Frequency interference between two mesa-shaped quartz crystal microbalances

The multichannel quartz crystal microbalance (MQCM) is very attractive for biosensor applications. The principle of the MQCM design involves fabricating arrays of quartz microbalances on a single substrate, and it is important that the individual sensor performance is not influenced by the neighboring devices. Feasible ways to control the coupling of acoustical energy within a MQCM structure are to increase the difference in the resonance frequency between the electroded and unelectroded portions of the substrate; and a practical way to achieve this is to use mesa structures. In this paper, the frequency interference between two mesa-shaped quartz crystal microbalances is investigated using Mindlin's theory. The results show that even a very small mesa height (/spl sim/5% of the plate thickness) can greatly reduce the frequency interference and more effectively trap the acoustic energy. This allows for a broader design window and higher packing density for MQCM applications.     

Detection of polycyclic aromatic hydrocarbons using quartz crystal microbalances

A chemically coated piezoelectric sensor has been developed for the determination of PAHs in the liquid phase. An organic monolayer attached to the surface of a gold electrode of a quartz crystal microbalance (QCM) via a covalent thiol-gold link complete with an ionically bound recognition element has been produced. This study has employed the PAH derivative 9-anthracene carboxylic acid which, once bound to the alkane thiol, functions as the recognition element. Binding of anthracene via pi-pi interaction has been observed as a frequency shift in the QCM with a detectability of the target analyte of 2 ppb and a response range of 0-50 ppb. The relative response of the sensor altered for different PAHs despite pi-pi interaction being the sole communication between recognition element and analyte. It is envisaged that such a sensor could be employed in the identification of key marker compounds and, as such, give an indication of total PAH flux in the environment.     

Molecular-imprinted, polymer-coated quartz crystal microbalances for the detection of terpenes

A piezoelectric sensor coated with an artificial biomimetic recognition element has been developed for the determination of L-menthol in the liquid phase. A highly specific noncovalently imprinted polymer (MIP) was cast in situ on to the surface of a gold-coated quartz crystal microbalance (QCM) electrode as a thin permeable film. Selective rebinding of the target analyte was observed as a frequency shift quantified by piezoelectric microgravimetry with the QCM. The detectability of L-menthol was 200 ppb with a response range of 0-1.0 ppm. The response of the MIP-QCM to a range of monoterpenes was investigated with the sensor binding menthol in favor of analogous compounds. The sensor was able to distinguish between the D- and L-enantiomers of menthol owing to the enantioselectivity of the imprinted sites. To our knowledge, this is the first report describing enantiomeric resolution within an MIP utilizing a single monomer-functional moiety interaction. It is envisaged that this technique could be employed to determine the concentration of terpenes in the atmosphere.     

Performances and limits of a parallel oscillator for electrochemical quartz crystal microbalances

This paper describes a driving circuit for an electrochemical quartz crystal microbalance (EQCM) adapted to a wide range of applications. The oscillator is a Miller-type parallel oscillator using an operational transconductance amplifier (OTA). A theoretical study of the oscillating circuit led to the analytical expression of the microbalance frequency as well as to an overestimation of the error on the mass measurement. The reliability of the EQCM was then experimentally verified through electrochemical copper deposition and dissolution. The limit of operation of the EQCM was also investigated, both analytically and experimentally. This work shows that parallel oscillators using few electronic components allow a very reliable EQCM to be obtained for mass measurements on metallic films, even if they are highly damped.     

Effects of interface slip and viscoelasticity on the dynamic response of droplet quartz crystal microbalances

In the present paper we first present a derivation based on the time-dependent perturbation theory to develop the dynamical equations which can be applied to model the response of a droplet quartz crystal microbalance (QCM) in contact with a single viscoelastic media. Moreover, the no-slip boundary condition across the device-viscoelastic media interface has been relaxed in the present model by using the Ellis-Hayward slip length approach. The model is then used to illustrate the characteristic changes in the frequency and attenuation of the QCM with and without the boundary slippage due to the changes in viscoelasticity as the coated media varies from Newtonian liquid to solid. To complement the theory, experiments have been conducted with microliter droplets of aqueous glycerol solutions and silicone oils with a viscosity in the range of 50 approximately 10,000 cS. The results have confirmed the Newtonian characteristics of the glycerol solutions. In contrast, the acoustic properties of the silicones oils as reflected in the impedance analysis are different from the glycerol solutions. More importantly, it was found that for the silicone oils the frequency steadily increased for several hours and even exceeded the initial value of the unloaded crystal as reflected in the positive frequency shift. Collaborative effects of interfacial slippage and viscoelasticity have been introduced to qualitatively interpret the measured frequency up-shifts for the silicone oils. The present work shows the potential importance of the combined effects of viscoelasticity and interfacial slippage when using the droplet QCM to investigate the rheological behavior of more complex fluids.     

