Polyvinylidene fluoride (PVDF) based fluoropolymers are promising materials for capacitors in pulsed power applications because of their high dielectric constant compared to other polymers. High energy losses, such as conduction losses or ferroelectric losses, impose great challenges for large-scale commercialization. Here, we present a systematic study on the high field electrical conduction of biaxially oriented PVDF films. The conductivity shows a surprising initial decrease, followed by a gradual increase, with increasing electric field. The unexpected decrease in conductivity arises from ferroelectric switching, and the electric field of the transition point in conductivity is consistent with the switching field for polarization reversal. This suggests that PVDF films with pre-aligned ferroelectric domains could simultaneously exhibit reduced high field conduction losses and ferroelectric losses.

Capacitors are critical components in high voltage pulsed power systems, such as pulse-forming networks (PFNs) and medical defibrillators.1,2 In these applications, development of high energy density and power density capacitors is highly in demand, as it will enable the miniaturization of electronic devices. This is especially true, considering that nowadays the capacitors still occupy a large fraction of volume and contribute to majority of their cost, while other active components have undergone dramatic size reduction in the last twenty years. Polyvinylidene fluoride (PVDF) and its derivatives have been extensively studied as candidates for high energy density capacitors due to their high dielectric constant.3 Discharge energy density above 6 J/cc has been achieved in large size prototype capacitors based on these high k fluoropolymers; over 25 J/cc can be achieved for lab-scale capacitor film samples.2,4

However, one of the most critical issues for PVDF-based fluoropolymers is the large energy losses due to electrical conduction and the hysteresis of ferroelectric switching under high fields, which limit their applications to pulsed power systems with low repetition rates. Over the past several years, numerous studies have been reported about improving the high field performance of fluoropolymers by adding nanoparticles,5,6 formulating blends,7 or fabricating multi-layered structures.8 But, most of these studies focus on reducing ferroelectric losses, with less attention to high field electrical conduction. In fact, in order to achieve high energy density, dielectric materials must be operated at >600 MV/m, close to their breakdown strength. It is known that the leakage current may increase exponentially with the electric field and could dominate the energy losses in capacitors at high fields and high temperatures.9 As a result, the knowledge of high field conduction behavior for PVDF-based polymers is essential for the successful implementation of these high k polymers in high power applications.

In this paper, we present our systematic studies on the electrical conduction of biaxially oriented PVDF (BO-PVDF) films using a special homemade test fixture, which allows us to measure the leakage current in air at high electric fields without premature specimen dielectric breakdown. The results are quite surprising as the conductivity of PVDF films exhibits an unexpected dependence on electric field. The implication of these results for developing PVDF-based capacitors for pulsed power systems is also discussed.

BO-PVDF films were melt-extruded and then biaxially oriented at an elevated temperature to maintain the high content of the nonpolar α phase. The nominal film thickness was 8.0 μm. A gold electrode of 6.2 mm diameter was sputtered on both surfaces of the films, respectively, for electrical measurements. High field electrical conduction was measured with a PK-SPIV17 (PolyK Technologies, USA). Specifically, the leakage current was recorded using a Keithley 6517A electrometer with a Stanford Research Systems PS 350 as a high voltage source in a thermal chamber set to 25 °C. High voltages were applied with a unique spring-loaded ball electrode to maintain a reasonable electrical connection without damaging the soft thin polymer film. Under a high DC electric field, the leakage current drops gradually as a function of test time and stabilization of current will take several hours or longer. For comparison purpose, for each voltage/temperature test, fresh BO-PVDF specimens were always used and leakage current after 15 min measurement was used to define resistivity or conductivity. Polarization loop measurement was performed in a PK-CPE1801 Ferroelectric and Dielectric Breakdown Strength test system (PolyK Technologies, USA). The samples were subjected to a unipolar/bipolar wave, with varied frequencies. Fourier transform infrared (FTIR) spectroscopy was performed with a Perkin Elmer Spectrum Two spectrometer at a resolution of 2 cm−1 with 32 scans.

