Download dielectric propertiies with barium sodium niobate

CHAPTER-4
DIELECTRIC PROPERTIIES WITH
BARIUM SODIUM NIOBATE NANO
COMPOSITES
Abstract
Dielectric properties of BNN-PS nanocomposites were measured over a
broad frequency range (100Hz to 13 MHz) and temperature range (280C1300C) to explore the possibility of their use as electronic materials, and
characterize them on the basis of existing theories. The composites
revealed marked departures from the law of physical mixtures for its
dielectric properties. The dielectric constant and dielectric losses increase
with increasing BNN content. At a constant temperature, the composites
follow a linear relationship between logarithm of their dielectric constant
and volume fraction of the ferroelectric filler. The system conforms to the
Claussis Mossotti equations. Dielectric permittivity values of the
composites are intermediate between Bottcher-Bruggeman and MaxwellWagner models. The presence of BNN nanofiller into polystyrene matrix
is generally responsible for an increase of glass transition temperature,
usually of about 90C, with respect to the neat polystyrene
The results of this chapter have been accepted for publication in the
International Journal of Material Science
Chapter IV
100
4.1 Introduction
The principal applications for ceramics and ceramic composites are as
capacitive elements in electronic circuits and as electrical insulation. For
these applications the properties of most concern are the dielectric constant
and dielectric loss factor.
A dielectric material has interesting electrical properties because of the
ability of an electric field to polarize the material to create electric dipoles. A
dipole is an entity in which equal positive and negative charges are separated
by a small distance, dl, the electric dipole moment is given
by µ= qdl
(4.1)
The electric dipole is a vector. In its simplest model, a dipole moment
consists of two point charges of opposite sign, +q and –q separated by a
distance.
Choosing the origin of the co-ordinate system to coincide with the negative
charge, the dipole moment in this case has a magnitude equal to qdl, and is
represented by a vector pointing from the negative charge in the direction of
positive charge [1-3]
It is fundamental that the capacitance of a condenser is increased if the space
between the conductors is filled with a dielectric material. If Co is the
capacitance of the condenser with region between the conductors evacuated
and C its capacitance when the region is filled with a dielectric, then the ratio
C
ε
= εr =
ε0
C0
(4.2)
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
101
where ε r is the relative permittivity or dielectric constant of the medium and
ε and ε 0 are the permittivity of the medium and free space respectively.
The dielectric constant is a measure of the extent to which the insulating
material’s surface interact with the electric field set up between the charged
plates. The constant is dependent on two molecular level properties; the
permanent ‘dipole moment’ and the ‘polarizability’ or the induced change in
dipole moment due to the presence of an electric field. The permanent dipole
moment is the average over the various dipole moments given rise to by
structural charge density differences over intramolecular distances.
Polarizability is the property which arises from changes in the molecular
electron distribution induced by the applied electric field.
Dielectrics are substances which do not possess free electric charges under
ordinary circumstances but they can modify the electric field into which they
are introduced. The most important property of dielectrics is their ability to
become polarized under the action of an external electric field. The atoms
and molecules of the dielectrics are influenced by an external field and hence
the positive particles are pushed in the direction of the field while the
negative particles in the opposite direction from their equilibrium position.
Hence dipoles are developed and they produce a field of their own. The
process of producing electric dipoles out of neutral atoms and molecules is
referred to as polarization.
Dielectrics may be broadly divided into non-polar materials and polar
materials. In non polar materials, the positive nuclei of charge q is
surrounded by a symmetrically distributed negative electron cloud of charge
–q. In the absence of an applied field the centre of gravity of the positive and
negative charge distribution coincide. When the molecule is placed in an
Chapter IV
102
external electric field the positive and negative charges experience electric
forces tending to move them apart in the direction of the external field. The
distance moved is very small (10 -10 m) since the displacement is limited by
the restoring forces which increases with increasing displacements. The
centers of positive and negative charges no longer coincide and the
molecules are said to be polarized. Dipoles so formed are known as induced
dipoles since when the field is removed the charges resume their normal
distribution and the dipoles disappear. For molecules q will be of the order
of electronic charge( 10-19C) and dl of the order of molecular dimensions(
10 -10 m) and so dipole moment will be of the order of 10 -29 Cm.
In considering a dielectric material from the macroscopic point of view, we
restrict our attention to average values over volumes which are sufficiently
small in comparison with the dimensions of the material specimen but large
enough to contain a sufficient number of molecules for the purpose of
averaging. The sum of the dipole moments in an element of volume ∆v is
N ∆v
_
∑ µi = N ∆v (µ ) = P∆v
(4.3)
i =1
_
where ( µ ) represents the average dipole moment of each molecule and N
the number of molecules per unit volume. The vector P is the dipole moment
per unit volume and is called electric polarization.
In polar dielectrics, the molecule, which are normally composed of two or
more different atoms, have dipole moments even in the absence of an electric
field, that is, the centers of their positive and negative charges do not
coincide. Normally these molecular dipoles are randomly oriented through
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
103
out the material owing to thermal agitation, so that the average moment over
any macroscopic volume element is zero. In the presence of an externally
applied field the molecules tend to orient themselves in the direction of the
field in such a manner that the elementary volume has a net dipole moment
In some polar materials a spontaneous dielectric polarization can exist even
in the absence of an applied electric field. Such materials are known as
ferroelectrics.