Analysis of a monolithic, two-dimensional array of quartz crystal microbalances loaded by mass layers with nonuniform thickness

We study free thickness-shear vibrations of a monolithic, two-dimensional, and periodic array of quartz crystal microbalances loaded by mass layers with gradually varying thickness. A theoretical analysis is performed using Mindlin's two-dimensional plate equation. It is shown that the problem is mathematically governed by Mathieu's equation with a spatially varying coefficient. A periodic solution for resonant frequencies and modes is obtained and used to examine the effects of the mass layers. Results show that the vibration may be trapped or untrapped under the mass layers. The trapped modes decay differently in the two in-plane directions of the plate. The mode shapes and the decay rate of the trapped modes are sensitive to the mass layer thickness.     

Quartz crystal microbalances for microscale thermogravimetric analysis

A new method for analyzing the chemical purity and consistency of microscale samples with a quartz crystal microbalance (QCM) sensor platform is described. The QCM is used to monitor submicrogram changes in the mass of a deposited thin film as a function of temperature, in a manner similar to that of a conventional thermogravimetric analyzer (TGA). Results correlated well with TGA measurements for a wide range of representative materials, including organic compounds, ionic detergents, oxidizing and inert powders, carbon nanotubes, and various mixtures of these samples. In each case, the sample mass was on the order of a few micrograms, compared to the need for several milligrams for conventional TGA analysis. This work illustrates the effectiveness of this approach for analysis of nanoparticles, thin films, and highly purified specimens on the microgram scale.     

Multichannel quartz crystal microbalance

Arrays of quartz crystal resonators are fabricated on a single quartz wafer as a multichannel quartz crystal microbalance (MQCM). Three types of four-channel array of 10-MHz resonators are prepared and tested. Mechanical oscillation of each channel is entrapped within the channel almost completely, so that the interference between the channels via the quartz crystal plate is almost negligible. A mass change on each channel is quantitatively evaluated on the basis of Sauerbrey's law. Thus, each channel of a MQCM device can be used as an independent QCM. Influence from a longitudinal wave generated from another channel is also negligible compared to the influence from the wave from the monitored channel itself. The simultaneous oscillation of channels is also possible. The potential applicability of MQCM to the two-dimensional mapping of mass changes is demonstrated.     

A parametric quartz crystal oscillator

Parametric oscillators have been well studied but currently are not used often. Nevertheless, they could be a low-phase noise solution, at least outside the frequency bandwidth of the resonant circuit. The theoretical aspect of parametric oscillations is briefly reviewed in this paper. Indeed, the basic theory of a simple resistance-inductor-capacitor (RLC) circuit working in parametric conditions easily can be extended toward a resonant loop that includes a quartz crystal resonator. Then, as an application, this study is transposed to a quartz crystal oscillator that has been modeled and tested as a first prototype. Simulation results are compared with those actually obtained.     

Controlled crystal dissolution applied to quartz

Quartz chemical lapping of AT and SC cuts was performed in NaOH·xH₂O medium and this controlled dissolution resulted in reasonable quality of surface texture. Activation energy was calculated from dissolution rates measured against temperature. The initial surface texture of the samples influenced roughness parameter evolution but not the final roughness value. The electrical response of piezoelectric devices made by chemical lapping has been compared against others obtained by the IBE process. The comparison has shown that the controlled dissolution process is at least as good as IBE for producing piezoelectric devices.     

Proximity effect in quartz crystal microbalance

When an object approaches a vibrating quartz crystal microbalance (QCM) the resonant frequency changes. This "proximity effect" was seen at the distance of 10 mm in air and became more pronounced as the distance decreased. This effect depends on the quality factor (Q-factor) value of a QCM, conductivity of the object, and electrical connection of the object to QCM electrodes. A special setup was constructed to test the impact of the proximity effect on a QCM. Damping fluid was placed on one side of QCM, to change the Q-factor. A conducting metal disk was brought close to the other side of the QCM exposed to air. By varying the distance between the QCM and an object (metal disk), a shift in frequency was observed. This proximity effect was largest (>200 Hz for 10 MHz QCM) when the Q-factor was low and a conducting metal disk (e.g., Cu) was electrically shorted to the proximal (nearest) QCM electrode. The finite element modeling showed that the proximity effect was likely due to interaction of the object with the fringing electromagnetic field of the QCM. A simple modified Butterworth Van-Dyke model was used to describe this effect. It must be recognized that this effect may lead to large experimental artifacts in a variety of analytical QCM applications where the Q-factor changes. Therefore, in order to avoid artifacts, QCM and similar mass acoustic devices should not operate in the low Q-factor (<1000) regime.     

