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- Curie transition (3)
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- dielectric relaxation spectroscopy (2)
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- ferroelectric polymers (2)
- fluoroethylenepropylene (FEP) copolymer (2)
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- (PEDOT (1)
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- piezoelectric nanogenerator (PENG) (1)
- piezoelectricity-polarization relation (1)
- poly(vinylidenefluoride-trifluoroethylene) P(VDF-TrFE) (1)
- polyethylene (1)
- polyethylene naphthalate (PEN) (1)
- polymer ferroelectrets (1)
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- polypropylene (1)
- polytetrafluoroethylene (PTFE) (1)
- printed electroacoustic thin-film transducers (1)
- printing (1)
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- pyroelectricity (1)
- relationships (1)
- relaxor-ferroelectric polymers (1)
- remanent polarisation (1)
- screen (1)
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- silicone based dielectric elastomer actuators (1)
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- space charge (1)
- space-charge and polarization profiles (1)
- spectroscopy (1)
- spin coating (1)
- static-pressure dependence (1)
- steel and concrete structures (1)
- strain gauges (1)
- strain sensors (1)
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- surface charge stability (1)
- surface morphology (1)
- surface reconstruction (1)
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- temperature dependence (1)
- thermal (1)
- thermally stimulated depolarization current (1)
- thin-film actuators (1)
- titanium dioxide (1)
- tubular-channel polymer systems (1)
- vinylidenefluoride(VDF)-based polymers (1)
- wearable (1)
- wearable electronics (1)
Institute
In this paper, two non-destructive thermal methods are used in order to determine, with a high degree of accuracy, three-dimensional polarization distributions in thin films (12 mu m) of poly(vinylidenefluoride- trifluoroethylene) (PVDF-TrFE). The techniques are the frequency-domain Focused Laser Intensity Modulation Method (FLIMM) and time-domain Thermal-Pulse Tomography (TPT). Samples were first metalized with grid-shaped electrode and poled. 3D polarization mapping yielded profiles which reproduce the electrode-grid shape. The polarization is not uniform across the sample thickness. Significant polarization values are found only at depths beyond 0.5 mu m from the sample surface. Both methods provide similar results, TPT method being faster, whereas the FLIMM technique has a better lateral resolution.
The prehistory of electrets is not known yet, but it is quite likely that the electrostatic charging behavior of amber (Greek: τò ηλεκτρoν, i.e., “electron”) already was familiar to people in ancient cultures (China, Egypt, Greece, etc.), before the Greek philosopher and scientist Thales of Miletus (6th century BCE)-or rather his disciples and followers-reported it in writing (cf. Figure 1). More than two millennia later, William Gilbert (1544–1603), the physician of Queen Elizabeth I, coined the term “electric” in his book De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (1600) for dielectric materials that attract like amber and that included sulfur and glass [1]. The second half of the 18th century saw the invention of the electrophorus or electrophore [2], a capacitive electret device, in 1762 by Johan Carl Wilcke (1732–1796).
Here, a promising approach for producing piezo-polymer transducers in a one-step process is presented. Using 3D-printing technology and polypropylene (PP) filaments, we are able to print a two-layered film structure with regular cavities of precisely controlled size and shape. It is found that the 3D-printed samples exhibit piezoelectric coefficients up to 200 pC/N, similar to those of other PP ferroelectrets, and their temporal and thermal behavior is in good agreement with those known of PP ferroelectrets. The piezoelectric response strongly decreases for applied pressures above 20 kPa, as the pressure in the air-filled cavities strongly influences the overall elastic modulus of ferroelectrets.
Due to their electrically polarized air-filled internal pores, optimized ferroelectrets exhibit a remarkable piezoelectric response, making them suitable for energy harvesting. Expanded polytetrafluoroethylene (ePTFE) ferroelectret films are laminated with two fluorinated-ethylene-propylene (FEP) copolymer films and internally polarized by corona discharge. Poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS)-coated spandex fabric is employed for the electrodes to assemble an all-organic ferroelectret nanogenerator (FENG). The outer electret-plus-electrode double layers form active device layers with deformable electric dipoles that strongly contribute to the overall piezoelectric response in the proposed concept of wearable nanogenerators. Thus, the FENG with spandex electrodes generates a short-circuit current which is twice as high as that with aluminum electrodes. The stacking sequence spandex/FEP/ePTFE/FEP/ePTFE/FEP/spandex with an average pore size of 3 mu m in the ePTFE films yields the best overall performance, which is also demonstrated by the displacement-versus-electric-field loop results. The all-organic FENGs are stable up to 90 degrees C and still perform well 9 months after being polarized. An optimized FENG makes three light emitting diodes (LEDs) blink twice with the energy generated during a single footstep. The new all-organic FENG can thus continuously power wearable electronic devices and is easily integrated, for example, with clothing, other textiles, or shoe insoles.
