Thermal stability, AC electrical conductivity and dielectric properties of N-(5-{[antipyrinyl-hydrazono]-cyanomethyl}-[1,3,4]thiadiazol-2-yl)-benzamide

Article abstract of DOI:10.1016/j.jallcom.2014.05.120

A novel organic compound containing antipyrine and thiadiazole moieties, N-(5-{[antipyrinyl-hydrazono]-cyanomethyl}-[1,3,4]thiadiazol-2-yl)-benzamide (ACTB) has been synthesized. The thermal properties, alternating current electrical conductivity (σ_AC) and electrical modulus of ACTB have been reported. The thermal properties were analyzed using differential scanning calorimetry and thermogravimetric measurements. The AC measurements of bulk ACTB were performed in frequency range 100 Hz-5 MHz and temperature range 303-503 K. The frequency dependence of AC conductivity is found to follow Jonscher's universal power law with the applicability of the correlated barrier hopping model. The temperature dependence of σ_AC could be described in terms of Arrhenius relation with two activation energies. The activation energy decreases witty and effectiveness of proposed USDA versus SSDA methods. Moreover, we propose a computationally efficient alternative to TGP (Bo and Sminchisescu 2010), and it's variants, called the direct TGP. We show that our model outperforms a number of baselines, on two public datasets: HumanEva and ETH Face Pose Range Image Dataset. We can also achieve 8-15 times speedup in computation time, over the traditional formulation of TGP, using the proposed direct formulation, with little to no loss in performance.

Full text of DOI:10.1016/j.jallcom.2014.05.120

Journal of Alloys and Compounds 611 (2014) 50–56
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Thermal stability, AC electrical conductivity and dielectric properties
of N-(5-{[antipyrinyl-hydrazono]-cyanomethyl}-[1,3,4]
thiadiazol-2-yl)-benzamide
b
a
c
E.M. El-Menyawy a, , I.T. Zedan , A.M. Mansour , H.H. Nawar
⇑
a Solid State Electronics Laboratory, Solid State Physics Department, Physics Division, National Research Center, Dokki, Cairo 12311, Egypt
b Basic Science Department, High Institute of Engineering and Technology, El-Arish, North Sinai, Egypt
c Department of Chemistry, Faculty of Education, Al Jabal Al Gharbi University, Libya
a r t i c l e i n f o
a b s t r a c t
Article history:
A
novel organic compound containing antipyrine and thiadiazole moieties, N-(5-{[antipyrinyl-
hydrazono]-cyanomethyl}-[1,3,4]thiadiazol-2-yl)-benzamide (ACTB) has been synthesized. The thermal
properties, alternating current electrical conductivity ( AC) and electrical modulus of ACTB have been
Received 12 February 2014
Received in revised form 24 March 2014
Accepted 17 May 2014
r
reported. The thermal properties were analyzed using differential scanning calorimetry and thermogravi-
metric measurements. The AC measurements of bulk ACTB were performed in frequency range 100
Hz–5 MHz and temperature range 303–503 K. The frequency dependence of AC conductivity is found
to follow Jonscher’s universal power law with the applicability of the correlated barrier hopping model.
Available online 28 May 2014
Keywords:
Antipyrine
Thiadiazole
The temperature dependence of rAC could be described in terms of Arrhenius relation with two activation
energies. The activation energy decreases with increasing frequency. The dielectric relaxation behavior is
explained in terms of electric modulus formalism. At relatively higher temperatures, the imaginary mod-
ulus spectra exhibit asymmetric maxima with peak-width much broader than that of the Debye peak and
are skewed toward the high frequency sides of the maxima with increasing temperature. The relaxation
time is calculated and exhibited thermally activated process with activation energy of 0.77 eV.
Ó 2014 Elsevier B.V. All rights reserved.