An aptamer-based quartz crystal protein biosensor

We developed a quartz crystal biosensor designed to detect concentrations and ligand affinity parameters of free unlabeled proteins in real time. Using a model system with human IgE as the analyte and single-stranded DNA aptamers or an anti-IgE antibody as immobilized ligands, we could demonstrate that aptamers were equivalent to antibodies in terms of specificity and sensitivity. Both receptor types selectively detected 0.5 nmol/L of IgE. In addition, the aptamer receptors tolerated repeated affine layer regeneration after ligand binding and recycling of the biosensor with little loss of sensitivity. Because of the small size and nonprotein nature of the aptamers, they were immobilized in a dense, well-oriented manner, thus extending the linear detection range to 10-fold higher concentrations of IgE. In addition to demonstrating for the first time that an aptamer-based biosensor can specifically and quantitatively detect an analyte in various complex protein mixes, the aptamer-ligand proved to be relatively heat resistant and stable over several weeks. Since aptamers consist of nucleic acids, well-established chemistry can be applied to produce optimized affine layers on biosensors that may be developed to specifically detect proteins in solution for analysis of proteomes.     

Torsional vibrations of quartz crystal beams

An exact solution of a partial differential equation including elastic compliance constant s'₅₆, with respect to stress function ψ has been found for torsional modes of vibration of an arbitrary (singly, doubly, triply) rotated beam with a pair of parallel free edges. The solution is obtained by relaxing the condition that the edge planes are perpendicular to the main faces of the beam. That is, the edges are off perpendicular by the angle Θ=arctan(-s'₅₆ /8'₅₅). The exact solution can reduce the difference of the calculated and measured values for a thickness-to-width ratio which gives the first-order temperature coefficient α=0. Also, a comparatively large inclination of the edge cuts is required to reduce the unwanted complicated mode shapes to simple ones     

The viscosity of thin water films between two quartz glass plates

Summary An apparatus for the determination of the viscosity coefficient of water in the neighbourhood of a quartz glass surface is described. The law of Stefan-Reynolds is applied in a special modification. The relative viscosity coefficient of water between two quartz glass plates having a distance smaller than 100 ? lies beyond 10 for small shearing stresses. Increasing shearing stresses lead to smaller values of the relative viscosity coefficient of such water zone, so that a non-Newtonian behaviour of flowing water in very thin layers can be accepted.

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Résumé On décrit un appareil pour la détermination du coefficient de viscosité de l'eau au voisinage d'une surface de quartz transparent. On applique ici une variante de la loi de Stefan-Reynolds. Le coefficient de viscosité relatif de l'eau entre deux plaques de quartz transparent maintenues à seulement 100 ? l'une de l'autre est de plus de 10 pour les faibles contraintes de cisaillement. Des contraintes de cisaillement croissantes déterminent des valeurs plus faibles du coefficient de viscosité relative, et l'on peut donc admettre que l'eau, sous forme de ces couches très minces, se caractérise par un écoulement non newtonien.

     

Computer aided design of quartz crystal oscillators

The latest development of a simulation program designed for quartz crystal oscillator analysis is presented in this paper. The simulator being developed uses the full nonlinear Barkhausen criterion method. It consists of finding the frequency ω₀ and the amplitude u₀ which nullify both the real and imaginary parts of a characteristic complex polynomial P(u,jω) describing the oscillator behavior. Most of the nonlinearities come from the amplifying transistor described by using large signal admittance parameters y(u) obtained by means of an analog circuit simulator (SPICE). This paper presents the method used to derive and code the characteristic polynomial coefficients. This method has been successfully implemented for a Colpitts oscillator and is currently being used to build an oscillator library covering the most widely used structures. The validity and the predictive power of the model have been checked experimentally and the comparison between experimental results and simulation is presented and discussed     

Frequency temperature coefficients of AT-cut quartz lenses

Conclusions A method of producing small, including zero values of the f.t.c. for quartz lenses was found and thus the possibility of their application was extended from standard oscillators with an underground thermostatic control to normal thermostatically controlled standard oscillators.     

Isolated electrodeless high-frequency quartz crystal microbalance for immunosensors

This paper presents a contactless technique to measure shear bulk wave resonance frequencies of an isolated quartz crystal in a flow cell. The line antenna placed outside the cell generates and detects the resonance frequencies in a wireless-electrodeless manner. It is revealed that this mechanism relies on the quasistatic electric field. A 0.3-mm-thick AT-cut quartz was used, and its overtone resonance frequencies up to 80 MHz were measured in liquids. Exact vibrational analysis was carried out for a triple-layered resonator system consisting of the adsorbed material layer, the electrode film, and the quartz plate. It predicts higher frequency sensitivity to the adsorbed material at higher modes when the electrode layer is removed. The 13th overtone (72-MHz resonance frequency) was used to detect human immunoglobulin G with concentrations between 0.1 and 20 microg/mL captured by protein A immobilized on one side of the crystal. The real-time measurement of the frequency response yielded the equilibrium constant KA=5.21 x 10(7) M(-1).