Dc and ac characterizations of electrical conducting nanoporous carbon structures based on resorcinol-formaldehyde

Article abstract of DOI:10.1016/j.jpcs.2011.12.007

Structural, electrical and morphological properties of electrical conducting nanoporous carbon structures, prepared at different pyrolysis temperatures by solgel method, were investigated. The effect of the measurement temperature on the electrical properties of the obtained sample pyrolysed at 675 °C was studied. The imaginary and real parts of the sample impedance versus frequency, in the range of 40 Hz100 MHz, are investigated. The Nyquist diagrams were used to identify an equivalent circuit and the fundamental parameters of the circuit are determined at different temperatures with the aim to study the contributions of the grains and boundary grains to the conductivity.

Full text of DOI:10.1016/j.jpcs.2011.12.007

Journal of Physics and Chemistry of Solids 73 (2012) 707–712
Contents lists available at SciVerse ScienceDirect
Journal of Physics and Chemistry of Solids
journal homepage: www.elsevier.com/locate/jpcs
dc and ac characterizations of electrical conducting nanoporous carbon
structures based on resorcinol-formaldehyde
n
I. Najeh a, N. Ben Mansour a, H. Dahman a, A. Alyamani b, L. El Mir a,c,
a
ꢀ
ꢀ
ꢀ
Laboratoire de Physique des Mate´riaux et des Nanomate´riaux Applique´e a l’Environnement, Faculte´ des Sciences de Gabes, Universite´ de Gabes, Cit´e Erriadh Manara Zrig,
ꢀ
6072 Gabes, Tunisie
b National Nanotechnology Research Centre, KACST, Riyadh, Saudi Arabia
c Al-Imam Muhammad Ibn Saud Islamic University, College of Sciences-Physics Department, 11623 Riyadh, Kingdom of Saudi Arabia
a r t i c l e i n f o
a b s t r a c t
Article history:
Structural, electrical and morphological properties of electrical conducting nanoporous carbon
structures, prepared at different pyrolysis temperatures by sol–gel method, were investigated. The
effect of the measurement temperature on the electrical properties of the obtained sample pyrolysed at
675 1C was studied. The imaginary and real parts of the sample impedance versus frequency, in the
range of 40 Hz–100 MHz, are investigated. The Nyquist diagrams were used to identify an equivalent
circuit and the fundamental parameters of the circuit are determined at different temperatures with
the aim to study the contributions of the grains and boundary grains to the conductivity.
& 2011 Elsevier Ltd. All rights reserved.
Received 6 December 2010
Received in revised form
16 November 2011
Accepted 14 December 2011
Available online 28 December 2011
Keywords:
A. Nanoporous materials
A. Organic compounds
B. Sol–gel
D. Electronic transport properties
1. Introduction
mechanisms in this material. By the complex impedance method,
we discuss the relation between the electric conductivity and
The electrical properties of carbon materials derived from
organic precursors have been studied extensively over the years
and it has been shown that they vary widely depending on the
nature of the precursor and the heat treatment temperature (HTT)
[1–6]. Due to their appropriate easiness at work and for their
fundamental interest, measures of electric resistance appeared
very early in the amorphous matter [7–11]. The study of the
electric behavior of RF-675 (RF-675) sample was achieved by
impedance spectroscopy. An amorphous material can be thus
modeled by a set of cells that are elementarily corresponding to
grains, separated by a grain boundary phase possessing different
conductivities. In most cases, after modeling samples by equiva-
lent circuits, it will be possible to understand their different
macroscopic behaviors of the electronic transport.
grains drivers and the boundary.
2. Experimental details
The synthesis of electrical conducting carbon (ECC) structures
has been done in three steps as described elsewhere [1]. The
samples were prepared by mixing formaldehyde (F) with dis-
solved resorcinol (R) in acetone (A) solution and using picric acid
as catalyst and pyrolysed at different temperatures in the range
600–1000 1C. The samples used for electrical measurements were
prepared by sculpting the ECC monolith on a parallelepiped shape
(10 ꢀ 10 ꢀ 2) mm3 and silver painted on two parallel faces for
ohmic contacts. The XRD patterns of ECC were carried out at room
temperature by a Bruker D5005 diffractometer, using Co K
˚
l¼1.78901 A) over the range of 5–801 (2y). Electrical
a
In the first part of this work, we describe the features of the
continuous conductivity and we show that the electric conduc-
tivity in asset coal is produced by hopping mechanism [12].