Thermal properties
AC conductivity
Modulus formalism
1. Introduction
materials in manufacturing devices including chemosensors [8]
and bulk heterojunction solar cells [9]. Bithiophene azo dyes func-
Most of high-performance devices are based on inorganic mate-
rials. However these materials are relatively expensive and their
fabrication processes are complicated. The target of very low-cost
devices is the main guideline in the research of new materials
and new technology. In this regard, organic materials have been
fanned due to their prospects in electronic and optoelectronic
applications owing to their multiple advantages such as low cost,
chemical and thermal stability, processability, and flexibility of
molecular design. They are currently used as active component in
fabricating various devices such as solar cells [1], photodiodes [2],
thin film transistors [3] and optical data storages [4].
tionalized with thiadiazole acceptor group exhibited second order
nonlinear optical properties [10]. N-(5-{[antipyrinyl-hydrazono]-
cyanomethyl}-[1,3,4]thiadiazol-2-yl)-benzamide (ACTB) with its
molecular structure shown in Scheme 1 belongs to both thiadiaz-
oles and antipyrines. Antipyrines are also important class of great
important in the field of organic chemistry and its applications.
They exhibited semiconductor behavior [11] and photovoltaic
properties [12].
We were thus motivated to undertake a systematic study of
preparation and characterization of a new organic containing anti-
pyrine and thiadiazole moieties. In this work, ACTB as novel com-
pound has been chemically synthesized and characterized. The AC
conductivity, electrical modulus and thermal properties of ACTB
are discussed. Conductivity and dielectric properties of a material
are sensitive to charge movement and storage in a device. It is a
powerful tool to study the physical processes, which are going on
in the active material of a device. Thermal properties are important
design parameters in different devices for the optimal operation.
Five-membered, hetero-aromatic compounds such as thiadia-
zole have been gained intensive attention, owing to their strong
electron-accepting ability and synthetic ease [5–7]. Organic mate-
rials containing thiadiazole moiety have been used as active
⇑
Corresponding author. Tel.: +20 1006021326; fax: +20 233709310.
E-mail address: emad_elmenyawy@yahoo.com (E.M. El-Menyawy).
http://dx.doi.org/10.1016/j.jallcom.2014.05.120
0925-8388/Ó 2014 Elsevier B.V. All rights reserved.

E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
51
100
CH3
N
90
N
CH3
80
70
60
50
H
N
O
N
N
S
C
O
H
C
N
C
N
N
Scheme 1. Molecular structure of ACTB compound.
2. Experimental
4000 3600 3200 2800 2400 2000 1600 1200
Wavenumber (cm-1
800
400
)
2.1. Synthesis of organic compound
Fig. 1. FTIR spectra of ACTB compound.
An aqueous solution of sodium nitrite (0.7 gm in 5 ml water) was added to a
cold (0 °C) solution of 4-aminoantipyrine (0.01 mole) in concentrated hydrochloric
acid (5 ml). The resulting diazonium salt solution was then added to a cold solution
of (0.01 mole) of N-(5-(cyanomethyl)-1,3,4-thiadiazol-2-yl)benzamide in ethanol
(50 ml) containing sodium acetate. The mixture was stirred at room temperature
for one hour and then the solid product was collected by filtration and re-crystal-
lized from ethanol/chloroform to give N-(5-{[antipyrinyl-hydrazono]-cyanometh-
yl}-[1,3,4]thiadiazol-2-yl)-benzamide as red crystals; in yield 77%, melting point.
241 °C. Anal. Calcd for C22H18N8O2S: C, 57.63%; H, 3.96%; N, 24.44%. Found: C,
57.60%; H, 3.99%; N, 24.41%.
vibrations of aromatic CAH groups and the band located at
2850 cmꢁ1 corresponds to stretching vibrations of aliphatic CAH
groups. The band appeared at 2215 cmꢁ1 is ascribed to the pres-
ence of cyano group. The band situated at around 1616 cmꢁ1 is
due to C@O vibrations and the band situated around 1574 cmꢁ1
is due to C@N vibrations.
The 1H NMR spectrum of ACTB is represented in Fig. 2. The spec-
trum shows two singlet signals at d = 2.30–3.07 ppm due to the
presence of two methyl groups of antipyrine moiety. The multiple
signals at d = 7.35–7.52 ppm are due to the five aromatic protons of
antipyrine moiety, whereas those at d = 7.53–8.07 ppm are due to
the five aromatic protons of benzamide moiety. The spectrum
shows also two singlet signals at d = 9.19–12.96 ppm. The former
is attributed to the NAH group linked to five-membered ring of
antipyrine, whereas the later is attributed to the NAH group linked
to five-membered ring of thiadiazole moiety.
