Conductivity and Space Charge in LDPE/BaSrTiO3
Nanocomposites
R. J. Fleming
School of Physics, Monash University, Victoria 3800, Australia
A. Ammala, P. S. Casey
CSIRO Materials Science and Engineering, Clayton, Victoria 3168, Australia
and S. B. Lang
Department of Chemical Engineering, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel
ABSTRACT
Nano-sized BaSrTiO3 particles and a dispersant were incorporated in samples of low
density polyethylene (LDPE). The nanoparticle loading was 2% or 10% by weight, and
the dispersant loading was 4 parts per hundred relative to BaSrTiO 3. dc conductivity
measurements were made in the temperature range 30-70 oC in vacuum, and in air at
30 oC. The vacuum dc conductivity in LDPE with 0.4% dispersant was approximately
five times larger than in LDPE, but in LDPE containing 0.4% dispersant and 10%
nanoparticles it was approximately a factor of 6-7 smaller than in LDPE. Since the
conductivity of the latter composite was smaller than that of its least conductive
component, it may be that the interface regions between the nanoparticles and the
LDPE control the dc conductivity. The dispersant and the nanoparticles both increased
, the real part of the relative permittivity. The  values for the nanoparticles, implied
by the Lichtenecker-Rother equation for a three-part composite, were of order several
hundred, much smaller than the value of at least 10,000 quoted by the nanoparticle
suppliers. Space charge measurements were made in air using the Laser Intensity
Modulation Method (LIMM), and the profiles calculated using the LIMM Monte Carlo
method. The maximum space charge density adjacent to the negative poling electrode
was 600 C/m3, for the pure LDPE and the LDPE with dispersant, and 200 C/m3 near
the positive electrode. The corresponding maxima in samples with dispersant and
nanoparticles were approximately an order of magnitude smaller. The Monte Carlo
method is more accurate than other methods of analyzing LIMM data, and this may
account for the very large densities close to the electrodes.
Index Terms — Low density polyethylene, barium-strontium-titanate nanoparticles, dc
conductivity, relative permittivity, space charge profiles, Monte Carlo method
1 INTRODUCTION
THE effects of nanosized particle additives on the
electrical properties of common dielectrics is currently of
considerable interest [1-5]. It is recognized that the interfaces
between the host dielectric and the nanometric particles can
strongly influence the dielectric properties of the composite
material as a whole. Thus the value of a given physical
property in the composite is not necessarily bounded by the
values of that property in the components [5].
Barium strontium titanate (BST) is a continuous solid
solution of ferroelectric BaTiO3 and paraelectric SrTiO3 [6].
Its paraelectric/ferroelectric transition temperature (Curie
temperature) decreases with increasing Sr content, e.g.,
approximately 0 oC for Ba0.6Sr0.4TiO3 and -70 oC for
Ba0.4Sr0.6TiO3 [7]. It is of considerable interest in the fields of
electroceramics and microelectronics [8-11]. Much work has
been done on BST thin films [12-15], particularly on their use
as integrated storage capacitors in gigabit DRAMs [16]. Such
films tend to have:
(a) high relative permittivity , which may exceed 103 but
falls to a few hundred due to residual tensile stress in films
grown on silicon substrates [12]. It increases with increasing
film thickness [13] and decreases with increasing applied field
[6]
(b) low tan δ, typically 0.01 to 0.05, increasing with increasing
film thickness [6]
Table 1. Dielectric data for polymer/BST composites
ε/Freq (Hz)
tan δ/Freq(Hz)
Ref
Cyclic olefin
Particle Size/
Volume Fraction %
-
2.4/109
10-4/109
17
Cyclic olefin
0.2-2 μm/100
0.2-2 μm/2.5
1757/105
2.6/109
10-3/105
10-4/109
"
“
"
0.2-2 μm/25
6.0/109
9 x 10-4/109
"
3 x 10-3/109
"
"
0.2-2 μm/60
21.4/10
9
9
-4
9
"
"
< 200 nm/2.5
< 200 nm/25
2.6/10
7.3/109
10 /10
2.3 x 10-3/109
"
“
"
< 200 nm/33
11.0/109
9 x 10-3/109
"
Silicone rubber
-
2.11/104
-
18
4
Silicone rubber
5-10 μm/100
5-10 μm/100
5-10 μm/18
6654/10
2000/107
13/104-11/107
-
"
"
"
"
5-10 μm/40
26/104-23/107
-
"
4
7
"
5-10 μm/52
35/10 -33/10
-
"
"
5-10 μm/64
166/104-125/107
-
"
*PP/P(s-dvb)
-
2.33/109
-
19
*PP/P(s-dvb)*
?/100
?/5
2112/109
2.98/109
6.1 x 10-4
"
"
"
?/40
15.73/109
61.7 x 10-4
"
*Polypropylene grafted to Poly(styrene-stat-divinylbenzene) without surfactant
(c) Low leakage current, typically less than 10-8 A/cm2 at 10
kV/mm [16].
