with PMMA, Synth. Met., 2005, 152, 349–352.

25 D. S. McLachlan, C. Chiteme, C. Park, K. E. Wise, S. E. Lowther,P. T. Lillehei, E. J. Siochi and J. S. Harrison, AC and DCpercolative conductivity of single wall carbon nanotube polymercomposites, J. Polym. Sci., Part B: Polym. Phys., 2005, 43,3273–3287.

26 Z. L. Wang, C. Hui, Electron Microscopy of nanotubes, KluwerAcademic Publishers, Boston, 2003, pp. 215–216.

This journal is � The Royal Society of Chemistry 2007 J. Mater. Chem., 2007, 17, 4846–4853 | 4853

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