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Magnetic field induced delocalization in multi-wallcarbon nanotube-polystyrene composite at highfields

0008-6223/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.carbon.2013.12.038

* Corresponding author: Fax: +91 (80) 2360 2602.E-mail address: bhatia.phy@gmail.com (R. Bhatia).

Ravi Bhatia a,*, Jean Galibert b, Reghu Menon a

a Department of Physics, Indian Institute of Science, Bangalore 560012, Indiab Laboratoire National des Champs Magnetiques Intenses, CNRS/UPS/INSA/UJF, F-31400 Toulouse, France

A R T I C L E I N F O

Article history:

Received 28 July 2013

Accepted 11 December 2013

Available online 17 December 2013

A B S T R A C T

In well dispersed multi-wall carbon nanotube-polystyrene composite of 15wt%, with room

temperature conductivity of �5 S/cm and resistivity ratio [R2 K/R200 K] of �1.4, the tempera-

ture dependence of conductivity follows a power-law behavior. The conductivity increases

with magnetic field for a wide range of temperature (2–200 K), and power-law fits to con-

ductivity data show that localization length (n) increases with magnetic field, resulting in

a large negative magnetoresistance (MR). At 50T, the negative MR at 8 K is �13% and it

shows a maximum at 90 K (�25%). This unusually large negative MR indicates that the field

is delocalizing the charge carriers even at higher temperatures, apart from the smaller

weak localization contribution at T < 20 K. This field-induced delocalization mechanism

of MR can provide insight into the intra and inter tube transport.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Although the charge transport in disordered quasi-one

dimensional systems like multi-wall and single-wall carbon

nanotubes (MWCNTs and SWCNTs) has been widely inves-

tigated [1–12], including MWCNT inside a polymer matrix

[13–17], subtle variations in the nanoscale organization of

carbon nanotubes (CNTs) can modify the results. The usual

temperature dependence of resistivity cannot fully clarify

the complexity among a wide range of transport mecha-

nisms, and sometimes it is possible to observe unexpected

outcomes. In the charge transport of CNT and its compos-

ites, the complications arising from intra versus inter tube

transport in presence of barriers are yet to be understood

in detail.

Earlier studies in both MWCNT and SWCNT have shown

that variations in defects, length and diameter of tubes can

affect the intra and inter-tube conduction mechanisms; as a

result hopping, tunneling and coherent transport processes

have been observed [2–12]. Nevertheless, in pristine and

doped CNT the low temperature conductivity data can iden-

tify the transport mechanism [4,5,7,9,12]. High quality CNT

tend to show metallic behavior with contributions from weak

localization (WL) and electron–electron interactions (EEI)

depending on disorder; and in highly defect prone and disor-

dered tubes the hopping transport dominates [3–5]. In our ear-

lier work we have shown that the contributions from these

mechanisms can be sorted out from both low temperature

conductivity and magnetoresistance (MR) data [5]. However,

in CNT composites the situation is quite ambiguous, and

there are two categories: one near the percolation threshold

(�0.4 wt%) and the other at rather higher weight fraction of

CNT (�5–30 wt%) [13–17]. In the former, the dominance of

hopping type transport is usually observed, and in latter a

combination of mechanisms has been envisaged, but not

thoroughly studied yet.

Fig. 1 – SEM micrograph of 15 wt%. MWCNT–PS composite.

C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8 373

The room temperature conductivity in CNT composites in-

creases with weight fraction, following the theory of percola-

tion [18]. It is known that in CNT-polymer composites the

temperature dependence of conductivity is quite pronounced

near percolation threshold and becomes weaker as the CNT

weight fraction increases [13–17]. However, this is not straight

forward as heterogeneous nanoscale materials and structures

are affected by several geometrical and physical factors, like

presence of imperfect interfaces [19], and in addition sample

preparation procedure affects the nanomorphology which

substantially modifies the low temperature charge transport.

