J Solid State Electrochem (2014) 18:595–605 DOI 10.1007/s10008-013-2286-x
ORIGINAL PAPER
Electrical impedance spectroscopy study of piezoelectric PVDF membranes M. T. Darestani & T. C. Chilcott & H. G. L. Coster
Received: 22 March 2013 / Revised: 3 October 2013 / Accepted: 4 October 2013 / Published online: 24 November 2013 # Springer-Verlag Berlin Heidelberg 2013
Abstract Piezoelectric poly (vinylidene fluoride) (PVDF) membranes were prepared from pre-fabricated membranes by electrically poling in an intense electric field. The electrical impedance of PVDF membranes measured over a frequency range of 10−2–105 Hz before and after poling is presented. The effect of pressure on the impedance characteristics of un-poled and poled PVDF membranes was also studied. A four element model circuit, including a constant phase element (CPE) was fitted to the impedance spectra. The elements of the circuit fitted to the poled sample were more conductive compared with those of the un-poled sample. Stronger CPE elements in the circuit were detected in the poled samples under pressure suggesting that the piezoelectric activity of PVDF is the major contributor to the constant phase angle seen at low frequencies. Keywords Piezoelectric membranes . Electrical poling . Impedance spectroscopy . Poly (vinylidene fluoride)
crystalline structure of PVDF from non-piezoelectric configurations (α, γ, and δ) to an all-trans (β) phase that is responsible for the piezoelectric properties of PVDF. Filtration experiments using the piezoelectric PVDF membranes showed that the vibrations of these membranes delayed membrane fouling significantly [2–4]. The poled membranes required to be energized for generating the vibration required to prevent fouling. Therefore, it was critical to study the electrical impedance properties of original membranes and the effect of electrical poling on them. Electrical impedance spectroscopy (EIS) has become a widely applied, non destructive and powerful tool to investigate the properties of polymer films [5–11], membranes [12–20] and piezoelectric materials [21–27]. However, the electrical impedance spectroscopy of porous PVDF films has not been studied. Here, we present the electrical impedance properties these membranes, with and without pressure, before and after poling in an intense electrical field.
Introduction
Materials and methods
Poly (vinylidene fluoride) (PVDF) is widely used in actuators and sensors in electrical industries because of its piezoelectric properties. PVDF is also used in fabrication of membranes for separation processes. Recently, piezoelectric PVDF membranes were fabricated by imparting piezoelectric properties to prefabricated membranes [1, 2]. It was shown that poling in intense electric fields under controlled conditions can change the
The membranes used in the present study were PVDF microfiltration membranes (Pall Fluoro Tran® W) supplied by PALL Life Sciences (Australia). The thickness and the nominal pore size of the membranes were 123 and 0.22 microns, respectively.
M. T. Darestani : T. C. Chilcott : H. G. L. Coster (*) School of Chemical and Biomolecular Engineering, University of Sydney, Sydney, NSW 2006, Australia e-mail:
[email protected]
Electrical poling Poling in an intense electric field was used to impart piezoelectric properties to PVDF membranes. Electrical poling was performed at 90±10 °C using a 2-kV potential difference, corresponding to field strength of 16.3×106 V/m across the membrane sample. For this, the samples were
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sandwiched between two electrodes and a Stanford Research Systems DC power supply was used to generate the electric potential difference between the electrodes. The voltage applied between the electrodes was increased gradually from zero to 2 kV at a rate of about 50 V/min. After keeping the sample in the 16.3×106 V/m electric field at the elevated temperature for 2 h, the temperature was decreased slowly to room temperature. The voltage then was decreased gradually from 2 kV to zero at a rate of about 50 V/min. It needs to be pointed out that electrical breakdown analysis showed that PVDF membranes were stable at voltages up to 4 kV [28, 29]. Further experiments showed that exposure to 2 kV for longer than 4 h caused minor internal breakdown [28].
