Ferroelectrets piezoelectric coefficient

Equation 7 includes the prediction that the ratio of the piezoelectric coefficient and the remanent polarization P3 = Pr should be approximately equal to the elastic compliance /Ym of the matrix phase for the dipole-density effect or to the elastic compliance HYd of the dipole phase for the dipole-moment effect, respectively (or inversely proportional to the respective elastic modulus). First results assembled from the literature and from our own experimental data on PVDF and on cellular-foam PP and tubular-channel FEP ferroelectrets (Altafim et al. 2009) are shown in Fig. 5 (Qiu et al. 2013, 2014). They provide experimental evidence that the direct piezoelectric thickness coefficient of polymer materials can indeed be roughly approximated by the product of the remanent polarization in the poled material and of its overall elastic compliance. Additional data from the literature on other... 

Fig. 5 The ratio of the relevant component of the piezoelectric coefficient d and the respective polarization is plotted vs. the reciprocal of the respective elastic modulus Y (i.e., the relevant component of the elastic compliance). From left to right Literature data for inorganic ferroelectrics squares) barium titanate (BaTiOs), lead zirconate titanate (PZT), and lead zirconate niobate (PZN). Ferroelectric polymers triangles) polyamide-11 (PA-11), poly(vinylidene cyanide-vinyl acetate) (P(VDCN-VAc)), polyurea-5, poly(vinylidene fiuoride (PVDF)), poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)), and poly(vinylidene-hexafiuoropropylene) (P(VDF-HFP)). Polymer ferroelectrets circles) cellular polypropylene (cellular-PP) and tubular-channel poly (fluoro-ethylene-propylene) (FEP) (Qiu et al. 2014)...

Bias-induced reverse piezoelectric response Broadband dielectric spectroscopy (BDS) Dielectric permittivity spectrum Dielectric resonance spectroscopy Elastic modulus Ferroelectrets Electrical breakdown Acoustic method Characterization Dynamic coefficient Interferometric method Pressure and frequency dependence of piezoelectric coefficient Profilometer Quasistatic piezoelectric coefficient Stress-strain curves Thermal stability of piezoelectricity Ferroelectric hysteresis Impedance spectroscopy Laser-induced pressure pulse Layer-structure model of ferroelectret Low-field dielectric spectroscopy Nonlinear dielectric spectroscopy Piezoelectrically generated pressure step technique (PPS) Pyroelectric current spectrum Pyroelectric microscopy Pyroelectricity Quasistatic method Scale transform method Scanning pyroelectric microscopy (SPEM) Thermal step teehnique Thermal wave technique Thermal-pulse method Weibull distribution... 

As reported, ferroelectrets are thin polymer films with open or closed cavities, such as a foamed material although they differ from those due to the trapped electrical charges on the inner void surfaces. These characteristics allow the material to exhibit high J33 piezoelectric coefficients. In this section we describe the most accepted model, which explains this electromechanical behavior. 

Thus, this simple model highlights the influence of the ferroelectret s mechanical and electrical properties on the obtainable values of piezoelectric coefficients. 

Fig. 7 Force measurement with a ferroelectret sensor coupled to a charge amplifier top). A rectangular varying compressive force is applied to the sample. Force rate measurement, when the ferroelectret sensor is connected to a digital oscilloscope bottom). Measurement signals can be calibrated to determine the piezoelectric coefficient of the ferroelectret foam sensor...

The optimized PETP and PENP ferroelectrets exhibit high piezoeleetrie J33 coefficient of 500 and 140 pC/N, respectively. The piezoeleetrie sensitivity of polyester ferroelectrets is stable at least up to 80 °C, slightly higher than that of cellular PP ferroelectrets. In particular, PENP ferroelectrets are still piezoelectrically active even after storage at 100 °C for 5 days. 

In this eontext, ferroelectrets actually represent a third elass of piezoelectric polymers in the sense that these cellular materials share features of charge electrets (real eharges) with those of ferroelectric polymers (hysteresis-type ED characteristics) (Bauer et al. 2004 Lekkala et al. 1996). Moreover, ferroelectrets are characterized by extremely high piezoelectric 33 coefficients as well as an extreme anisotropy in their mechanical and electromechanical properties, which partially require speeifie characterization techniques (Dansachmiiller et al. 2005). 

Table 1 Measuring methods for piezoelectric t/33 coefficient in ferroelectrets...

To calculate the dynamic piezoelectric d- j, coefficient from the microphone sensitivity, the pressure sensitivity of the ferroelectret microphones is required. This sensitivity is defined as Mp = V/p, where p is the actual sound pressure p in front of the microphone after it is positioned in the sound field. This sound pressure differs at higher frequencies from the free-field value pf, due to diffraction effects. The value ofp can be determined from p hy means of the free-field correction factor (Xiaoqing Zhang et al. 2014 Zhang et al. 2012). From such evaluations Mp was obtained, and the dynamic piezoelectric 33 coefficient of the ferroelectret is obtained by means of (Zhang et al. 2007)... 

The above experimental methods were devoted to the study of the piezoeleetric coefficient as this one is flie relevant parameter of ferroelectrets. Ferroelectric polymers Uke PVDF and its copolymers show transversal and longitudinal piezoelectric activity depending on the degree and type of stretching (uniaxial vs. biaxial) causing molecular orientation. 

The pressure dependence of the coefficient is significant since it not only reveals the linearity of the piezoelectric effect in the material but also allows one to draw conclusions about the structure of the ferroelectrets (Hillenbrand and Sessler 2004 ... 

Fig. 16 Piezoelectric J33 coefficient determined by step response and interferometrically for two PP (Type VHD50) samples expanded at 80 °C and 160 °C, respectively, and for a commercial cellular PP ferroelectret (Type HSOl, VTT) sample (Reprinted from Zhang et al. (2004) with permission)...

Fig. 6 Experimental setup for testing ferroelectret sensors. The arrangement allows for measurements of the elastic modulus (when the LCR meter is applied) or for the characterization of the piezoelectric 1 33 coefficient (when the electrometer is employed). Force is applied to the sensor by a Teflon bar the force magnitude is adjusted by pressurized air (Redrawn with permission from (Dansachmuller et al. 2005))...

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