Study on the Polarization and Relaxation Processes of Ferroelectric

Article

Study on the Polarization and Relaxation Processes of Ferroelectric Polymer Films Using Sawyer-Tower Circuit with Square Voltage Waveform Jingjing Liu, Yifei Zhao, Chao Chen, Xiaoyong Wei, and Zhicheng Zhang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 30 May 2017 Downloaded from http://pubs.acs.org on June 4, 2017

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The Journal of Physical Chemistry

Study on the Polarization and Relaxation Processes of Ferroelectric Polymer Films Using Sawyer-Tower Circuit with Square Voltage Waveform Jingjing Liu1, Yifei Zhao1, Chao Chen2, Xiaoyong Wei2, Zhicheng Zhang1 * 1

Department of Applied Chemistry, MOE Key Laboratory for Nonequilibrium Synthesis and

Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Xi’an, P. R. China, 710049. 2

Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education &

International Center for Dielectric Research, Xi’an Jiaotong University, Xi’an, P. R. China, 710049.

ACS Paragon Plus Environment

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ABSTRACT

Displacement-vs-electric field hysteresis (D-E) loops constructed on the Saywer-Tower circuit has been widely utilized to characterize the ferroelectric performance of ferroelectric materials. To overcome the disadvantages of current Sawyer-Tower (ST) circuit in overestimated polarization from conduction loss and the disability in reflecting the polarization and relaxation processes, a ST circuit with square voltage waveform is developed for measuring the displacement of ferroelectric materials as a function of time under fixed electric field. By eliminating the conduction loss from the polarization and fitting the experimental results with the theoretical one, the characteristic parameters of a model ferroelectric material, poly(vinylidene fluoride-trifluoroethylene), have been obtained. The polarization and relaxation processes of the dipoles along the electric field have been finely illustrated for the first time, which cannot be given by the traditional ST possibly. Besides, more accurate parameters are obtained from ST circuit with square voltage waveform than the traditional one to give in-depth understanding of the energy storage and energy loss. This work might offer a robust method for the measuring of the polarization and relaxation processes in ferroelectric materials with desired accuracy.


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1. INTRODUCTION Poly(vinylidene fluoride) (PVDF) based ferroelectric polymers have been extensively investigated during past decades for their excellent dielectric1,2, ferroelectric3-5, piezoelectric6,7 and pyroelectric8 performances. The copolymers of VDF and trifluoroethylene (TrFE) are wellknown normal ferroelectrics and exhibit the best ferro- and piezo-electric properties with tunable ferro-to para-electric (F-P) transition temperature depending onto its chemical composition9-12. Besides direct copolymer of VDF and TrFE, they could be alternatively synthesized from the hydrogenation of corresponding copolymers of VDF and chlorotrifluoroethylene (CTFE)13. Their ferroelectric properties are mostly originating from the ferroelectric domains constructed on the high polar chains in TTTT conformation14-16. Inserting defects chemically or physically into the long sequence TTTT polymer chains may turn the normal ferroelectric performance of P(VDFTrFE) into the relaxor ferroelectrics with suppressed remnant polarization (Pr) at zero electric field and accelerated charging-discharging efficiency17,18. That allows them to be designed for actuators, artificial muscles and soft robots applications19-24. After grafting polystyrene (PS)25,26 or poly(acrylate ester)s (PXMA)27-29 onto the side chain of P(VDF-CTFE) and P(VDF-TrFECTFE), they could be even converted into anti-ferroelectric like materials characterized with double hysteresis profiles. The abnormally improved displacement under high electric field together with the near zero Pr at zero electric field brings them significant advantages in energy storage capacitors including the high energy density and high releasing efficiency. Displacement-electric field (D-E) hysteresis loops are one of the mostly utilized measurement to characterize the ferroelectric performances of these polymers under elevated electric field30-32, which is usually established based on the Sawyer-Tower (ST) circuit33 with a triangular wave form as shown in Figure 1(a). From which, the polarization (P) as a function of


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time t could be detected under a linearly increased AC or DC electric field as shown in Figure 1(a). By correlating the polarization and the electric field at the consistent time t, the D-E loops would be obtained with characteristic parameters such as spontaneous polarization, remnant polarization (Pr) and coercive electric field (Ec). D-E loops of a P(VDF-TrFE) sample measured from the traditional ST circuit are shown in Figure 7 for comparison.