The microscopic concept of polarization
Dielectric polarization is nothing but the displacement of charged particles
under the action of the electric field to which they are subjected. Devices
based on this manifestation are numerous. They range from condensers and
switch-gear equipment in power and distribution installations to rectifiers,
resonators, amplifiers and transducers- converters of electrical energy to
other forms of energy- in communication technology. They include memory
devices used for storage of information in modern computers.
The above said displacement of electric charges results in the formation of
electric dipole moment in atoms, ions or molecules of the material. The four
important types of polarization are (1) electronic polarization (2) ionic
polarization and (3) orientational polarization (4) space charge polarization.
[4-6]
4.1.1 Electronic Polarization
It is the displacement of electrons with respect to the atomic nucleus, to be
more precise the displacement of the orbits under the action of an external
electric field Electronic polarization can be observed in all dielectrics
irrespective of whether other types of polarization are displayed in the
Chapter IV
104
dielectric. When the system is subjected to an external field of intensity E,
the nucleus and the electron experience Lorentz forces of magnitude ZeE in
opposite directions. As they are pulled apart, a coulomb force develops
between them, which tends to counter the displacement and hence the actual
magnitude of displacement is very small, αe is the electronic polarizability.
The electronic dipole moment is given by
µe = α e E
(4.4)
Fig 4.1 Demonstration of electronic polarization
4.1.2 Ionic Polarization
When atoms form molecules, electronic polarization is still possible but
there may be additional polarization due to a relative displacement of the
atomic components of the molecule in the presence of an electric field.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
105
When a field is applied to the molecule, the atoms in the molecule are
displaced in opposite directions until ionic binding force stops the
process, thus increasing the dipole moment. It is found that this induced
dipole moment is proportional to the applied field and an ionic
polarizability α i is introduced to account for the increase.
µi = α i E
(4.5)
Of course, the individual ions experience polarization in addition. For
most materials, the ionic polarizability is less than electronic
polarizability
4.1.3 Dipole or Orientation Polarization
This type of polarization only occurs in polar substances. The permanent
molecular dipoles in such materials can rotate about their axis of
symmetry to align with an applied field which exerts a torque in them.
This additional polarization effect is accounted by an orientation
polarizability term α o. With electronic and ionic polarization processes,
the force due to externally applied field is balanced by elastic binding
forces, but for orientation polarization no such forces exist. In thermal
equilibrium with no field applied the permanent dipoles contribute no net
polarization since they are randomly oriented. However, since it is
observed that the orientation polarization is of the same order as the other
forms of polarization but it is temperature dependent, since at higher the
temperature the grater is the thermal agitation and that lowers α
o.
The
polarizability factors, α e and α i are functions of molecular structure and
are largely independent of temperature
Chapter IV
106
4.1.4 Space charge polarization (αs)
Space charges must be considered as extraneous charges which collect on
the interfaces. Space charge polarization involves a limited transport of
charge carriers until they are stopped by a potential barrier, possibly a
grain boundary or a phase boundary. This also depends on temperature
and this effect is more frequently knew as the Maxwell- Wagner effect,
arising in heterogeneous samples.
4.1.5 The Total Polaris ability is the sum of αe, αi, α0 and αs and is
shown in the fig 4.2
Fig 4.2 Total contribution of polarizability
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
107
4.1.6Clausius-Mosotti Relation
Clausius- Mosotti relation relate the dielectric constant of a material to the
polarizability of atoms comprising it. The dipole moment of a single atom
is proportional to local field i.e. dipole moment = α EL where α is the
polarizability of the atom and EL is the local field.
4.1.7 Evaluation of local field
The electric field which an atom sees or the total electric field at the atom
site is called the internal field or local field. If the dielectric is placed
between two charged plates, the electric field experienced by the molecule
of the dielectric, is given by EL, and
EL = E1 + E2 + E3
(4.6)
Where E1 is the field intensity due to charge density on the plates of the
capacitor (with no dielectric), E2 is the field at the atom due to polarized
charges, and E3 is the field due to neighboring dipoles. If there are N
atoms per unit volume, the electric moment per unit volume which is
called polarization and EL given by
Now P = Nα EL
(4.7)
4.1.8 Polarization in Polymers
Dry polymers are poor conductors of electricity and can be regarded as
insulators. Field-induced orientational polarization caused by permanent
or induced dipole moments is a very well known fact in dielectric theory.
Application of an electric field to a polymer can lead to polarization of the
sample, which is a surface effect, but if polymer contains groups that can
act as permanent dipoles then the applied field will cause them to align in
108
Chapter IV
the direction of the field. When the electric field is released, the dipoles
can relax back into a random orientation, but due to frictional resistance
experienced by the groups in the bulk polymer this will not be
instantaneous. The process of disordering can be characterized by a
relaxation time, but may not be easily measured. It is more convenient to
apply a sinusoid ally varying voltage to the sample and to study the dipole
polarization under steady state conditions [7].
Polystyrene, which is considered to be non polar, does in fact possess a very
very small dipole moment due to the asymmetry at the phenyl side group in
atactic polystyrene [8]. Because of their anisotropic polarizablility, phenyl
groups tend to orient with their greatest main axis of polarizabilitiy in the
direction along which the E vector of an electric field and an induced
dipole moment is produced in some phenyl groups. On the other hand, the
induced dipole moments interact with other phenyl groups present in an
ensemble of polystyrene. Both effects render it possible that the dielectric
data of Polystyrene become ac field dependent if there is an internal
degree of freedom concerning the phenyl-phenyl arrangement below the
glass transition temperature (Tg) [9]
4.2 Results and Discussions
Dielectric constants of the composites are found out and modeling is done
with different experimental predictions. The observed peak in the
dielectric loss factor is related to the glass transition temperature of PS.