The electrical conduction of the pristine BO-PVDF thin film under high electric fields is presented in Fig. 1(a). After a brief increase in conductivity from 5 MV/m to 30 MV/m, an unexpected decrease is observed until a transition field is reached, beyond which the conductivity increases again with further increasing e-field. The abnormal decrease in conductivity cannot be explained by any high-field conduction theories for typical dielectric materials and might be associated with the ferroelectric nature of PVDF. It is known that PVDF can undergo electric field-induced phase transitions if poling voltages are strong enough;10 besides, the ferroelectric β phase of PVDF can be permanently polarized under high fields.11 Figure 1(b) compares the FTIR spectra of the BO-PVDF before and after the conductivity measurement. The two curves are largely overlapped and the relative content of the β phase [Eq. (S1)] is almost identical, only reducing from 31.6% before the measurement to 29.3% after the measurement. The FTIR comparison indicates that the initial decrease in conductivity is not due to the phase transformation during the conductivity measurement, which can be understood as usually a much higher E-field is required to trigger the phase transition [e.g., above 300 MV/m (Ref. 12)]. Note that the slight decrease in the β phase content actually reflects the field-induced alignment of the –CH2CF2– dipoles in the β crystals. The IR absorption bands at 841 and 1280 cm−1, corresponding to the symmetric and asymmetric stretching modes of the CF2 groups in the β-phase, will show a reduced intensity when these β dipoles are oriented parallel to IR radiation (i.e., lying in the thickness direction of the film).

FIG. 1.

(a) Conductivity as a function of electric field for the pristine BO-PVDF film and the prepoled film; the latter was subjected to an E-field of 220 MV/m for 15 min before the conductivity measurement. (b) FTIR spectra of the BO-PVDF film before and after the conductivity measurement. Major bands for α and β phases are assigned.

FIG. 1.

(a) Conductivity as a function of electric field for the pristine BO-PVDF film and the prepoled film; the latter was subjected to an E-field of 220 MV/m for 15 min before the conductivity measurement. (b) FTIR spectra of the BO-PVDF film before and after the conductivity measurement. Major bands for α and β phases are assigned.

Close modal

On the other hand, the effects of ferroelectric polarization reversal on conductivity can be illustrated by comparing the pristine BO-PVDF film with the prepoled film. As also included in Fig. 1(a) is the result of the BO-PVDF which has been subjected to an electric field of 220 MV/m for 15 min before measurement. The conductivity of the prepoled sample exhibits a monotonic increase with the E-field and coincides with that of the pristine BO-PVDF in the electric field which happens to be the transition point in conductivity for the pristine film. These results strongly imply that the abnormal reduction of conductivity is related to the ferroelectric polarization switching, which should be accomplished at an E-field of ca. 90–100 MV/m.

However, it is intuitively expected that an e-field much higher than 90–100 MV/m is required to polarize the ferroelectric phase of PVDF.13,14 In fact, based on the polarization loop measurement on BO-PVDF (Fig. S1), the ferroelectric polarization reversal occurs at a minimum electric field of 350 MV/m, as the remanent polarization and the maximum polarization become stabilized afterward. But, it is also known that the dipole orientation is a relaxation process, where the longer the poling duration is the lower the E-field is needed to achieve the same polarization.15 In order to verify whether this lower transition field is related to the prolonged poling time during the conductivity measurement, the polarization loops of the BO-PVDF are measured over a wide range of frequencies, as shown in Fig. S2, and the representative results are presented in Fig. 2(a).

FIG. 2.

(a) Representative displacement vs. electric field (D-E) hysteresis loops for BO-PVDF at different measurement frequencies. (b) Derivative curves of D, (∂D/∂E)/ε0, as a function of electric field for BO-PVDF at different frequencies.

FIG. 2.

(a) Representative displacement vs. electric field (D-E) hysteresis loops for BO-PVDF at different measurement frequencies. (b) Derivative curves of D, (∂D/∂E)/ε0, as a function of electric field for BO-PVDF at different frequencies.