Figure 1. The triangle waveform of traditional ST circuit (a) and the square waveform of ST circuit (b) In this circuit, the conductivity has been regarded as the polarization as well as the charges stored on the surface of the dielectrics. For the ultra-low conductive materials, the conductivity leads to the negligible contribution to the polarization. However, for PVDF based ferroelectric polymers, their relatively high conductivity (10-7-10-13 S/cm) would lead to the overestimated polarization. Especially, high electric field and sufficient time are essentially required to fulfill the polarization since ferroelectric polymers usually have much higher Ec (c.a. 50–100 MV/m) and much longer switching time for the dipoles. Unfortunately, the current ST circuit is not possibly to distinguish the contribution of ferroelectric relaxation and conduction loss to the polarization. The ST circuit has to be modified to compensate the distortions34-36 and to extract the P(E) hysteresis from the recorded data by means of suitable numerical processing37-40.


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Introducing microcomputer into measurement to simulate process of circuit correction with different capacitances and resistances is the most popular one. However, limited success has been achieved in the correction of the hysteresis loop for the changed conductivity under variational electric field. In addition, P(E) hysteresis of ferroelectric polymers were determined by measuring and analyzing the polarization in specimens with voltage-dependent conductivity, voltage-dependent capacitance and significant amount of space charge.41-43 The recorded current was divided into three parts correlated to charging of capacitance, conductivity from sample and the orientation of dipole polarization, respectively. By subtracting the contributions of the conductivity and the sample-capacitance charging process from a poling scheme with more than one bipolar cycle or a combination of bipolar and unipolar semi-cycles, the remained current could be obtained ascribing to the dipole orientation. In an effort to precisely detect the polarization and depolarization processes of dipoles in these ferroelectric polymers, ST circuit with a square voltage waveform is presented in this contribution by displacing the triangle waveform as shown in Figure 1(b). As a function of time, the apparent polarization and the depolarization in the film could be facilely detected under desired electric field. Taking a P(VDF-TrFE) bearing 20 mol% TrFE units as an instance, the dependence of internal conductivity and ferroelectric polarization onto time could be well determined from ST circuit with square voltage waveform. After the contribution of internal conductivity is subtracted from the polarization, the real polarization and relaxation of dipoles in the film are determined as a function of time. Most importantly, the contribution of ferroelectric relaxation and conductivity to Ul could be clearly identified. This work might offer a robust strategy for investigating the polarization and relaxation processes of dipoles in the ferroelectric materials.


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2. EXPERIMENTAL SECTION 2.1 Materials P(VDF-CTFE) (with 20 mol% CTFE) was purchased from China Bluestar Chengrand Chemical Co. Ltd. N,N-dimethylformamide (DMF, Tianjin Reagents Co. Ltd AR grade) was used as received without further purification. P(VDF-TrFE) (80/20) was synthesized from a hydrogenation process of P(VDF-CTFE) (80/20) following the procedure as described in ref13. A fresh sample was used in each measurement. 2.2 Films fabrication P(VDF-TrFE) film with a thickness of around 13 µm were prepared by casting the copolymer solution (about 3wt% in DMF) onto glass plates at 70 oC. After the solvent was evaporated completely, gold electrodes were sputtered onto both surfaces of the film with a thickness around 80 nm using a JEOL JFC-1600 auto fine coater (Japan). 2.3 Instruments and programing Polarization and depolarization results were recorded on a Premiere II ferroelectric tester from Radiant Technologies equipped with a 10kV Trek high voltage amplifier (610E, Trek, INC., USA). The program of a square wave signal with the maximum voltage of 4,000V and the lasting time of 100 ms as shown in Figure 1(b) was input as a txt file in notepad as indicated in Figure 2. ‘300’ in the first line means there are 300 points in the signal generated. ‘1’ in the second line suggests the time interval between two points is 1ms. ‘0’ from line 3 to line 102 are setting the output voltage as 0 V in the first 100 points namely 100 ms, followed by the output voltage of 4,000 V in the next 100 points (line 103 to line 202) in second 100 ms. From line 203