In the second part, we used these results to study the
disorganization of coal, and to better understand the conductivity
radiation (
measurements in a temperature range of 80–300 K were investi-
gated using a liquid nitrogen cryostat where the samples were
kept under vacuum during the measurements. Current–voltage
measurements were performed using
a computer-controlled
setup comprising a Keithley 220 current source and an Agilent
34401A multimeter. For ac measurements, an Agilent 4294A
impedance analyzer was used to collect impedance measurements
over a wide frequency range (40 Hz–100 MHz). We employed a
parallel mode to measure conductance G using an alternating
signal with voltage amplitude of 50 mV. The experimental results
n Corresponding author at: Laboratoire de Physique des Materiaux et des
´
ꢀ ꢀ
a l’Environnement, Faculte´ des Sciences de Gabes,
Nanomate´riaux Applique´e
ꢀ
ꢀ
Universite´ de Gabes, Cite´ Erriadh Manara Zrig, 6072 Gabes, Tunisie.
Tel.: þ216 97408756; fax: þ216 75 392 421.
E-mail address: Lassaad.ElMir@fsg.rnu.tn (L. El Mir).
0022-3697/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2011.12.007

708
I. Najeh et al. / Journal of Physics and Chemistry of Solids 73 (2012) 707–712
were fitted using the Z-View software to obtain the absolute values
of all components of the proposed equivalent electrical circuits.
3. Results and discussion
Fig. 1 exhibits the XRD patterns of the (ECC) synthesized
product as dried at 150 1C (RF-150) and after heat treatment at
675 1C (RF-675) and 1000 1C (RF-1000) in nitrogen atmosphere.
According to these diffractograms, the samples are partly amor-
phous even after pyrolysis. However, for RF-1000 two small bands
centered at around 251 and 441, corresponding to (0 0 2) and
(1 0 1) planes, respectively, appear, indicating the beginning of a
graphitization . In fact, detected bands are related to the most
intensive diffraction peaks of crystalline graphite phase. The
average grain size can be calculated using the Scherer equation
[13] as follows:
50 nm
0:9
l
G ¼
ð1Þ
BcosyB
Fig. 2. TEM micrograph of RF-675 sample.
where is the X-ray wavelength,
l
yB is the maximum of the Bragg
diffraction peak (in radians) and B is the line width at half
maximum. After a correction for the instrumental broadening,
the average value of the crystallites was found to be about 2 nm.
Fig. 2 displays TEM micrograph of RF-675; the sample exhibits
significant nanoporous morphology in which pore sizes are about
50 nm in diameter. The dc bulk conductivity results as a function
of the pyrolysis temperature for measurement temperature in the
range (80–300) K are plotted in Fig. 3.
It is well known that all conductive composites show a percola-
tion threshold characteristic, which may depend on the nature, the
particles sizes and the spatial distribution of the conductor into the
used insulating polymer matrix [2,3]. Furthermore, there is a region
in the percolation curve where the conductivity of the composite
changes abruptly as the conductor content is increased. This change
occurs near the percolation threshold and has the same behavior of
the plots illustrated in Fig. 3. According to the fact that percolation
theory predicts a critical concentration of percolation threshold at
which conductive paths are formed in the composite, leading to a
conversion from an insulator to a more conductor material [14–18],
it is useful to define in our study the percolation threshold by a
critical conduction temperature (CCT) TC as illustrated in Fig. 3. It
means that when the RF xerogel is heated, the polymeric particles
can be transformed to electrical conductive carbon particles and the
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
100 K
140 K
180 K
220 K
260 K
300 K
600
650
700
750
Tp (°C)
800 850 900 950 1000 1050
Fig. 3. The dc conductivity isotherms versus pyrolysis temperatures.