The results are neatly discussed below.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
109
4.2.1 Dielectric constant of the composites
It is perceptible that higher concentrations of ferroelectric filler lead to
higher dielectric constant composites. The dielectric constant of BNN is
greater than that of polystyrene, so the addition of BNN to the polymer
matrix will result an increase in dielectric constant. At a temperature of
about 300C, and for a frequency of 1MHz, the dielectric constant of the
composites are found out and reported in the second column of table 4.1.
Because no significant contribution for electrode polarization is observed,
the increment in dielectric constant of PS is attributed mainly to the
addition of BNN, which increases the dipoles in the system. Since the
values of ‘ ε ’of the two ingredients, polystyrene and BNN are 2.55 and
430 respectively, it is also clear that this composites does not obey the law
of physical mixtures, as stated by
ε c = ε f v1 + ε p (1 − v1 )
(4.9)
where v1 is the volume fraction of the filler, ε c , ε p , ε f are the dielectric
constant of composites, polymer and filler respectively. The calculated
values of dielectric constants are reported in the third column of table 4.1
Table4.1 Dielectric constant of BNN-PS
Name
Dielectric constant (experimental) Calculated Dielectric constant
PS
2.55
2.55
BNN10
3.75
45.29
BNN20
6.05
88.04
BNN30
10.75
130.78
BNN40
23.05
173.02
Chapter IV
110
The present system of composites is a binary phase mixture of two
dielectrically different materials where BNN is ionic and polycrystalline
and polystyrene is amorphous atactic and non-polar. A great variety of
formulae has been suggested for the calculation of permittivity of
heterogeneous mixtures. These formulae are derived on the basis of
various theoretical assumptions and experimental data [9-11].
Fig (4.3-4.7) illustrates the dielectric interaction pattern of the mixed
system with respect to composition. It is found from Fig 4.3 that ε c , the
dielectric constants of the composites are non linearly dependent on
volume % of BNN. This shows that the constituent capacitors formed by
dielectrics fillers and polymer in the composites are not in parallel
combination in the composites.
BNN-PS
Linear fit
25
Dielectric constant
20
15
10
5
0
0
5
10
15
20
25
30
35
40
Volume of BNN, %
Fig 4.3 Dielectric constant versus volume fraction of BNN
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
111
From the plot 4.4 of the inverse of the dielectric constant ( ε c ) = ∫ ( ε c )
−1
the law of harmonic mixture), is curvilinear, which indicates that the twocomponent dielectrics are not in series combination in their composites.
When two capacitors are connected in series, the resultant is
C1 * C2
and
C1 + C2
their inverse obey harmonic series conditions
BNN-PS
0.40
0.35
0.30
(ε )
∋ −1
0.25
0.20
0.15
0.10
0.05
0
5
10
15
20
25
30
35
40
Volume of BNN, %
Fig 4. 4 Inverse dielectric constant vs. volume fraction of filler.
Physically these composites resemble porous structures which generally
conform to (eqn 4.10), the relation assumes the form of Lichteneker and
Rother’s [12, 13] more appropriate to layered structures which are neither
parallel nor perpendicular to the electric field i.e., the valid averages are
neither arithmetic nor harmonic. Suppose we have a particulate two phase
material we could use the model of composites to predict upper and lower
112
Chapter IV
bounds of the composite capacitances. One can choose to model
composites as having capacitance in parallel (upper bound) or in series
(lower bound). In practice the answer will lie somewhere between the
two. Lichtenecker’s rule predicts that a better approximation than either of
these is given by using the logarithemic dependence of the effective
capacitance values. Fig 4.8 shows that the plots of the dielectric constant
vs. frequency and the curves are practically equidistant in logarithmic
scale for equally spaced BNN volume fractions. This indicates the
logarithm of the dielectric constant is linearly proportional to the volume
fraction of BNN at all frequencies. Hence it is believed that the
composites follow the “log law” relationship, originally proposed by
Lichtenecker in which the dielectric constant of clean two component
system can be represented by (equ 4.10) where v1, is the volume fraction
of filler. The logarithmic law of mixtures (equ 4.10) firmly confirms a
logarithmic dependence of the dielectric constant of the composite on the
volume fraction of the filler.
The log ε c vs. filler volume % plot is linear for 10 to 40% of filler
volume and when extrapolating we get the log (dielectric constant) of
pure PS. This confirms the logarithmic dependence of the dielectric
values of the composites in fig 4.5. So we can apply Lichtenecker’s rule.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
113
BNN-PS
Linear fit
1.4
1.2
log (ε)
1.0
0.8
0.6
0.4
0
5
10
15
20
25
30
35
40
Volume of BNN,%
Fig 4.5 log ε vs filler volume % of composites.
log ε c = log ε
p
ε
+ v1 log  f
εp




 ε −1 
The plot of specific polarization  c

 εc + 2 
(4.10)
versus volume fraction as
presented in fig4.6. It is also linear with slope and intercepts of 1.4 and
0.35 respectively are as expected in accordance with Clausius-Mossotti
equation modified by Lorentz and Lorentz [14] applicable to the overall
composite dielectrics
Chapter IV
114
B
Linear Fit of Data1_B
0.9
specific polarisation
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
25
30
35
40
volume of BNN, %
Fig 4.6 Specific polarization vs.volume fraction of the composite
It implies that not only the square of the dipole moment per unit particle
of the combination but also the polarizability of a unit particle directly
decrease proportionally to the increase of the quantity of the polystyrene.