Much work has also been done on the dielectric properties
of polymer/BST composites.
A Finnish group [17]
synthesized composites of a thermoplastic cyclic olefin
copolymer and BST, the BST particle size being either 0.2–2
μm with an average of 1 μm (microcomposite), or less than
200 nm (nanocomposite). The thickness of the composite
samples on which measurements were made was 1.5-2 mm.
See Table 1 for  and tan δ values. The  values in the
microcomposites were well fitted over the whole BST volume
fraction range by a modified Lichtenecker-Rother logarithmic
law (see below), but only up to a BST volume fraction of 10%
in the nanocomposites, assuming the microsized BST  value.
The authors suggest that discrepancies at higher nanosized
BST loadings could be due to the increased interfacial bonding
areas between polymer and BST nanoparticles.
Liou and Chiou [18] fabricated composites of silicone
rubber (10 parts of RTV 630A and one part of RTV 630B)
and laboratory-synthesized BST. The BST volume fractions
were 18, 40, 52 and 64 %, and the thickness of the composite
samples was 0.4 mm. The BST particle size was 5-10 μm.
The authors considered each composite as a two-phase
dielectric mixture, consisting of a silicone rubber matrix with
= 2.11 and a BST additive. See Table 1 for  and tan δ
values. At the three lower volume fractions the  values were
consistent with the Maxwell-Garnett mixing formula (see
section 3.2).
Sonoda et al [19] studied the effect of a surfactant on the
dielectric properties of composites of polypropylene grafted to
poly(styrene-stat-divinylbenzene) and BST. No information is
given on the size of the BST particles. The surfactants were
caproic acid, lauric acid, stearic acid and behenic acid. See
Table 1 for  and tan δ values. Surfactant treatment had little
effect on the tan δ values but slightly increased the  values at
the higher BST loadings. The latter followed a modified
Lichtenecker-Rother equation containing an additional
parameter which varied slightly with BST loading. A particle
distribution study showed that the surfactants with longer
chains gave better dispersion of the BST particles in the
polymer matrix.
Low density polyethylene (LDPE) is one of the most widely
studied and utilized polymers. To the best of our knowledge the
effects of adding nanosized BST particles on its dielectric
properties have not been reported. In this paper we present dc
conductivity, ac impedance and space charge profile data for
LDPE films in which nanosized BST particles and a dispersant
had been incorporated.
2 EXPERIMENTAL
2.1 SAMPLES
The base polymer was an additive-free LDPE (Lotrene
FB3003 from Qatar Petrochemical Company), melt flow index
0.30 g/10 min, density 920 kg/m3 at 23 oC, and crystalline
melting point 109 oC. The suppliers of the BST nanopowder
(TPL Inc.) quoted a nominal particle size of 50 nm and  =
10,000-15,000; the barium/strontium ratio was 60/40. The
powder was chemically and mechanically pretreated using a
proprietary process and a hyperdispersant based on carboxylic
acid functionality (Solsperse S21000 from Lubrizol
Corporation, a viscous liquid at room temperature, density 900
kg/m3, possibly the stearate ester of poly(12-hydroxystearic
acid)). After drying in a vacuum oven, the selected powder
was blended with the cryoground LDPE at loadings of 2 and
10 % w/w. The dispersant loading was 4 parts per hundred
relative to BST. Samples were then compounded using a
DSM Micro 15 cm3 Compounder under controlled conditions
with a barrel and die temperature of 200 °C. Molten samples
were extruded in the form of rods and cut into pellets after
drying. A hot press was used to form the pellets into films
150-200 m thick, from which circular samples of 80 mm
diameter were cut. Aluminium electrodes 45 mm in diameter
and 100 nm thick, and a guard ring, were deposited on the
samples by sputtering.
