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Electrical conductivity and dielectric relaxation study of polyvinyl acetate/poly methyl methacrylate blends

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  • Physics Department, Faculty of Science, Zagazig University, Egypt

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Transparent films of PMMA (poly methyl methacrylate), PVAc (polyvinyl acetate) and their blends, have been prepared by using a solution-casting technique. The dielectric properties and the electrical conductivity are reported. The frequency and temperature dependence of the dielectric constant, ε′ and tan δ, have been investigated for the studied samples in the frequency range from 1 kHz to 5 MHz and over a range of temperature from 303–413 K. In addition, AC conductivity values were calculated from the dielectric data and the conduction mechanism is discussed. The frequency-dependent conductivity behavior at different temperatures provides a qualitative description of the conduction mechanism. Also, differential scanning calorimetry (DSC) scans have been measured for the studied samples.
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September 18, 2012 11:28 WSPC/Guidelines-IJMPB S0217979212501597
International Journal of Modern Physics B
Vol. 26, No. 29 (2012) 1250159 (10 pages)
c
World Scientific Publishing Company
DOI: 10.1142/S0217979212501597
ELECTRICAL CONDUCTIVITY AND DIELECTRIC
RELAXATION STUDY OF POLYVINYL ACETATE/POLY
METHYL METHACRYLATE BLENDS
R. M. AHMED
Physics Department, Faculty of Science, Zagazig University,
Zagazig 44519, Egypt
rania8 7@hotmail.com
Received 7 May 2012
Accepted 2 July 2012
Published 30 September 2012
Transparent films of PMMA (poly methyl methacrylate), PVAc (polyvinyl acetate) and
their blends, have been prepared by using a solution-casting technique. The dielectric
properties and the electrical conductivity are reported. The frequency and temperature
dependence of the dielectric constant, εand tan δ, have been investigated for the studied
samples in the frequency range from 1 kHz to 5 MHz and over a range of temperature
from 303–413 K. In addition, AC conductivity values were calculated from the dielectric
data and the conduction mechanism is discussed. The frequency-dependent conductivity
behavior at different temperatures provides a qualitative description of the conduction
mechanism. Also, differential scanning calorimetry (DSC) scans have been measured for
the studied samples.
Keywords: Conductivity; glass transition temperature; polymer blends; polymer films.
1. Introduction
Dielectric analysis is one of the most convenient and sensitive methods of studying
polymeric structure and its physical and chemical state.1In addition, it provides an
excellent means of characterizing the electrical properties of polymeric materials as
it allows one to study the two fundamental electrical characteristics of a material,
capacitance and conductance, as a function of temperature and frequency. In the
case of highly insulating polymers, the capacitive nature of the material dominates
their properties below the glass transition temperature and above this temperature
the conductive processes prevail.2
Blending of polymers has been extensively studied due to its significant im-
portance in applied as well as basic polymer science3,4; easy preparation and easy
control of their physical properties within the compositional regime is often pos-
sible. In some cases; a modification in the electrical properties can be obtained to
meet a specific requirement.5
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R. M. Ahmed
Poly (methyl methacrylate) (PMMA) is a hard, rigid, transparent thermoplastic,
which has good outdoor weatherability and is more impact resistant than glass. In
addition, in PMMA, being essentially an insulating material, the number of free
charge carriers is very small and their mobility is very low. In an electric field it is
expected that a redistribution of charges that are mobile enough to respond to the
time scale of the applied field will occur. PMMA also contains electron releasing
methyl groups, which supply electrons.6
On the other hand, polyvinyl acetate (PVAc) is also transparent and a good
insulating material with low conductivity; it has a great importance in the micro-
electronic industry. Its electrical conductivity depends on the thermally generated
carriers and also on the addition of suitable dopants.
Herein, I discuss a trial that was carried out to prepare transparent films of
PMMA, PVAc and their blends to study the miscibility in PMMA/PVAc blends and
also to enhance the electric properties of the individual homo-polymers. Dielectric
constant, tan δand AC conductivity measurements were performed for the samples
in the temperature and frequency range from 303–413 K and 1–5 MHz, respectively.
The miscibility of the blends was investigated by using DSC studies of their Tg(s).