That is why at v1 =0, the value of specific polarization term becomes the
specific polarization of polystyrene is exactly 0.34 (the diel. constant of
PS lies between 2.5 and 2.6). The Clausius-Mossotti equation itself does
not consider any interaction between filler and matrix [15]. So we used
the same equation for the calculation of dipole moment of BNN particle.
4.2.2 Calculation of Dipole Moment of BNN Particle
This discussion may be further extended to calculate dipole moments of
BNN particles. The Clausius-Mossotti equation for a single –component
system can be written as
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites

115

_
εc −1
N 
(µ )2 
α+
=
εc + 2
3ε 0 
3 K BT 

(4.11)

Where N is the number of molecules per unit volume, α is the
deformational polarizability (both electronic and ionic polarization.),
_
_
( µ )2
is the dipolar polarizability, ( µ ) is the dipole moment, K B is the
3 K BT
Boltzman’s constant, and T is absolute temperature.
Equation (4.11) is an appropriate one and becomes precise when polar
molecules are separated from each other, i.e. when polar molecules are
distributed in a different non polar environment. The present system more
or less conforms to this situation, where ionic BNN particles are
distributed in a polystyrene matrix. For such a system the equation
becomes
_
ε c −1
(µ )2
=(1/ 3ε 0 )( N1α1 + N1
+ N 2α 2 )
εc + 2
3 K BT
(4.12)
Where ‘N1’ and ‘N2’ are the number of molecules of BNN and
polystyrene per unit volume of the composite respectively. α1 and α2 are
_
deformational polarizability, (electronic & ionic) and ( µ ) is the average
dipole moment of BNN particles in the polystyrene matrix.
_
( µ )2
of the intensely polarized system is
The dipolar polarizabilitiy,
3 K BT
usually much higher than the deformation polarizabilities α1 and α2
Chapter IV
116
.Neglecting the two terms involving subscripts 1 and 2 in (eqn 4.12) and
substituting in N1=(d1/M1) NAv1 where density of BNN d1=5950 K g cm-3,
molecular weight of BNN is M1 =1651g, and NA, Avogadro number
NA=6.06*10
23
mol-1 and v1 is the volume fraction of BNN (eqn 4.12)
reduces to
_
ε c − 1 N A d1 ( µ ) 2
=
*v
ε c + 2 9 K BTM 1ε 0 1
(4.13)
The plot of specific polarization versus. v1 is linear and its slope is
_
N A d1 ( µ ) 2
ie in Cm
9 K BTM 1ε 0
_
( (µ ) )
2 1/2
 N A d1 
=

 9 K BTM 1ε 0 
−1/ 2
* ( slope) ½
(4.14)
T=300K and the slope is 1.4.
The calculated dipole moment of BNN in polystyrene matrix is
17.3439x10-30 Cm. This dipole moment of BNN particles and the high
induced polarization of BNN under electric field contribute for the high
dielectric constant of the composites. This dipole moment may be
considered as the dipole moment of a unit particle of the combination.
The two phase mixtures are also represented by the Bottcher-Bruggeman
formula [16] based on the spherical particle model where the filler is
interacting with polymer. According to this formulae
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
εc =
1
H + ( H 2 + 8ε f ε p )1/ 2 )
(
4
117
(4.15)
where
H = (3v1 − 1)ε f + (2 − 3v1 )ε p
with
ε f =430,the dielectric constant of the filler, and ε p =2.55, the
dielectric constant of PS. The values of dielectric constant of the
composites may be calculated from this equation and plotted against v1
.However, the Maxwell-Wagner-Sillars [17, 18] equation predicts as a
complete solution of the Wagner-Raleigh theory for a system of one
spherical particle uniformly distributed in another
εc = ε p
2ε p + ε f + 2v1 (ε f − ε p )
2ε p + ε f − v1 (ε f − ε p )
(4.16)
The behavior of the present system is in agreement with both of these
equations up to v1 =0.3 i.e. up to 30% volume fraction as revealed by the
plots of ε c versus v1 as in Fig4.7 in accordance with the calculated values
from the Bottcher-Bruggeman formulae and the Maxwell-Wagner-Sillars
equation. Beyond this point, the experimentally observed values of ‘ εc ’ lie
between the two plots, Bottcher-Bruggeman and the Maxwell-WagnerSillars. The experimental values are coinciding with Logarithmic laws.
This indicates that the shape, particle size, distribution and concentration
of the dispersed component do not permit a very high degree of physical
interaction as envisaged by Bottcher-Bruggeman.
Chapter IV
118
Bottcher-Bruggeman
Mawell-Wagner
Lichteneker
Experimental value
60
Dielectric constant
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
Volume of filler, %
Fig 4.7 Comparison of the calculated dielectric constant by different
laws governing mixing.
