Piezoelectricity, shear

The dynamic press allows measurements of the longitudinal, transverse and shear piezoelectric coefficients in the frequency range from 0.01 Hz to about 100 Hz. The lower limit is determined by the insulation resistance of the sample and cables, and charge drifts associated... 

Davis et al. [42] have recently introduced the terms rotator and extender for a variety of ferroelectrics based on oxygen octahedra, in order to classify them with respect to whether the shear or the collinear effect dominates in the piezoelectric response. In extenders, the dominant polarization extension is directly related to the collinear piezoelectric effect, whereas in rotators the dominant contribution to the piezoelectric effect is the polarization rotation, that is directly related to the shear piezoelectric effect. Thus, extenders are ferroelectrics with a large longitudinal piezoelectric coefficient 33 that is related to a large relative dielectric susceptibihty %33, while rotators are ferroelectrics with large shear coefficients dis and 24. which are related to transverse susceptibilities and %2z. correspondingly. Electrostrictive... 

Application of a shear stress to most natural biopolymers produces shear piezoelectricity. The polarization is measured by using an apparatus such as a Rheolo-graph Solid (Toyo Seiki Co.) upon application of an oscillatory shear stress (typically 20 Hz) to the biopolymer sample [13,14]. A typical piezoelectric matrix for materials displaying shear piezoelectricity is shown in Table 1. The three components of polarization, P, related to the six components of stress, T,... 

For materials displaying shear piezoelectricity, it is evident that the relationship between polarization and shear stress reduces to the following equation at zero applied field [13] ... 

The piezoelectric coefficients d, and d, do not cancel each other, as we saw previously with the shear piezoelectric biopolymers, but contribute to a small but finite value of tensile piezoelectricity. The tensile piezoelectric coefficient, d, can be measured with a Berlincourt piezometer [38]. The pyroelectric response can be measured with an apparatus in which the temperature is altered at 0.5°/min by circulating water and the pyroelectric current is measured using a low-impedance current amplifier [39]. 

The electrical response of a piezoelectric material is a function of the electrode configuration relative to the direction of the applied mechanical stress. For a coefficient dy, the first subscript is the direction of the electric field or charge displacement, and the second subscript gives the direction of the mechanical deformation or stress. The C2v crystallographic symmetry typical of S5mthetic oriented, poled polymer film leads to cancellation of all but five of the dtj components W31, ds2, ds3, di5, and 24)- If the film is poled and biaxially oriented or unoriented, dsi = ds2 and di5 = 24. Most natural biopolymers possess Pco symmetry which yields a matrix that possesses only the shear piezoelectricity components dis and 25. Because the dss constant is difficult to measure without constraining the lateral dimension of the sample, it is typically determined from equation 7 which relates the constants to the hydrostatic piezoelectric constant, dsh. 

Coefficients d, d2i and d-ij, describe the longitudinal piezoelectric effect (see symbol L in Table 5.1). The normal mechanical stress component causes piezoelectric polarization parallel to it in such case. Second possibihty is the piezoelectric polarization perpendicular to the applied normal mechanical stress. Such piezoelectric effect is so called transversal effect (see symbol T in Table 5.1) and it is characterized by one of the coefficients di2, d -i, J21, dj2, dn or J32. Application of shear mechanical stress might result in the piezoelectric polarization perpendicular to the plane of applied shear. Such shear piezoelectric effect is called longitudinal shear (see symbol 5l in Table 5.1) and it is characterized by one of the piezoelectric coefficients du, d25 or d e- Second possibility of shear piezoelectric effect is the piezoelectric polarization parallel to the plane of the applied shear stress. Such effect is called transversal shear (see symbol in Table 5.1 and in Fig. 5.2). This effect is related to one of the piezoelectric coefficients J15, di, d24, d26, d- orc 35. 

Validation of such flap actuation solutions have been performed in wind tunnel tests on a one-seventh downscaled Bell-412 Mach-scaled rotor hub [87]. It has been shown that trailing edge deflections of 4° to 5° can be achieved at up to 1800 rpm which allowed suppression of vibratory bending moments imder an open loop control condition. Even some preliminary closed-loop tests using a neural network controller were performed which however required simultaneous actuation of all four blades. In [88] an induced-shear piezoelectric actuator has been described to actuate trailing edge flaps... 

Centolanza, L.R. Smith, E.C. and Munsky, B. Induced-shear piezoelectric actuators for rotor blade trailing edge flaps. Smart Mater. Struct., 11 (2002), pp. 24-35... 

The study of the shear piezoelectric polymers has advanced in the last few decades, and their practical application to sensor and actuator devices has progressed. In this section, the fundamental properties and applications of shear piezoelectric polymers are discussed. 

Poly-L-lactic acid is a chiml polymer with two optical isomers, and its chain molecules form a helical structure owing to its chiraUty. One is PLLA and the other is poly-D-lactic acid (PDLA). The helical structure of PLLA is right handed, whereas the hehcal structure of PDLA is left handed. The shear piezoelectric constant of PLLA is high compared with those of other shear piezoelectric polymers, as shown in Table 5. 