2. Materials and Method
2.1. Materials
Both PMMA and PVAc were obtained from Sigma–Aldrich Co. (USA); they were
reported to have molecular weights of 996,000 and 167,000 g ·mol1, respectively.
Chloroform with a purity of 99.8%, purchased from Sigma–Aldrich Co. (USA), was
used as a common solvent for both PMMA and PVAc.
2.2. Preparation of the samples
Transparent films (thickness 35–45 µm) of PMMA and PVAc and their blends were
prepared by using a solution-casting technique. PMMA and PVAc were dissolved
separately in chloroform for 48 h at room temperature. Afterwards, the dissolved
homo-polymers were mixed with different concentrations and then cast onto glass
dishes and left at 55C for 48 h in an air oven. After curing; the samples were re-
moved and were cut to various shapes as desired. The blends of PMMAx–PVAc100x
were prepared with different concentrations where xhad the values 100, 80, 60, 40,
20 and 0 wt.%.
2.3. Differential Scanning Calorimeter (DSC)
The DSC thermograms were performed for the studied samples by using a differ-
ential scanning calorimeter, model DSC 50, Shimadzu, Japan. A heating rate of
5C/min from room temperature up to 200C was utilized under nitrogen atmo-
sphere. The glass transition(s) were determined from the inflection point(s) of the
curves.
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Electrical Conductivity and Dielectric Relaxation Study of Polyvinyl Acetate
2.4. Electrical measurements
The samples were cut in the form of circular discs of a diameter (1 cm). The two
parallel surfaces of each disc were coated with carbon paste and checked for good
conduction.
The dielectric properties as a function of frequency (from 1 to 5 MHz) and also as
a function of temperature (from 303–413 K) were measured using a programmable
automatic multi frequency RLC bridge, (3532-Z Hitester, Hioki, Japan). The dielec-
tric properties are considered as an important tool in studying structural transitions
and molecular mobility in polymers. The dielectric permittivity ε, of a material is
represented by two parts: ε=ε′′ where εis the real part (dielectric constant)
and ε′′ the imaginary part (dielectric loss).7
The dielectric constant ε, represents the amount of the dipole alignment (both
induced and permanent). It was determined from ε=C/Co, where Cis the sample
capacitance and Cois the vacuum capacitance of the cell. Co=εoA/d, where A
is the area of the electrode, dis the thickness of the sample and εois the free
space permittivity (εo= 8.86 ×1012 F/m). In addition, the dielectric loss ε′′ ,
which measures the energy required to align dipoles or move ions, was calculated
by ε′′ =εtan δwith tan δbeing measured.8
The ac conductivity of all samples was calculated from the dielectric losses
according to the relation σac =ωε′′εo, where ω= 2πf is the angular frequency.7
3. Results and Discussion
3.1. DSC
It is well known that a blend of two polymers is considered miscible if it gives,
for each blend composition, a single glass transition, Tg.9DSC measurements per-
formed on the samples showed that the glass transition temperature, Tg, values for
pure PMMA and PVAc were 371.8 and 317.4 K, respectively. In addition, single
Tgvalues for (80/20, 60/40, 40/60 and 20/80) PMMA/PVAc blends were obtained
at 349.3, 345.1, 341 and 321.8 K, respectively. According to the criterion of mis-
cibility and these values of Tg, PMMA and PVAc appeared to be miscible for all
concentrations of their blends.9,10
Moreover, in order to explain the blend dependence of the glass temperature
of blends of miscible polymers, the glass transition temperature Tgvalues were
calculated using the Fox equation11: 1/Tg(blend) =W1/Tg1+W2/Tg2, where W1
and W2are the weight fractions and Tg1and Tg2are the respective glass transition
temperatures of the individual polymers. Figure 1 illustrates the theoretical and
experimental values of Tgfor the samples as a function of the blend composition.
3.2. AC conductivity
The dependence of AC conductivity, σac , on frequency at different temperatures
was nearly the same for all studied blends and the individual polymers. A typical
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R. M. Ahmed
Fig. 1. Dependence of Tgon the concentration of PMMA in PVAc/PMMA blends.
plot is shown in Fig. 2(a) for (PMMA/PVAc 40/60) blend, which clearly illus-
trates that there was an increase in the conductivity with increasing the applied
frequency. Moreover, for all the samples, two linear segments were observed one
at low (frequency 100 ±50 kHz) and the other at high frequency (frequency
100 ±50 kHz).
