Piezoelectric matrix

In general, the strains resulting from an applied field increase with the magnitude of the piezoelectric constants C/y 0 that lithium niobate, for example, exhibits larger strains than does gallium arsenide for a given electric field. However, die particular strain pattern found depends on the form of the piezoelectric matrix (and hence, on the crystal class involved) as well as the electric field direction. 

TABLE 1 Piezoelectric Matrix for Materials with D, Symmetry [10]... 

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,... 

Many biopolymers display the piezoelectric matrix shown in Table 1. The origin of piezoelectricity lies in the internal rotation of the CONH peptide bond with a dipole moment of 3.4 debye [9]. Most natural biopolymers have 25 values of the order of 0.1 pC/N [7,9]. A common crystalline structure for proteins such as p-... 

TABLE 2 Piezoelectric Matrix for Materials with Syminetry [101... 

The piezoelectric matrix for stretched and polarized polymers with symmetry has the form shown in Table 3. Note that the tensile piezoelectric coefficients t/, and t/33 have finite values. 

This representation presumes that the c—axis is aligned with the 0 3—direction. For a cubic crystal, such as gallium arsenide, only three components of the piezoelectric matrix are nonzero, and these are specified in terms of a single constant according to... 

In the past four decades, four kinds ttf piezoelectric matrix have beat found in different polymers as shown below. 

Piezocomposite transducers are an advancement of piezoelectric ceramics. Instead of the classic piezoceramic material, a compound of polymer and piezoceramic is used for the composite element to improve specific properties. The 1-3 structure, which is nowadays mostly used as transducer material, refers to parallel ceramic rods incorporated in an epoxy-resin matrix (see Fig. 1). 

A piezo-composite consists of a piezoelectric active phase and a passive plastic phase [2]. In the 1-3-configuration adopted in our case, piezoelectric rods parallely aligned in thickness direction are imbedded in a three-dimensional plastic matrix (Fig. 1). The distance between the rods has to be chosen inferior to the half wave length of the shear wave in the matrix material ensuring that the whole compound is vibrating as a quasi-homogeneous material. 

Ferroelectric Ceramic—Polymer Composites. The motivation for the development of composite ferroelectric materials arose from the need for a combination of desirable properties that often caimot be obtained in single-phase materials. For example, in an electromechanical transducer, the piezoelectric sensitivity might be maximized and the density minimized to obtain a good acoustic matching with water, and the transducer made mechanically flexible to conform to a curved surface (see COMPOSITE MATERIALS, CERAMiC-MATRix). 

CH2—CI2—) —(—CF2— CFH—) (39). Ceramic crystals have a higher piezoelectric efficiency. Their high acoustic impedance compared to body tissues necessitates impedance matching layers between the piezoelectric and the tissue. These layers are similar in function to the antireflective coatings on a lens. Polymer piezoelectric materials possess a more favorable impedance relative to body tissues but have poorer performance characteristics. Newer transducer materials are piezoelectric composites containing ceramic crystals embedded in a polymer matrix (see Composite materials, polymer-MATRIX Piezoelectrics). 

The Chemical Inkjet Printer (ChIP), an inkjet printer-like device which is equipped with a piezoelectric reagent-dispensing system, has been developed by Shimadzu Corporation. The ChIP can dispense picoliter volumes of matrix solution onto a tissue section, which has four printing heads and nozzles that have no contact with the tissue section surface. 

Non-labelled immunosensors rely on various principles (Fig. 3.27.A). Either the antibody or the antigen is immobilized on the solid matrix to form a sensing device. The solid matrix should be sensitive enough at the surface to detect immunocomplex formation. Electrode, membrane, piezoelectric and optically active surfaces may in principle be used to construct non-labelled immunosensors. The antigen or antibody to be determined is dissolved in a solution and reacted with the complementary matrix-bound antibody or antigen to form an immunocomplex that alters the physical e.g. the electrode potential or intrinsic piezofrequency) or optical properties of the... 

