Probing colloid-substratum contact stiffness by acoustic sensing in a liquid phase

In a quartz crystal microbalance, particles adhering to a sensor crystal are perturbed around their equilibrium positions via thickness-shear vibrations at the crystal's fundamental frequency and overtones. The amount of adsorbed molecular mass is measured as a shift in resonance frequency. In inertial loading, frequency shifts are negative and proportional to the adsorbed mass, in contrast with "elastic loading", where particles adhere via small contact points. Elastic loading in air yields positive frequency shifts according to a coupled resonance model. We explore here the novel application of a coupled resonance model for colloidal particle adhesion in a liquid phase theoretically and demonstrate its applicability experimentally. Particles with different radii and in the absence and presence of ligand-receptor binding showed evidence of coupled resonance. By plotting the frequency shifts versus the quartz crystal microbalance with dissipation overtone number, frequencies of zero-crossing could be inferred, indicative of adhesive bond stiffness. As a novelty of the model, it points to a circular relation between bandwidth versus frequency shift, with radii indicative of bond stiffness. The model indicates that bond stiffness for bare silica particles adhering on a crystal surface is determined by attractive Lifshitz-van der Waals and ionic-strength-dependent, repulsive electrostatic forces. In the presence of ligand-receptor interactions, softer interfaces develop that yield stiffer bonds due to increased contact areas. In analogy with molecular vibrations, the radii of adhering particles strongly affect the resonance frequencies, while bond stiffness depends on environmental parameters to a larger degree than for molecular adsorption.     

Influence of diquat on growth and death of HepG2 cells using quartz crystal and micro CCD camera

Diquat is widely used agent which produces toxicity in human and implicated as an environmental toxicity. HepG2 cell was cultured onto an indium tin oxide (ITO) surface of quartz crystal modified a collagen film. In this paper, we investigated the physical properties and the morphological change of the HepG2 cells cultured onto the ITO electrode of the quartz crystal sensor with micro CCD camera. The resonance responses of the quartz crystal and the morphological change were directly monitored. After seeding the cells and diquat injection into the chamber, the resonance frequency and the resonance resistance were obtained with real time morphologies. From the resonance characteristics and the series of morphologies, we could know the diquat to be death and weakening of the cells.     

Analytical and finite element method design of quartz tuning fork resonators and experimental test of samples manufactured using photolithography 1—significant design parameters affecting static capacitance C0

Resonance frequency of quartz tuning fork crystal for use in chips of code division multiple access, personal communication system, and a global system for mobile communication was analyzed by an analytical method, Sezawa’s theory and the finite element method (FEM). From the FEM analysis results, actual tuning fork crystals were fabricated using photolithography and oblique evaporation by a stencil mask. A resonance frequency close to 31.964 kHz was aimed at following FEM analysis results and a general scheme of commercially available 32.768 kHz tuning fork resonators was followed in designing tuning fork geometry, tine electrode pattern and thickness. Comparison was made among the modeled and experimentally measured resonance frequencies and the discrepancy explained and discussed. The average resonance frequency of the fabricated tuning fork samples at a vacuum level of 3×10⁻² Torr was 31.228-31.462 kHz. The difference between modeling and experimentally measured resonance frequency is attributed to the error in exactly manufacturing tuning fork tine width by photolithography. The dependence of sensitivities for other quartz tuning fork crystal parameter C₀ on various design parameters was also comprehensively analyzed using FEM and Taguchi’s design of experiment method. However, the tuning fork design using FEM modeling must be modified comprehensively to optimize various design parameters affecting both the resonance frequency and other crystal parameters, most importantly crystal impedance.     