2.2 MEASUREMENTS
TEM images were obtained by sectioning composite
samples and mounting them between two 50 mesh copper
grids. A Philips CM30 transmission electron microscope
operating at an accelerating voltage of 200kV was used to
image the samples. Electron-transparent areas existed near
the edges and towards the centres of these samples.
dc conductivity measurements were made in the temperature
range 30-70 oC, and in vacuum (pressure 1.3 x 10-3 Pa or 10-5
torr) in order to avoid oxidation of the LDPE. Measurements
were also made in air at 30 oC. Before measurements were
commenced each sample was held between grounded
electrodes at 70 oC in vacuum for at least 24 hr, so that excess
charge might dissipate. Before another measurement at
different field or temperature was commenced, the sample was
again held between grounded electrodes until the current fell to
a negligible level.
ac impedance measurements were made under vacuum over
the same temperature range, and in air at 30 oC, using a
Solartron SI1260 Impedance/Gain-Phase Analyzer, in
conjunction with a Solartron 1296 Dielectric Interface. The
frequency range was 10 mHz to 100 kHz. Ten measurements
were taken at each frequency, and the resulting data averaged.
The applied voltage was 3 V rms, with zero dc bias.
Space charge profile measurements were made in air at
room temperature using the laser-intensity-modulated method
(LIMM) [20]. Each sample was exposed to a dc voltage of
3100 V for 24 hours at room temperature.
LIMM
measurements were made immediately after poling, and 24 hr
thereafter (without further poling). Both electrodes were laserirradiated separately, in order to obtain data to a depth of
approximately 15 μm below each electrode. Measurements of
the real and imaginary components of the pyroelectric currents
generated by the laser irradiation were made at 50 different
logarithmically-spaced frequencies between 10 Hz and 50
kHz. In order to eliminate external electrical interference, the
sample holder and the current amplifier were placed in a
Ramsey Portable RF Shielded Test Box.
3 RESULTS & DISCUSSION
3.1 TEM
Figure 1 is a TEM image of a small piece of a composite
sample, approximately 10 μm thick, containing 0.4% w/w
dispersant and 10% w/w BST nanoparticles. It shows
reasonably well and homogeneously dispersed nanoparticles of
higher electron density (dark spots) embedded in a lower
electron density medium (LDPE).
Figure 1. TEM image of a composite sample containing 0.4% w/w
dispersant and 10% w/w BST nanoparticles. The dark spots are the BST
nanoparticles.
3.2 DC CONDUCTIVITY
The current flowing at least 20 hrs after the application of
the field was taken as the "steady state" current; at such times
the rate of current decrease was very slow in all samples.
Figure 2 shows log (steady state dc current) versus 1000/T,
measured in vacuum on samples with various additive
contents, at an applied field strength of 20 kV/mm.
Addition of the dispersant to the LDPE increased the current
by a factor of approximately 5, at all but the lowest
temperature. A similar increase was observed in our earlier
work [21,22]. Addition of the dispersant and 2% w/w
nanoparticles gave currents slightly larger than those in LDPE
without dispersant, while addition of the dispersant and 10%
nanoparticles decreased the currents by a factor of 6-7 relative
to LDPE without dispersant. The same ordering was observed
at 10 kV/mm.
Another well-established formula is that of Bruggeman
(sometimes called the symmetric Bruggeman or effective
medium formula) [24]. It is widely used in electromagnetics.
It reads, for a mixture with N isotropic spherical inclusions,
log (current pA)
5
4
(3)
3
.