The standard charging process for polymer ferroelectrets, e. g., from polypropylene foams or layered film systems involves the application of high DC fields either to metal electrodes or via a corona discharge. In this often-used process, the DC field triggers the internal breakdown and limits the final charge densities inside the ferroelectret cavities and, thus, the final polarization. Here, an AC + DC charging procedure is proposed and demonstrated in which a high-voltage high-frequency (HV-HF) wave train is applied together with a DC poling voltage. Thus, the internal dielectric-barrier discharges in the ferroelectret cavities are induced by the HV-HF wave train, while the final charge and polarization level is controlled separately through the applied DC voltage. In the new process, the frequency and the amplitude of the HV-HF wave train must be kept within critical boundaries that are closely related to the characteristics of the respective ferroelectrets. The charging method has been tested and investigated on a fluoropolymer-film system with a single well-defined cylindrical cavity. It is found that the internal electrical polarization of the cavity can be easily controlled and increases linearly with the applied DC voltage up to the breakdown voltage of the cavity. In the standard charging method, however, the DC voltage would have to be chosen above the respective breakdown voltage. With the new method, control of the HV-HF wave-train duration prevents a plasma-induced deterioration of the polymer surfaces inside the cavities. It is observed that the frequency of the HV-HF wave train during ferroelectret charging and the temperature applied during poling of ferroelectrics serve an analogous purpose. The analogy and the similarities between the proposed ferroelectret charging method and the poling of ferroelectric materials or dipole electrets at elevated temperatures with subsequent cooling under field are discussed.
In recent communications from these laboratories, we observed that amine-rich thin organic layers are very efficient surfaces for the adhesion of mammalian cells. We prepare such deposits by plasma polymerization at low pressure, atmospheric pressure, or by vacuum-ultraviolet photo-polymerization. More recently, we have also investigated a commercially available material, Parylene diX AM. In this article we first briefly introduce literature relating to electrostatic interactions between cells, proteins, and charged surfaces. We then present certain selected cell-response results that pertain to applications in orthopedic and cardiovascular medicine: we discuss the influence of surface properties on the observed behaviors of two particular cell lines, human U937 monocytes, and Chinese hamster ovary cells. Particular emphasis is placed on possible electrostatic attractive forces due to positively charged R-NH3+ groups and negatively charged proteins and cells, respectively. Experiments carried out with electrets, polymers with high positive or negative surface potentials are added for comparison.
The addition of nano-Al2O3 has been shown to enhance the breakdown voltage of epoxy resin, but its flashover results appeared with disputation. This work concentrates on the surface charge variation and dc flashover performance of epoxy resin with nano-Al2O3 doping. The dispersion of nano-Al2O3 in epoxy is characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The dc flashover voltages of samples under either positive or negative polarity are measured with a finger-electrode system, and the surface charge variations before and after flashovers were identified from the surface potential mapping. The results evidence that nano-Al2O3 would lead to a 16.9% voltage drop for the negative flashovers and a 6.8% drop for positive cases. It is found that one-time flashover clears most of the accumulated surface charges, regardless of positive or negative. As a result, the ground electrode is neighbored by an equipotential zone enclosed with low-density heterocharges. The equipotential zone tends to be broadened after 20 flashovers. The nano-Al2O3 is noticed as beneficial to downsize the equipotential zone due to its capability on charge migration, which is reasonable to maintain flashover voltage at a high level after multiple flashovers. Hence, nano-Al2O3 plays a significant role in improving epoxy with high resistance to multiple flashovers.