The AC conductivity, σac , for all blends and the individual polymers, were found
to obey the power law formula σac =s, where Ais a constant that depends on
the temperature, ωis the angular frequency and sis the frequency exponent.12
The values of the frequency exponent s, and the constant A, calculated from the
slope of the straight-line as depicted in Fig. 2(a) at high frequency and different
temperatures, are tabulated in Table 1. In all cases swas less than unity. It could
be observed that the values of the constant Aand the frequency exponent swere
temperature dependent.
Moreover, Table 1 shows that the values of sincreased with the temperature
up to a certain temperature, Tp, which is close to the Tgfor each sample, and
then decreased. For T < Tp, the increase in the values of scould be attributed to
increasing transport of the charge carriers according to the quantum mechanical
tunneling model.13 On the other hand, at T > Tp, the decrease in the values of s
can be due to a change occurring in the conduction mechanism to one based on a
correlated barrier hopping model14 in which the charge transport between localized
states is mainly due to hopping over the potential barrier separating the states.
Moreover, the observed enhancement in the conductivity by increasing the applied
temperature, Fig. 2(a), could be attributed to the increase of the mobility of charge
carriers for hopping and/or tunneling.15
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Electrical Conductivity and Dielectric Relaxation Study of Polyvinyl Acetate
Table 1. The estimated values of the glass transition temperature Tg(K), the frequency exponent (s), the dependent temperature constant (A) and
the effective energy barrier for a single electron hopping (WH).
PMMA/PVAc The
(wt%) Tg(K) Parameters 303 (K) 313 (K) 323 (K) 333 (K) 343 (K) 353 (K) 363 (K) 373 (K) 383 (K) 393 (K)
A×1010 9.33 8.12 6.61 5.89 4.78 3.98 2.63 3.39 3.63 5.37
(100/0) 371.8 s0.414 0.426 0.443 0.448 0.464 0.478 0.507 0.487 0.483 0.476
WH(eV) 0.380 0.375 0.382 0.387
A×1010 0.18 0.10 0.10 0.08 0.15 0.22 0.41 0.47
(80/20) 349.3 s0.703 0.748 0.749 0.765 0.741 0.712 0.652 0.648
WH(eV) 0.731 0.683 0.632 0.538 0.547
A×1010 3.02 2.18 2.09 1.86 6.03 8.32
(60/40) 345.1 s0.511 0.537 0.541 0.547 0.458 0.438
WH(eV) 0.379 0.327 0.324
A×1010 18.2 14.1 10.9 6.31 7.59 8.32
(40/60) 341 s0.326 0.343 0.368 0.419 0.407 0.406
WH(eV) 0.264 0.296 0.298 0.307
A×1010 6.31 3.24 5.89 10.7 12.6
(20/80) 321.8 s0.530 0.560 0.535 0.493 0.480
WH(eV) 0.367 0.358 0.339 0.340
A×1010 1.07 1.02 1.62 2.34 3.31 4.79 7.08 12.0 16.2
(0/100) 317.4 s0.613 0.615 0.586 0.547 0.520 0.493 0.476 0.453 0.439
WH(eV) 0.404 0.420 0.403 0.379 0.369 0.359 0.357 0.352 0.352
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R. M. Ahmed
Fig. 2. (a) Frequency dependence of AC conductivity at different temperatures, (b) temperature
dependence of AC conductivity at different frequencies, both for the (PMMA/PVAc 40/60) blend.
On the other hand, the exponent s increased towards unity as Tdecreased to Tg
according to the relation16 s= 1 [(6k T )/WH] where WHis the effective energy
barrier for single electron hopping. Its values are also listed in Table 1.