2
1
2.9
3
3.1
3.2
3.3
1000/(Temp K)
Figure 2. log (dc current) versus 1000/T, at 20 kV/mm in vacuum.  LDPE,
□ LDPE + 0.4% dispersant, Δ LDPE + 0.08% dispersant + 2% nanoparticles,
 LDPE + 0.4% dispersant + 10% nanoparticles.
If the dc conductivity  (T) followed the familiar Arrhenius
relationship
 (T) = o exp(-Ea/kT)
(1)
where o is a constant, Ea is the activation energy for the
charge transport mechanism, k is Boltzmann‘s constant and T
is the absolute temperature, a plot of log current against 1/T
would be a straight line. This is clearly not the case in Figure
2, the nearest approach being that of the sample with 0.4 %
dispersant and 10% nanoparticles. For that sample a fit to (1)
yielded Ea = 1.18 eV with a correlation coefficient R2 = 0.987,
the corresponding values at 10 kV/mm being 1.27 eV and
0.995. However, approximate values of Ea, obtained over the
narrow temperature ranges accessed through the temperature
controller overshoots, decreased from 1.5 eV at 30 oC to 0.9
eV at 70 oC. A similar range was obtained for a sample
containing 0.08% dispersant and 2% nanoparticles. These
results suggest that a range of activation energies, rather than
one discrete value, exists in a given sample.
Many approximate formulae have been proposed for the
relative permittivity εeff of a composite of two homogeneously
mixed weakly-conducting materials, specifically a host with
relative permittivity εh and an inclusion of spherical particles
with relative permittivity εi [23-25]. They proceed by
calculating the average electric field < E > and the average
electric displacement < D > over the sample volume, and
defining εeff as the ratio < D >/< E >. Identical formulae apply
to dc conductivity  [26-28]. Several of these formulae can be
expressed in the form
eff = {(1-f) h + f Κ i}/(1-f + f Κ)
(2)
where f is the volume fraction of the inclusion and Κ is the
ratio of the average electric field in the inclusion to that in the
host. K may depend on the ratio i/h, f, and the shape, size
and orientation of the inclusion particles [23]. Thus K = 3h
/(i + 2 h) for the case of spherical inclusions randomly
distributed through the host, leading to the classical Maxwell
Garnett mixing formula [24].
where eff is the conductivity of the mixture and the fj are the
volume fractions of the inclusions. It is symmetrical in the
sense that each term on the left-hand-side is of the same form,
representing the contribution from one component of the
mixture.
Finally, the Lichtenecker-Rother logarithmic mixing
formula applied to conductivity is [29]
log eff = f log i + (1-f) log h
(4)
where f is again the volume fraction of the inclusion.
Although it was developed specifically for the relative
permittivity of mixtures, one might expect it to apply to dc
conductivity since the same mathematical formulation is
involved in both [30,31]. Some work on sulgin-talc mixtures
[32] suggests that it is indeed applicable to dc conductivity,
provided the volume fractions are replaced by weight
fractions. It has been criticized on the grounds that there are
logical errors in its formulation [25, 33]. However, Zakri et al
[34] showed that by combining a beta function distribution of
the geometrical shapes of inclusions with effective medium
theory, and assuming self-consistency, Lichtenecker‘s
formulae [35] can be derived. Furthermore, it has been shown
very recently [36] that the Lichtenecker-Rother logarithmic
formula [29] can be derived by applying Maxwell‘s equations
and the principle of charge conservation to a mixture in which
the shapes and orientations of the components are randomly
spatially distributed, and that the symmetric mixture formula
of Bruggeman (3) can be obtained from the LichteneckerRother formula. There is also considerable experimental
support for the Lichtenecker-Rother formula, based on data for
chaotic mixtures with near-spherical inclusions (see references
in [33]). According to [34] it is applicable to composites with
more than two components.
In our earlier work [21,22] we ignored the increase in
conductivity, typically by a factor of five, when the dispersant
was added to the LDPE, because it was numerically much
smaller than the reduction in conductivity, typically by two
orders of magnitude, when the nanoparticles were added to
the LDPE/dispersant. This is not the case for the present BST
nanoparticles, and so the increase due to the dispersant must
be considered.