Close modal

The loops assume a half-propeller shape, a characteristic of typical ferroelectric materials. The charge density (or electric displacement, D) measures the total polarization—that is the amplitude of the dipole orientation under a certain electric field, and the dielectric constant evaluates the motion of the dipoles in that field.12,13 The high field dielectric constant (εr) can be calculated from the D-E loops as expressed by Eq. (1), where D represents the electric displacement, E the applied field, and ε0 the vacuum permittivity16 

εr=1ε0×DE.
(1)

The results of (∂D/∂E)/ε0 as a function of electric field in the charging process are shown in Fig. 2(b). εr at low fields is consistent with the dielectric constant value measured with an LCR meter (Fig. S3). For each poling cycle, a peak appears in the derivative curve of the D-E loop, corresponding to the maximum switching rate of dipoles. Before the peak, εr increases with the electric field, indicating that more and more crystal dipoles are aligned with the E-field. These dipoles are mainly associated with the ferroelectric β crystals, as α crystals are of nonpolar phase. After the peak, the oriented dipoles are gradually saturated, accounting for the decrease in εr. Across different poling cycles, as unipolar cycles continue to higher fields, more ferroelectric domains are polarized and cannot switch back upon the removal of the e-field during the discharging process. As a result, the peak value of (∂D/∂E)/ε0 will keep decreasing until the completion of ferroelectric switching. At high poling fields (e.g., >300 MV/m), the peak values stabilize and the derivative curves almost overlap. This behavior is similar to that of relaxor ferroelectrics,17 implying the presence of reversible dipole orientations. It has been reported that there exist nanoconfined decoupled dipoles or ferroelectric domains in PVDF.18 These crystals have a small crystallite size, so that they can exhibit fast reversible polarization.

The effect of poling frequency on crystal polarization can be demonstrated in Fig. 2(b) and more clearly in Fig. 3. Under the same poling condition, the peak of (∂D/∂E)/ε0 moves to lower electric fields with decreasing poling frequency. This behavior is analogous to thermally activated processes, where the temperature of thermal relaxation will be reduced as heating rates become slower and the temperature decrease can be determined by the activation thermal energy. Likewise, the ferroelectric switching should be a field-activated process, with the activation field dictating the shift of the peak field with the poling frequency [vide infra, Eq. (2)]. In fact, it is generally believed that the ferroelectric polarization reversal proceeds via a nucleation-growth mechanism,15,19 i.e., initiated by the nucleation of antiparallel domains, followed by the growth and overlapping of these domains throughout the sample. The domain nucleation is the rate-limiting step, as it is more time-consuming than the expansion of domains. The nucleation time has an exponential dependence on the applied field via Eq. (2), where τs is the switching time at the electric field of E, Ea is the activation field, and τ0 is the time constant, representing the switching time at E = Ea14,15

τs=τ0e(Ea/E).
(2)

Figure 4 presents the poling frequency as a function of the peak field of (∂D/∂E)/ε0 at different poling cycles. The experimental results can be fitted very well by Eq. (2), confirming the nucleation-dominated kinetics for the polarization switching. The fitted curve shifts to higher frequencies (i.e., lower 1/f) with increasing poling field, i.e., the time constant (τ0) becomes smaller as the D-E loops proceed to higher fields; nevertheless, the activation fields (Ea) derived from different poling cycles are similar, ranging from 480 to 500 MV/m. As mentioned before (Fig. 2), with the continuation of D-E loop cycles, more and more large ferroelectric domains are permanently aligned, leaving only small-sized decoupled domains that can switch back and participate in the next poling cycle. The decrease in the time constant at higher electric fields reflects the faster switching dynamics of the small domains than the large ones.20 However, regardless of the domain size, the polarization reversal always progresses through the rotation of carbon-fluorine and carbon-hydrogen bonds around the main chains of polymer molecules, which could explain the similar activation field at different poling cycles. It is also worth mentioning that the calculated Ea (480–500 MV/m) is a little lower than the results based on β-PVDF or PVDF copolymers (∼700 to 1000 MV/m).15,21 This could be due to the high content of α phase in the BO-PVDF, which dissociates the coupling between ferroelectric domains.