Investigations on LGS and LGT crystals to realize BAW resonators

The LGS family are promising materials for the design of high quality bulk acoustic wave resonators. We have manufactured many plano-convex 10 MHz 5th overtone Y-cut resonators using langasite (LGS, La₃Ga₅SiO₁₄) and langatate (LGT, La₃Ga_5.5Ta_0.5O₁₄) crystals. We observed that the quality factor strongly depends on the polishing method, the supplier of the material, and on the energy trapping. For quartz crystals, we have found that resulting IR spectra exhibit absorption peaks more or less deep, linked to defects. These predominant criteria are not surprising, but they have to be defined in manner similar to that used for quartz crystal. A satisfying machining and polishing method has been first applied to elaborate high Q resonators, and a comparison between samples of LGS and LGT materials from different suppliers is established. In addition, LGT resonators are characterized by their motional parameters and frequency-temperature curves. Nevertheless, one of the main results is that the measured Q × f product is not the expected one. We present results of Q-factor versus radius of curvature: it appears that an optimization should be performed and that this last one cannot be directly transposed from that of quartz crystal resonator. Currently, the best resonator that we have made has a Q × f product of 1.4 × 10¹³ on its 5th overtone (1.7 × 10¹³ on its 9th overtone). This result is slightly higher than the similar parameter obtained on a state-of-the-art SC-cut quartz crystal resonator working at the same frequency.     

Modeling of a short-term stability measuring system of quartz crystal resonators

A new numerical model of a short-term stability measuring system of quartz crystal resonators is presented. It is based on the phase bridge method using a pair of resonators driven by a low-noise source. The output signal, obtained with a phase detector, is proportional to the phase difference introduced by the resonators. The numerical transfer function of each bridge path is given by the model. The output spectral density of the phase fluctuations is computed from these transfer functions and the numerical approximation of the low-noise source. The model was applied to third overtone, SC-cut, 10 MHz BVA quartz crystal resonators. It enables the rejection of the source noise versus the resonant frequency of quartz crystal resonators to be quantified.     

Self-temperature-testing of the quartz resonant force sensor

Temperature characteristics of a quartz resonant force sensor are important features, which should be seriously considered in the sensor's practical application. This paper analyzes the temperature characteristics of a quartz resonant force sensor and presents a self-temperature-testing method for the sensor by analyzing the different temperature characteristics when the quartz resonator vibrates in its fundamental mode and in its third overtone mode. A beat frequency results from the resonator's fundamental and third overtone frequencies. Experimental result show that the sensor's operating temperature can be measured by making use of this beat frequency rather than applying a temperature sensor     

Electrochemical quartz crystal nanobalance to detect solvent displacement by pH-induced conformational changes of proteins at Pt

The electrochemical quartz crystal nanobalance (EQCN) techniques of simultaneous measurements of frequency and cyclic voltammetry (CV) were used to investigate protein adsorption behavior resulting from pH-induced conformational changes at the Pt electrode at 298 K. The adsorption behavior of holo- and apo-alpha-lactalbumin was studied in electrolyte solutions of pH < 2, 7.4, and 11. The EQCN frequency measurements did not directly monitor the mass of the adsorbed protein at anodic potentials, but instead, at a potential characteristic of the double layer for platinum, gave a measure of the extent of solvent displacement by the adsorbed protein (i.e., a "footprint"), which correlated well with known pH-induced conformational changes of the protein. Simultaneous CV charge transfer measurements provided information on the number of layers of protein adsorbed to the surface. This ability of the EQCN to detect solvent displacement by protein adsorption is potentially useful for biosensors to detect and to monitor protein conformational changes in the bulk and during the adsorption process. The Langmuir adsorption isotherm provided the Gibbs energy of adsorption, DeltaG(ADS), and showed excellent agreement between the CV and EQCN frequency measurements.     

Analytical and finite element method design of quartz tuning fork resonators and experimental test of samples manufactured using photolithography 2: comprehensive analysis of resonance frequencies using Sezawa's approximations

Resonance frequency of a quartz tuning fork crystal for use in chips of code division multiple access, personal communication system, and a global system for mobile communication was comprehensively analyzed by an analytical method, Sezawa's approximations and the finite element method. A comparison was also made in a more detailed and comprehensive manner among resonance frequencies calculated by the Sezawa's approximations. From the finite element method analysis results, actual tuning fork crystals were fabricated using mass-production capable positive (subtractive) photolithography, selective etching and subsequent positive (subtractive) photoresist spray coating method. A target resonance frequency of was aimed at and a general scheme of commercially available 32.768 kHz tuning fork resonators was also followed in designing tuning fork geometry, tine electrode pattern and thickness. Comprehensive comparison was made among the modeled and experimentally measured resonance frequencies and the discrepancy explained and discussed. Finite element method analysis results quite closely agreed with the experimentally measured resonance frequencies (32.676-32.933 kHz) of the fabricated tuning fork samples measured at a vacuum level of 10⁻⁵ Torr. The difference between modeling and experimentally measured resonance frequency is attributed to the error in exactly manufacturing tuning fork tine width by photolithography. However, the tuning fork design using finite element method modeling must be modified comprehensively to optimize various design parameters affecting both the resonance frequency and other crystal parameters, most importantly crystal impedance (series resistance).     

