Plate Mode Oscillators

Surface acoustic-wave (SAW) elements Plate-mode oscillators Interface impedance elements Fiber optic elements sensitive to elastic constants... 

Figure 49, Lamb waves propagating in a thin plate-mode oscillator (PMO) [226], [231] (with permission from Plenum Publishing. New York)...

Plate-Mode Oscillators (PMOs). Lamb Wave Oscillators. In all the SAW devices discussed above, the acoustic wave propagates in a slab of material whose thickness is infinitely larger than the wavelength A of the propagating wave. When the thickness of the plate is reduced to such an extent that it becomes comparable to A, the entire plate becomes involved in the periodic motion, producing a symmetric and antisymmetric Lamb wave (LW) (Fig. 49). This behavior is observed in plate-mode oscillators with thicknesses of a few micrometers. A cross-sectional view through a typical PMO is shown in Figure 50. 

This happens in Acoustic plate-mode (Apm) oscillators, which have a thickness of only a few microns. The eigenfrequency of the Apm oscillators is given by the interdigitated electrode spacing p and by the plate thickness t. 

Fig. 4.21 Bulk Lamb waves in Acoustic plate-mode (Apm) and Flextural Plate Wave (FPW) oscillators...

A number of interactions can affect plate-mode propagation characteristics, particularly in a liquid environment. In the following sections, models of several of the important modes of interaction will be outlined and compared to experimental results. These include (1) mass accumulation on the device surface, (2) viscous entrainment of the contacting liquid medium by the oscillating device surface, and (3) acoustoelectric coupling between evanescent plate mode electric fields and the liquid. 

In modeling the interaction of a liquid with plate modes, the high frequency of operation necessitates the consideration of viscoelastic response by the liquid. For the simple liquids examined, good agreement was obtained by modeling the liquid as a Maxwellian fluid with a single relaxation time r. When the Maxwellian fluid is driven in oscillatory flow with cot < 1, it responds as a Newtonian fluid characterized by the shear viscosity, rj. For wt > 1, the oscillation rate approaches the rate of molecular motion in the liquid and energy ceases to be dissipated in... 

Most immunochemically based sensors to date have been developed for liquid-phase measurements thus, the TSM resonator has been the device of choice. Of course, other plate-mode devices (SH-APM, FPW) would be equally well suited for liquid-phase detection and may have advantages in terms of sensitivity. A low-frequency (20 MHz) SAW liquid-phase immunoassay device has been reported [27], but operation of SAWs of higher frequencies in liquids is not feasible due to excessive attenuation of the SAW by the liquid. An alternative to in-situ detection is to expose a protein-coated AW device to a liquid-phase sample for a period of time, then dry it [226] the observed frequency shift is proportional to analyte concentration. When using this technique, it is crucial that careful control experiments in the absence of analyte be performed to obtain an accurate idea of the reproducibility of the baseline oscillation frequency throughout the procedure. 

Continuity of particle displacement across the solld/llquld interface requires that the surface displacement of the APM generate motion in the liquid. Solution of the Navler-Stokes equation in the liquid, subject to this non-slip boundary condition at the solid/li-quld interface, indicates that the liquid undergoes a shear motion which decays rapidly with distance from the surface (11). For an angular frequency of oscillation the velocity field decay length S of the liquid entrained by the plate mode is approximated by ... 

Figure 4. Perturbations in a) plate mode velocity and b) attenuation due to liquid entrainment by the APM device surface. Data are for glycerol/water mixtures which only contact the surface between transducers. The solid lines are calculated from a viscoelastic model for the liquid the dashed lines are calculated using a Newtonian model, c) Perturbation in oscillator frequency due to acoustoelectric interactions between APM and ions and dipoles in solution. Solid lines are calculated using best-fit values for the dielectric coefficient of each solvent.

A series of viscoelastic fluids based on SE-30 (General Electric, polydimethyl siloxane gum, = 450,000) were used in the evaluation of the Differential Rheometer (DR) for viscoelastic fluids. The samples were prepared with a serial dilution technique starting with a 8.874% mixture of low molecular weight PDMS (Scientific Polymer Products, Inc., = 103,400) in SE-30. Portions of this mixture were serially diluted with pure SE-30 to obtain four different viscoelastic fluids. The samples were characterized on a Rheometrics Mechanical Spectrometer (RMS) in the oscillating parallel plate mode. The measurements were taken at 22 C using 25-mm fixtures and a strain amplitude of less than 5 percent. 