FIG. 3.

Effect of D-E loop frequency on the derivative curve [(∂D/∂E)/ε0] at the same poling fields of (a) 300 MV/m, (b) 400 MV/m, and (c) 500 MV/m.

FIG. 3.

Effect of D-E loop frequency on the derivative curve [(∂D/∂E)/ε0] at the same poling fields of (a) 300 MV/m, (b) 400 MV/m, and (c) 500 MV/m.

Close modal
FIG. 4.

Correlation of the poling time (1/f) and the poling field (1/E) for polarization switching in BO-PVDF.

FIG. 4.

Correlation of the poling time (1/f) and the poling field (1/E) for polarization switching in BO-PVDF.

Close modal

Along these lines, the electric field to accomplish the ferroelectric switching should also obey the same frequency dependence. As shown in Fig. S1, in order to reverse ferroelectric polarization, an electric field of 350 MV/m is needed at a poling frequency of 10 Hz; based on the time-field superposition (Fig. 4), it is equivalent to applying a lower field of 94 MV/m if the poling time is prolonged to 15 min, the duration of the leakage current measurement. The reduced electric field is in good agreement with the transition field observed in the conductivity measurement for the pristine BO-PVDF [Fig. 1(a)], confirming again that the abnormal decrease in conductivity arises from the ferroelectric switching. In light of what has been discussed so far, the leakage current measured before the transition field [ca. 90–100 MV/m, Fig. 1(a)] is apparently not stabilized, as the ferroelectric domains are still being polarized. In fact, at any reasonable measurement duration, the measured value of leakage current under a low/medium field is not a stabilized one, as it takes an extremely long time to complete the polarization reversal. However, the field-dependent electrical conduction under different measurement conditions can be derived based on the same time-field superposition, as shown in Fig. 4.

In the progress of ferroelectric polarization reversal, more crystal dipoles are oriented with the external electric field; these oriented dipoles will create a strong depolarization field, opposite to the direction of the external field.13 As a result, the mobility of charge carriers will be reduced and the leakage current will be decreased accordingly. Besides, it has also been reported that charges need to be trapped at the interfaces of ferroelectric domains to stabilize the polarization.6,22 The decrease in the leakage current may also originate from the lower populations of available free charges. It is worth mentioning that similar effects have been observed in ferroelectric ceramics.23 It has been reported that the electrical resistivity of some ferroelectric oxides can exhibit an anomalous increase by several orders of magnitude near the phase transition temperature. This behavior of positive-temperature-coefficient-of-resistivity (PTCR) is generally attributed to the ferroelectric domains lowering barriers to electron transport.24 However, there are few studies investigating the field effects, perhaps due to the high conductivity and low breakdown strength of these oxide materials, which makes it rather difficult to perform the long-time high-voltage measurement. This study of the field-dependent abnormal electrical conduction for the PVDF ferroelectric polymer can shed some light on the relevant research in the area of ferroelectric ceramics.

For PVDF based polymers, their high dielectric loss restricts the practical applications of these high-K polymers to low repetition pulsed power systems. At high repetition rates, there may be issues with thermal runaway if the capacitor is not appropriately designed to facilitate heat dissipation.25 This study implies that pre-poling can be used as an effective approach to mitigate the high field dielectric losses. In addition to the reduced conduction loss (as shown in this work), the ferroelectric loss can also be constrained, as the aligned ferroelectric domains will not switch back and participate in subsequent charging/discharging cycles under pulsed power conditions, thus reducing remanent polarization and improving recoverable energy density and efficiency.

In summary, the electrical conductivity of BO-PVDF exhibits abnormal dependence on the electrical field: the conductivity decreases with the electric field first, until a transition field is approached, and then it begins to increase with further increasing field. The initial unexpected decrease in conductivity arises from ferroelectric switching, which could create a strong depolarization field and/or trap charges at the interfaces of aligned ferroelectric domains; the transition field agrees well with the E-field for polarization reversal based on time-field superposition. This study implies that the performance of ferroelectric capacitor films, such as BO-PVDF, can be further improved by simple pre-poling, as it will effectively reduce high field conduction losses and ferroelectric losses.