The temperature dependence of AC conductivity at certain frequencies was
measured for all the blends and the individual polymers; a typical plot is shown
in Fig. 2(b). The AC conductivity increased by increasing the applied frequency,
same as Fig. 2(b), which could be attributed to the fact that the increase of the
applied field could enhance the carrier jumping and, consequently, the conductivity
value.17
The AC conductivity was both frequency and temperature dependent and was
enhanced with increasing of both the frequency and the temperature. Indeed, the
rise of conductivity upon increasing the frequency and temperature is a common
respond for polymeric samples. It is due to the tremendous increase of the mobility
of charge carriers in the sample.18 The charge carriers could contribute significantly
to AC conductivity by hopping backward and forward at places with jump proba-
bility.19
The temperature dependence of σac is represented by σac =σoexp(Eac/kT ),
where σois a constant and ∆Eac is the activation energy for the conduction.12 The
activation energy was calculated from the negative of the slope in plot log σac versus
1/T as seen in Fig. 2(b). The activation energy values were evaluated and are listed
in Table 2 for the various blends and the individual polymers. ∆Eac decreased with
increasing PMMA content in the blend.
3.3. Dielectric properties
The dielectric constant, ε, showed a frequency dependence at all temperatures.
Figure 3(a) illustrates the dielectric constant, ε, of different concentrations of
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Electrical Conductivity and Dielectric Relaxation Study of Polyvinyl Acetate
Table 2. The activation energy, ∆Eac, and the
constant, σo, obtained for the studied samples.
PMMA/PVAc (wt%) Eac (eV) Ln σo
100/0 0.198 15.52
80/20 0.223 14.27
60/40 0.274 12.84
40/60 0.308 11.51
20/80 0.327 10.00
0/100 0.367 8.09
Fig. 3. Frequency dependence of the dielectric constant, ε, (a) for different blendes at constant
temperature 303 K, (b) for the (PMMA/PVAc 80/20) blend at different temperatures.
PVAc/PMMA blends and the individual polymers at constant temperature 303 K
as a function of frequency. An increase in the values of the dielectric constant, ε,
is clearly observed by increasing the PVAc content in the blends in which the po-
lar nature of the blend increases since PVAc is more polar than the weakly polar
polymer, PMMA.20
In all cases, a strong frequency dependence of the dielectric constant, ε, was
observed followed by a nearly frequency dependent behavior at high frequencies,
see Fig. 3(b) as a typical plot for the studied samples.
In fact, the behavior of dielectric constant, ε, with frequency is related to the
application of the field. When the frequency is increased the dipoles will no longer
be able to rotate rapidly, so that, their oscillation will begin to lag behind this field,
which explains the observed decrease in the dielectric constant, ε, with increasing
the frequency.21
Moreover, the observed increase in the value of dielectric constant, ε, by in-
creasing the investigated temperature could be explained as reported by Psarras
et al.15,22 in which the increase in the temperature could increase the dielectric con-
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September 18, 2012 11:28 WSPC/Guidelines-IJMPB S0217979212501597
R. M. Ahmed
Fig. 4. Isochronal (constant frequency) plot of εversus temperature Tat several frequencies.
Table 3. The temperature of the three regions, T(K), of the
peaks of tan (δ) for the different samples.
PMMA/PVAc (wt%) I II III
100/0 T < 363 363 < T < 383 383 < T
80/20 T < 343 343 < T < 373 373 < T
60/40 T < 333 333 < T < 363 363 < T
40/60 T < 373 373 < T < 393 393 < T
20/80 T < 333 333 < T < 363 363 < T
0/100 T < 343 343 < T < 383 383 < T
stant due to increased segmental mobility of the polymer molecules, which leads to
an increase in dielectric constant.
Figure 4 shows the variation of the dielectric constant, ε, as a function of
temperature at different frequencies for several samples. It could be observed that
for pure PMMA, the dielectric constant increases with temperature above Tgdue to
an increase of total polarization arising from dipoles and trapped charge carriers. On
the other hand, for pure PVAc and its blends with PMMA, the dielectric constant,
ε, first increased up to Tgof each sample and then decreased with further increase
in temperature. Moreover, the dielectric constant decreased with increasing the
frequency in the case of all blends and their homo-polymers which may be due to
the tendency of dipoles in the polymer to orient themselves in the direction of the
applied field.20
Figure 5 shows the variation of tan (δ) with frequency at various fixed tem-
perature of (PMMA/PVAc 80/20) blend as a typical plot for the studied blends.
The peaks of tan (δ) have three different trends for different regions of temperature
which are shown in Table 3. This reveals the existence of three relaxation peaks
which are originated from three relaxation modes, β-relaxation at low temperature,
α-relaxation at higher temperature and αβ process between them.23
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Electrical Conductivity and Dielectric Relaxation Study of Polyvinyl Acetate
Fig. 5. Frequency dependence of tan δfor the (PMMA/PVAc 80/20) blend at different temper-
atures.