2.2. Sample preparation and measurements
ACTB in powder form was grounded in a mortar to obtain fine powder. Then, it
was compressed under a pressure of 1.96 ꢀ 108 N/m2 to make a disk. The thickness
and effective area of the disk were 0.06 cm and 0.8 cm2, respectively. Symmetrical
gold electrodes were made on both sides of the disk by using thermal evaporation
technique. Edward E306A coating unit was used for electrode deposition under base
pressure of 10ꢁ4 Pa. The thickness of gold film and the rate of deposition were con-
trolled by quartz thickness monitor. The gold0 film thickness was about 150 nm and
the rate of deposition was between 2 and 3 ÅA/s.
3.2. Thermal properties
Fourier transform infrared (FTIR) spectra are recorded on ATI Mattson infrared
spectrophotometer in spectral range 4000–400 cmꢁ1. Nuclear magnetic resonance
(1H NMR) spectra are measured by using varian Mercury-vx-300 NMR spectrome-
The thermal properties of ACTB were characterized by TG and
DSC curves. The measurements were conducted at a heating rate
of 10 °C/min under nitrogen atmosphere. The TG data were
recorded in temperature range of 34–950 °C as depicted in Fig. 3.
The results reveal that the ACTB starts to decompose at temperature
of 235 °C, indicating that good thermal stability, which is adequate
for the application in electronic and optoelectronic devices. The
thermally induced phase transition behavior of ACTB was investi-
gated with differential scanning calorimetry (DSC) under a nitrogen
atmosphere. The experimental DSC data of ACTB are shown in Fig. 4.
It can be seen that there is one endothermic peak appeared at
ter. Deuterated dimethyl sulfoxide (DMSO-d6) was used as
a solvent. The
percentage compositions of the elements of ACTB powder are determined by using
PERKIN-ELMER 2400 CHN elemental analyzer.
Thermogravimetric analyzer SDTQ 600 TA instruments were used to record the
thermogravimetric and differential scanning calorimetry (TG/DSC) data. The mea-
surements were achieved at heating rate of 10 °C/min in nitrogen environment.
The AC measurements were carried out by using a programmable automatic
LCR bridge; model Hioki 3532-50 Hitester. The organic disk sample was placed in
a holder specially designed to minimize the stray capacitance. The electrical con-
tacts were equipped with copper wires, which were connected to the metal elec-
trodes of the disk using conducting sliver paste. The measurements were
achieved in frequency range 100 Hz–5 MHz and temperature range 303–503 K.
The temperature of the sample was recorded by using a NiCr–NiAl thermocouple
with an accuracy of 1 K. The thermocouple was placed in contact with the sample.
The LCR Bridge allowed measuring the capacitance, C, and loss tangent, tan d. These
values were used to calculate the dielectric constant, e0, and dielectric loss, e00, using
the following expressions [11]:
72.8 °C, giving a
peaks at 191 and 241 °C with
D
H value of 148 J gꢁ1 and there are two exothermic
D
H 10.7 and 139.8 J gꢁ1 respectively.
These peaks are due to the phase change of ACTB [13].
The glassy state is characterized by vibrational motion of the
atoms constituting the chain about an equilibrium position. There-
fore, the glass-glass transition peak at 72.8 °C may apparently be
due to unfreezing of the motion of comparatively small kinetic
vinyl groups, i.e., b-relaxation of ACTB [14].
Cd
e0
¼
ð1Þ
e
oA
and e00
¼
e00 tan d
ð2Þ
On the other hand, the peak observed at a higher temperature
(i.e. 191 °C), can be assigned to the glass transition, i.e., the glass
where d is the distance between the two electrodes, eo is the permittivity of free
space (8.854 ꢀ 10ꢁ12 F mꢁ1) and A is the cross section area of the film.
to rubber-like state or
a-relaxation [15]. On further heating, the
sample start to re-crystallize and consequently show a melting
3. Results and discussion
point at higher temperature (i.e. Tm = 241 °C) [16].
3.1. FTIR and NMR spectra
3.3. AC conductivity
The FTIR spectrum of the synthesized ACTB is shown in Fig. 1.
The signal appeared at 3122 cmꢁ1 is attributed to NAH vibrations.
The band located at 2939 cmꢁ1 corresponds to stretching
Electrical conductivity is an important quantity for revealing
reliable information about the electrical conduction mechanisms

52
E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
Fig. 2. 1H NMR spectra of ACTB compound.