QCM露点传感器水粘性影响的抑制方法研究

为了解决基于主控温式的石英晶体微天平（Quartz Crystal Microbalance, QCM）露点测量系统中冷凝水粘弹特性影响露点识别准确性的问题,对QCM电极进行疏水处理,改善凝结特性,减小水粘性引起的频率耗散,实现液态水质量变化引起的谐振频率偏移测量。在QCM电极上制备静态水接触角为133° ± 2°的疏水层并对其进行表征,将疏水电极与未经处理的电极用于露点识别实验,并与精密露点仪获得的标准露点进行比对。实验证明,通过疏水处理电极凝结面的方法能够有效提升QCM露点传感器的露点识别精度,为主控温式露点传感器结构的优化设计提供理论和实验依据。     

Effects of a liquid layer on thickness-shear vibrations of rectangular AT-cut quartz plates

Thickness-shear vibrations of rectangular AT-cut quartz with one face in contact with a layer of Newtonian (linearly viscous and compressible) fluid are studied. The two-dimensional (2D) governing equations for vibrations of piezoelectric crystal plates given previously are used in the present study. The solutions for 1D shear wave and compressional wave in a liquid layer are obtained, and the stresses at the bottom of the liquid layer are used as approximations to the stresses exerted on the crystal surface in the plate equations. Closed form solutions are obtained for both free and piezoelectrically forced thickness-shear vibrations of a finite, rectangular AT-cut quartz plate in contact with a liquid layer of finite thickness. From the present solutions, a simple and explicit formula is deduced for the resonance frequency of the fundamental thickness-shear mode, which includes the effects of both shear and compressional waves in the liquid layer and the effect of the thickness-to-length ratio of the crystal plate. The formula reduces to the widely used frequency equation obtained by many previous investigators for infinite plates. The resonance frequency of a rectangular AT-cut quartz, computed as a function of the thickness of the adjacent liquid layer, agrees closely with the experimental data measured by Schneider and Martin (Anal. Chem., vol. 67, pp. 3324-3335, 1995)     

QCM Operation in Liquids: An Explanation of Measured Variations in Frequency and Q Factor with Liquid Conductivity

Recently, several reports have shown that when one side of a quartz crystal microbalance (QCM) is exposed to a liquid, the parallel (but not the series) resonant frequency is influenced by the conductivity and dielectric constant of the liquid. The effect is still controversial and constitutes a serious complication in many applications of the QCM in liquid environments. One suggestion has been that acoustically induced surface charges couple to charged species in the conducting liquid. To explore this effect, we have measured the parallel and the series mode resonance frequencies, and the corresponding Q factors, for a QCM with one side facing a liquid. These four quantities have all been measured versus liquid conductivity, using a recently developed experimental setup. It allows the simultaneous measurement of the resonant frequency and the Q factor of an oscillating quartz crystal, intermittently disconnected from the driving circuit. Based on these results, a simple model together with an equivalent circuit for a quartz crystal exposed to a liquid is presented. The analysis shows that it is not necessary to infer the existence of surface charges (or other microscopic phenomena such as electrical double layers) to account for the influence of the liquid's electrical properties on the resonant frequency. Our results show that the contacting conductive liquid, in effect, enlarges the electrode area on the liquid side and thereby changes the parallel resonant frequency. By proper design of the QCM measurement, perturbing effects due to the liquid's electrical properties can be circumvented.     