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to 302, the output signal is set as 0 V again and last for 100 ms. The parameters including the output voltage, number of points, time length of interval, and overall period could be adjusted to meet the properties of materials. The program in text file could be loaded into the ferroelectric test system by choosing ‘QuikLook’ and ‘Hysteresis’ in the interface followed by clicking ‘From File’ and ‘Browse to File’ to select the program file by name e.g. 1ms-4000V-100ms.txt for a unipolar testing as indicated in Figure 2(a). The programing command for bipolar testing is listed in Figure 2(b) as well. The corresponding waveforms for unipolar and bipolar testing are shown in Figure 2(c) and (d), respectively.

Figure 2. Programing commands (a, b) and generated square voltage waveforms (c, d) of ST circuit under DC and AC fields. 3. Results and discussion 3.1 Polarization and depolarization processes under fixed electric field


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It has been well recognized that the relaxor ferroelectric property of P(VDF-TrFE) is originated from its polar β-crystalline phase. However, due to the complexed contribution of conduction loss and relaxation to the overall polarization, the real polarization and depolarization processes of the ferroelectric polymers could hardly be identified by traditional ST method. Under different electric fields, the polarization of P(VDF-TrFE) film as a function of t could be measured with square voltage waveform as shown in Figure 3(a). A fixed electric field (from 50 MV/m to 250 MV/m in Figure 3(a)) is immediately added onto the film and maintained for desired time period (c.a. from 100 ms to 200 ms in Figure 3(a)). After the polarization process is completed, the electric field is suddenly removed and the relaxation process is undergoing under zero external electric field (from 200 ms to 300 ms in Figure 3(a)). After the conduction loss is excluded, the real polarization curve of the sample was obtained as displayed in Figure S1.

Figure 3. Polarization and relaxation of P(VDF-TrFE) film under elevated electric field with square voltage waveform (a), the measured displacement with square voltage waveform under 250 MV/m (b) and the comparison of displacement curves before and after subtracting conduction loss (c). Taking the results measured under 250 MV/m electric field as an instance, the polarization as a function of t is re-scaled. The first and second 100 ms are referring to the polarization and


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relaxation processes of the sample, respectively. As shown in Figure 3(b), at the first 1ms once the electric field is applied, an instantaneous polarization (P0) of 4.99 µC/cm2 is observed immediately, which could be obtained from the starting point where the polarization curve deviates from the linear increasing trend. That means P0 is responding to the external electric field forthwith. As polarization time increases, the polarization is increasing continuously but the increasing speed is gradually reduced to a constant. Namely, the polarization as a function of t is improving in linear when t is over 16 ms, whose slope could be obtained from the fixed line in red as shown in Figure 3(b). No polarization saturation could be observed at all due to the conduction loss. In this case, the conductivity of P(VDF-TrFE) film could be treated as a constant under the consistent electric field and the contribution of conduction loss to the polarization (Pc) should be linearly increased from 0 µC/cm2 as a function of t as suggested by the straight line in blue, which is parallel to the red straight line and expressed as Pc=k×t, where k is the slope of the blue line and related to the conductivity (σ) and the size (area and thickness) of the samples. Therefore, after the conduction loss is excluded, the real polarization curve of the sample under 250 MV/m could be obtained as a function of t as illustrated in red in Figure 3(c). From which, the saturation polarization (P∞) of P(VDF-TrFE) film could be detected, which would be discussed in detail later on. Besides the polarization process, the depolarization process of dipoles in P(VDF-TrFE) films could be measured from the ST circuit with square voltage waveform. The polarization obtained at 100 ms (c.a. 10.70µC/cm2) is taken as the maximum polarization (Pmax). As soon as the electric field is removed, the polarization is immediately dropped to a low polarization (c.a. 6.34 µC/cm2 in Figure 3(b)) before the relaxation process is started, which is identified as PR0. As t increases from 100ms to 200ms, the polarization (PRt) is quickly reduced and reaches a