4
3
100
80
60
40
20
0
2
1
0
-1
-2
-3
-4
0
200
400
600
800
1000
0
50
100
150
200
250
300
t (°C)
t (°C)
Fig. 3. Thermogravimetry curve for ACTB compound.
Fig. 4. DSC thermogram for ACTB compound.
in materials. The AC conductivity of ACTB is computed by using the
expression given by [17]:
illustrated in Fig. 5. It is clear that rac increases with increasing
frequency and temperature. It can also be seen that the high-fre-
quency dispersion region of the AC conductivity decreases slightly
as the temperature increases. This feature signifies the presence
of a thermally activated process caused by the increase in the
charge-carrier energy. At low frequencies, the applied electric field
forces the charge carriers to drift over large distances [18]. When
rAC
ðx
Þ ¼
e
oxe00 ¼ 2
pf
eoe0 tan d
ð3Þ
where
x
is the angular frequency (
x
= 2pf, f is frequency of the
applied AC field). The frequency dependence of the AC conductivity
of ACTB, at different temperatures in the range 303–503 K, is

E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
53
-11
-12
-13
-14
-15
-16
-17
-18
-19
-20
of charge carriers is reduced. The AC conductivity in terms of this
model is given by:
p
3N2ee
24
rAC
ð
x
Þ ¼
o xR6x
ð5Þ
where N is the concentration of localized states and R is the hop-
x
ping length expressed by:
303 K
323 K
343 K
363 K
383 K
403 K
423 K
443 K
463 K
483 K
503 K
e2
Rx
¼
ð6Þ
p
eoe½Wm þ kBT lnð soÞꢂ
x
where e is the electronic charge, Wm is the energy required to
remove the electron completely from the site to the excited state,
kB is Boltzmann’s constant, T is the absolute temperature and so is
the characteristic relaxation time (10ꢁ13 s). The frequency exponent
s in the CBH model is given by:
4
6
8
10
12
14
16
6kBT
s ¼ 1 ꢁ
ð7Þ
ln (
f, Hz)
½Wm þ kBT lnð soÞꢂ
The first approximation of this equation takes the form:
x
Fig. 5. Frequency dependence of the AC conductivity at various temperatures for
ACTB compound.
6kBT
Wm
s ¼ 1 ꢁ
ð8Þ
the frequency is increased, the mean displacement of the charge
carriers is reduced and the AC conductivity follows the universal
Jonscher’s power law expressed by [19]:
The value of Wm is calculated as 0.6 eV from the slope of the
straight line in Fig. 6. By neglecting the frequency term in Eq. (6),
the value of R is determined as 4.44 nm. Substituting this value
x
in Eq. (5), the value of N is determined as 1.89 ꢀ 1017 cmꢁ3. The
rAC
ðx
Þ ¼ Bxs
ð4Þ
obtained values of N and R are better than those obtained for
x
DOPNA compound [11]. These results indicate the compound
under investigation can be recommended in solar cells
applications.
The temperature dependence of the AC conductivity for ACTB at
fixed frequencies is depicted in Fig. 7. It is clear that lnrAC
increases with increasing temperature showing two linear straight
lines with distinct slopes (regions I and II). This implies that the AC
conductivity is a thermally activated process and the dependence
of AC conductivity on temperature can be described by Arrhenius
relation in the form:
where B is a temperature dependence constant and s is the fre-
quency exponent which is less than or equal to unity [20]. The uni-
versal Jonscher’s law of AC conductivity is not limited to the case of
glasses but also for amorphous, crystalline and ionic single crystal
materials [21].
The frequency exponent s is obtained by the least squares
straight-line fit of the experimental data shown in Fig. 5 and is
plotted as a function of temperature in Fig. 6. It can be observed,
that the exponent s decreases from 0.52 (at 303 K) to 0.32 (at
503 K). There are many models [22–25] explaining the behavior
of exponent s and its variation with frequency and temperature.