Electrical impedance spectroscopy (EIS) involves the measurement of the electrical potential ν0 and the phase shift φ of a system in response to an alternating current of small amplitude i 0 and known angular frequency ω [13, 30]. The voltage across the sample is v and has the same frequency as the current (i). However, the current and voltage are out of phase by φ. The impedance (Z) is defined by its magnitude (|Z |=ν0/i 0) and its phase angle (φ) which is the phase angle between the AC voltage and the AC current. The impedance which is generally frequency-dependent can be expressed in terms of the conductance (G ) and capacitance (C ) as shown below. GðwÞ ¼ 1=jZ jcosðφÞ
ð1Þ
Scanning electron microscopy (SEM)
C ðwÞ ¼ −1=ðwjZ jÞ sinðφÞ
ð2Þ
A Field Emission Scanning Electron Microscope (Zeiss, ULTRA plus), equipped with a Schottky field emission gun (10 kV) was used to analyse the morphology of the membranes. For this, the membrane specimens were coated with a 15-nm gold layer using a sputtering technique.
More information about the impedance spectroscopy and its application can be found elsewhere [13, 31].
Piezoelectric response analysis
Effect of poling on microstructure and filtration properties
The membrane samples were sputter-coated, on both sides with gold. AC signals were applied to the membranes by connecting the gold coatings to an AC signal generator (Topward TFG-8114). The vibration of the membrane surface when subjected to the electric signal was measured using a laser Doppler vibrometer (Polytec PDV 100).
The SEM images of the microstructure of the membranes before and after poling are shown in Fig. 1. It can be seen that poling in an intense electric field changed the microstructure of the membranes from a random porous structure to an anisotropic layered structure [1]. Filtration experiments showed that this affected the filtration properties of the membranes. As shown in Fig. 2, poled membranes had lower average flux but higher rejection. The improvement in rejection was more significant than the decline in flux [32]. Effects of poling on microstructure and filtration properties of membranes were investigated and were discussed in detail elsewhere [1, 32]. The change in porosity and microstructure of the membrane is likely to affect the electrical properties of the membrane. This hypothesis is examined in the present study.
Electrical impedance spectroscopy An INPHAZE™ high resolution impedance spectrometer (INPHAZE, Australia) was used to measure the impedance of the samples. Dielectric structure refinement software (INPHAZE™) was employed to analyse the results and to model an equivalent circuit for the samples. For EIS measurements, the membrane samples with surface area of about 80×10−6 m2 were sputter coated with a 30-nm gold layer on either side and sandwiched between two thin, flat copper electrodes that made contact with the gold films and acted as electrodes for the impedance measurements. A clamp with a flat 40×20 mm rectangular surface was used to apply pressure on samples to explore the effect of pressure on the impedance characteristics. To achieve comparable pressures on poled and un-poled samples, both samples were clamped at the same time using one clamp. Three spectra in the frequency range of 10−2 to 105 Hz were collected and the average spectra with error bars were used in the analysis. The two electrodes and the sample had exactly the same surface area, and all the data were normalized to the surface area.
Results and discussion
Piezoelectric and anti-fouling properties of poled membranes To evaluate the effectiveness of electrical poling in inducing piezoelectric properties the vibration of the poled and unpoled when energized by AC signals was compared. Figure 3 gives an example of the vibration measured using the laser vibrometer. This Figure shows the vibration responses of unpoled membrane (blue line) and poled membrane to a 5-Hz sinusoidal stimulus of 10 volt amplitude. The manifestation of a sharp peak of 1.7 nm amplitude in the vibration response at 5 Hz arising from the application of the 5 Hz stimulus indicates that poling in an intensive electric field was effective
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Fig. 1 SEM micrographs of a cross section of a PVDF membrane before electrical poling (a) and after poling (b) [1]
and had yielded a piezoelectrically active PVDF membrane. Effects of parameters such as frequency and amplitude of the AC signal on the piezoelectric vibration of poled membranes has been presented previously [1]. The results of the filtration experiments using the piezoelectric membranes showed that the vibrations out of the plane of these membranes (i.e. in the direction of the flux) increased the flux and delayed membrane fouling significantly. The relative antifouling effect of piezoelectric induced vibration was enhanced with increasing cross flow velocity. Figure 4 compares the effect of vibration on flux decline pattern of piezoelectric PVDF membranes. More examples of filtration results using these membranes are discussed elsewhere [4]. The filtration experiments showed that the most suitable frequency range for operating the piezoelectric membranes
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Fig. 2 Effect of poling on flux (a) and rejection of a PVDF microfiltration membrane under identical constant pressure and cross-flow filtration conditions [32]