Fig. 6. The dielectric strength, ∆ε, as a function of temperature for the studied blends.
Moreover, the dielectric strength ∆ε=εoε, where εoand εare the low
and high frequency limits of dielectric constant, εwere evaluated. Figure 6 illus-
trates the relaxation between ∆εand temperature Tfor the studied blends in three
regions. It is obvious that the dielectric strength εincreased with temperature
in region (I) corresponding to β-relaxation and in region (II) corresponding to αβ-
relaxation with different in slope. On the other hand, a decrease in the dielectric
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September 18, 2012 11:28 WSPC/Guidelines-IJMPB S0217979212501597
R. M. Ahmed
strength ∆εwas observed in region (III) which is often considered as a character-
istic of α-relaxation.24
4. Conclusions
The results presented above clearly show that PVAc/PMMA blends have a higher
compatibility that is manifested by the fact that the DSC thermo-grams show one
Tglocated at an intermediate temperature within the range of those of the individ-
ual polymers. Moreover, trends in dielectric constant as a function of temperature
and frequency reveal that dielectric properties are drastically affected by blending
PMMA and PVAc. Also, the conductivity behavior of the blends is frequency-
dependent and the variation follows the simple power law.
Acknowledgement
I would like to express my gratitude to Prof. Dr. Ahmed El Falaky for allowing
me doing the dielectric measurements in his lab at physics department, faculty of
science, Zagazig University, Zagazig, Egypt.
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In the work described in this paper the dielectric properties of solid solutions of p-nitroaniline in poly(methyl methacrylate), poly(ethyl methacrylate) and poly(n-butyl methacrylate) were measured in the frequency range from 20 to 106 Hz and the results obtained were compared with those of the pure polymers. It is shown that the presence of the solute has a strong influence on the relaxation process of poly(methyl methacrylate), and this is ascribed to the formation of hydrogen bonds between the amino group of the solute and the side groups of the polymer. In poly(ethyl methacrylate) this effect is less pronounced and it is absent in the case of poly(n-butyl methacrylate), suggesting that the increasing size of the n-alkyl group prevents hydrogen bond formation between the solute and the polymer.
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Viscometric behavior of poly(methyl methacrylate) (PMMA) (referred to as the guest polymer) in various solvents containing poly(vinyl acetate) (PVAc) (referred to as the host polymer) at constant concentration was thoroughly investigated. It has been found that, using PVAc and tetrahydrofuran (THF) to form polymer solvent of (PVAc+THF), the intrinsic viscosity of PMMA in polymer solvent was less than in pure solvent of THF, indicating that repulsive interaction between PMMA and PVAc existed in THF. With the increasing of the concentration of PVAc in polymer solvent of (PVAc+THF), the intrinsic viscosity of PMMA decreased, indicating that repulsive interaction between PMMA and PVAc increased in concentrated polymer solvent. On the contrary, if using PVAc and chloroform, or, PVAc and cyclohexanone to form polymer solvent, the intrinsic viscosity of PMMA in polymer solvent is larger than in pure solvent of chloroform or cyclohexanone, indicating that attractive interaction between PMMA and PVAc existed in either chloroform or cyclohexanone. With the increase of the concentration of PVAc in polymer solvent, the intrinsic viscosity of PMMA increased accordingly, and reached its maximum at the concentration of 0.2 g/dl in polymer solvent of (PVAc+chloroform) or 0.3 g/dl in polymer solvent of (PVAc+cyclohexanone). With the further increase of the concentration of PVAc in polymer solvent, the intrinsic viscosity of PMMA, either in (PVAc+chloroform) or in (PVAc+cyclohexanone), decreased. On this occasion, the increased concentration-dependent intermolecular excluded volume effect is believed to be dominant, resulting in the contraction of PMMA coils and thus the decrease of the intrinsic viscosity of PMMA in polymer solvent. Viscometric behavior of PMMA/PVAc blends with the weight ratio of 1/1 in various solvents was also investigated and several criteria to predict polymer–polymer compatibility by viscosity measurement were determined to interpret the phase behavior of PMMA/PVAc blends cast from different solvents.