The behaviors of the exponent s and the corresponding conduction
mechanism are summarized in our previous work [26]. The
observed temperature dependence of frequency exponent s reveals
that the correlated barrier hopping (CBH) is the mechanism
responsible for AC conduction in ACTB. In CBH model, hopping of
carriers is most likely to takes place between adjacent localized
states. When the frequency is increased, the mean displacement
ꢀ
ꢁ
ꢀ
ꢁ
ꢁ
D
kBT
EI
ꢁ
D
kBT
EII
rAC
¼
rI exp
þ
r
II exp
ð9Þ
where
DEI and DEII are the conduction activation energies at low
and relatively high temperatures, respectively, and rI and rII are
the corresponding pre-exponential factors. The AC activation ener-
gies of ACTB in two regions are calculated from the slopes of the lin-
ear parts. The frequency dependence of
DEAC is depicted in Fig. 8. It
0.55
0.50
0.45
0.40
0.35
0.30
-11
Region II
Region I
-12
-13
-14
-15
-16
-17
-18
-19
-20
0.1 kHz
0.3 kHz
0.8 kHz
3 kHz
8 kHz
30 kHz
80 kHz
250 kHz
600 kHz
2 MHz
2.0
2.2
2.4
2.6
2.8
103/T (K-1)
3.0
3.2
3.4
300
350
400
450
500
T (K)
Fig. 7. Temperature dependence of the AC conductivity at fixed frequencies for
Fig. 6. Variation of the frequency exponent with the temperature.
ACTB compound.

54
E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
0.24
0.20
0.16
0.12
0.08
0.04
0.00
303 K
323 K
343 K
363 K
383 K
403 K
423 K
443 K
463 K
483 K
503 K
102
103
104
f (Hz)
105
106
Fig. 9. Frequency dependence of the real part of electric modulus at several
temperatures for ACTB compound.
Fig. 8. Dependence of the activation energy on the applied frequency.
can be observed that the activation energy in both regions
decreases with increasing frequency. The increase of AC conductiv-
ity with increasing frequency indicates that hopping conduction is
the dominant current transport mechanism. Thus, the increase of
the applied frequency enhances the electronic jumps between the
localized states; consequently, the activation energy decreases with
increasing frequency. Therefore, at high frequencies the conductiv-
ity is taken by mobility of charge carriers over short distances and
need lower energy than that necessary for mobility over longer dis-
tances at low frequencies.
303 K
323 K
343 K
363 K
383 K
403 K
423 K
443 K
463 K
483 K
0.07
0.06
0.05
0.04
503 K
0.03
0.02
0.01
0.00
3.4. Electric modulus
The dielectric properties of materials can be expressed in vari-
ous ways, using different representations. The electric modulus
formalism study of organic materials provides the information of
bulk phenomenon property as average conductivity relaxation
times. The modulus formalism is based on the concept of complex
102
103
104
f (Hz)
105
106
Fig. 10. Frequency dependence of the imaginary part of electric modulus at several
temperatures for ACTB compound.
dielectric modulus, M⁄(
x) and is defined as the reciprocal of the
complex dielectric permittivity [27]:
(i) A relaxation peak is clearly observed at higher temperatures.
This peak is related to the relaxation of mobile charge carri-
ers and the re-orientation of dipoles [29]. The region to the
left side of the peak is where the positive charge carriers
are mobile over long distances and the region to the right
is where the charge carriers are spatially confined to their
potential wells. The frequency range where the peak occurs
is indicative from short-range to long-range mobility at
decreasing frequency. The full width at half maximum of
the modulus peak is greater than 1.14 decades displaying a
stretched exponential function. It is a non-Debye behavior
and can be interpreted as the consequence of distributions
of relaxation time.
(ii) The relaxation peak shifts towards high frequency with
increasing temperature indicating that the relaxation is
thermally activated. This behavior can be explained by the
faster movement of the charge carriers at high temperatures,
leading to decrease in relaxation time. Relaxation time is
decreased with increasing temperature as the dissipated
thermal energy assists the formed dipoles to follow the
motion of alternating applied field.
1
Mꢃ ¼ ¼ M0 þ iM00
ð10Þ
eꢃ
where M0 and M00 are the real and imaginary parts of the complex
electric modulus respectively, and i = (ꢁ1)1/2. The values of M0 and
M00 are calculated by using the following relations:
e0
þ
M0 ¼
and
ð11Þ
e02
e002
e00
þ
M00 ¼
ð12Þ
e02
e002
Fig. 9 shows the frequency dependence of the real part of elec-
tric modulus for ACTB at different temperatures. It is characterized
by low values of M0 at low frequency. The values of M0 increase
with increasing frequency and tends to saturate at M (M = 1/
e1, e1 is the dielectric constant at high frequency) which is attrib-
uted to the conduction phenomena due to short-range mobility of
charge carriers [28]. It is also clear from the figure that the value of
M0, at fixed frequency, decreases with elevated temperatures.