The composite under investigation consists of ionic BNN dispersed in
polystyrene medium. Hence it is likely that the magnitudes of both the
short range and the long range interactions possible between the ions in
the filled matrix are lessened by the imposition of a plastic environment
on the ionic BNN. However, the charge density, the dipole moment of a
unit particle of the combination, the energy of the dipole and the overall
dielectric constant are not uniquely determined by the degree of
engulfment of BNN by polystyrene only. Other balancing factors such as
particle size, degree of packing and space charge effects also gain
prominence as percentage of polystyrene in the system is varied. The best
reproduction was obtained by the use of ‘Lichteneker relations’
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
119
4.2.3 Effect of frequency on the dielectric properties of the polymer
and the composites
25
PS
BNN10
BNN20
BNN30
BNN40
Dielectric constant
20
15
10
5
0
2
3
4
5
6
7
Log(f) Hz
Fig 4. 8 Dielectric constant versus frequency of PS and the composites
When the dielectric material is subjected to an alternating field the
orientation of dipoles, and hence the polarization, will tend to reverse
every time the polarity of the field changes. At low frequencies the
polarization follows the alterations of the field without any significant lag
and the permittivity is independent of frequency and has the same value
as in static field. When the frequency is increased the dipoles will no
longer be able to rotate sufficiently rapidly so that their oscillations will
begin to lag behind those of the field. The above effect leads to a fall in
dielectric constant of the material with frequency [19, 20]
Dielectric permittivity variation can be fitted to the Maxwell- Wagner
type of interfacial polarization in many cases. In this model materials are
assumed to be composed of polarizable grains separated by poorly
120
Chapter IV
conducting grain boundaries. In nanomaterials there is an additional
chance of getting a high dielectric constant because of the large space
charge polarization owing to the large surface area of a large number of
individual grains. The interface contact area changes inversely as the
radius of the particle (1/r). In a low frequency regime electronic, ionic
dipolar and space charge polarization plays a dominant role in
determining the dielectric properties of the materials [21, 22]. In the
BNN-PS composites, there is a finite contribution from the above
mentioned polarization, which gives an initial high value for dielectric
constant and that slightly decreases with frequency due to the slight
changes in orientational polarization with frequency.
It is observed that, upto one MHz, the permanent dipoles can follow the
field quite closely and so dielectric constant is high because the dipoles
can easily align with change in polarity. This observation is evidenced
from fig4.8 that the high dielectric constant values for the prepared
samples which fall slightly with frequency for the composites [23]. This
indicates that at high frequency the mobility of polar groups in polymer
chains is unable to contribute to the dielectric constant. At low frequency
the dielectric constant of the composite strongly depends on the dielectric
properties of both polymer and ceramic contents, while at high frequency
the dielectric constant becomes dependent primarily of the ceramic filler
and its concentration. The frequency dispersion relation given by Habery
and coworkers [24], in which dielectric constant decreases with increasing
frequency and reaches a constant value for all samples.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
121
4.2.4 Impedance-Frequency Spectra
The composites were analyzed by means of complex impedance
spectroscopy as a function of temperature and frequency. Fig 4.10 shows
the impedance spectra of each of the composites analyzed at room
temperature. A.C measurements are often made with a Wheatstone bridge
type of apparatus in which the resistance, ‘R’, and capacitance, ‘C’ of the
sample are balanced against variable resistors and capacitors as in fig 4.9.
The central problem with a.c measurements arises over the interpretation
of the data. This is because the sample and the electrode arrangement is
electrically a ‘black box’ whose equivalent circuit (i.e. its representation
by some combination of R and C elements) is often unknown.
Fig 4.9 Measurement of R and C with bridge& Vector Representation of
Capacitive and Resistive current
The impedance spectra thus obtained were then processed through
computer assisted electrochemical data analysis software that ideally fit to
the experimental data [25].
Chapter IV
122
Z=
where
RX c
( R + X c 2 )1/ 2
2
(4.17)
( R 2 + X c 2 )1/ 2 is the vector addition of
the resistance and
capacitive reactance. The impedance of a parallel RC circuit is always less
than the resistance or capacitive reactance of the individual branches. The
relative values of ‘Xc’ and ‘R’ determine how capacitive or resistive the
circuit line current is. The one that is the smallest and therefore allows
more branch current to flow is the determining factor. Thus if ‘Xc’ is
smaller than ‘R’, the current in the capacitive branch is larger than current
in the resistive branch, and the line current tends to be more capacitive.
Frequency of the applied voltage determines many of the characteristics
of a parallel RC circuit. Frequency affects the value of the capacitive
reactance and so also affects the circuit impedance, line current and phase
angle, since they are determined to some extend by the value of ‘Xc’. The
higher the frequency of a parallel RC circuit, the lower is the value of
‘Xc’. This means that for a given value of R, the impedance is also lower,
making the line current larger and more capacitive.
The impedance measurement of the composites revealed that when the
volume fraction increased from 10 to 40%, the composites remain in their
capacitive characteristics. The a.c conductivity is a measure of resistive
component and it depends on the value of ‘δ’. No significant changes are
observed for ‘δ’ value from 10 to40% volume fraction. The impedance Zfrequency curves were parallel curved lines and the phase angle θ about
900, which are like ideal capacitors {Z depends on 1/ j (2πf C)}
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
123
7.0
6.5
logZ ( ohms)
6.0
5.5
5.0
PS
BNN10
BNN20
BNN30
BNN40
4.5
4.0
3.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
logf ( Hz)
Fig 4.10 Impedance frequency Plot of the composites
Capacitive reactance is proportional to the frequency of the applied voltage
and so the impedance depends on the applied voltage. Furthermore,
although a voltage drop occurs when current flow through either of the
components a phase relationship between the current and the voltage drop
is established and it is a measure of the opposition to the current flow [26].
