Resonant oscillation frequency

Figure 7.9. Change in resonant oscillation frequency of a piezoelectric transducer (a) with, and (b) without poly(A) immobilized to the surface. Step 1 is surface modification with copolymer, Step 2 is poly(A) immobilization, and Step 3 is hybridization to target poly(U).10 [Reprinted, with permission, from N. C. Fawcett, J. A. Evans, L.-C. Chien, and N. Flowers, Anal. Lett. 21, 1988, 1099-1114. Nucleic Acid Hybridization Detected by Piezoelectric Resonance . Copyright 1988 by Marcel Dekker, Inc.]...

Surface Acoustical Have Devices. As Illustrated in Fig. 2(middle), application of an AC potential bias between a pair of adjacent, closely spaced (by 1/4 of the acoustical wavelength) electrodes will produce (2,39) an undulatory surface oscillation, or surface wave, that is propagated toward a similar pair of detecting electrodes at a rate determined primarily by the properties of the quartz piezoelectric material (ca. 10 m/s) but also by any mass that contacts the quartz crystal in the region between the two sets of electrodes. Changes in the surface wave propagation rate, and in the amplitude of the surface oscillation, can be detected as a changes in the resonant oscillation frequency. 

If a drop carries a uniformly distributed surface charge Qg, the modified resonant oscillation frequency is given by ... 

The attachment of cells to CG hydrogel layered onto a surface of a quartz crystal sensor (QCM) reduces the resonant oscillation frequency by A/, = -75 Hz after the first cell injection (Figure 5.49, curve 1 at t<600 s). The second cell injection leads to the total A/i2 -105 Hz, i.e., IA(2lgain controller voltage (Figure 5.49, curve 2) that indicates cells interactions with the CG matrix. These frequency shifts can be interpreted in terms of mass addition at the sensor surface according to the equation... 

The linearized and Laplace-transformed equations of the models described above are used to evaluate the various system transfer functions as functions of the Laplace variables s = cr + jco, where a is the real part and co is the imaginary part of the complex variable s. a refers to the damping constant (or damped exponential frequency) and co refers to the resonant oscillation frequency of the system. 

Figure Bl.5.3 Magnitude of the second-order nonlinear susceptibility x versus frequency co, obtained from the anliannonic oscillator model, in the vicinity of the single- and two-photon resonances at frequencies cOq and coq 2> respectively.

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

These piezoelectric crystal oscillators are very accurate mass sensors because their resonant frequencies can be measured precisely with relatively simple electronic circuitry. For certain quartz crystals, the resonant frequency is inversely related to the crystal thickness. A crystal resonating at 5 megahertz is typically 300 micrometers thick. If material is coated or adsorbed on the crystal surface, the resonant frequency will change (decrease) in proportion to the amount of material added. The effect of adsorbed mass on the oscillator frequency varies according to the operational mode of the device. In any case, interpretation of mass via changes in frequency or amplitude assumes that the coated films are rigidly elastic and infinitesimally thin (that is, an extension of the crystal). 

CRYSTAL OSCILLATOR. This device is a precise mechanical resonator and frequency generator. The need for a stable, accurate, and... 

Let us first consider the case of Y/D 1. This means that at certain values of the compound nucleus excitation energy, individual levels of the compound nucleus can be excited (i.e., when the excitation energy exactly equals the energy of a given CN level). When this happens, there will be a sharp rise, or resonance, in the reaction cross section akin to the absorption of infrared radiation by sodium chloride when the radiation frequency equals the natural crystal oscillation frequency. In this case, the formula for the cross section (the Breit-Wigner single-lev el formula) for the reaction a + A —> C b + B is... 

Sensors using quartz crystal are very sensitive and can detect samples of the order of pg. Usually, an organic thin film is pasted on quartz surface since the crystal surface hardly absorbs any chemical species. The organic thin film provides the potential to detect various kinds of volatilities with high selectivity and sensitivity. The principle of the gas sensor is based on Eq. (1) [32]. The quartz oscillator has a specific resonance frequency with an oscillating circuit. Its frequency is decreased by the absorption of volatilities on the quartz surface due to the increase in mass. The frequency shift caused by exposure to a volatile depends on the amount adsorbed. With a 9 MHz quartz oscillator, the frequency is decreased by 400 Hz upon adsorption of 1 pg of a compound. A resonance oscillator with a higher resonance frequency can detect smaller amounts. 

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