Numerical algorithms and results for SC-cut quartz plates vibrating at the third harmonic overtone of thickness shear

Finite element matrix equations, derived from two-dimensional piezoelectric high frequency plate theory are solved to study the vibrational behavior of the third overtone of thickness shear in square and circular SC-cut quartz resonators. The mass-loading and electric effects of electrodes are included. A perturbation method which reduces the memory requirements and computational time significantly is employed to calculate the piezoelectric resonant frequencies. A new storage scheme is introduced which reduces memory requirements for mass matrix by about 90% over that of the envelope storage scheme. Substructure techniques are used in eigenvalue calculation to save storage. Resonant frequency and the mode shapes of the harmonic third overtone thickness shear vibrations for square and circular plates are calculated. A predominant third overtone thickness shear displacement, coupled with the third overtone of thickness stretch and thickness twist, is observed. Weak coupling between the third order thickness shear displacement and the zeroth-, first-, and second-order displacements is noted. The magnitudes of the lower order displacements are found to be about two orders smaller than that of the third overtone thickness shear displacement.     

Temperature dependence of piezoelectric properties for textured SBN ceramics

Temperature dependences of piezoelectric properties were studied for h001i textured ceramics of bismuth layer-structured ferroelectrics, SrBi(2)Nb(2)O(9) (SBN). The textured ceramics with varied orientation degrees were fabricated by templated, grain-growth method, and the temperature dependences of resonance frequency were estimated. Excellent temperature stability of resonance frequency was obtained for the 76% textured ceramics. The resonance frequency of the 76% textured specimens varied almost linearly over a wide temperature range. Therefore, the variation was slight, even in a high temperature region above 150 degrees C. Temperature stability of a quartz crystal oscillator is generally higher than that of a ceramic resonator around room temperature. The variation of resonance frequency for the 76% textured SrBi(2)Nb(2)O(9) was larger than that of oscillation frequency for a typical quartz oscillator below 150 degrees C also in this study. However, the variation of the textured SrBi(2)Nb(2)O(9) was smaller than that of the quartz oscillator over a wide temperature range from -50 to 250 degrees C. Therefore, textured SrBi(2)Nb(2)O(9) ceramics is a major candidate material for the resonators used within a wide temperature range.     

Design analysis of miniature quartz resonator using two-dimensional finite element model

This study focused on 2-D miniature quartz plates. By assigning appropriate boundary condition using finite element modeling (FEM), the vibration of a quartz plate was analyzed for converse piezoelectric effect. The quality and stability of the resonance of a quartz plate was determined by examining changes on the response curve of resonant frequency when the length of plate was decreased or increased. A graphical user interface (GUI) was adopted to assist the finite element software to calculate the frequency responses with different length of a large number of quartz plates, and to conclude a detailed curve of resonant frequency versus size. With this diagram, changes of the resonant mode for quartz plates caused by length variation can be easily observed. An optimum size of the quartz plate is obtained from the curve. Moreover, analyses were also conducted on the electrode coverage of a quartz plate and the mass-loading effect of metallic electrodes for this study, to discuss the influence on the resonant frequencies of quartz plates.     

An in-depth analysis of electric cell-substrate impedance sensing to study the attachment and spreading of mammalian cells

The attachment and spreading of fibroblast cells on a gold surface coated with fibronectin or ovalbumin were studied by a modified electric cell-substrate impedance sensor. In this system, cells were cultured in a well, equipped with a detecting gold electrode (surface area of 0.057 mm2) and a gold counter electrode (18 mm2). Based on a comprehensive theoretical framework, the impedance of the electrode-electrolyte interface and a cell layer was precisely obtained for frequencies ranging from 1 to 10 kHz. Surface concentrations of the protein adsorbed on the gold surface were determined by a surface plasmon resonance biosensor. The resistance change of the electrode-electrolyte interface at 4 kHz increased linearly with the number of fibroblast cells attached on the detecting electrode. The slope of the linear relationship appeared to depend on the type of coating protein. As the surface area occupied by the cells was also proportional to the cell number, the resistance change was in turn proportional to the area covered by the cells.     

Analysis of the Internal Noise of Quartz-Crystal Oscillators

This paper describes the influence of the parallel capacitance of a quartz-crystal resonator on the amplitude-frequency coupling and particularly on the internal noise spectra of the oscillator working at the series resonance. A theoretical analysis which is a first order perturbation method is used. It is shown that the parallel capacitance of the quartz-crystal resonator increases the amplitude-frequency coupling and drastically modifies both amplitude and phase spectra of the internal noise. The 1/f2 phase spectrum of the internal thermal noise is transformed into a white phase spectrum for noise component frequencies greater than f0 + f? or less than f0 - f?, where f0 is the resonator series resonant frequency and f?, the difference between antiresonant and resonant frequencies of the quartz crystal. A "noise quieting" phenomenon appears when the noise component frequencies are in the vicinity of the antiresonant frequency fp. A good agreement between theoretical and experimental results for different values of the parallel-capacitance proves the validity of the mathematical model.     