At 20 kV/mm in vacuum, Figure 2 indicates eff ≈ 5h for
LDPE containing 0.4% dispersant over most of the
experimental temperature range. The conductivity of the
dispersant in vacuum is not known, but we measured it in air at
room temperature at low field strength (33 V/mm) and
obtained 8.9 x 10-12 Sm-1. The measured conductivity of
LDPE at 30 oC and 20 kV/mm was 2.7 x 10-15 Sm-1. Then:
(a) (2) yields Κ = 0.30, a surprisingly large figure given that
the conductivity of the dispersant is more than three orders of
magnitude greater than that of the LDPE.
(b) (3) is inconsistent with the data, the two terms in the
summation differing by a factor of 90.
(c) (4) is also inconsistent with the data, the left-hand-side
being 50 times the right-hand-side.
In air at 30 oC , addition of 0.4% dispersant to the LDPE
increased the current by a factor 2-3. At 10 kV/mm (2) gave K
= 0.14, while (3) and (4) were again inconsistent with the data.
Addition of 2% and 10% nanoparticles decreased the
conductivity in vacuum and at 20 kV/mm relative to that of
LDPE samples containing dispersant only (Figure 2).
Assuming that the current magnitude is controlled by the bulk
conduction mechanisms, we would then deduce that the
conductivity of the nanoparticles is less than that of LDPE
with dispersant only. Eqs. (3) and (4), which apply to
composites containing two or more components, certainly
imply that the conductivity of the composite will be greater
than that of the least conductive component, and less than that
of the most conductive component. Conductivity values for
nano-BST are not readily available, but a figure of 1.6 x 10 -10
Sm-1 at an applied field of 12.5 kV/mm in air at room
temperature has been published for excimer laser ablated BST
thin film [37]. The conductivity may be lower in vacuum than
in air, but is unlikely to be less than 3.8 x 10 -15 S/m obtained
here for LDPE containing 0.4 % dispersant at 30 oC in vacuum
at 20 kV/mm. The reduction in conductivity following the
addition of the nanoparticles is therefore surprising; it could be
due to the influence of the LDPE-nanoparticle interfaces in the
sample bulk, since it has been found that the value of a given
physical property in a nanocomposite is not necessarily
bounded by its values in the components [5]. Alternatively it
may be that the measured currents are controlled
predominantly by the charge injection mechanism operating at
the electrode-LDPE interface, which would also be influenced
by the LDPE-nanoparticle interfaces.
In air at 30 oC, addition of 0.08% dispersant and 2%
nanoparticles gave a current of comparable magnitude with
that in the LDPE. However, addition of 0.4% dispersant and
10% nanoparticles increased the current at 10 kV/mm by a
factor of about 2.5 (relative to LDPE without dispersant) but
left it largely unchanged at 20 kV/mm.
It may be concluded that
(a) the conductivity of the LDPE + 0.4% dispersant samples in
vacuum and in air is consistent with the classical mixing
formula, although the field ratio is surprisingly large. It may
be that the dispersant reacts chemically with LDPE. However,
this would not be expected given the likely identity of the
dispersant.
(b) the conductivity of the LDPE + 0.4% dispersant + 10%
BST nanoparticles samples in vacuum and in air is not
consistent with the 3-component symmetric Bruggeman or
Lichtenecker-Rother formulae, in that the measured values are
less than the conductivity of the least conductive component
(LDPE). This may be an indication of the influence of the
interfacial regions between the nanoparticles and the LDPE
matrix [1].
3.3 AC IMPEDANCE
Figure 3 shows the real part  of the complex relative
permittivity of various samples measured in vacuum at 30 oC,
as a function of frequency. Essentially identical data were
obtained in air at 30 oC. There is some unexpected localized
variation of the values with frequency, also seen in Figure 4,
which is probably due to instrumental artefacts. If such
variation is ignored, we may conclude that the permittivity is
independent of frequency over the experimental frequency
range. The values for LDPE quoted in the commercial
literature lie mostly in the range 2.25-2.30, so that the value
around 2.34 for the base LDPE is a little higher than would be
expected, possibly due to the samples being slightly thicker at
the edges than at the centre.