Cellular polypropylene (PP) ferroelectrets combine a large piezoelectricity with mechanical flexibility and elastic compliance. Their charging process represents a series of dielectric barrier discharges (DBDs) that generate a cold plasma with numerous active species and thus modify the inner polymer surfaces of the foam cells. Both the threshold for the onset of DBDs and the piezoelectricity of ferroelectrets are sensitive to repeated DBDs in the voids. It is found that the threshold voltage is approximately halved and the charging efficiency is clearly improved after only 10(3) DBD cycles. However, plasma modification of the inner surfaces from repeated DBDs deteriorates the chargeability of the voids, leading to a significant reduction of the piezoelectricity in ferroelectrets. After a significant waiting period, the chargeability of previously fatigued voids shows a partial recovery. The plasma modification is, however, detrimental to the stability of the deposited charges and thus also of the macroscopic dipoles and of the piezoelectricity. Fatigue from only 10(3) DBD cycles already results in significantly less stable piezoelectricity in cellular PP ferroelectrets. The fatigue rate as a function of the number of voltage cycles follows a stretched exponential. Fatigue from repeated DBDs can be avoided if most of the gas molecules inside the voids are removed via a suitable evacuation process.
Polymer foams with electrically charged cellular voids, the so-called ferroelectrets, are soft piezoelectric transducer materials. Several polymers such as polyethylene terephthalate or cyclo-olefin copolymers are under investigation with respect to their suitability as ferroelectrets. Here, the authors report an additional ferroelectret polymer, cellular polyethylene-naphthalate (PEN), which was prepared from commercial uniform polymer films by means of foaming in supercritical carbon dioxide, inflation, biaxial stretching, electrical charging, and metallization. Piezoelectric d(33) coefficients of up to 140 pC/N demonstrate the suitability of such cellular PEN films for transducer applications. Their piezoelectricity is partially stable at elevated temperatures as high as 100 degrees C.
Polymer foams are in industrial use for several decades. More recently, non-polar polymer foams were found to be piezoelectric (so-called piezoelectrets) after internal electrical charging of the cavities. So far, few studies have been carried out on the electrical-insulation properties of polymer foams. Here, we compare the piezoelectric and the DC-voltage electrical-insulation properties of cellular polypropylene (PP) foams. Their cavity microstructure can be adjusted via inflation in high-pressure nitrogen gas in combination with a subsequent thermal treatment. While inflation is effective for improving the piezoelectricity, it is detrimental for the electrical-insulation properties. The original cellular PP foam shows a breakdown strength of approximately 230 MV/m, within the same range as that of solid PP. The breakdown strength decreases with increasing degree of inflation, and the dependence on the foam thickness follows an inverse power law with an exponent of 1.2. Nevertheless, up to a thickness of 140 mu m (3.5 times the original thickness), the breakdown strength of cellular-foam PP films is at least 7 times that of an air gap with the same thickness. In addition, the influence of high temperatures and high humidities on the piezoelectricity and the breakdown strength of cellular PP was studied. It was found that the piezoelectric d(33) coefficient decays rapidly already at 70 degrees C, while the breakdown strength slightly increases during storage at 70 or 90 degrees C. Under a relative humidity of 95%, the breakdown strength increases with storage time, while the piezoelectric d(33) coefficient slightly decreases.
Characterization and calibration of piezoelectric polymers in situ measurements of body vibrations
(2011)
Piezoelectric polymers are known for their flexibility in applications, mainly due to their bending ability, robustness, and variable sensor geometry. It is an optimal material for minimal-invasive investigations in vibrational systems, e.g., for wood, where acoustical impedance matches particularly well. Many applications may be imagined, e. g., monitoring of buildings, vehicles, machinery, alarm systems, such that our investigations may have a large impact on technology. Longitudinal piezoelectricity converts mechanical vibrations normal to the polymer-film plane into an electrical signal, and the respective piezoelectric coefficient needs to be carefully determined in dependence on the relevant material parameters. In order to evaluate efficiency and durability for piezopolymers, we use polyvinylidene fluoride and measure the piezoelectric coefficient with respect to static pressure, amplitude of the dynamically applied force, and long-term stability. A known problem is the slow relaxation of the material towards equilibrium, if the external pressure changes; here, we demonstrate how to counter this problem with careful calibration. Since our focus is on acoustical measurements, we determine accurately the frequency response curve - for acoustics probably the most important characteristic. Eventually, we show that our piezopolymer transducers can be used as a calibrated acoustical sensors for body vibration measurements on a wooden musical instrument, where it is important to perform minimal-invasive measurements. A comparison with the simultaneously recorded airborne sound yields important insight of the mechanism of sound radiation in comparison with the sound propagating in the material. This is especially important for transient signals, where not only the long-living eigenmodes contribute to the sound radiation. Our analyses support that piezopolymer sensors can be employed as a general tool for the determination of the internal dynamics of vibrating systems.