However, in the composites the impedance values were still fairly high and
showed a frequency dependence indicating that the particle-particle
contacts are very weak and there are thin dielectric layers between the
particles, which give strong capacitive effects (dominated by 1/(2πfC)).
The high normal surface resistance of the powder may also contribute to the
contact resistance between the particles, and hence to the composite
resistance. In short, it should be emphasized that temperature play an
important role in the dielectric and conducting properties
Chapter IV
124
4.2.5
Effect of Temperature on the dielectric properties of the
polymer and the composites
The dielectric constant of the composites increases with increase in
temperature. It is essentially due to the different thermal expansion of the
polymer (50*10-6K-1-300*10-6K-1) on one hand and the ceramics (0.5*10-6
K-1-15*10-6K-1) on the other. The increase in dielectric constant is attributed
to the higher orientation polarization of the polymer at higher temperature
due to the greater mobility of molecules.
It is observed that the rate of variation of dielectric constant with
temperature is steeper for higher volume fraction samples [27]. This is
attributed to the internal field generated by the ceramic particles, which
favors the orientation of polymer molecules. Fig 4.11 shows the
temperature dependence of dielectric constants for polymer and the
composites. It is noteworthy that the curves for various BNN-PS
composites parallel to each other in fig 4.9 and 4.11. This indicates that the
composites follow the ‘log-law’ relationship within the entire range of
temperature studied.
The dielectric constant of BNN is slightly increased by the temperature
variations within a temperature limit of 280 C to 1200 C because of its
ferroelectric nature in the above temperature range[28] The ferroelectric
transition temperature of BNN is at 5300C (reported in chapter 9) and so
BNN is ferroelectric in the studied temperature. Electronic and ionic
polarizations are partially independent of temperature but space charge
polarization and orientation polarization depends upon temperature.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
Polystyrene
BNN10
BNN20
BNN30
BNN40
30
25
Dielectric constant
125
20
15
10
5
0
20
40
60
80
100
120
0
Temperature( C)
Fig 4.11
Temperature dependence of dielectric constant of PS and
Composites
The number of space charge carriers governs the space charge
polarization. As the temperature increases the number of carriers
increases, resulting in an enhanced build up of space charge polarization
and hence an increase in dielectric properties. In space charge
polarization, the increases of temperature facilitate the diffusion of ions
[29]. Thermal energy may also aid in overcoming the activation barrier
for orientation of polar molecules in the direction of the field. In such
cases relative dielectric constant increases when the temperature
increases, the orientation of these dipoles is facilitated and this increases
the dielectric polarization. But at very high temperatures the chaotic
thermal oscillations of molecules are intensified and the degree of
orderliness of their orientation is diminished and thus the permittivity
passes through a maximum [30]. In orientation polarization, the
randomizing action of thermal energy decreases the tendency of the
Chapter IV
126
permanent dipoles to align themselves in the applied field at very high
temperature. These result a decrease in dielectric constant with
temperature at and above 1000C, nearly the glass transition temperature of
PS. The same effect is observed in the case of YBCO filled PS
composites and that are reported in chapter 5.
Table 4.2 Dielectric constant of the Samples at different temperatures at
frequency 1 MHz
Temper(0C)
PS
BNN10
BNN20
BNN30
BNN40
30
2.5
3.918
6.109
9.55
23
60
3.
4.7
7.32
11.4
25.2
90
3.3
6.1
9.7356
16.25
29.3
120
3.1
5.7
9.19
15.8
27.1
The composites at lower volume fraction follow the path of polystyrene in
its dielectric properties. Fig 4.11 and table 4.2 give evidences for the
same [31-33].
4.2.6 Conductivity and Glass transition temperature
The ac conductivity (σ) of the prepared composites were calculated using
the formulae
σ = 2π f ε 0ε c tan(δ ) (4.18)
where ε0 is the dielectric constant of vacuum εc, the relative dielectric
constant of the composites, ‘f’ the applied frequency i.e., one MHz.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
127
Dielectric loss factor(tan δ)
0.020
0.015
0.010
Polystyrene
BNN10
BNN20
BNN30
BNN40
0.005
0.000
20
40
60
80
100
120
140
160
180
200
220
0
Temperature ( C)
Fig4. 12 Temperature versus dielectric loss for PS and the composites
At sufficiently low temperatures all polymers are hard rigid solids. As the
temperature rises, each polymer eventually obtains sufficient thermal
energy to enable its chains to move freely enough for it to behave like a
viscous liquid (assuming no degradation has occurred). Although the
glass-rubber transition itself does not depend on polymer structure, the
temperature at which ‘Tg’ the glass transition is observed depends largely
on the chemical nature of the polymer chain i.e., chain flexibility,
molecular structure etc. The dielectric loss is responsible for conductivity
and the peak temperature is characterized as the glass transition
temperature by dielectric theory. The glass transition temperature of the
composites increases with the increment of filler content and the nature is
represented in fig 4.12. The peak values are reported in table 4.3 and are
128
Chapter IV
justified by the homogeneity of dispersion of the nanofillers into PS, as
revealed by SEM analysis, and by the enormous interfacial area of the
nanoparticles, as the strong reinforcement between the two phases reduce
the mobility of PS chains. This is schematically represented in fig 4.13.