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constant value referred as PR (c.a. 4.94 µC/cm2 in Figure 3(b), which is defined as the polarization remained after the relaxation is completed. It has to be notified that during the depolarization process the conduction loss could be neglected since no external electric field is applied onto the sample any longer. Therefore, the polarization in the relaxation process against t could be obtained by subtracting the conduction loss at 100 ms (Pc100) from the measured curve, which is re-plotted in Figure 3(c) as well. The parameters P0, Pmax, PR0, and PR∞ could be directly obtained from Figure 3(a) and are listed in Table 1. Table 1. The parameters directly obtained from ST circuit with square voltage waveform

Entry

P0 (µC/cm2)

Pmax (µC/cm2)

PR0 (µC/cm2)

PR∞ (µC/cm2)

50MV/m

0.55

0.74

0.16

0.12

100MV/m

1.86

3.31

1.32

0.81

150MV/m

3.00

4.50

1.66

0.99

200MV/m

3.80

5.56

2.15

1.28

250MV/m

4.99

10.70

6.34

4.94

3.2 Polarization dependence onto testing parameters Different materials show varied polarization dependence onto the polarization time and electric field to reach the polarization equilibrium. To determine the above polarization parameters precisely, the polarizing time period under fixed electric field, which should be larger than the polarization equilibrium requested τP, has to be determined firstly. As shown in Figure 4(a), three polarizing time scales, including10 ms, 100 ms, and 1000 ms corresponding to the frequency of 100 Hz, 10 Hz, 1 Hz, are examined for P(VDF-TrFE) film under the same electric field of 200 MV/m. The results show that 10 ms is too short to reach the polarization equilibrium


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since the polarization is still increasing after removing the conduction loss. In contrast, 1000 ms is too long for the polarization since the polarization starts to increase linearly after polarized for 10-30 ms. Meanwhile, the longer the polarization time, the more Joule heat would be generated from the conductivity. 100 ms is long enough for P(VDF-TrFE) film to reach the polarization equilibrium, which agrees well with the frequency of 10 Hz utilized in traditional D-E hysteresis loops under linear increased electric field. Meanwhile, as shown in Figure 4(b), 100 ms is sufficient for the relaxation of the oriented dipoles as well. Therefore, in this work, the polarization and depolarization periods are both set as 100 ms. According to the polarization and relaxation performance of the varied materials, the periods could be facilely programed as discussed above in the experimental section.

Figure 4. Polarization (a) and relaxation (b) processes of film under different time period at 200 MV/m. Besides the polarization time, the external electric field is another important parameter dominating the polarization and relaxation behavior of the ferroelectric materials. In the traditional ST testing, the increased electric fields are set and added across the samples step-bystep and a series of D-E loops under varied electric fields would be observed. In this ST method, the increased electric fields are applied as well with an interval of 50 MV/m. To eliminate the


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polarization accumulation, fresh samples are used in each testing. As shown in Figure 3(a), the polarization and relaxation curves as a function of t under elevated electric fields are rather different. The higher the electric field is added, the larger polarization would be observed. Both the increasing speed of the polarization against testing time and the Pr after the discharging process completes are improved due to the increased conductivity under elevated electric field. 3.3 Data manipulation of simulating testing curves During the polarization process, the measured polarization from the ST circuit with square voltage waveform consists of two parts including the Pc and Pt in equation (1). Therefore, the dependence of polarization on t could be expressed as equation (2), −t /τ p

d(Pt − P0 ) / dt = (P∞ − P0 ) − (Pt − P0 )e −t/τ p

Pt = P∞ +(P0 −P∞)e −t/τ p

P = Pe 0

(1) −t/τ p

+P∞(1− e

)+k×t

(2)

where, P0 is the instantaneous polarization, P∞ is the saturated polarization, Pt is the polarization at time t, τP is the time required for the polarization to reach saturated value under the applied electric field, and k is the slope of the linear curve for fitted polarization contribution from conduction loss. Therefore, the measured polarization curves could be simulated with equation (2) by adjusting the parameter τp, where all the contributions to the polarization are accounted. The simulated results in red solid lines with equation (2) are presented in Figure 5 (from 100-200 ms) together with the tested polarization results from ST circuit with square voltage waveform in scattered hollow symbols. By subtracting the conduction loss (Pc) from the measured


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polarization curves as a function of t, the real polarization curves of the samples could be obtained. All the parameters listed in equation (2), including Pc at the end of charging circle (Pc100), P∞, and τp, could be certainly determined as listed in Table 2.