See supplementary material for the detailed D-E loop curves and the low field dielectric properties as measured with an LCR meter.

The work at Penn State University was supported in part by the U.S. National Science Foundation under Award No. 1433993.

1.
H. S.
Nalwa
,
Handbook of Low and High Dielectric Constant Materials and Their Applications
(
Academic Press
,
San Diego
,
1999
), pp.
423
491
;
B.
Li
,
P. I.
Xidas
,
K. S.
Triantafyllidis
, and
E.
Manias
,
Appl. Phys. Lett.
111
(
8
),
082906
(
2017
);
Z.
Dang
,
J.
Yuan
,
S.
Yao
, and
R.
Liao
,
Adv. Mater.
25
(
44
),
6334
(
2013
);
[PubMed]
H.
Chen
,
T.
Cong
,
W.
Yang
,
C.
Tan
,
Y.
Li
, and
Y.
Ding
,
Prog. Natl. Sci.
19
(
3
),
291
(
2009
).
2.
S.
Zhang
,
C.
Zou
,
D. I.
Kushner
,
X.
Zhou
,
R. J.
Orchard
,
N.
Zhang
, and
Q. M.
Zhang
,
IEEE Trans. Dielectr. Electr. Insul.
19
(
4
),
1158
(
2012
).
3.
B.
Chu
,
X.
Zhou
,
K.
Ren
,
B.
Neese
,
M.
Lin
,
Q.
Wang
,
F.
Bauer
, and
Q. M.
Zhang
,
Science
313
(
5785
),
334
(
2006
);
[PubMed]
X.
Zhou
,
X.
Zhao
,
Z.
Suo
,
C.
Zou
,
J.
Runt
,
S.
Liu
,
S.
Zhang
, and
Q. M.
Zhang
,
Appl. Phys. Lett.
94
(
16
),
162901
(
2009
).
4.
Y.
Wang
,
X.
Zhou
,
Q.
Chen
,
B.
Chu
, and
Q. M.
Zhang
,
IEEE Trans. Dielectr. Electr. Insul.
17
(
4
),
1036
(
2010
).
5.
V.
Tomer
,
E.
Manias
, and
C. A.
Randall
,
J. Appl. Phys.
110
(
4
),
044107
(
2011
);
B.
Li
and
E.
Manias
,
MRS Adv.
2
(
06
),
357
(
2017
).
6.
B.
Li
,
P. I.
Xidas
, and
E.
Manias
,
ACS Appl. Nano Mater.
1
(
7
),
3520
(
2018
).
7.
X.
Zhang
,
Y.
Shen
,
Z.
Shen
,
J.
Jiang
,
L.
Chen
, and
C.
Nan
,
ACS Appl. Mater. Interfaces
8
(40),
27236
(
2016
);
[PubMed]
S.
Wu
,
M.
Lin
,
S.
Lu
,
L.
Zhu
, and
Q. M.
Zhang
,
Appl. Phys. Lett.
99
(
13
),
132901
(
2011
).
8.
M. A.
Wolak
,
M. J.
Pan
,
A.
Wan
,
J. S.
Shirk
,
M.
Mackey
,
A.
Hiltner
,
E.
Baer
, and
L.
Flandin
,
Appl. Phys. Lett.
92
(
11
),
113301
(
2008
);
E.
Baer
and
L.
Zhu
,
Macromolecules
50
(
6
),
2239
(
2017
).
9.
J.
Ho
and
T. R.
Jow
, in
2012 IEEE International Power Modulator High Voltage Conference
, San Diego, CA, USA, June
2012
, pp.
399
402
;
J.
Ho
and
T. R.
Jow
,
IEEE Trans. Dielectr. Electr. Insul.
19
(