TC is the pyrolysis temperature corresponding to the beginning of
conductive path formation. It is shown from Fig. 3 that the CCT for
this material is located between 600 and 700 1C. In order to
determine the critical conduction temperature values, the conduc-
tivity versus pyrolysis temperatures was fitted to a power law
proposed by El Mir et al. [19] and given by
(002)
(101)
n
s
¼ AðTPꢁTCÞ
ð2Þ
where
s
is the dc conductivity of the ECC, TP is the pyrolysis
(c)
temperature, TC is the critical conduction temperature, A and n are
the fitting parameters. The studies of resorcinol formaldehyde have
shown that the electrical characteristics are highly dependent on the
pyrolysis temperature and that there is a sample conductivity
change of about seven orders of magnitude when the HTT is varied
between 600 1C and 1000 1C. This increase may be due in part to the
conversion of amorphous carbon into a semi-crystalline phase. The
emergence of XRD graphite related bands for sample pyrolysed at
1000 1C, as shown in Fig. 1, may consolidate this hypothesis.
Reported values of the critical exponent, n, are ranging between
3 and 3.2. Lee et al. [20–22] found an exponent n¼3.1 in a material
presenting insulator spherical inclusions distributed in a driver.
The V–I characteristics of RF-675 sample, at different tempera-
tures, are shown in Fig. 4. At To200 K, some regions with negative
differential resistance (NDR) are observed. As the bias current
(b)
(a)
10 20 30 40 50 60 70 80 90
0
2θ (degree)
Fig. 1. XRD patterns of: (a) RF-150, (b) RF-675, and (c) RF-1000.

I. Najeh et al. / Journal of Physics and Chemistry of Solids 73 (2012) 707–712
709
exceeds a threshold value Ith, the NDR behavior (dV/dIo0) appears.
For instance, at 80 K an increase of the current breaks ohmic relation
at around 0.9 mA. After that, an increase in current will cause a
decrease in voltage. A symmetric V–I curve may indicate that
contacts are ohmic; furthermore, Nyquist investigations show no
significant effect of used contacts. From the results shown in Fig. 4,
one can outline that the threshold value of the current Ith increases
with increasing temperature while the voltage across the sample
decreases. The Ith is 0.9 mA at 80 K and up to 80 mA at 260 K.
The inset of Fig. 4 shows the non-linear region of V–I character-
carry most of the current. This leads to a voltage decrease across the
sample. Other possible origin of this behavior has been proposed
such as the effect of the charge density wave and quantum
tunneling effects [24–27]. According to Ja¨ger investigations, electron
tunneling is the major conduction mechanism in carbon black
polymers. In carbon based nanocomposites, electrons may jump
easily from one particle to another when the distance between
particles is within several nanometers [28].
The study of the electric properties of an amorphous material
[29–31] requires taking into account the contribution of the bulk
conductivity. The measurements were carried out in the tem-
perature range 80–300 K and frequency range between 40 Hz and
100 MHz. The analysis of complex impedance spectra shown in
Fig. 5 permits to have access to information concerning the
analyzed sample material. The experimental impedance data,
obtained by impedance spectroscopy may be modeled, at low
temperature measurements, with a circuit composed by a con-
stant phase element (CPE) in parallel with a resistor R in series
with a resistor R0 as depicted in the inset of Fig. 5. The CPE acts
like a capacitor with a small distribution of relaxation time. The
complex impedance of single parallel R-CPE [32,33] is given by
istics for RF-675 sample. The plots behavior which may follow the
b
relationship of V–Iꢁ , and from fitting data one can obtain
b¼0.3 in
agreement with results reported in [23]. A simple scenario may be
proposed to explain the results. The observed phenomenon is
probably due to the presence of as like metallic filaments which
100
80 K
100 K
80
60
40
120 K
140 K
160 K
180 K
200 K
220 K
240 K
260 K
280 K
300 K
R
Z ¼
ð3Þ
1þRCðjo a
Þ
20
Thus, the total equivalent circuit impedance can be given by
0
R
Z ¼ R0 þ
ð4Þ
1þRCðjo a
Þ
-20
-40
-60
-80
The CPE describes an ideal capacitor with a capacitance C for
¼1 and an ideal resistor R for ¼0. A value less than
a
a
a
1 indicates in general certain electric property heterogeneity
within the material [34]. In Fig. 5 we give Nyquist plots and their
fits according to the proposed equivalent sample circuit depend-
ing on the measurement temperatures regions. The total con-
ductivities were calculated from the impedance data. The values
of the equivalent circuit parameters were obtained by using the
least squares fitting routine in Z-view Scribner Associates
-15
-10
-5
0
5
10
15
Current (mA)
Fig. 4. V(I) characteristics of RF-675 for different measurement temperatures
(80–300) K.