Finally, metallic fibers find some limited applications as reinforcement in composites. They are generally not desirable due to their inherently high densities and because they present difficulties in coupling to the matrix. Nonetheless, tungsten fibers are used in metal-matrix composites, as are steel fibers in cement composites. There is increasing interest in shape memory alloy filaments, such as Ti-Ni (Nitanol) for use in piezoelectric composites. We will discuss shape-memory alloys and nonstructural composites in later chapters of the text. 

A code has been written to enable the velocities of surface waves in multilayered anisotropic materials, at any orientation and propagation and including piezoelectric effects, to be calculated on a personal computer (Adler et al. 1990). The principle of the calculation is a matrix approach, somewhat along the lines of 10.2 but, because of the additional variables and boundary conditions, and because the wave velocities themselves are being found, it amounts to solving a first-order eight-dimensional vector-matrix equation. A... 

Example 15.4-3 Both the piezoelectric effect and the Pockels effect involve coupling between a vector and a symmetric 7(2). The structure of K is therefore similar in the two cases, the only difference being that the 6 x 3 matrix [rqi is the transpose of the 3x6 matrix [diq where i 1, 2, 3 denote the vector components and q= l,. .., 6 denote the components of the symmetric 7(2) in the usual (Voigt) notation. Determine the structure of the piezoelectric tensor for a crystal of C3v symmetry. 

T. Miliotis, S. Kjellstrom, J. Nilsson, T. Laurell, L. E. Edholm, and G. Marko-Varga, Capillary liquid chromatography interfaced to matrix-assisted laser desorption/ionization time-of-flight mass spectrometry using an on-line coupled piezoelectric flow-through microdispenser, J. Mass Spectrom., 35 (2000) 369-377. 

The piezoelectric coefficients are third rank tensors, hence the piezoelectric response is anisotropic. A two subscript matrix notation is also widely used. The number of non-zero coefficients is governed by crystal symmetry, as described by Nye [2], In most single crystals, the piezoelectric coefficients are defined in terms of the crystallographic axes in polycrystalline ceramics, by convention the poling axis is referred to as the 3 axis. 

The piezoelectric strain coefficients now take the form d and the relation between the applied stress, o- , and induced polarization, P,-, can be expressed in final matrix-like form as ... 

The currently most frequently applied method for LC-MALDI-MS is automated post-column fractionation and on-plate collection in discrete spots of the LC colunm effluent. After the solvent is evaporated, the matrix solution can be added, and MALDI-MS analysis of the various spots can be performed. The procedure requires a liquid-handling robot, capable of disposition of effluent fractions at discrete spots on the MALDI target. A number of ways were proposed for deposition in discrete spots on the MALDI target, e.g., blotting via direct contact between droplet and target [139-140], piezoelectric flow-through microdispensing [141], pulsed electrical-mediated droplet deposition [142], and a heated droplet interface [143], Commercial LC-MALDI-MS devices were recently reviewed [144],... 

Despite their high cost and the long process involved in their development, immunochemical techniques may soon have broad applicability in the environmental field. Antibody production is the key step of any immunochemical technique. Immunosensors yield the best results for pesticides determination104 in terms of both accuracy and reliability. The most reliable immunosensors are piezoelectric. They assure a good sensitivity and limit of detection.105 The main problem for piezoelectric immunosensors utilization for water analysis is their low sensitivity, which results in a decrease in the S/N ratio because of the impurities present in water (from matrix or other sources). 

C. S. I. Lai, G. J. Moody, and J. D. R. Thomas, Piezoelectric Quartz Crystal Detection of Ammonia Using Pyridoxine Hydrochloride Supported on a Polyethoxylate Matrix. Analyst, 111 (1986) 511. 

These matrix equations relating the various electrical and mechanical quantities in piezoelectric media form the basis for the derivation of the FEM. The electric field E and mechanical strain S are related to the electrical potential and mechanical displacement, respectively, as follows ... 

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