3
),
990
(
2012
);
B.
Li
,
C. I.
Camilli
,
P. I.
Xidas
,
K. S.
Triantafyllidis
, and
E.
Manias
,
MRS Adv.
2
(
06
),
363
(
2017
).
10.
S.
Zhang
,
B.
Chu
,
B.
Neese
,
K.
Ren
,
X.
Zhou
, and
Q. M.
Zhang
,
J. Appl. Phys.
99
(
4
),
044107
(
2006
).
11.
12.
F.
Guan
,
J.
Pan
,
J.
Wang
,
Q.
Wang
, and
L.
Zhu
,
Macromolecules
43
(
1
),
384
(
2010
).
13.
F.
Guan
,
J.
Wang
,
J.
Pan
,
Q.
Wang
, and
L.
Zhu
,
Macromolecules
43
(
16
),
6739
(
2010
).
14.
T.
Furukawa
and
G. E.
Johnson
,
Appl. Phys. Lett.
38
(
12
),
1027
(
1981
).
15.
T.
Furukawa
,
T.
Nakajima
, and
Y.
Takahashi
,
IEEE Trans. Dielectr. Electr. Insul.
13
(
5
),
1120
(
2006
).
16.
T.
Furukawa
,
A. J.
Lovinger
,
G. T.
Davis
, and
M. G.
Broadhurst
,
Macromolecules
16
(
12
),
1885
(
1983
).
17.
L.
Yang
,
X.
Li
,
E.
Allahyarov
,
P. L.
Taylor
,
Q. M.
Zhang
, and
L.
Zhu
,
Polymer
54
(
7
),
1709
(
2013
).
18.
F.
Guan
,
J.
Wang
,
J.
Pan
,
Q.
Wang
, and
L.
Zhu
,
Chin. J. Polym. Sci.
29
(
1
),
65
(
2011
).
19.
D.
Mao
,
I.
Mejia
,
H.
Stiegler
,
B. E.
Gnade
, and
M. A.
Quevedo-Lopez
,
J. Appl. Phys.
108
(
9
),
094102
(
2010
).
20.
R.
Han
,
J.
Jin
,
P.
Khanchaitit
,
J.
Wang
, and
Q.
Wang
,
Polymer
53
(
6
),
1277
(
2012
).
21.
F.
Xia
,
H.
Xu
,
F.
Fang
,
B.
Razavi
,
Z.
Cheng
,
Y.
Lu
,
B.
Xu
, and
Q. M.
Zhang
,
Appl. Phys. Lett.
78
(
8
),
1122
(
2001
);
W.
Hu
,
D.
Juo
,
L.
You
,
J.
Wang
,
Y.
Chen
,
Y.
Chu
, and
T.
Wu
,
Sci. Rep.
4
,
4772
(
2015
).
22.
M.
Womes
,
E.
Bihler
, and
W.
Eisenmenger
,
IEEE Trans. Electr. Insul.
24
(
3
),
461
(
1989
);
B.
Li
,
F.
Salcedo-Galan
,
P. I.
Xidas
, and
E.
Manias
,
ACS Appl. Nano Mater.
1
(
9
),
4401
(
2018
).
23.
Y.
Chen
and
S. F.
Yang
,
Adv. Appl. Ceram.
110
(
5
),
257
(
2011
).
24.
B.
Huybrechts
,
K.
Ishizaki
, and
M.
Takata
,
J. Mater. Sci.
30
(
10
),
2463
(
1995
);
W.
Heywang
,
J. Am. Ceram. Soc.
47
(
10
),
484
(
1964
).
25.
Q.
Chen
,
Y.
Wang
,
X.
Zhou
,
Q. M.
Zhang
, and
S.
Zhang
,
Appl. Phys. Lett.
92
(
14
),
142909
(
2008
);
S. A.
Boggs
,
B.
Li
, and
S.
Zhang
, in
2017 IEEE Conference on Electrical Insulation and Dielectric Phenomenon
, Fort Worth, TX, USA, January
2018
, pp.
274
277
.

Supplementary Material