2.6
2.56
2.52
 ' 2.48
2.44
2.4
2.36
2.32
-2
-1
0
1
2
3
4
5
log freq(Hz)
Figure 3.  versus log frequency in vacuum at 30 OC for  LDPE, □ LDPE
+ 0.4% w/w dispersant, Δ LDPE + 0.08% w/w dispersant + 2% w/w
nanoparticles,  LDPE + 0.4% w/w dispersant + 10% w/w nanoparticles.
Addition of 0.4% dispersant to LDPE increased  from
approximately 2.34 to 2.49. By comparing the capacitance
values of a concentric cylindrical capacitor, in air and when
filled with the dispersant, we deduced ε' for the dispersant to
be3.0 ± 0.1 at room temperature, over the frequency range 25
Hz to 200 kHz. The increase in ε' on adding the dispersant is
therefore surprisingly large, given the very small dispersant
volume fraction and the similar  values. Using (2) in its
relative permittivity form, and substituting c =2.49, i = 3.0
and h = 2.34, we obtain K= 75, which seems unduly large.
Similarly, the two terms in (3) differed by a factor of 100, and
(4) implies i > 107.
In some recent work [38], micro-sized (300 nm) and nanosized (15 nm) rutile TiO2 particles were incorporated in a
styrene-ethylene-butadiene-styrene copolymer, using sorbitan
monopalmitate as a surfactant (or dispersant).
 for the
copolymer was 2.2 over the range 20 Hz – 1 MHz. It
increased steadily to 3.4 at 2% surfactant volume fraction,
again largely independent of frequency, but did not change
with further increases in surfactant volume fraction.  for the
surfactant is not quoted, but it would be expected to be similar
to that of the dispersant used in the present work.
Consequently the increase in  due to addition of the
surfactant is also surprisingly large for this system.
Turning now to the LDPE + 0.4% dispersant + 10%
nanoparticles plot in Figure 3, (3) yields a negative  value for
the BST. However, (4) (with three terms on the right-handside) yields a value around 450. While this is much smaller
than the minimum value (10,000) quoted by the suppliers of
the BST, the value for the composite (≈ 2.58) is consistent
with the greatly reduced values reported in [18,19].
Figure 4 shows  measured in vacuum at 70 oC. The
ordering of Figure 2 is reproduced, but all the  values are
smaller. Again (3) yields a negative  value for the BST, but
(4) gives 145.
If we assume that the samples are only weakly polar,
consistent with the nanoparticle material being above its Curie
temperature, we can estimate the change in  with temperature
by differentiating the Clausius-Mossotti equation [39] with
respect to temperature. We obtain
(d/dT) = - T ( - 1) ( + 2)
(5)
2.44
2.4
2.36
'
2.32
2.28
2.24
2.2
-2
-1
0
1
2
3
4
5
log freq(Hz)
Figure 4.  versus log frequency in vacuum at 70 OC.  LDPE, □ LDPE +
0.4% dispersant,
Δ LDPE + 0.08% dispersant + 2% nanoparticles,

LDPE + 0.4% dispersant + 10% nanoparticles.
where T is the thermal expansion coefficient of LDPE. T
values in the commercial literature average around 3 x 10 -4/oC.
Integrating (5) from 30 oC to 70 oC , and assuming T
independent of temperature, we expect  for LDPE in vacuum
to decrease from 2.34 at 30 oC to 2.27 at 70 oC. The
experimental value around 2.25 is in reasonable agreement,
given the uncertainty in T and its likely increase with
increasing temperature. T for the dispersant is unknown, but
the reduction in  for LDPE + 0.4% dispersant from 30 oC to
70 oC implies T = 4.33 x 10-4/ oC. This value, more than 40%
larger than that assumed for LDPE, is surprising, given the
very small volume fraction of dispersant. The value for the
LDPE + 0.4% dispersant + 10% nanoparticles composite,
calculated in the same way, is 5.54 x 10-4/ oC. Thus the
nanoparticles also appear to affect thermal expansion
significantly.
Figure 5 shows tan δ measured at 30 oC in vacuum versus
frequency. The main feature is the unexpected absorption
around 30 kHz (a corresponding feature is visible in Figures 3
and 4). There is little magnitude variation between samples. A
similar plot was obtained at 30 oC in air.
