Piezoelectric modulus

Emura,T. Temperature variation of complex piezoelectric modulus... 

Date,M., Hara,K. Temperature dispersion of complex piezoelectric modulus of wood. Japan. J. Appl. Phys. 8,151 (19 ). 

The polymeric materials are utilized in industry and an ordinary household with the characteristic that a natural organic material does not have. Research and development are performed actively now because the polymers are materials with a variety of functionality (Imai et al., 2002 Ishii et al., 2009 Ishimoto et al., 2009 Varlow Li, 2002). By such a background, we aimed at the polymer system piezoelectric material which let it give piezoelectricity as the sensor function. For typical piezoelectric material(Koga Ohigashi,1985 Lindner etal.,2002), PZT and BaTiCb are well known until now. In contract, the PVDF of the polymer system piezoelectric material immobilized CF2 dipolar orientation. Piezoelectric modulus d.33 of the pwrous polymer electrets is higher than PVDF, and in a polymer system, polaristation reversal happens. 

The first convincing experiment of this kind was performed by Graham (1972, 1974) whose setup is shown schematically in Fig.6.1. An X-cut a-quartz plate Qi is mounted in an epoxy bed E in an evacuated cylindrical tube. A second X-cut a-quartz plate Q2, mounted on a piston serves as a projectile accelerated by a compressed gas to collide head on with Qi. Careful ahgnment of the two quartz faces and a special ratio of thickness to diameter of Qi insure that upon impact a plane compressive shock wave is generated in Qi. From the impact velocity, measured independently, and from the known material properties the deformation is calculated. The polarization resulting from this deformation by the direct piezoelectric effect is obtained from the electric signal detected from the electrodes of Qi. From measurements at differerrt impact velocities values for the piezoelectric modulus en at different deformations were calculated and fium these a value for em as a measure for the deformation dependence was derived. 

Iwataki et al. (2001) also shows relationship between Ali/Al2 and piezoelectric modulus I dn I as shown in Figure 18. Here, Ali is same length with Al as shown in Fig.l7, and Al2 is length along [120] of A-polyhedron. As seen from Figure 18(b), the ratio Ali/Al2 increases... 

E Pukada. M. Dale, and K. Hara, Temperature disperaicia of complex piezoelectric modulus of wood. Jpn. J. AppL Pkys 8 151 (1969). 

Relaxations of a-PVDF have been investigated by various methods including dielectric, dynamic mechanical, nmr, dilatometric, and piezoelectric and reviewed (3). Significant relaxation ranges are seen in the loss-modulus curve of the dynamic mechanical spectmm for a-PVDF at about 100°C (a ), 50°C (a ), —38° C (P), and —70° C (y). PVDF relaxation temperatures are rather complex because the behavior of PVDF varies with thermal or mechanical history and with the testing methodology (131). 

The piezoelectricity of polymeric materials has in general a relax-ational nature and the piezoelectric stress constant e is a function of the frequency of the applied strain in a similar way to the elastic modulus and dielectric constant. The induced polarization has in-phase and out-of-phase components to the strain and the e-constant is expressed as a complex quantity, as in Eq. (32). 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e", does not necessarily imply an energy loss (Holland, 1967). In the former two, G"/G and e"/e express the ratio of energy dissipation per cycle to the total stored energy, but e"/e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e" is not a positive definite quantity in contrast to G" and e". In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e ... 

Fig. 11. Complex piezoelectric strain constant (20 Hz), complex Young s modulus (30 Hz), and complex dielectric constant (1kHz) of uniaxially drawn poly(D-propylene oxide) film plotted against temperature. Draw-ratio = 1.5. Degree of crystallinity=40%. Drawn after Furukawa and Fukada [Nature 221,1235 (1969)] by permission of Macmillan (Journals) Ltd.

Kohara,J., Okamoto.H. Dynamic Young s modulus and piezoelectric... 

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