Charging properties and time-temperature stability of innovative polymeric cellular ferroelectrets
(2007)
After appropriate mechanical and electrical treatments, some cellular polymers become able to retain space charge for a long time, i.e. they acquire electret behavior. The electrical treatment consists of charging under high levels of DC electric field. The mechanical treatment, based on the application of stretching forces to cellular polymer slabs that were before expanded under pressurized gas, affects the cavity size and shape, and therefore also the effectiveness of the charging process itself. An investigation of charging mechanisms, as well as of mechanical treatment, is therefore fundamental for optimizing the ferro- and piezo-electret properties. The aim of this paper is to discuss the effect of the physical dimension of the cavities on the charging behavior of cellular ferroelectrets and to focus on the time-temperature stability for two families of polymeric cellular ferroelectrets based on polypropylene (PP) and on a cyclo-olefin copolymer (COC). Emphasis will be given to the stretching process and in particular to the expansion rate applied during the manufacturing process (which affects the radial dimension and the height of the cavities, respectively). Space-charge and partial-discharge measurements as a function of time and temperature are the main tools to infer the influence of the cavity size on charging and stability characteristics.
The low surface-charge stability of polypropylene (PP) frequently limits its application as an electret material. In this paper, we demonstrate how the treatment of PP-film surfaces with orthophosphoric acid (H3PO4) enhances their charge stability. To discriminate between the effects of chemical modification and thermal treatment, as-received and annealed PP films are used as reference samples. The electret properties of treated and non-treated PP films are characterized with thermally stimulated discharge (TSD) and isothermal surface-potential decay (ISPD) experiments, from which considerable improvement in thermal and temporal charge stability is observed for samples modified with H3PO4. The half-value temperature (T-1/2) observed on TSD curves of chemically treated PP increases to 131 and 145 degrees C for positive and negative charges, respectively. The enhancement might be attributed to the phosphoric compounds detected on the H3PO4-modified surfaces via attenuated-total-reflection infrared spectroscopy. Deeper surface traps formed at the "foreign" phosphorus-containing structures are able to capture the charges over longer time periods and at higher temperatures, thus leading to significant improvements in the temporal and thermal surface-charge stabilities of PP electrets. Published by AIP Publishing.
Coating of porous polytetrafluoroethylene films with other polymers for electret applications
(2001)
Complete relaxation map of polyethylene : filler-induced chemical modifications as dielectric probes
(2001)
When exposed to sufficiently high electric fields, polymer-foam electret materials with closed cells exhibit ferroelectric-like behavior and may therefore be called ferroelectrets. In cellular ferroelectrets, the influence of the cell size and shape distributions on the application-relevant properties is not yet understood. Therefore, controlled inflation experiments were carried out on cellular polypropylene films, and the resulting elastical and electromechanical parameters were determined. The elastic modulus in the thickness direction shows a minimum with a corresponding maximum in the electromechanical transducer coefficient. The resonance frequency shifts as a function of the elastic modulus and the relative density of the inflated cellular films. Therefore, the transducer properties of cellular ferroelectrets can be optimized by means of controlled inflation. (C) 2004 American Institute of Physics
In the present study, the charge distribution and the charge transport across the thickness of 2- and 3-dimensional polymer nanodielectrics was investigated. Chemically surface-treated polypropylene (PP) films and low-density polyethylene nanocomposite films with 3 wt % of magnesium oxide (LDPE/MgO) served as examples of 2-D and 3-D nanodielectrics, respectively. Surface charges were deposited onto the non-metallized surfaces of the one-side metallized polymer films and found to broaden and to thus enter the bulk of the films upon thermal stimulation at suitable elevated temperatures. The resulting space-charge profiles in the thickness direction were probed by means of Piezoelectrically-generated Pressure Steps (PPSs). It was observed that the chemical surface treatment of PP which led to the formation of nano-structures or the use of bulk nanoparticles from LDPE/MgO nanocomposites enhance charge trapping on or in the respective polymer films and also reduce charge transport inside the respective samples.