The variation of imaginary part of electric modulus with fre-
quency at different temperatures is demonstrated in Fig. 10. The
variation of M00 as a function of frequency is characterized by:
1
1
The characteristic relaxation time is related to frequency of the
maximum position as smꢄ(2
pfm) = 1. The relation between the
value of fm and the reciprocal temperature is represented in

E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
55
9
8
7
6
5
in the sample (for a Debye relaxation, b = 1). Lopes et al. [32] found
that the value of b is practically constant from 0.57 at 60 °C to 0.63
at 150 °C.
00
00
Normalization plot of M /M
versus ln(f/fm) (fm is the fre-
max
00
quency corresponding to M
value) for ACTB, at fixed tempera-
max
tures, is demonstrated in Fig. 12. The relaxation peak observed at
low frequencies indicates that the charge carriers can perform suc-
cessful hopping to neighboring sites [33]. The near perfect overlap-
ping between the obtained curves at different temperatures
indicates that all dynamical processes are temperature indepen-
dent in the investigated range [34]. This overlapping is observed
in organic and inorganic materials [32,35].
4
4. Conclusions
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
103/T (K-1)
Organic compound containing both antipyrines and thiadiazole
moieties, N-(5-{[antipyrinyl-hydrazono]-cyanomethyl}-[1,3,4] thia
diazol-2-yl)-benzamide (ACTB) has been synthesized. The thermal
properties denote the good thermal stability of ACTB up to 241 °C.
The AC measurements of bulk ACTB were investigated in frequency
range 100 Hz–5 MHz and temperature range 303–503 K. The cor-
related barrier hopping (CBH) is the most mechanism which is
responsible for AC conduction. In terms of CBH model, the values
of maximum barrier height, hopping length and density of local-
ized states are determined as 0.6 eV, 4.44 nm and 1.89 ꢀ
1017 cmꢁ3, respectively. The activation energy is found to decrease
with increasing frequency. The imaginary part of dielectric modu-
lus showed a peak, at higher temperatures, which shifted towards
high frequency by increasing temperature. The relaxation time is
thermally activated process with activation energy of 0.77 eV. Elec-
tric modulus analysis has confirmed the presence of non-Debye
type of relaxation in ACTB compound. Using the scaling of modulus
data at relatively higher temperatures, it is observed that the relax-
ation dynamics of charge carriers is independent of temperature.
Fig. 11. Relation between ln fm and 103/T for ACTB compound.
443 K
463 K
483 K
503 K
1.0
0.8
0.6
0.4
0.2
0.0
10-2
10-1
100
101
102
103
104
f / fm
References
Fig. 12. Plot of M00/Mm00 ax versus ln(f/fm) for ACTB compound.
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Fig. 11. The relation exhibits straight line indicating, that the rela-
tion can be described by Arrhenius relation:
ꢀ
ꢁ
ꢁ
D
T
E
fm ¼ fo exp
ð13Þ
where fo is pre-exponential factor and
D
E is the activation energy
for dielectric relaxation process. The obtained value of
DE is calcu-
lated from the slope of the relation as 0.77 eV. This value is greater
than those obtained from AC conduction indicating that it is related
to the direct current conduction.
The electric field relaxation due to the motion of charge carriers
is given by the empirical Kohlrausch–Williams–Watts function
(K–W–W) [30,31]:
[12] H.M. Zeyada, M.M. El-Nahass, E.M. El-Menyawy, Sol. Energy Mater. Sol. Cells
92 (2008) 1586.
[13] K. Liu, Q-A. Wu, E. Wanga, Thermochim. Acta 428 (2005) 77.
[14] M. Sato, Y. Manabf, T. Sasaki, Y. Ohtomo, F. Komatsu, Eur. Polym. J. 27 (1991)
1391.
ꢀ
ꢁ
b
t
sM
u
ðtÞ ¼ exp ꢁ
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_
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56
E.M. El-Menyawy et al. / Journal of Alloys and Compounds 611 (2014) 50–56
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