Quartz crystal, resonant frequency

Keywords Quartz crystals Resonance frequencies Oscillators Network analysis... 

Table II contains room-temperature internal-friction values and Young s moduli, the latter both at the quartz-crystal resonant frequency (30 to 90 kHz) and at zero frequency. Linear...

Fig. 2 Quartz crystal microbalance frequency shifts for cycles of alternate myoglobin/ds-DNA and cytochrome P450cam/ds-DNA adsorption on gold resonators coated with mixed mono-layers of mercaptoproionic acid/mercaptopropanol as first layer and PDDA as second layer. DNA was from salmon testes (ST) and calf thymus (CT). Average values are shown for five replicates of [Mb/ST ds-DNA] (0) and four replicates of [cyt P450cam/ST ds-DNA] ( ) films. (From Ref. [15] with permission. Copyright American Chemical Society.)...

To mimic the PG electrode surface for QCM measurements of layers adsorbed on the gold-quartz resonators, we first chemisorb a mixed monolayer of mercaptopropionic acid/mercaptopropanol. This layer is represented by the first point in Fig. 2, labeled MPA. The second layer is PDDA. Quartz crystal microbalance frequency decreasing in a roughly linear fashion and at regular intervals for the multiple adsorption steps demonstrates repeatable adsorption for the two DNA/en-zyme films. Relative precision of layer formation on multiple resonators within 15% can be achieved. Film thicknesses and component weights in Table 1 were obtained by analyzing the QCM data with Eqs. 1 and 2. 

Figure 12.4 depicts a typical admittance parametric plot for the quartz crystal resonator. Note that the effect of the static capacitance C0 in the parallel branch is to shift the admittance circle upward by resonance frequency top which now depends on C0, in addition to the series resonance frequency to, = 2irfa. Changes in the resonance frequency are related to changes in the equivalent inductance L and broadening of the admittance curve near resonance (decrease in the circle diameter l/R in Fig. 12.4) are related to equivalent resistance R. 

Oyama and Tatsuma measured the resonant frequency and resonant resistance of quartz crystal resonators coated with several redox active polymers [58-60], DNA [61] and tungsten oxide [62]. 

The EQCM comprises a quartz crystal oscillator, in which one of the Au exciting electrodes is also exposed to the solution and acts as the working electrode in a conventional (here, three electrode) cell. Provided any surface film is rigidly coupled to the underlying electrode changes in inertial mass (Am) of the electrode result in crystal resonant frequency changes (A/) that are described by the Sauerbrey equation [11] ... 

The electrochemical quartz crystal microbalance is a versatile technique for studying several aspects of electroactive polymer film dynamics. For rigid films, it is a sensitive probe of mobile species (ion and solvent) population changes within the film in response to redox switching. For non-rigid films, it can be used to determine film shear moduli. In the former case, one simply follows changes in crystal resonant frequency. In the latter case, the frequency dependence of resonator admittance in the... 

As the readers may see, quartz crystal resonator (QCR) sensors are out of the content of this chapter because their fundamentals are far from spectrometric aspects. These acoustic devices, especially applied in direct contact to an aqueous liquid, are commonly known as quartz crystal microbalance (QCM) [104] and used to convert a mass ora mass accumulation on the surface of the quartz crystal or, almost equivalent, the thickness or a thickness increase of a foreign layer on the crystal surface, into a frequency shift — a decrease in the ultrasonic frequency — then converted into an electrical signal. This unspecific response can be made selective, even specific, in the case of QCM immunosensors [105]. Despite non-gravimetric contributions have been attributed to the QCR response, such as the effect of single-film viscoelasticity [106], these contributions are also showed by a shift of the fixed US frequency applied to the resonator so, the spectrum of the system under study is never obtained and the methods developed with the help of these devices cannot be considered spectrometric. Recent studies on acoustic properties of living cells on the sub-second timescale have involved both a QCM and an impedance analyser thus susceptance and conductance spectra are obtained by the latter [107]. 

Multilayer films were fabricated directly on one side of preliminary cleaned in a piranha solution quartz crystal resonators with gold working surface having the basic oscillation frequency of 5 MHz. The resonators were covered with a PEI/PSS layer if needed. The adsorption of PEI and PSS was carried out from 1 mg/mL polyelectrolyte solutions. Each adsorption step was followed by washing the resonator with the film in distilled water to remove an excess polyelectrolyte. 

Figure 2. Frequency shift upon HRP/PSS alternate adsorption from the aqueous solution on a (PEI/PSS>2-covered quartz crystal resonator.

Another resonant-frequency thermometer is the quartz crystal resonator (Benjaminson and Rowland, 1972), which, if the crystal is properly cut, is quite linear from about 190 to 525 K. Although this thermometer has excellent resolution, it does exhibit hysteresis and drift. The principle of quartz crystal thermometry is based on the temperature dependence of the piezoelectric resonant frequency of a quartz crystal wafer of a given dimension. The angle of cut of the quartz crystal is selected to give as nearly a linear and yet sensitive correspondence between resonant frequency and temperature as possible. This angle of cut is referred to as an LC (linear coefficient) cut. The temperature sensitivity of the quartz crystal thermometer is about 1000 Hz/°C. 

Abstract Oscillators are the standard interface circuits for quartz crystal resonator sensors. When applying these sensors in gases a large set of circuits is available, which can be adapted to particular applications. In liquid applications viscous damping accompanied by a significant loss in the Q factor of the resonator requires specific solutions. We summarize major design rules and discuss approved solutions. We especially address the series resonance frequency and motional resistance determination and parallel capacitance compensation. We furthermore introduce recent developments in network analysis and impulse excitation technique for more sophisticated applications. Impedance analysis especially allows a more complete characterization of the sensor and can nowadays be... 