This scenario can be evaluated from the resistivity ratio [R2 K/

R200 K] of samples, and it decreases considerably at the onset

of dominant coherent transport [14]. This qualitative feature

has to be understood in detail from the relaxation and scat-

tering mechanisms involved in nanoscale transport, by inves-

tigating how the magnetic field alters low temperature

conductivity. In the case of CNT-polymer composite of inter-

mediate weight fraction (10–20 wt%) the conductivity is ob-

served to decrease exponentially with temperature and

models like variable range hopping (VRH) and fluctuation in-

duced tunneling (FIT) are used to describe the conduction

mechanisms [14]. However, if the conductivity is weakly

dependent on temperature, i.e. it lies near the metal–insula-

tor boundary; it is possible to observe power law behavior

[17]. In CNT and its composites both positive and negative

magnetoconductance (MC) are observed at low temperatures,

the positive MC indicates towards the dominance of WL and

negative MC shows the presence of EEI [3–5,7,9,12]. Also, a

crossover from positive MC (at lower magnetic field) to nega-

tive MC (at higher magnetic field) is observed in SWCNT indi-

cating the dominance of both WL and EEI mechanisms

[7,9,12]. Most of the magnetotransport studies in CNT systems

are carried out at fields below 20T [1–7,9,12–17]. However,

Ksenevich et al. [20] have studied the low temperature charge

transport at fields up to 40T in SWCNT fibers and observed a

positive (showing a maximum of 25% @ 2.2 K @ 40T) MR. How-

ever, the temperature dependence of conductivity and MR are

often not in agreement with the used models, since a large

positive MR in VRH and a weakly temperature dependent

small MR in FIT model is expected [21,22].

In this work the charge transport properties of multi-wall

carbon nanotube–polystyrene (MWCNT–PS) composite of

15 wt% are investigated down to 2 K and at fields up to 50T.

The temperature dependence of conductivity does not follow

the usual hopping models and a large negative MR, even at

T > 30 K, has been observed. These results are not consistent

with the conventional models of charge transport in disor-

dered systems.

2. Experimental

MWCNT were grown by chemical vapor deposition of a mix-

ture of toluene and ferrocene [5]. The average length and

diameter of tubes are 100 lm and 50 nm, respectively. Polysty-

rene (PS, from Sigma Aldrich) and 15 wt% of MWCNT are

mixed in toluene by ultrasonication, and then casted onto

alumina substrate to obtain composite film of thickness

�60 lm. FEI Quanta 200 is used to obtain scanning electron

microscope (SEM) image of well-separated and randomly dis-

tributed MWCNT in PS matrix, as in Fig. 1. The transport mea-

surements were performed on samples of dimensions around

8 mm · 2 mm by the standard linear four-probe technique.

Electrical contacts were made by conducting silver paste; with

the separation between contacts �1.5 mm. For conductivity

measurements, constant currents in the range of 0.1–1 lA

were used to avoid any sample heating at low temperatures,

and the voltages were measured by the standard low fre-

quency lock-in amplifier. Temperature and magnetic field

dependence of the resistance are measured down to 2 K and

fields up to 50T using a pulsed magnet with pulse duration

�400 ms. Transverse magnetoresistance measurements were

carried out at Laboratoire National des Champs Magnetiques

Intenses, CNRS-Toulouse, France.

3. Results and discussion

The weight fraction of MWCNT in PS matrix is in the interme-

diate range so that a balanced intra versus inter tube trans-

port is expected to occur. At 15 wt% of MWCNT, it is well

above the percolation threshold, and at higher wt% the intrin-

sic metallic transport in MWCNT could overwhelm the bulk

transport as the inter-tube interaction increases. The SEM

micrograph of 15 wt% in Fig. 1 shows a combination of both

inter-tube junctions and uninterrupted portions of long tubes

present in the sample. It is interesting to compare the trans-

port properties of this 15 wt% MWCNT–PS sample to a similar

one published in literature, and the closest one we found is a

20 wt% MWCNT–polymethylmethacrylate (PMMA) composite

[14], as shown in Fig. 2. Although the room temperature con-

ductivity of these samples is of the same order of magnitude,

the temperature dependence of conductivity is quite differ-

ent. The temperature dependence of conductivity down to

2 K is rather weak for 15 wt% MWCNT–PS sample and the ra-

tio of zero field conductivity (rr) from 200 to 2 K is 1.4, which is

considerably low. Whereas the conductivity shows pro-

nounced temperature dependence in the case of 20 wt%

Fig. 2 – Conductivity (r) vs. temperature (T) of 15 wt%

MWCNT–PS composite at various magnetic fields and r vs. T

of 20 wt% MWCNT–PMMA composite. (A color version of

this figure can be viewed online.)

Fig. 3 – (a) Temperature dependence of reduced activation

energy (W) of 15 wt% MWCNT–PS and 20 wt% MWCNT–

PMMA composites. (b) Linear fits to the conductivity data of

15 wt% MWCNT–PS composite at various magnetic fields

(log–log scale) according to Eq. (1). (A color version of this

figure can be viewed online.)