R, M. White, P. W, Wicher, S. W. Wenzel. E. T. Zellers "Plate-Mode Ultrasonic Oscillator Sensors," IEEE Trans. Ultrason. Dev. Ferroelectr. Fretj. Contr. UFFC-34(I987) 162-171. 

Compression. The sample in this geometry is sandwiched between horizontal parallel plates, and the upper plate is oscillated so as to apply a small-amplitude strain. This mode of deformation is also useful with soft samples. 

The mechanical properties of frozen materials can be difficult to study due to the enormous stiffness and moduli involved and the fact that changes can occur rapidly over small temperature ranges. The Ares rheometer (Rheometrics Corporation/TA Instrument, Delaware, USA) has a wide range of modulus measuring capability and has been used in the oscillating plate mode in studies of sugars at comparatively low moisture contents (15% —10°C) with and without hydrocolloids [141]. 

It is suggested that the mode of subduction of the Pacific Plate since the middle Miocene age related to Jackson s episode, hence oscillation of direction of lateral movement of Pacific plate. Synchronized igneous and hydrothermal activities and Jackson s episode indicate that the formations and characteristics of hydrothermal ore deposits (Kuroko and epithermal vein-type deposits) are largely influenced by plate tectonics (mode of subduction, direction of plate movement, etc.). For example, sulfur isotopic composition of sulfides is not controlled by /o and pH, but by of... 

AT-cut, 9 MHz quartz-crystal oscillators were purchased from Kyushu Dentsu, Co., Tokyo, in which Ag electrodes (0.238 cm2) had been deposited on each side of a quartz-plate (0.640 cm2). A homemade oscillator circuit was designed to drive the quartz at its resonant frequency both in air and water phases. The quartz crystal plates were usually treated with 1,1,1,3,3,3-hexamethyldisilazane to obtain a hydrophobic surface unless otherwise stated [28]. Frequencies of the QCM was followed continuously by a universal frequency counter (Iwatsu, Co., Tokyo, SC 7201 model) attached to a microcomputer system (NEC, PC 8801 model). The following equation has been obtained for the AT-cut shear mode QCM [10] ... 

Dynamic melt viscosity studies on the star blocks and a similar triblock were carried out using a Rheometric Mechanical Spectrometer (RMS) (Rheometrics 800). Circular molded samples with -1.5 mm thickness and 2 cm diameter were subjected to forced sinusoidal oscillations (2% strain) between two parallel plates. The experiment was set in the frequency sweep mode. Data were collected at 180 and 210 °C. 

More recently methods have also been developed to measure the adsorbed amount on single surfaces and not onto powders. Adsorption to isolated surfaces can, for instance, be measured with a quartz crystal microbalance (QCM) [383]. The quartz crystal microbalance consists of a thin quartz crystal that is plated with electrodes on the top and bottom (Fig. 9.11). Since quartz is a piezoelectric material, the crystal can be deformed by an external voltage. By applying an AC voltage across the electrodes, the crystal can be excited to oscillate in a transverse shear mode at its resonance frequency. This resonance frequency is highly sensitive to the total oscillating mass. For an adsorption measurement, the surface is mounted on such a quartz crystal microbalance. Upon adsorption, the mass increases, which lowers the resonance frequency. This reduction of the resonance frequency is measured and the mass increase is calculated [384-387],... 

The crystal cut determines the mode of oscillations. Shear vibrations are generated if one large crystal face moves parallel with respect to the underlying planes as in QCMs with AT-cut a-quartz crystals. This crystal wafer is prepared by cutting the quartz at approximately 35.17° from its Z-axis. A typical crystal plate is a cylindrical disk of a diameter 10 mm and thickness about 0.7 to 0.1 mm for resonant operation in the 2 to 15 MHz frequency range. This type of crystals shows weak dependence of the resonant frequency on the temperature and stress for room temperature operation. 

---