Fig 4.13 Schematic representation of the two phase mixture
The increasing relaxation temperature of the composites with increasing
BNN concentration may be due to an interfacial or Maxwell-WagnerSillars polarization [34].The relaxation arises from the fact that the free
charges, which were present at the stage of processing, are now
immobilized in the materials. At sufficiently high temperature, the
charges can migrate in the presence of an applied electrical field. These
charges are then blocked at the interface between the two media of
different conductivity and dielectric constant. In BNN-PS composites,
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
129
interfacial polarization is always present. Although this phenomenon is
clear in a conductive filler such as metal reinforced polymer composites
[35], polarizable filler-reinforced polymer composites have also been
shown to exhibit the MSW effect [36] The interpretation of the
impedance, dielectric and conductivity spectra and their electrical
characteristics support the statement that these materials, are essentially
insulating, although a slight increase in conductivity is observed with
increasing filler content. This trace of conductivity may be attributable to
an incipient tunnel effect known [37, 38] to allow the electrons to flow
from one conductor particle to the next through the polymer film
sandwiches between the particles, thus establishing an electric current.
The lesser the filler content, less likely are the electrons to leap from one
particle to the next, so for BNN10 the conductivity is minimum and the
composite exhibits purely capacitive behavior. As the filler content
increases, chances are given for electrons to flow through it and as a
consequence a drop in electrical resistivity of the polymer composite is
experienced. This fact confirms that, particle percolation is not achieved.
The filler particles cannot even be bought close enough together to give
rise to percolation condition. The particles are no longer in contact, but
surrounded by a fine polymer film and hence infinitesimal gaps among
the adjacent particles may conduct an electric current by tunneling effect.
Chapter IV
130
Table 4.3 Peak of dielectric losses at a frequency I MHz
Name of Sample Glass Transition Temp(0 C)
PS
108.7
BNN10
109.37
BNN20
112.13
BNN30
116.04
BNN40
117.12
This conductivity is dictated by nearest neighbour tunneling. The
percolation like behaviour is observed only when the radius of the particle
is superior to tunneling range.
4.2.7 Arrhenius Relation
By Arrhenius relation of activation, the conductivity of the composites is
− Eg
calculated by applying the relation σ
= σ 0 e K BT
(4.18)
where Eg is activation energy, KB is Boltzman’s constant. The results are
graphically represented in the fig 4.14.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
131
Polystyrene
BNN10
BNN20
BNN30
BNN40
32
30
28
26
-6
Conductivity * 10 (S/m)
24
22
20
18
16
14
12
10
8
6
4
2
0
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
(1000/T) K
Fig 4.14 Arrhenius plot of PS and composites.
4.2.8Variation of conductivity with frequency at a fixed temperature
The variation of ac conductivity with frequency is shown in figure 4.15 ,
((σ)ac is a temperature and frequency dependent term, and it is attributed
to the dielectric relaxation caused by localized electric charge carriers
which obey the following power law where B and ‘n’ are composition and
temperature dependent parameters by Koop’s equation for conductivity
[39]. Also the slope of the graphs gives values of ‘n’ which determines
the conducting behaviour of the grains.
(σ)ac (f, T)= Bfn at a fixed temperature
(4.19)
Log (σ)ac) = logB+ n log(f)
(4.20)
132
Chapter IV
Hence the slope of log (σ)ac) versus log(f) graph provides the value of
‘n’ while the intercept gives the value of extrapolated conductivity
expected at zero applied frequency. The enhancement of conductivity
properties is explained on the basis of correlated barrier hopping model.
The zero frequency value and ‘n’ increases with increase in filler content
The conduction is due to the hopping and tunnelling of electrons. As the
frequency of the applied field increases, the polarizable grains become
more active by promoting the hopping between Nb+4 and Nb+5 ions on the
octahedral sites, thereby increasing the hopping conduction [40-43]. These
electronic exchanges determine the polarization in the composites. The
polarization decreases with increase in frequency as in fig 4.8, and then
reaches a constant value due to the fact that beyond certain frequency of the
external field, the electronic exchange between Nb+4 and Nb+5 ions cannot
follow the alternating field. Thus we observe a gradual increase in
conductivity with frequency upto a frequency of one MHz.. It is found that
the conductivity saturates at high frequencies [44-46]. This means that
electronic exchange cannot follow field variations and saturation in the
generation of charge carriers was reached at high frequency [47-50].
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
133
18
Conductivity (S/m) *1e-6
16
14
PS
BNN10
BNN20
BNN30
BNN40
12
10
8
6
4
2
0
2
3
4
5
6
7
Log (f) Hz
Fig 4.15
Variation of ac conductivity with logarithmic frequency at
room temperature
4.3 Conclusion
Composites do not obey the law of physical mixtures for dielectric mixing.
The logarithmic law of mixtures confirms a logarithmic dependence of the
dielectric constant of the composite on the volume fraction of the filler.
Dipole moment of BNN in polystyrene matrix is 17.3439x10-30 Cm. This
dipole moment of BNN particles and the high induced polarization of BNN
under electric field contribute for the high dielectric constant of the
composites. For 10 to 40%, volume fraction of the filler, the composites
remain in their capacitive characteristics. Dielectric permittivity variations
can be fitted to Lichteneker relations. The dielectric constant of the
composites increases with increase in temperature. The glass transition
temperature of the composites increases with the increment of filler content.
Chapter IV
134
References
1
Meiya L, Min N, Yungai M A; J. Phys.D: Appl.Phys 40 (2007) 1603.