374 C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8

MWCNT–PMMA sample, with rr around 500 [14], indicating

that the presence of an additional 5 wt% of more MWCNT

could not make the system more metallic. Obviously this

low value of rr < 2 in 15 wt% MWCNT–PS suggests that the

system is at the metal–insulator boundary, and the 20wt%

MWCNT–PMMA (rr � 500) is in the insulating regime. Thus,

the low value of rr in the former indicates that tubes are of

high quality and its dispersion in polymer matrix is very good

in the present work, as in the SEM image (see Fig.1). This qual-

itative feature in the temperature dependence of conductivity

is further verified by taking the logarithmic derivative [i.e., re-

duced activation energy, W = d( lnr)/d(lnT)] and its tempera-

ture dependence is shown in Fig. 3(a). The temperature

independent W(T) plot for 15 wt% MWCNT–PS sample clearly

shows that the system is near the metal–insulator transition;

whereas in case of 20wt% MWCNT–PMMA the linear negative

temperature coefficient is similar to that observed in usual

exponential model for insulating systems. The temperature

independent W(T) for 15 wt% MWCNT–PS indicates that the

conductivity follows a power-law behavior, as shown by Lar-

kin and Khmelnitskii (Ref. 23). Further, it is interesting to ob-

serve that the conductivity increases with magnetic field and

tends to saturate above 25T, though the field does not alter

the feature of the drop in conductivity around 20 K (see

Fig. 2), indicating that the usual metallic behavior in pristine

MWCNT is being modified; however this decrease in conduc-

tivity of 15 wt% MWCNT–PS composite is not substantial en-

ough to show an insulating behavior with hopping transport.

This unusual scenario in 15 wt% MWCNT–PS indicates

that both the temperature and magnetic field dependence of

conductivity do not follow conventional models, and this is

possibly due to the complex transport within the MWCNT

network, in which both intra and inter-tube transport play

major roles. This is verified from a log–log plot of the temper-

ature dependence of conductivity as in Fig. 3(b). The straight

line fits, even at high fields, show that the data follow a

power-law, i.e. r / Tb. Although such a power-law behavior

has been predicted for systems near the critical regime of me-

tal–insulator transition, and the value of b is expected to be in

the range of 0.3–1 (Ref. 23); and the fits to data in Fig. 3(b)

show that b is around 0.1. Hence the conductivity data neither

follow the disordered metallic model nor the exponential

behavior [21,22]. Though other alternatives can be considered

due to charging or tunneling mechanisms [24], but it is not

consistent with the power-law fit. The interesting feature in

this unusual behavior is that the field increases the conduc-

tivity significantly without any deviation from the power-

law fit, though the value of b increases marginally at higher

fields. This indicates that the mechanism involves a field-in-

duced delocalization of carriers to enhance the conductivity.

Hence the essential ingredients that could play a role in this

field-induced delocalization involve the localization length,

the presence of barriers for inter-tube transport and thermal

activation to some extent. Since the field is not expected to

Fig. 4 – Resistance vs. magnetic field of 15 wt% MWCNT–PS

composite at various temperatures in the magnetic fields up

to 50T. (A color version of this figure can be viewed online.)

C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8 375

modify the latter two parameters significantly, the increase in

localization length at higher fields could augment the con-

ductivity. To our knowledge, the theoretical models taking

all these factors into account are lacking since the complexity

involved in the charge transport in such a network is yet to be

fully understood. However, we find that a phenomenological

model could explain this field-induced delocalization, as ex-

pressed below:

rðTÞ ¼ r�nw

� �kBTEA

� �b

ð1Þ

where w is the barrier width at the inter-tube interface, n is

the localization length, EA is the activation energy for inter-

tube transport, r� is the extrapolated value of conductivity

at very low temperatures and b is the exponent. The Eq. (1)

is modified form of power-law equation and phenomenologi-

cal model which explains the observed weak temperature

dependence of conductivity and large negative magnetoresis-

tance by considering various parameters such as localization

length, activation energy and barrier width [23]. Although

there are many variables in Eq. (1) to obtain a good fit, the va-

lue of these parameters are constrained within a certain

range. An average value for w can be obtained from the statis-

tical analysis of transmission electron microscopy images of

the inter-tube junctions, which is around 5 nm. Since the

sample is nearly metallic, as inferred from the temperature

dependence of conductivity, the value of b is expected to be

slightly lower than that of 0.3. From previous studies in sim-

ilar CNT systems it is known that value of n is within the

range of 10–20 nm [16,25]. Since the temperature dependence

of conductivity is rather weak, the value for EA is expected to

be in few meV range, and also suggesting that the barriers

present at inter-tube junctions are rather thin. The fits to

Eq. (1) at various fields are shown in Fig. 3(b) and the values

are listed in Table 1. Only the values of b [0.08 (at 0T) and

0.12 (at 25T)] and n [10.06 nm (at 0T) and 14.1 nm (at 25T)] vary

with the field, as indicated by the increasing slopes at higher

fields. Hence the random potential barriers present at the in-

ter-tube junctions are sufficiently thin [barrier width,

w � 4 nm] to facilitate field-induced delocalization of carriers.