was ∼500–1,000 Hz and the anti-fouling effect was improved by increasing the AC voltage amplitude as shown in Fig. 5b. The flux increase versus the voltage was not linear and the deviation from the line was increased by raising the voltage amplitude. This was in agreement with the trend of vibration amplitude versus the signal amplitude [1] shown in Fig. 5a. These observations suggested that the electrical properties of the piezoelectric (i.e. poled) membrane were different from that of a simple circuit. There is not much published information on electrical properties of piezoelectric PVDF films. Therefore, in the present study, the electrical properties of poled and un-poled membranes were compared using EIS. To investigate the effect of piezoelectric activities of poled membranes, the effect
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1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
with other reports indicating an increase in the conductivity of PVDF films as a result of poling in an intense electrical field [33, 34]. The higher conductivity of the poled sample is probably due to alignment of the PVDF molecules and the structural changes of the PVDF membrane due to the poling process depicted in Fig. 1 and discussed in detail elsewhere [1]. Applying a pressure to the poled sample (filled diamond) resulted in a higher capacitance, while a slightly lower capacitance was detected on applying pressure to the un-poled (filled square) sample. Application of pressure did not change the conductance or the impedance of the un-poled membranes noticeably, whereas the pressure applied to the poled membrane resulted in a significant increase in the conductance shown in Fig. 6b. Higher conductance and capacitance of the poled membranes as a result of applying pressure can be attributed to the piezoelectric properties of this sample. In other words, the potential difference generated as a result of outside mechanical stress could increase the charge storage capacity and increase the charge mobility through the poled sample. Pressure did not change the phase angle of the un-poled sample over the whole frequency range. In contrast, the phase angle profile for the poled sample in the mid frequency range shifted to higher frequencies with a concomitant increased frequency range at lower frequencies where the phase angle was constant with frequency (see Fig. 6c). The higher conductivity of the poled PVDF membranes under pressure correlates with piezoelectric electric potential generation of this sample under pressure. The voltage generation of the piezoelectric PVDF films under pressure has been reported and, of course, is widely employed in pressure and acoustic sensors [35, 36]. The effect of poling on the imaginary components of the electrical impedance can also be readily discerned in Cole– Cole plots as is illustrated in Fig. 7. Both the real and imaginary impedances decreased as a result of electrical poling, which was also reflected in the effect of poling on the conductance and capacitance plots in Fig. 6. The
Poled membrane 0.2 0.1 0.0 4 5 6 Un-Poled membrane 1
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Frequency(Hz) Fig. 3 An example of the vibration amplitude measured in air by a laser Doppler vibrometer at 5 Hz when a signal at 5 Hz was applied to the poled (piezoelectric) membrane. For comparison, the response for an un-poled membrane is shown in blue. The molecular changes of PVDF structure resulting from electrical poling is schematically depicted in the left insert to this figure
of pressure on electrical properties of poled and un-poled membranes was also compared. Electrical impedance spectroscopy Figures 6 and 7 show the electrical impedance results of the poled and un-poled membranes. The results of the compressed samples are also shown in these graphs and an arrow shows the direction of the shift as a consequence of compression in each graph. The capacitance, conductance, impedance and phase angle versus frequency are shown in Fig. 6a–c, respectively. It can be seen that both the capacitance and conductance of the poled sample (filled circle) were significantly higher than those of un-poled membrane (filled square); by almost two orders of magnitude at the lower ends of the spectra. The difference between the poled and un-poled samples was enhanced at lower frequencies. These results are in agreement 100
Normalized flux (%)
Fig. 4 Comparison of the flux decline for non-vibrating (0 V) membranes and a membrane excited by a 10-V AC signal at a frequency of 500 Hz. Experiments were performed at constant 25 kPa pressure using 35 l/h (0.24 m/s) crossflow velocities
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Fig. 5 Effect of AC signal voltage on vibration (a) and average flux of the piezoelectric membranes (b) as a function of the AC signal voltage (at 500 Hz) during filtration of 1 g/l PEG solution at 100 kPa pressure and 24 l/h cross-flow velocity (∼0.17 m/s)
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imaginary component of the impedance of the un-poled sample was almost 10 times greater than that of the poled membrane. It needs to be pointed out that an inductive-like resonance at high frequencies has been reported as piezoelectric materials [25, 26], but that was not observed here. This could be because the resonance amplitude is proportional to the square of the piezoelectric coefficient [26, 27] and hence in case of materials with a low piezoelectric coefficient such as PVDF, the height of the resonance can be of the order of the resolution limit of the impedance measurements. Alternatively,
the resonant frequency may be at a frequency >1 MHz which was the limit of the instrument used in this study.