Figure 5. The fitted polarization and relaxation curves of P(VDF-TrFE) film under the elevated electric field For the discharging circle, the dependence of the measured polarization (PRt) onto the relaxation time could be expressed by equation (3),

PRt = PR0 -(PR0 − PR∞ )e−t/τ R

(3)

where, PR0 is the instantaneous polarization when the electric field is removed, PR∞ is the constant polarization after the discharging process is completed, and τR is the lowest time for film to reach PR∞. The polarization results during the discharging circles are fitted with the equation (3). As shown in Figure 5 (from 200-300 ms), the scattered hollow symbols are obtained directly from ST circuit with square voltage waveform under varied electric fields, and the solid curves in red are the simulated results by equation (3) with the best fitted τR. It has to be notified that the conduction loss during the polarization process causes the constant contribution


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(Pc at 100ms) on the measured polarization during relaxation process. Therefore, the real remnant polarization (Pr) could be calculated by subtracting the Pc at 100 ms from the PR∞. The instantaneous releasable polarization (PIR), referring to the charges could be immediately discharged, could be determined by subtracting the PR0 from Pmax. Both Pr, PIR and τR are presented in Table 2 as well. Table 2. The parameters obtained from fitted curves of P(VDF-TrFE) film

a

Entry

P∞ (µC/cm2)

Pc100 (µC/cm2)

50MV/m

0.68

0.06

8

10

0.06

0.58

100MV/m

2.60

0.71

10

12

0.10

1.99

150MV/m

3.63

0.87

12

14

0.12

2.84

200MV/m

4.51

1.05

14

15

0.23

3.41

250MV/m

6.47

4.23

16

22

0.71

4.36

τP (ms)

τR (ms)

Pra (µC/cm2)

PIRb (µC/cm2)

Pr = PR∞ − Pc100 ; b PIR = Pmax − PR 0

3.4 Polarization and relaxation performance of P(VDF-TrFE) film After eliminating the influence of conduction loss onto the polarization, the accurate polarization and relaxation processes of P(VDF-TrFE) film could be detected with the square voltage waveform. The characteristic parameters reflecting the ferroelectric performance of the materials including P0, P∞, PIR, Pr, τP and τR are plotted against electric field as shown in Figure 6(a) and 6(b), respectively. Under low electric field, P0 and P∞ are rather close suggesting the invisible polarization of large ferroelectric domains. As electric field increases, the gap between P∞ and P0 is enlarged due to the orientation of ferroelectric phase. Interestingly, the PIR is rather


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close to P0 and both are increasing linearly as electric field increases, which is about 80% of the overall polarization. The quick response to the electric field character allows this part of polarization to be facilely utilized for storing and releasing the electric energy for capacitors. In the contrast, the fairly small (less than 10% of P∞) real Pr indicates that the P(VDF-TrFE) film could hardly be polarized for piezoelectric applications. It has to be notified that the contribution of conduction loss to the polarization (Pc100) is quickly enhanced with the increase of electric field and an incredible high Pc100 is observed at 250 MV/m.