Instead, if the barriers were thicker [w P 14 nm] the effect of

field could not have such a significant effect on the conductiv-

ity. This is justified from the rather weak temperature depen-

dence of conductivity and the increase in conductivity at high

fields in 15 wt% MWCNT–PS sample. In order to highlight

these features a comparison of the charge transport in

20 wt% MWCNT–PMMA shows contrasts in behavior. Further,

the appropriateness of this model is explained below in the

analysis of MR data.

Table 1 – The fitting parameters for the low temperature condu

Applied Magneticfield (T)

r� (S/cm) Barrier width,w (nm)

Locn (n

0 2.61 4.46 10.4 2.75 4.41 11.

10 2.85 4.40 12.25 2.91 4.38 14.

The variation of resistance in 15 wt% MWCNT–PS as a

function of magnetic field, from 2 to 200 K, is shown in

Fig. 4. At all temperatures the resistance decreases with

increasing field, and the initial drop at lower fields is larger

and then it tends to saturate at higher fields. The relative

changes in the resistance at different temperatures can be ob-

served in the usual MR plot as shown in Fig. 5, and the max-

imum negative MR is observed at 90 K and the minimum at

8 K. The interesting finding is that the field increases the con-

ductivity even at temperatures as high as 200 K, which is

rarely observed in CNT and its composites, since the effect

of field on conductivity usually occurs at T < 30 K, with the

exceptions in giant magnetoresistance systems. To our

knowledge, this large negative MR for such a wide range of

temperature is not observed in usual systems. The well-

known models for negative MR in disordered metals due to

WL cannot explain the data at all fields and temperatures,

since the negative MR due to WL is typically below 5% at

T < 20 K. To bring these results in perspective a comparison

of the MR data (up to field of 9T) of both 15 wt% MWCNT–PS

and 20 wt% MWCNT–PMMA samples is necessary, which is

shown in Fig. 6. In latter both the magnitude (�5% at 5 K

and 9T) and temperature dependence of MR (�2% at 30 K

and 9T) can be explained within the WL framework; on the

contrary a large positive MR is expected if the hopping trans-

port is rather significant. However, in 15 wt% MWCNT–PS, MR

vs. H data show quite different trend with a large negative MR

(12% at 50 K and 9T) which is not consistent with the WL

ctivity data according to Eq. (1).

alization length,m)

Activation energy,EA (meV)

Exponent, b

6 14.2 0.084 13.8 0.095 13.6 0.111 13.3 0.12

Fig. 5 – Magnetoresistance vs. magnetic field of 15 wt%

MWCNT–PS composite at various temperatures. (A color

version of this figure can be viewed online.)

Fig. 6 – Comparison of magnetoresistance data of 15 wt%

MWCNT–PS and 20 wt% MWCNT–PMMA composites at

various temperatures in the magnetic fields up to 9T. (A

color version of this figure can be viewed online.)

Fig. 7 – Magnetoresistance vs. temperature of 15 wt%

MWCNT–PS composite at various fields. (A color version of

this figure can be viewed online.)

376 C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8

model. The main difficulty is that the existing theoretical

models for the behavior of MR in such complex systems are

lacking to provide an explanation for this field-induced delo-

calization of carriers for a wide range of temperature. The

temperature dependence of MR does not follow any particular

model and its trend is mixed up, since the negative MR in-

creases from 8 K (�13% at 50T) to 90 K (�25% at 50T), and

the values at 2 and 200 K are in between, as in Fig. 5. This indi-

cates that several mechanisms are dominating at different

temperature ranges, and to sort them out is not trivial.

The MR data show that the transport mechanism as a

function of temperature and magnetic field are entangled.