5x103
4x103
3x103
2x103
80 K
100 K
120 K
140 K
160 K
180 K
200 K
220 K
240 K
260 K
280 K
300 K
1x103
0
0
1x103
2x103
3x103
Z' (Ω)
4x103
5x103
6x103
7x103
Fig. 5. Nyquist plots at different temperatures and equivalent electric circuit of the simplified model for RF-675 sample.

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I. Najeh et al. / Journal of Physics and Chemistry of Solids 73 (2012) 707–712
software. The obtained simulated results are given in the table. As
it can be seen from Fig. 5, a best fit with experimental data is
obtained, indicating the validity of the proposed equivalent
circuit. From Table 1, one can notate that the value of C increases
from 0.3 to 3 nF with measurement temperatures, while the
resistor value decreases, this is an indication of semiconductor
measurement temperature. The differential activation energy (DAE)
Ea, was introduced and used by several authors. In fact, the
temperature dependence of DAE seems to be a good method for
distinction between VRH and band conduction models [35–40], and
it can be calculated from the linear regression within the relation
given by
behavior. At the same time, we can observe that
a seems to be
Ea
dðlnsÞ
lnð
s
Þ ¼ s0
ꢁ
thus Ea ¼ ꢁ
ð7Þ
less temperature dependent and close to 0.9. At low temperature,
the resistor R0 may be neglected; however, it increases when the
temperature is increased, indicating a metallic behavior. Indeed,
the increase of R0 at high temperature, which may be interpreted
by the increasing role of grains, the whole material behavior still
be dominated by boundary grain effect.
The dc conductivity versus 1000/T is presented in semi-log
scale in Fig. 6(a). The straight line, fitting the experimental points,
reveals a thermally activated process, thus the dc electrical
conductivity can be given by
KT
dð1=KTÞ
By using Eqs. (6) and (7), one can deduce the form of DAE
associated with VRH conduction model, given by
!
ꢀ
ꢁ
0:25
T0
T
dðlnsÞ
pT0:75
s
¼
s
00 exp
ꢁ
therefore Ea ¼ ꢁ
ð8Þ
dð1=KTÞ
The temperature dependence of the DAE is plotted in Fig. 7. As
it can be seen, the DAE varies linearly with T0.75 in the low
temperature region and tends to be stabilized at higher tempera-
tures. This behavior leads to think that, at low temperatures
(To200 K), the conduction occurs within the VRH conduction
model, while at high temperatures domain, the nearest neighbor
hopping (NNH) instead of band conduction probably dominates.
The variation of electrical conductivity with frequency for RF-675
sample at different measurement temperatures is shown in Fig. 8.
The conductivity is increasing slowly at low frequency, while it
increases strongly at high frequency region. One can notate that,
as the frequency increases the conductivity becomes more
and more frequency dependent. The very basic fact about ac
conductivity in disordered solids is its increase with frequency.
In the hopping model, it is possible to distinguish different
characteristic regions of frequency [41]. At low frequencies where
the conductivity representing the dc conductivity is constant, the
ꢀ
ꢁ
Ea
sðTÞ ¼
s
0 exp ꢁ
ð5Þ
KT
where
s
0 is the conductivity prefactor, Ea is the activation energy,
and K is the Boltzman constant.