There has been remarkable progress in the development and application of the quartz crystal microbalance (QCM) principle in sensitive devices for the detection and concentration measurement of specific molecules in gaseous and liquid media [1]. Since the behavior of quartz crystal resonator (QCR) sensors in gases is similar to quartz crystals technically used as frequency standards, a large set of circuit configurations is available, whose known properties can merely be adapted to particular applications [2-5]. In many cases quartz crystals used in electronic circuitry, sometimes even from mass production, are employed. 

In its original application as timing reference, special care has been taken to minimize the perturbations on frequency of the selected mode of vibration caused by unavoidable variations in the environment, first of all temperature and acceleration. The breakthrough of quartz crystal resonators in timekeeping is very much correlated to the existence of a specific crysfal cuf, at which the device resonance frequency provides a zero temperature coefficient of frequency at 25 °C and a remarkable temperature stability around room... 

Fig. 12 Characteristic resonance frequencies of quartz crystal resonators, shown in the locus of impedance, Z = R+jX (a), and admittance, Y = G+jB (b). is the parallel resonant frequency/p at Umax, O is the parallel resonant frequency/a at X = 0, O is the parallel resonant frequency/ at 2 max, i Ih series resonance frequency/s at Gmax, is the series resonant frequency/r at = 0, and is the series resonant frequency/m...

The classical sensing application of quartz crystal resonators is microgravimetry [1,5]. Many commercial instruments are around. These devices exploit the Sauerbrey relation (Eq. 28). For thin films, the resonance frequency is—by and large—inversely proportional to the total thickness of the plate. The latter increases when a film is deposited onto the crystal surface. Monolayer sensitivity is easily reached. Flowever, when the film thickness increases, viscoelastic effects come into play, as was for instance recognized by Lu and Lewis, who derived a refined version of the Sauerbrey equation [6]. These authors mainly intended to improve the microweighing procedure. Actually measuring viscoelastic properties with the QCM was not a major issue... 

A standard model has emerged for the calculation of the resonance frequencies of quartz crystal resonators coated with planar layers [37,42-45]. We first... 

The quartz crystal resonator is a useful device for the study of thin-layer and interfacial phenomena. The crystals commonly employed have a fundamental resonance frequency of 5 -10 MHz and a resolution of the order of 0.1 -0.5 Hz. This high resolution makes the device sensitive to a myriad of physical phenomena, some of which are interrelated and some quite independent of each other. It cannot be overemphasized that the quartz crystal resonator acts as a true microbalance (more appropriately a nanobalance) only if in the course of the process being studied, the nature of the interface (its roughness, sHp-page, the density and viscosity of the solution adjacent to it, and the structure of the solvent in contact with it) is maintained constant. 

For a quartz thermometer, the resonant frequency of a quartz crystal resonator is strongly related to the temperature variation. With high resolution, the temperature change can be directly determined from the frequency change of a quartz crystal thermometer. A quartz thermometer developed for use between -80 and 250°C [85] has a resolution of 0.1 mK. If used at the same temperature, a comparable precision can be achieved. However, with temperature cycling, hysteresis can reduce its repeatability. An accuracy of 0.05°C can be achieved with calibration. Nevertheless the temperature resolution for the quartz resonator is found to be less accurate at lower temperatures Over the temperature range from 4.2 to 400 K, the temperature resolution with the resonant frequency change for a YS cut quartz crystal thermometer drops from 1 kHz/K at 300 K to 80 Hz/K at 4.2 K [86]. 

Usually, the properties of a quartz crystal resonator with respect to frequency can be discerned from admittance plots, where the abscissa represents the real part of the admittance (conductance, G) and the ordinate the imaginary component (susceptance, B). Resonance occurs at two frequencies where the admittance locus crosses the real axis, fs and fp, which are the series and parallel resonance frequencies, respectively. If Rt is negligible, the series and parallel frequencies at which resonance occurs are given by eqn.(5) [2],... 

Figure 7 shows the results of solubilization experiments in a static system. Each line indicates the resonance frequency change over time under different conditions. There are two types of lines - solid lines and lines with symbols. Solid lines are the results attained in the liquid state of CO2 (10 MPa, 20 C), while lines with symbols are in the supercritical state (10 MPa, 45 C). Since the resonance frequency of a quartz crystal is directly affected by the properties of the ambient fluid, reference measurements using a bare quartz crystal resonator were performed before the experiment. Noisy signals were observed when CO2 was purged into the system. The results of the reference measurements indicate that about 70-80 seconds are required until the stabilization of the system. The data recorded during this stabilization period in ignored. 

Figure 9. Frequency change of a quartz crystal resonator in a dynamic process.

Kasemo s laboratory at Chalmers University of Technology and Goteborg University was the source of the QCM-D technique [10], now embodied in instrumentation offered by Q-Sense AB. They define the dissipation, A as the inverse of the quality factor Q of the quartz crystal resonator [47] (see equation (4)). In the Q-Sense instrumentation, the driving RF power to the oscillator, causing it to respond at resonant frequency f, is switched off and the exponentially damped sinusoidal wave decays with a time constant r, where D -. .More than 100... 

R. Lucklum, P. Hauptmaim and R.W. Cemosek, Thin Film Material Properties Analysis with Quartz Crystal Resonators, IEEE Intemational Frequency Control Symposium, (2001) 542-50. 

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