Fig. 8. As a result, the C=0 bond, whieh has a larger dipole moment flian the other bond, is displaeed. The rotation of the C=0 bond ehanges the polarization of the entire long-ehain molecule, resulting in the shear piezoelectricity of PLLA. Thus, the macroscopic piezoelectricity of a drawn PLLA film is a result of its intrinsic piezoelectricity due to its crystal state. However, in general, translational symmetry does not exist in a PLLA film because of its complex high-order structure (Tajitsu 2010). In other words, amorphous components are always present in the complex high-order structure. No one-to-one correspondence has been foxmd between macropiezoelectric properties and crystal characteristics. The mechanism of macroscopic piezoelectricity is made complicated by the existence of the complex high-order structure. We emphasize that the point group in the macroscopic state is different from that in the crystal state (Tajitsu 2013).

PLLA films, with a larger shear piezoelectric constant than the oflier polymers in Table I and non-pyroelectricity, are greatly anticipated to be used as sensors and actuators for realizing unconventional HMIs because of their excellent fiexibility and transparency. A PLLA sensor has been combined with a projected capacitive touch panel to realize a deformation-sensitive touch panel (Ando et al. 2012). The touch sensor comprises a PLLA film, and the electrode of tiie touch sensor has a diamond stracture. A polycarbonate (PC) plate is used as tiie surface plate of the touch panel. The electrode consists of three layers, as shown in Fig. 9 (Ando et al. 2013). On layer 1, an RX electrode was... 

Nix and Wird (10 have developed a technique for the measurement of the shear piezoelectric coeffi nte. They glued uniaxially orienled PVDF sheets between blocks of Perspex and attached electrodes on the edges of the sample perpendicular to the 1 and 2 directions. When the sample and blocks of Perspex were mounted in an appropiiate rig, a simple shear could be applied in the 1-3 plane and the change in polarization detected by the electrodes perpendicular to the 1 direction to determine d. Similarly, shear in the 2-3 plane and detection of the change in polarization with the electrode mounted perpendicular to the 2 direction gives d, ... 

Another popular crystalline structure for protein is the structure formed by extended protein molecules. A pleated sheet structure is formed by hydrogen bonds between adjacent extended molecules aligned in parallel. Piezoelectricily in B-form protein was first observed by Fukada in 1956 for silk fibroin [3]. Since there is no intrinsic pt -zation in the B structure, pyroelectricity and ten piezoelectricity are not observed. However, the piezoelectricity due to shear is observed. If the shear is applied such as to cause slip between oriented molecules, polarizatioo is induced in the direction perpendicular to the plane of the shear. Shear piezoelectricity is observed for most natural biopolymers, not only keratin but abo trumy other proteins. 

Shear piezoelectricily far polysaccfaarkles was first Investigated in detail for wood cellulose by Bazhenov in 1951 [4]. Shear piezoelectricity for bone and tendon coUagen was first reported by Fukada and Yasuda in 1957 [5] and 1964 [6]. 

Starting from these initial studies, a Urge number of works have been published on the piezoelectric properties of biopolymers of both natural and synthetic origin. This chapter outlines the work carried out for the shear piezoelectricity of biopolymers as well as optically active polymers. 

The synunetry of D. is observed for most natural biopolymers, which show only shear piezoelectricity. The 3 axis is taken as the axis of orientation. In this symmetry the lelaboo da s -d holds. The symmetry of C. is found in certain structures of living systems such as bone and tendon. The preferred alignment of the polar axis of polymer crystallites in the 3 axis provides the piezoelectric constants d d as well as the pyroelectric effect in the 3 axis, although they are not so large. 

Shear piezoelectricity is observed almost universally for the oriented textures of bio> polymers. It is also observed for the oriented films of a variety of synthetic polymers with optical activity. Rcctangplar coordinates are assigned to the film sample as shown in Figure 1. The 3 axis is taken in the direction of orientatiao, and the 1 axis is perpendicular to the plane of the film. The film Is cut at a slant, at an angle 9 with the 3 axis. The tension applied at 8 a 45 gives a shear stress r , which is positive. Then the polarization or the electric displacement 0, which is negative for L polymers and positive for D polymers, is induced in the direction of the 1 axis. 

Shear piezoelectricity b observed in oriented films of many synthetic polymers. During casting from solution, the polar axes of polymer crystab are oriented at random in the film. Therefore, after ekmgation of the fil the polar axes of polymer crystallites arc distributed with equal probability in both the positive and negative directions of the 3 axb. Thus the constants d and d become null, although the piezoelectric constanb d and dit of crystab may have finite values. 

In the following description, the piezoelectric constant d indicates the shear piezoelectric constant -d, or d . For symmetry C. and D the relation -d, d d holds. In most cases, a sinusoidal stress at 10 Hz is given to the sample and both in-phase component and v/2 out-of-phase component of the resulting sinusoidal polarization are detected. The ratio of polarization to stress is the conqdex piezoelectric strain constant d d - id, and the ratio of polarization to strain is the complex stress constant e t - id. ... 

If the sense of the dipole moment of a helixes oouM be oriented in the same diiec tioo. there would be a possibility to obtain a dipolar ekctrct with a huge remanent polarization, which should exhibit very large pyrockctricily as well as both tensile and shear piezoelectricity. 

The estimated piezoelectric constants in the crystalline phase for PLXA are as large as Cm fi0 mC/m and d,/ s -30 pCTN, respectively. If the degree of crystallinity is assumed to be > 0.5, these becomes approximately Cu -40 mCTm and d,t -20 peVN. These are the highest values so far obtained for the shear piezoelectric constant in polymer crystals [46]. 

---