0.008
0.006
 δ0.004
tan
0.002
0
-2
-1
0
1
2
3
4
5
log freq(Hz)
1
Figure 5. tan δ versus log frequency in vacuum at 30 OC.  LDPE, □
LDPE + 0.4% dispersant,
Δ LDPE + 0.08% dispersant + 2%
nanoparticles,  LDPE + 0.4% dispersant + 10% nanoparticles.
Figure 6 shows the corresponding data in vacuum at 70 oC;
note the dramatic increase at frequencies below 0.1 Hz.
Addition of the dispersant resulted in a smaller increase, and
addition of the dispersant and nanoparticles gave a much
smaller increase. It is logical to seek a correlation between tan
δ at low frequencies with dc conductivity ; the smaller increase
in the former in samples containing nanoparticles seems
consistent with the decrease in dc conductivity. However,
addition of the dispersant gave a smaller increase in tan δ but
an increase in dc conductivity.
0.05
0.04
tanδ
0.03
0.02
0.01
0
-
-1
0
1
2
3
4
5
log freq (Hz)
Figure 6. tan δ versus log frequency in vacuum at 70 OC.  LDPE, □
LDPE + 0.4% dispersant,
Δ LDPE + 0.08% dispersant + 2%
nanoparticles,  LDPE + 0.4% dispersant + 10% nanoparticles.
It may be concluded that
(a) The increase in ε on adding 0.4 % dispersant to LDPE is
larger than would be expected, given the small volume fraction
of the dispersant. This observation supports the earlier
suggestion that a chemical reaction may be occurring between
the two components.
(b) The ε value for the LDPE + 0.4% dispersant + 10% BST
nanoparticles samples is consistent with the 3-component
Lichtenecker-Rother formula, but implies an effective ε for
the nanoparticles much smaller than that quoted by the
suppliers.
3.4 SPACE CHARGE PROFILES
The relationship between the measured pyroelectric currents
and the space charge distribution is given by a Fredholm
integral equation of the 1st kind. This is an ill-conditioned
problem with multiple solutions. There are several different
methods for solving the equation. The recently developed
Monte Carlo technique, which has high accuracy, was used to
solve this equation. The complete algorithm is given in [40].
The accuracy of the method was checked by solving for the
electric field in one of the sets of experimental data, using the
field values to calculate the real and imaginary components of
the pyroelectric current at each of the measurement
frequencies, and then comparing the calculated currents with
the experimental current data. The agreement was very good,
confirming that the Monte Carlo method produces accurate
solutions of the LIMM equation. The calculated space charge
profiles (in air at room temperature) are shown in Figure 7.
Figure 7. Space charge profiles in air at room temperature. (a) LDPE poled at 19.9 kV/mm; (b) LDPE + 0.4% dispersant poled at 17.4 kV/mm; (c) LDPE +
0.08% dispersant + 2% BST poled at 18.8 kV/mm; (d) LDPE + 0.4% dispersant + 10% BST poled at 19.4 kV/mm.
Several interesting features should be noted:
(a) The space charge densities in the LDPE and LDPE +
dispersant samples close to the electrodes (Figure 7 (a) and
(b) respectively) are much larger than those commonly
reported for LDPE. However, they are comparable with
those measured using the LIMM technique in nominally
identical samples poled for much the same time but at
slightly higher applied fields (27 kV/mm) [22]. The high
spatial resolution of LIMM near the electrodes (typically 12 μm) would be expected to yield space charge densities in
those regions which are more accurate than those obtained
using the more popular LIPP or PEA techniques; the latter
have spatial resolution of approximately 10 μm in samples
150-200 μm thick.
(b) In the sample without additive (Figure 7(a)) the
maximum negative space charge density near the
negatively-poled electrode increased by a factor of
approximately 1.6 during the 24 hr interval between the first
and second measurements. An even larger multiplication
occurred in the sample with dispersant and 2% BST
particles (Figure 7(c)), although the absolute densities were
smaller and the charge positive. There is no obvious
explanation for these counter-intuitive increases.