From Fig. 6(a) one can notate a deviation of experimental data, in
the low temperature region, from Arrhenius law. This behavior is
probably due to the presence of other conduction mode at low
temperature. Fig. 6(b) shows results of dc conductivity versus Tꢁ1=4
The obtained straight lines indicate that the VRH model can describe
the conduction mechanisms in the studied material. It worth
noticing, that for large number of materials, including various types
of amorphous carbon, electronic conduction may follow the Tꢁ1=4
law, which is related to VRH conductivity in a three dimensional
space. In this case, the dc conductivity is given by
.
"
#
ꢀ
ꢁ
1=4
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
T0
T
s
¼
s
00 exp ꢁ
ð6Þ
where s00 is a prefactor and T0 denotes material parameter related
to the distribution of localized electronic states. Another way to
confirm the presence of this type of conduction mechanism model is
to determine the evolution of differential activation energy versus
Table 1
Values of equivalent circuit parameters deduced from experimental data fits.
T (K)
C (nF)
a
R (
O
)
R0
(O)
80
0.3535
0.4617
0.8711
1.3660
1.9650
3.0860
0.95687
0.93371
0.89377
0.88661
0.87672
0.89684
357,200
13,081
1525
607
140
200
240
260
300
20
30
40
50
60
70
80
11
33
74
T0.75 (K0.75
)
370
128
Fig. 7. The differential activation energy (DAE) Ea versus T0.75 for RF-675 sample.
10-3
10-4
10-5
10-3
10-4
10-5
10-6
2
10-6
4
6
8
10
12
14
0.24 0.26 0.28 0.30 0.32 0.34
1000/T (K-1)
T-0.25 (K-0.25
)
Fig. 6. dc conductivity evolution versus 1000/T (a) and Tꢁ1/4 (b) in a semi-logarithmic scale for RF-675 sample.

I. Najeh et al. / Journal of Physics and Chemistry of Solids 73 (2012) 707–712
711
The frequency exponent in the CBH model is given by [49]
10-2
10-3
10-4
10-5
10-6
10-7
6KT
sð
o
,TÞ ¼ 1ꢁ
ð11Þ
Wm þKT Lnðotoh
Þ
where Wm is the energy required to remove an electron from one
site (activation energy), and toh is the relaxation time.
At low temperature and at
o
¼106 Hz, using the best fit is
obtained Wm¼0.3 eV and toh¼10ꢁ13 s. This result is compatible
with the assumption of electronic hopping between localized
sites and the values agree well with those given in Ref. [50].
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Frequency measurement=1MHz
The value of sdc can be estimated from the plateau of s(o)
plotted in Fig. 8. For each temperature there is a critical frequency
o0 beyond which a power law is followed. Kilbride et al. [51]
proposed an experimental definition of the critical frequency by
80 K
100 K
160 K
220 K
280 K
120 K
180 K
240 K
300 K
140 K
200 K
260 K
the following the formula:
s(o
0)¼1.1sdc. The dependency
between sdc and o0 is shown in the inset of Fig. 9. It is clear that
sdc and o0 increases linearly with increasing temperature, indi-
cating a linear relationship. The scaling frequency for a number of
systems obeys to o0aTqsdc law [52]. This equation is also known
as BNN (Barton, Nakijama and Namikawa [53,54]) relation. The
value of q depends on material nature, however the observed
linearity in the inset of Fig. 9 implies that q¼0.
100 150
250
50
200
300
T (K)
101
102
103
104
105
106
107
Frequency (Hz)
Fig. 8. ac conductivity versus frequency at different measurement temperatures.
Inset: Temperature dependence of the frequency exponent for RF-675 sample.