Direct monitoring of paraquat induced cell death using quartz crystal sensor

Paraquat, a nonselective herbicide and pesticide, has been implicated as an environmental toxicity which caused cell death. In order to investigate the influence of paraquat, we used a quartz crystal sensor with a micro CCD camera that measured morphology and resonance characteristics simultaneously. Human hepatoma cell line (HepG2) was cultured onto an indium tin oxide (ITO) surface of quartz crystal modified on a collagen film. After the growth of the cells, paraquat was injected to the chamber and the resonance responses of the quartz crystal were directly monitored with morphology. We analyzed changes of the cells by the resonance frequency (F) and the resonance resistance (R) responses (F–R diagram). With this analysis, we also observed the morphologies during cell culturing. From the data, we could know that paraquat caused the weakening and death of the cells. Namely, paraquat plays an important role in the free radicals production that led to apoptosis and cell death.     

Voltage-controlled double-resonance quartz oscillator using variable-capacitance diode

In this work, we present a variable-frequency quartz crystal oscillator that is able to oscillate at LC resonance under frequency locking of a quartz crystal resonance, with the frequency tuning realized by variable-capacitance diodes. This circuit shows a steep transition between LC oscillation modes to quartz crystal double-resonance, which shows a characteristic change in the oscillation frequency. Control voltage of this diode is precisely adjusted from the low side to higher values and conversely in the vicinity of the oscillation mode transition. The transition of the oscillation modes is experimentally demonstrated and compared with an algebraic analysis.     

A novel microcomputer temperature-compensating method for an overtone crystal oscillator

In this paper, a novel microcomputer temperature-compensating method for an overtone crystal oscillator (MCOXO) is presented. In this method, a ceramic oscillator is chosen, and its output frequency is mixed with the output frequency of an overtone crystal oscillator. A crystal filter is used to suppress the spurious mixing products. A microcomputer is used to control the switch capacitance array that is connected to the ceramic oscillator circuit. The frequency deviation of the crystal oscillator is directly compensated by the output frequency of the ceramic oscillator. As a result, the method is able to overcome the disadvantages of frequency stability degradation and phase noise deterioration that are provoked by adding inductance or frequency multiplication in traditional compensating approaches. At the same time, this method is able to compensate a quite wide frequency range and many types of oscillators, not just crystal oscillators. The experimental compensating results show that, using this method, the frequency-temperature stability of a 100 MHz 5th overtone temperature-compensated crystal oscillator can achieve /spl les/ /spl plusmn/2/spl times/10/sup -6/ for 0-70/spl deg/C.     

High-frequency overtone TCXO based on mixing of dual crystal oscillators

To implement a high-stability and high-frequency overtone temperature-compensated crystal oscillator (TCXO) conveniently, an improved design of the novel overtone TCXO is described in this paper. A 120-MHz TCXO based on mixing of dual crystal oscillators is implemented. It utilizes a 100-MHz AT-cut 5th-overtone crystal oscillator mixed with a 20-MHz AT-cut voltage-controlled crystal oscillator (VCXO). The 120-MHz mixed product is filtered to produce the output signal. The total frequency deviation of 20-MHz and 100-MHz crystal oscillators is compensated by adjusting the output frequency of the 20-MHz oscillator to produce the stable 120-MHz output frequency. In this work, verifying experimental results of the compensation are presented. The stability of the experimental 120-MHz overtone TCXO with microprocessor temperature compensation achieves +/-2 X 10(-7) over the temperature range from -30 degrees C to +70 degrees C. A phase noise level of -133 dBc/Hz at 1 kHz offset has been initially measured for the prototype TCXO. The experimental result demonstrates this approach can conveniently implement the high-frequency overtone temperature compensation with a relatively high stability, and it is available for a wider frequency range as well.