Fig. 6 The effect of poling and pressure on the impedance properties of the PVDF membranes: the capacitance (a), the conductance (b) and the phase angle (c) vs. frequency. The electrical parameters of the poled membrane without (red-filled circle) and with (filled black diamond)
pressure are compared with those of the un-poled without (blue-filled square) and with (filled black triangle) pressure. Note that the scales for the capacitance, conductance and plots are logarithmic and the differences between the plots are therefore very significant
Modelling the electrical impedance properties Identification of the most appropriate equivalent circuit to represent the electrical properties of a sample simplifies the characterization of its properties. However, choosing the most appropriate equivalent circuit can be difficult because usually more than one circuit can be used to represent a particular impedance spectrum. In addition, there are no well-accepted
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Fig. 7 The effect of poling and pressure on the imaginary impedance vs. the real impedance (Cole–Cole plot) of the PVDF membranes. The electrical impedance of the poled membrane without pressure (red-filled circle) and with pressure (filled back diamond) are compared with those of the un-poled membrane without (blue-filled square) and with pressure (filled black triangle ). The imaginary impedance for the poled membranes was an order of magnitude smaller than that of the un-poled membranes. The lower graph presents the results for the poled membrane on an expanded scale
criteria to decide which of these circuits in the most appropriate [37]. Figure 8a illustrates the proposed electrical impedance model used in this study. This particular equivalent circuit was chosen to be consistent with the structure of the samples determined from the SEM images. This circuit contains a resistance element (1) which dominates the impedance at high frequencies. The properties of the Maxwell–Wagner element (2) consisting of a parallel combination of a resistor and a capacitor were most evident in the region where the minimum phase angle was observed (e.g. region 2 in Fig. 6c). Another Maxwell–Wagner element (3) in parallel with a frequency dependent element (4) dominated the impedance properties in lower frequency range. The frequency dependent element exhibits constant phase angle behaviour at low frequencies (e.g. region 4 in the EIS spectra shown in Fig. 8b). The concept of a constant phase element (CPE) dates back to Fricke (in 1932) who reported the phenomenon to explain the impedance properties of various biological systems [13, 38]. Non-uniform distribution of the current is believed to be the origin of this behaviour [37, 39, 40].
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Fig. 8 The proposed circuit model (a ) and the typical impedance spectroscopy results of the samples (b). The numbers shown on the experimental impedance results in (b) refer to the elements numbers identified in (a)
An assortment of chemical and physical processes including the porosity of the polymer films [5, 6, 8, 20] and the non-uniform film thickness [9, 10] have been reported as sources of this pseudo-capacitive behaviour that leads to regions of constant phase angle in the impedance spectra [10, 11]. This could apply here for both poled and un-poled membranes since both have porous structures. The impedance of piezoelectric materials has also been reported in the literatures to reveal a frequency dependent capacitance dispersion at low frequencies [21–24] that cannot be described by simple elements such as capacitances, resistances, inductances or connective diffusion (e.g., Warburg) elements. This behaviour for piezoelectric ceramics [21–24] and polymers [6, 22, 41] has also been described in term of constant-phase elements (CPE)s. The conductance and capacitance of a CPE can be described by the following functions. In these equations, A, B and α (0