Figure 6. Characteristic parameters of P(VDF-TrFE) film under elevated electric field determined from the ST circuit with square voltage waveform. Besides the polarization value presented above, τP and τR are important parameters to characterize the polarization and depolarization processes of P(VDF-TrFE) film as shown in Figure 6(b). Both τP and τR are increasing as a function of electric field. That means the elevated electric field would drive the more dipoles aligning along the electric field. On the other hand, longer time is required for the orientation of all the dipoles as well. It could be imagined that if the electric field is sufficient high to polarize all the dipoles in the sample, τp should be reduced for the enlarged driving force. Unfortunately, the film would be broken down under electric field


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over 300 MV/m, and the results under higher electric field could not be presented. Under the fixed electric field, the period of polarization is slightly lower than the relaxation period. As discussed above, the relaxation of the oriented dipoles is totally free with no assistance of external electric field. The disorientation of dipoles has to overcome the coupling forces among them together with the intermolecular force. The larger τR indicates the delayed disorientation should attribute to the enlarged coupling force. The more dipoles aligned along the electric field, the larger the coupling force among them, thus the increased τR would be obtained. However, τR is significantly increased at 250 MV/m comparing with the linear increasing tendency under lower electric field. That suggests the ferroelectric domains in bigger size start to orient, which requires rather long time to disorientate. It is logical to believe that τR under further elevated electric field would be dramatically improved as well indicating the high stability of the oriented ferroelectric domains in film. The orientation of this part dipoles is the resource of ferro- and piezoelectric performance of P(VDF-TrFE). That means the samples in this work require at least 250 MV/m electric field to polarize the film for piezoelectric application at ambient temperature. As a piezoelectric performance parameter, piezoelectric coefficients (d33) is only observed as -2 pC/N in the samples polarized at 250 MV/m and no visible d33 could be detected in the other samples. That agrees well with the polarization results as discussed above. 3.5 Comparison of traditional ST circuit from ST circuit with square voltage waveform To show the difference between the ST circuit with square voltage waveform and the traditional ST circuit, the D-E loops of the same samples observed from the two circuits are compared. As shown in Figure 7, the traditional D-E loops of P(VDF-TrFE) film obtained under linearly increased electric field are presented. Each fresh sample is polarized under only one electric field twice, and the results from the first and the second circles are presented as Figure


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7(a) and Figure 7(b), respectively. As shown in Figure 7(a), the displacement is increasing continuously as a function of electric field and the polarization saturation could hardly be identified before internal conductivity is subtracted. Meanwhile, the conductivity is continuously increasing in every D-E loop as the electric field increase. That means the subtraction of conduction contributed to polarization have to be treated differently depending onto the maximum electric field applied, which makes the compensation rather tricky. As a result, the characteristic ferroelectric parameters including Pr and P∞ obtained from which are far from accuracy, although they are very important for evaluating the performance of ferroelectric materials.

Figure 7. D-E hysteresis loops of P(VDF-TrFE) film for the first (a) and second (b) run under elevated electric fields As depicted in Figure 7(b), the difference between first and second runs is mostly in the DE loops measured under high electric field (200 and 250 MV/m). The starting polarization of the second run at 200 and 250 MV/m is negative, which is different from the zero in the first run. Apparently, the starting negative polarization is remained in the samples from the first polarization. The invisible starting polarization in the second run of under electric field below 200 MV/m suggests the negligible polarization remained from the last polarization circle.


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Meanwhile, the difference between the polarization obtained at the ending of first circle and the starting of the second run under the same electric field could be ascribed to both the conduction loss and the polarization relaxation. Unfortunately, the contribution of conducting loss to the polarization could hardly be estimated under the elevated electric field, neither could the relaxation polarization. Under AC electric field, the polarization of P(VDF-TrFE) films measured with single (a) (one positive square voltage circle followed by one negative one) and double (b) square voltage waveforms (two positive square voltage cycles followed by two negative ones) are presented for comparison as shown in Figure 8. Obtained under single AC square waveform field, the slopes of the curves in 100-200 ms and 300-400 ms are consistent in Figure 8(a). Namely, the contribution from conduction in the 100-200 ms (positive direction) and 300-400 ms (negative direction) are the same as expected. If the films are polarized in one direction twice before switching the field direction, as shown in Figure 8(b), the repeated polarization in one direction would lead to continuously increased polarization for the accumulation of conductive contribution. By subtracting the maximum polarization of first polarity waveform from the second one as suggested by red dash line in Figure 8(b), the polarization from conductivity referred as P’c100 could be directly obtained. Therefore, by subtracting P’c100 from PR∞ of the first circle, the remnant polarization (P’r) could be determined as presented in Figure 8(c). Pc100 and Pr obtained from the linear fitted method of the first circle as discussed above are listed in Figure 8(c) for comparison. Under the consistent field, both P’c100 and P’r are rather close to Pc100 and Pr, which suggests that it is reasonable to treat the conductivity of the sample under consistent electric field as a constant. Meanwhile, it demonstrates that both ways may precisely distinguish the conduction contribution from the real remnant polarization. It has to be notified that all the