In this paper, a measuring technique is presented for the detection of radial oscillations of tube walls excited by changes in internal air pressure. On organ pipes, the oscillations were investigated by means of piezoelectric polymer films slightly tensioned around the pipe bodies. Employing sensors with patterned electrodes, the well-known elliptical oscillation of the cross section as well as an additional monopole breathing of the organ-pipe body were detected. For the monopole breathing, a close relationship between the pressure distribution of the air-column resonances inside the pipe and the circumference variations along the pipe was observed
Here, piezoelectric transducers consisting of a P(VDF-TrFE) layer with either silver or PEDOT:PSS screen-printed electrodes are studied. The influence of electrodes on the dielectric and electroacoustic properties are studied in dielectric-spectroscopy and ferroelectric-hysteresis measurements. Only when both the bottom and the top electrodes are made of silver, the typical dielectric relaxation of the P(VDF-TrFE) layer is clearly observed. When one or two of the electrodes are of PEDOT:PSS, a Debye-like relaxation is present. Compared with silver electrodes, PEDOT:PSS electrodes allow for moderate self-healing. Consequently, samples with bottom and top PEDOT:PSS electrodes can be poled to saturation, while samples with silver electrodes can hardly be poled to saturation due to destructive electric breakdown. Acoustic transducer measurements show that silver electrodes facilitate higher and broader frequency operation, while PEDOT:PSS electrodes bring slightly lower total harmonic distortion. Overall, the acoustic performance shows no significant deviations between differently electroded samples so that silver electrodes do not offer any advantages for the transducers studied here due to their much higher tendency for destructive electric breakdown.
Organic materials with non-centrosymmetric chromophores are known to be susceptible to a number of photochemical processes, including reversible isomerization reactions as well as irreversible photo-oxidation or photo- reduction reactions. Reversible isomerization is the basis for a variety of applications, such as photo-induced poling, optical data storage and optical grating formation. The irreversible processes that involve the destruction of the chromophores have been found useful for the fabrication of optical waveguides, but they also limit the life times of polymeric photonic devices. In this paper, it is demonstrated that dielectric measurements allow for an in-depth investigation of non-reversible chromophore degradation processes in a typical side-chain polymer. The time- and temperature-dependent dielectric function of the polymer at 1 kHz enables us to follow the chromophore-degradation kinetics and to monitor the bleaching depth as a function of time at room and elevated temperatures
Dielectric materials for electro-active (electret) and/or electro-passive (insulation) applications
(2019)
Dielectric materials for electret applications usually have to contain a quasi-permanent space charge or dipole polarization that is stable over large temperature ranges and time periods. For electrical-insulation applications, on the other hand, a quasi-permanent space charge or dipole polarization is usually considered detrimental. In recent years, however, with the advent of high-voltage direct-current (HVDC) transmission and high-voltage capacitors for energy storage, new possibilities are being explored in the area of high-voltage dielectrics. Stable charge trapping (as e.g. found in nano-dielectrics) or large dipole polarizations (as e.g. found in relaxor ferroelectrics and high-permittivity dielectrics) are no longer considered to be necessarily detrimental in electrical-insulation materials. On the other hand, recent developments in electro-electrets (dielectric elastomers), i.e. very soft dielectrics with large actuation strains and high breakdown fields, and in ferroelectrets, i.e. polymers with electrically charged cavities, have resulted in new electret materials that may also be useful for HVDC insulation systems. Furthermore, 2-dimensional (nano-particles on surfaces or interfaces) and 3-dimensional (nano-particles in the bulk) nano-dielectrics have been found to provide very good charge-trapping properties that may not only be used for more stable electrets and ferroelectrets, but also for better HVDC electrical-insulation materials with the possibility to optimize charge-transport and field-gradient behavior. In view of these and other recent developments, a first attempt will be made to review a small selection of electro-active (i.e. electret) and electro-passive (i.e. insulation) dielectrics in direct comparison. Such a comparative approach may lead to synergies in materials concepts and research methods that will benefit both areas. Furthermore, electrets may be very useful for sensing and monitoring applications in electrical-insulation systems, while high-voltage technology is essential for more efficient charging and poling of electret materials.