The scaling function of ac conductivity in extended pair
approximation (EPA) and CBH models is similar. Our experimen-
tal data supports CBH model but the behavior of scaling frequency
are quite different than EPA model.
charge transport may take place on infinite paths [42]; however,
for a region of frequencies where the conductivity increases
strongly with the frequency, the transport is dominated by
contributions from hopping infinite clusters [42]. Fig. 8 shows
In Fig. 9 we present the scaled conductivity
s(o)/sdc as a
function of the scaled frequency o0 at various measurement
o
/
temperatures for the R F-675 sample. The scaling behavior of the
conductivity of various conducting polymers and their blends
[55–59] can be described by the following relation [60–63]:
the temperature dependence of the conductivity
ent frequencies from 40 Hz to 100 MHz.
independent at low frequency region and equal to
from the ohmic conductivity, in almost the whole temperature
range. In general, the total conductivity ,T) of the sample
s
(
o
,T) at differ-
,T) is frequency
dc, deduced
s(o
s
ꢀ
ꢁ
m
s
sdc
o
o0
¼ 1þc
ð12Þ
s(o
obeys to the empirical Jonscher’s universal power law given by
where m and c are constants. In this scaling law, the exponent m,
lying between zero and unity, is characteristic of hopping in a
disordered material where the hopping charge carriers are subject
to spatially randomly varying energy barriers [62]. As it can be
clearly seen from plots in Fig. 9, the scaled conductivity of all our
blends, as a function of the scaled frequency, follow a master
curve represented by Eq. (12), and the best fit to our experimental
data is obtained for an exponent value close to 0.8, independent of
measurement temperatures indicating the universality in the ac
conduction regime.
the relation [43,44]:
o
Þ
sð
o
,TÞ ¼ sdcðTÞþAðTÞosðT,
ð9Þ
where dc(T) is the dc conductivity, A is temperature dependant
s
parameter and s(T, ) is the angular frequency exponent which is
o
determined from the relation given by
dlnsac
dln
ðo,TÞ
sðT,
o
Þ ¼
ð10Þ
o
o
)
where sac
(
o
,T) is the ac conductivity and equal to A(T)os(T,
.
The variation of the exponent s(T,
o
) with temperature, shown
10-3
101
in the inset of Fig. 8, can give useful information about the
involved specific conduction mechanism. As clearly mentioned
in this figure, the angular frequency exponent s is temperature
dependent; in fact, s decreases with increasing temperature and
tends to a constant value near to zero. This behavior which was
previously observed by other authors in ceramic samples of WO3
added (Na1/2Bi1/2) TiO3 [45,46], indicates that transport mechan-
ism may occur within different types of conduction models. At
low temperatures (To200 K), s is less than 1, corresponding to a
hopping process; however s values decrease with the increase of
temperature. Moreover, for T4200 K, the exponent s approaches
zero indicating that NNH mechanism dominates in higher tem-
perature domain. Eq. (10) confirms this tendency, in fact for
80 K
100 K
120 K
140 K
160 K
180 K
200 K
10-4
10-5
103
104
σdc (Ω.cm)-1
105
100
T4200 K s-0 and sac(o,T)-sdc.
On the light of the exponent s variation with the measurement
temperature, sac can be interpreted either by quantum-mechan-
ical tunneling (QMT) [47] or correlated barrier hopping (CBH) [48]
models. If the ac conductivity is originated from QMT, s is
expected to be temperature independent but in the CBH model,
the exponent s decreases with increasing temperature.
10-4
10-3
10-2
10-1
ω/ω0
100
101
102
Fig. 9. Scaling behavior of
s
/
sdc versus o/o0 at different measurement tempera-
tures for RF-675 sample. Inset: Correlation between the onset frequency o0 and
static conductivity sdc at various pyrolysis temperatures.

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I. Najeh et al. / Journal of Physics and Chemistry of Solids 73 (2012) 707–712
4. Conclusion
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related, and can be both attributed to bulk hopping transport. An
equivalent circuit, composed of a capacitor CPE connected in
parallel with a resistor R, well represent the impedance of the
studied sample. The non-linearity observed in the V–I character-
istics, resulting from NDR phase, has been discussed and found to
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follow the relationship V–Iꢁ . The calculated DAE outlined a
competition between two transport mechanisms: VRH for
To200 K and NNH instead of band conduction were found to
dominate at higher temperatures.
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