However, a plot of MR vs. temperature at various fields, as

in Fig. 7, suggests that it is possible to deconvolute the regions

in which a particular mechanism is dominant. Fig. 7 shows

that there are four distinct regions: from 2 to 8 K (region I), 8

to 20 K (region II), 20 to 90 K (region III) and 90 to 200 K (region

IV). In regions I and IV the magnitude of the negative MR de-

creases upon increasing the temperature and in other two it

increases. However, the variation in slopes of regions II and

III are different, in former the negative MR increases rapidly.

This behavior in MR is consistent at all fields with slight vari-

ations, except at fields below 2T. In region I, the negative MR

at 2 K is larger than that at 8 K indicating that an additional

contribution from WL at T < 8 K is playing a role, and its effect

gradually decreases by T � 20 K. In region II, the negative MR

increases rapidly due to the dominant contribution from

field-induced delocalization. However, it weakens in region

III due to the increasing electron–phonon scattering, as ob-

served by the slope change in Fig. 7. At T > 90 K, (region IV)

the thermally activated scatterings dampen the effect of field;

though the MR is still negative suggesting that field-induced

delocalization cannot be easily smeared off and it can persist

to temperatures as high as 200 K. Hence the MR data for a

wide range of temperature and field show that apart from

the conventional WL contribution at T < 20 K, the additional

dominant contribution from field-induced delocalization is

necessary to explain this large negative MR that extends to

higher temperatures.

Both conductivity and MR data show that the mechanism

of charge transport undergoes some variation at T � 10 K. At

T > 10 K, the role of inter-tube transport becomes important

due to thermal activation; however at T < 10 K it is possible

to observe the role of intra-tube transport as indicated by

the additional WL contribution to negative MR, since the long

and well-dispersed highly conducting MWCNT are expected

to have quantum corrections at very low temperatures. The

low field MC due to WL is given by the following expression

[17].

DrðH;TÞ ¼ ½ð1=12 p2Þðe=�hÞ2G0ðlinÞ3H2� ð2Þ

where G0 ¼ e2=�h and lin is the inelastic scattering length. The

low field (H < 1T) H2 fits of the MC data at T < 20 K are shown

in Fig. 8, the values of lin at various temperatures can be deter-

Fig. 8 – Dr vs. H2 fits 15 wt% MWCNT–PS composite at low

magnetic fields, according to Eq. (2). (A color version of this

figure can be viewed online.)

C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8 377

mined from the slopes of linear fit to Eq. (2). The values of linat 2 and 20 K are 3.2 and 2.5 nm, respectively. The value of linprobes the intrinsic intra-tube transport; and it is interesting

to compare this number with the barrier width of �4 nm

which is one of the representative parameter involved in in-

ter-tube transport. The numbers for both of these parameters

are rather close indicating that both intra and inter tube

transport are important in bulk transport. However, the value

of localization length (n = 10–14 nm) is larger than lin and w

indicating that in CNT the delocalized states can be well ex-

tended due to its tubular structure. In tubular structures the

mesoscopic wave function of delocalized states can circum-

vent point-like imperfections or barriers at the inter-tube

junctions, unlike in case of nanorod-like structures. The

observation of this large value of localization length implies

that the extent of inter-tube delocalization of electronic states

in MWCNTs can be substantial, especially when the inter-

tube barriers are thinner. In typical random network of nano-

scale conductors the localization of carriers is rather strong,

and this usually results in large positive MR due to hopping

transport. On the contrary, the observation of large negative

MR in MWCNT–PS system due to the delocalization of elec-

tronic states, for a wide range of temperature and fields, is a

rather special case due to the presence of thinner inter-tube

barriers.

4. Conclusions

The temperature dependence of conductivity is observed to

be rather weak in 15 wt% MWCNT–PS sample and it follows

a power-law behavior. At ultra-high magnetic fields the con-

ductivity increases, which is indicative of the delocalization

of carriers. A large negative relative magnetoresistance has

been observed for a wide range of temperature (2–200 K) in

the magnetic fields up to 50T. The data analysis shows that

localization length (n) increases at high fields in accordance

with the power-law.

Acknowledgments

We acknowledge the support of the LNCMI-CNRS, member of

the European Magnetic Field Laboratory (EMFL).

R E F E R E N C E S

[1] Langer L, Stockman L, Heremans JP, Bayot V, Olk CH, VanHaesendonck C, et al. Electrical resistance of a carbonnanotube bundle. J Mat Res 1994;9(4):927–32.

[2] Langer L, Bayot V, Grivei E, Issi JP, Heremans JP, Olk CH, et al.Quantum transport in a multiwalled carbon nanotube. PhysRev Lett 1996;76(3):479–82.

