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