Polymer-dispersed liquid crystals (PDLCs) are prepared from poly(vinylidene fluoride-trifluoroethylene) (P(VDF- TrFE)) and a nematic liquid-crystal (LC). The anchoring effect was studied using dielectric relaxation spectroscopy. Two dispersion regions are observed in the dielectric spectra of the pure P(VDF-TrFE) film. They are related to the glass transition and to a space-charge relaxation. In PDLC films containing 10 wt% of LC, an additional, bias field-dependent relaxation peak is found that can be attributed to the motion of LC molecules. Due to the hindered movement of the LC molecules, this relaxation process is considerably slowed down, compared with the related process in the pure LC.
Ferroelectric polyamide 11 films were prepared by melt-quenching, cold-drawing and electrical poling. Their ferroelectricity was studied by means of dielectric-hysteresis measurements. A remnant polarisation of up to 35 mC/m(2) and a coercive field of 75 MV/m were obtained. The piezoelectric d(33) coefficient and the pyroelectric coefficient of the films are reduced by annealing just below the melting region, but remain at about 3 pC/N and 8 muC/(m(2)K), respectively, during further heat treatment. Differential scanning calorimetry (DSC), dielectric relaxation spectroscopy (DRS) and thermally stimulated depolarisation (TSD) were applied for investigating the conformational changes induced by melt-quenching, cold-drawing and annealing. The results indicate that the cold-drawn film mainly consists of a rigid amorphous phase which exhibits considerably lower conductivity, no glass transition and consequently no dielectric a relaxation. Instead, an a, relaxation is found, which is related to chain motions in regions of the rigid amorphous phase where the amide-group dipoles are not perfectly ordered. Annealing removes imperfectly ordered structures, but does not affect the ferroelectric polarisation. Therefore, it may be concluded that essentially the a, relaxation causes the thermally non-stable part of the piezo- and pyroelectricity in polyamide 11
Dielectric spectra of a partially fluorinated chromophore / amorphous Teflon AF guest-host system
(1999)
By means of pyroelectrical measurements and dielectric spectroscopy as well as structural information from differential scanning calorimetry, it is shown that, in a poly(vinyl alcohol) with azobenzene-alkoxy side chains, pyroelctricity and dielectric hysteresis which are usually related to each other have different origins. The pyroelectric effect is explained with reversible dipole-density changes upon thermal expansion, whereas the dielectric hysteresis is proposed to result from a charge-carrier polarisation.
Direct hysteresis measurements on ferroelectret films by means of a modified Sawyer-Tower circuit
(2013)
Ferro- and piezo-electrets are non-polar polymer foams or film systems with internally charged cavities. Since their invention more than two decades ago, ferroelectrets have become a welcome addition to the range of piezo-, pyro-, and ferro-electric materials available for device applications. A polarization-versus-electric-field hysteresis is an essential feature of a ferroelectric material and may also be used for determining some of its main properties. Here, a modified Sawyer-Tower circuit and a combination of unipolar and bipolar voltage waveforms are employed to record hysteresis curves on cellular-foam polypropylene ferroelectret films and on tubular-channel fluoroethylenepropylene copolymer ferroelectret film systems. Internal dielectric barrier discharges (DBDs) are required for depositing the internal charges in ferroelectrets. The true amount of charge transferred during the internal DBDs is obtained from voltage measurements on a standard capacitor connected in series with the sample, but with a much larger capacitance than the sample. Another standard capacitor with a much smaller capacitance-which is, however, still considerably larger than the sample capacitance-is also connected in series as a high-voltage divider protecting the electrometer against destructive breakdown. It is shown how the DBDs inside the polymer cavities lead to phenomenological hysteresis curves that cannot be distinguished from the hysteresis loops found on other ferroic materials. The physical mechanisms behind the hysteresis behavior are described and discussed.
In this paper, a recently developed numerical method to analyze dielectric-spectroscopy data is applied to alpha-phase polyvinylidene fluoride (PVDF). The numerical procedure is non-parametric and does not contain any of the extensively used empirical formulas mentioned in the literature. The method basically recovers the unknown distribution of relaxation times of the generalized dielectric function representation by simultaneous application of the Monte Carlo integration method and of the constrained least-squares optimization. The relaxation map constructed after the numerical analysis is compared to a-phase PVDF data presented in the literature and results of the parametric analysis with a well- known empirical formula. (c) 2005 Elsevier B.V. All rights reserved
Elastic properties and electromechanical coupling factor of inflated polypropylene ferroelectrets
(2006)
Electrets
(1999)