2
Myounggu P, Hyonny K, Jeffry P Y; Nanotech 19 (2008) 055705.
3
Yun K Y, Ricinschi D, Kanashima T, Okuyamma M; Appl. Phys.
Lett. 89 (2006) 192902.
4
Andre R S, Elena T V, Ludwig J. G ; J. Am. Ceram.Soc 89 (2006)
1771.
5
Antony J B ; Polymer, 26, (1985)567.
6
Montedo O R K, Bertan F M, Piccoli R, Oliveria A P N; Am. Ceram.
Soc. Bull, 87 (2008) 34.
7
Kuryan S, Abraham R., Isac J; Interl J of Matel Scie 3 (2008) 47.
8
Kumar V, Packia Selvam, Jithesh K, Divya P V; J. Phys. D:
Appl.Phys 40 (2007) 2936.
9
Borcia G, Brown N M D, J. Phys.D: Appl.Phys 40 (2007) 1927.
10
Devan R S , Despande S B, Chougule B K; J. Phys.D:
Appl.Phys 40 (2007) 1864.
11
Soumya K B, Amitha P, Panchanan P; J. Am. Ceram. Soc. 90
(2007) 1071.
12
Lichteneker K; J .Appl.Phys,27 (1956) 824.
13
Vemulapally G. K; Theoretical Chemistry Publ Asoke Ghosh,
Prentice Hall, New Delhi (2004).
14
Tareev B; Physics of Dielectric Material, Mir Publishers, Moscow
(1979).
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
15
135
Blythe A.R; Electrical properties of Polymers, Cambridge
University Press, London, (1974).
16
Bottcher C J F; Physics, 9, (1942)937.
17
Grossman D G, Isard J O; J. Phys. Appl. Phys.3 (1970)1061.
18
Van Beek L K H; Progr. Dielectr 7(1967) 60.
19
Galasso F G; Structure Properties and Preparation of Perovskite
Compound. Pergamon, Oxford, 1969.
20
Vrejoiu J D, Pedarnig M, Dinescu; J Appl. Phys. A 74 (2002) 407.
21
Newnham RE, Wolfe R W, Dorian ; Mater Res Bull 6, (1971)
1029.
22
Nakano H, Kamegashira , Urabe K; Mater. Res. Bull 36 (2001) 57.
23
Yang H, Shi J, Gong M; J Mater. Sci 40, (2005) 6007.
24
Habery F, Wiju HP ; J. Physic Statu Solidi 26, (1968)231.
25
Saxena N, Kumar K, Srivastava G. P; J Phys.Status.Solidi 127,
(1991) 231.
26
Jainwen XU, Wong C.P; J.Electronic materials 35, (2006).1087.
27
Parker R, Elewell D; J. Appl. Phys. 17, (1966)1269.
28
Brisco B. J; in Friction and Wear of Polymer Composites
Vol.published by R. B. Pipe Series editor(Elsheveir, Amsterdam
(1986).
29
Sichel E K; Appl.Phys.Commun 1, 83 (1981).
30
Suzhu Yu, Peter Hing , Xiao Hu; Jl of Appld Phys 88, (2000) 398.
Chapter IV
136
31
Pramod K S, Amreesh C ;J Phys D: Appl. Phys 36, (2003) L93.
32
Mark.G. B, John V. H, Kevin J P, Dan S P; J. Am. Ceram. Soc 90
(2007)1193.
33
Jose L A, Jose R J; J of Appl Poly Scie. 57 (1955) 431.
34
Sillars R. W; J Inst. Electr. Eng. 80 (1937)378.
35
Satish B, Sridevi K , Vijaya M S; J. Phys D: Appl. Phys 35 (2002)
2048.
36
Chiang C K, Popielarz R, Sung L P;Mat. Res. Soc. Symp. Proc.
Vol. 682 E (c) 2001 Material Research Society.
37
Mathew G, Nair S S, Anantharaman; J Phys. D: Appl. Phy. 40,
(2007).1593.
38
Hong X K, Hu G J, Chen J; J Amer. Ceramic Soc 90, (2007) 1280.
39
Koops C G; Phys. Rev 83 (1951) 121.
40
Gim Y, Hudson Y, Fan C K; Appl Phys Lett, 77 (2000) 1200.
41
Park W. Y, Ahin K. H. Hwang C. S; Appl. Phys Lett 83, (2003) 4387.
42
Hu G J, Chen J, An D L, Chu J H ;Appl Phys Lett 86 (2005) 162905.
43
Chen X Q, Qi HY, Qi Y J, Lu C; J Phys Lett A 346 (2005) 204.
44
Singh N K, Choudhary R.N. P; J Matel Science, 23, (2000). 239.
45
Joshna. S; J. Chemical Reviews, 99 (1999) 3604.
46
Reddy P V, Sathyanarayana R, Rao T S; J Phys. Status. Solidi ,
78, (1983) 109.
Dielectric Studies on Barium Sodium Niobate – Polystyrene Composites
47
137
Lee D, Wang Z, Zhang L,Yao X, Zhou H; J Mater. Res, 17
(2002) 723.
48
Popielarz R, Chiang C K, Nozaki R, Obrzut J; Macromol 34 (2001)
5910.
49
Wagner K W; Am..Phys., 40, (1973)317.
50
Yonglai Y, Mool C G, Kennath L D; Nanotech 15 (2004) 1545.