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results have to be determined from the same sample since the crystalline and ferroelectric properties of P(VDF-TrFE) could be easily varied in a wide range.

Figure 8. Polarization of (P(VDF-TrFE) (80/20)) under elevated electric field with single square voltage waveform (a), double square voltage waveform (b), and Pc100 and Pr obtained from the linear fitted results in first circle compared with P’c100 and P’r (c). As the most important parameters, the maximum polarization (Pmax) and Pr under certain electric field could reflect the ferroelectric performance of materials clearly. The Pmax and Pr obtained from traditional ST circuit are compared with the ST circuit with square voltage waveform as a function of electric field in Figure 9. Under low electric field, P∞ is slightly larger than Pmax due to the longer polarization time in ST circuit with square voltage waveform than triangular one. Under high electric field, P∞ and Pmax are rather close, which might be attributed to the contribution of conduction loss in traditional ST method. Pr detected from the ST circuit with square voltage waveform is much lower than that from the traditional ST, especially under electric field over 150 MV/m. As finely discussed above, Pr obtained from traditional ST contains both the Pc and partial releasable polarization, which is significantly overestimated and could be confirmed by d33 results as well. Apparently, after eliminating the contribution of conduction loss and the releasable polarization, Pr measured from the ST circuit with square voltage waveform is more accurate and better reflecting the real condition.


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Figure 9. Comparison of P∞ and Pr from ST circuit with triangular voltage waveform and ST circuit with square voltage waveform under elevated electric field. 4. CONCLUSION A method of Sawyer-Tower circuit with square voltage waveform has been proposed in present work for the precise measurement of the polarization and relaxation processes of P(VDFTrFE) based ferroelectric materials. Instead of increased electric field against time, a fixed electric field is added onto the film for the designed time period to fulfill the polarization. The depolarization process is conducted by fully removing the electric field immediately, which is different from the linear decreasing electric field in the traditional ST. By monitoring the polarization as a function of t and fitting the experimental results with the theoretical equation under different electric field, parameters including P0, P∞, Pc, PR0, PR∞, Pr, τP and τR could be obtained with high accuracy. As a consequence, the polarization and depolarization processes of the dipoles in P(VDF-TrFE) could be more clearly illustrated by eliminating the contribution of the conduction loss. The polarization of P(VDF-TrFE) requires 10-30 ms to reach the equilibrium and the elevated electric field leads to the prolonged polarization and relaxation period together with the improved polarization and conduction loss. Comparing with the traditional ST circuit, the ST circuit with square voltage waveform may not only measure the


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parameters reflecting the polarization and relaxation processes of ferroelectric materials but also provide the polarization results with higher accuracy. The convenient program and the data processing procedure make the method a robust tool to give a deep insight into the polarization of ferroelectric materials. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications Website. See supporting information for information about additional illustration and figure. AUTHOR INFORMATION Corresponding Author *(Zhicheng Zhang). E-mail: [email protected]. ORCID Zhicheng Zhang: 0000-0003-1871-117X Present Addresses Department of Applied Chemistry, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Xi’an, P. R. China, 710049. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally.


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Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was financially supported by the National Nature Science Foundation of ChinaNSFC (No. 51573146, 10976022, 51103115, 51603167), Fundamental Research Funds for the Central Universities (xjj2013075, cxtd2015003), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JQ2010), and China Postdoctoral Science Foundation Funded Project (2015M582633).

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TOC Graphic


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Study on the Polarization and Relaxation Processes of Ferroelectric

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