(c) In the samples containing BST, the space charge
densities adjacent to both electrodes were much smaller
than those in the samples without BST. In all samples the
maximum densities (absolute values) adjacent to the
negatively-poled electrode were much greater than those
adjacent to the positively-poled electrode. Clearly the
nanoparticles strongly affect the charge transfer mechanisms
between both electrodes and the LDPE.
4 CONCLUSIONS
The following tentative conclusions regarding the influence of
BST nanoparticles incorporated in LDPE may be drawn from
this work:
(a)They reduce dc conductivity, suggesting that the interface
areas between the nanoparticles and the LDPE are particularly
influential
(b) They increase ε in accordance with the 3-component
Lichtenecker-Rother logarithmic formula, but the implied
effective ε for the nanoparticles is very much smaller than that
quoted for the ―free‖ nanoparticles.
(c) They reduce the space charge density adjacent to both
electrodes.
(d) The effect of the dispersant on the studied properties,
relative to that of the dispersant combined with the
nanoparticles, is significant, and cannot be neglected in the
analysis.
ACKNOWLEDGMENTS
RJF acknowledges more than thirty years friendship with
Professor Gerhard Sessler, and many fruitful discussions of
charge transport and space charge accumulation in insulating
polymers. SBL also sends his warmest greetings and thanks
for many years of friendship, and advice and guidance in
numerous scientific matters.
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Robert
Fleming
graduated
in
mathematics and physics from Queen‘s
University, Belfast in 1959, and
subsequently obtained the Ph.D. and
D.Sc. degrees from the same university.
He moved to the Department of Physics,
Monash University, Australia in 1967,
and formally retired from that
Department in December 2000. He was
then appointed as a Senior Honorary
Research Fellow and is continuing his
research on the electrical properties of
polymers, particularly charge transport
and trapping and space charge
accumulation. He is a Fellow of the
Australian Institute of Physics, an Associate Editor of the IEEE Transactions on
Dielectrics and Electrical Insulation, and Co-Editor-in Chief of the IEEE
Electrical Insulation Magazine.
Anne Ammala completed her B.Sc.
(Honours) (1990) and Ph.D. degrees in
chemistry (1994) at the University of
Newcastle,
Australia.
After
postdoctoral studies in Geneva,
Switzerland (1995), she worked at
Monash University, Australia before
joining CSIRO (1997) where she is
now a senior research scientist. Her
current areas of interest include the
development
of
new
oxobiodegradable
polymers
and
nanoparticle additives for polymers
and coatings, encompassing several
application areas such as nucleating agents, UV protection, flame
retardants and reduced gas permeability.
Phil Casey received his chemistry
degree from the University of
Canterbury, New Zealand and
postgraduate
qualifications
inIndustrial Chemistry and Chemical
Engineering from the University of
NSW, Australia in 1982 in
heterogeneous catalysis.
He is
currently Research Group Leader
(Polymers) at CSIRO (Materials
Science and Engineering) and Stream
Leader (High Performance Materials
and Coatings). His current interests
include the
design
of
lattice
engineered
nanoparticles
for multifunctional polymer (nano) composites and coatings, adaptive and
responsive polymers including thermochromic, shape memory and
electroconductive systems.
Sidney Lang (SM99) received a
petroleum refining engineer degree from
the Colorado School of Mines in 1956
and a Ph.D. degree in chemical
engineering from the University of
California at Berkeley in 1962. He
entered academia as an Associate
Professor of Chemical Engineering at
McGill University, Montreal, Canada
from 1968 to 1973. He has been a
Professor of Chemical Engineering at
Ben-Gurion University of the Negev,
Beer Sheva, Israel since 1973. His research interests are in applications of
pyroelectricity and piezoelectricity, and electrical properties of biological
materials. He is a Senior Member of the IEEE, a member of the American
Physical Society and a member of the Russian Academy of Engineering
Science. He is an Associate Editor of several journals: IEEE Transactions on
Ultrasonics, Ferroelectrics and Frequency Control; Ferroelectrics; and
Ferroelectrics Letters. He is the Departmental Academic Advisor of the
Department of Applied Physics, Hong Kong Polytechnic University, Hong
Kong.