[3] Yosida Y, Oguro I. Variable range hopping conduction inmultiwalled carbon nanotubes. J Appl Phys 1998;83(9):4985–7.

[4] Baxendale M, Mordkovich VZ, Yoshimura S, Chang RPH.Magnetotransport in bundles of intercalated carbonnanotubes. Phys Rev B 1997;56(4):2161–5.

[5] Bhatia R, Prasad V, Menon R. Probing the inter-tube transportin aligned and random multiwall carbon nanotubes. J ApplPhys 2011;109(5):053713.

[6] Wang DP, Feldman DE, Perkins BR, Yin AJ, Wang GH, Xu JM,et al. Hopping conduction in disordered carbon nanotubes.Solid State Commun 2007;142(5):287–91.

[7] Jaiswal M, Wang W, Fernando KAS, Sun YP, Menon R. Chargetransport in transparent single-wall carbon nanotubenetworks. J Phys Condens Matter 2007;19(44):446006.

[8] Fuhrer MS, Cohena ML, Zettla A, Crespic V. Localization insingle-walled carbon nanotubes. Solid State Commun1999;109(2):105–9.

[9] Jaiswal M, Wang W, Fernando KAS, Sun YP, Menon R.Magnetotransport in transparent single-wall carbonnanotube networks. Phys Rev B 2007;76(11):113401.

[10] Cumings J, Zettl A. Localization and nonlinear resistance intelescopically extended nanotubes. Phys Rev Lett2004;93(8):086801.

[11] Vavro J, Kikkawa JM, Fischer JE. Metal-insulator transition indoped single-wall carbon nanotubes. Phys Rev B2005;71(15):155410.

[12] Choudhury PK, Jaiswal M, Menon R. Magnetoconductance insingle-wall carbon nanotubes: electron–electron interactionand weak localization contributions. Phys Rev B2007;76(23):235432.

[13] Chauvet O, Benoit JM, Corraze B. Electrical, magneto-transport and localization of charge carriers innanocomposites based on carbon nanotubes. Carbon2004;42(5–6):949–52.

[14] Kim HM, Choi MS, Joo J, Cho SJ, Yoon HS. Complexity incharge transport for multiwalled carbon nanotube andpoly(methyl methacrylate) composites. Phys Rev B2006;74(5):054202.

[15] Choudhury PK, Ramaprabhu S, Ramesh KP, Menon R.Correlated conformation and charge transport in multiwallcarbon nanotube-conducting polymer nanocomposites. JPhys Condens Matter 2011;23(26):265303.

[16] Benoit JM, Corraze B, Chauvet O. Localization, Coulombinteractions, and electrical heating in single-wall carbonnanotubes/polymer composites. Phys Rev B2002;65(24):241405.

[17] Bhatia R, Sangeeth CSS, Prasad V, Menon R. Unusualmetallic-like transport near the percolation threshold. ApplPhys Lett 2010;96(24):242113.

[18] Stauffer D, Aharony A, editors. Introduction to percolationtheory. London: Taylor & Francis Press; 1992.

378 C A R B O N 6 9 ( 2 0 1 4 ) 3 7 2 – 3 7 8

[19] Pavanello F, Manca F, Palla PL, Giordano S. Generalizedinterface models for transport phenomena: unusual scaleeffects in composite nanomaterials. J Appl Phys2012;112(8):084306.

[20] Ksenevich VK, Odzaev VB, Martnas Z, Seliuta D, Valusis G,Galibert J, et al. Localization and nonlinear transport insingle walled carbon nanotube fibers. J Appl Phys2008;104(7):073724.

[21] Mott NF, Davis EA, editors. Electronic processes innoncrystalline materials. Oxford: Clarendon Press; 1979.

[22] Sheng P, Sichel EK, Gittleman JI. Fluctuation-inducedtunneling conduction in carbon–polyvinylchloridecomposites. Phys Rev Lett 1978;40(18):1197–200.

[23] Larkin AI, Khmelnitskii DE. Activation conductivity indisordered systems with large localization length. Sov PhysJETP 1982;56(3):647–52.

[24] Augelli V, Ligonzo T, Masellis MC, Muscarella MF, Schiavulli L,Valentini A. Electrical properties of gold–polymer compositefilms. J Appl Phys 2001;90(3):1362.

[25] Choi ES, Brooks JS, Eaton DL, Al-Haik MS, Hussaini MY,Garmestani H, et al. Enhancement of thermal and electricalproperties of carbon nanotube polymer composites bymagnetic field processing. J Appl Phys 2003;94(9):6034.