Comparison of lumped-element and transmission-line models for thickness-shear-mode quartz resonator sensors

A study of the contact mechanics of a probe tip interacting with a quartz crystal microbalance ͑QCM͒ has been performed, involving simultaneous measurements of normal load, displacement, and contact stiffness with changes in QCM resonant frequency. For metal-metal and glass-metal contacts in air, the QCM frequency shifts were observed to be positive, and directly proportional to the contact area as inferred from the contact stiffness. Interfacial characteristics of the probe-tip contact ͑elasticity, contact size, and an estimate of the number of contacting asperities͒ were deduced by extending a prior model of single asperity contact to the case of multiple contacts. The extended model clarifies a number of seemingly disparate experimental results that have been reported in the literature.

Section: Modelingmentioning

confidence: 99%

Measuring nanomechanical properties of a dynamic contact using an indenter probe and quartz crystal microbalance

Borovsky

Krim

Asif

et al. 2001

“…In liquid phase operation the quartz crystal also has a dissipation. The quartz crystal can also be used in electrochemical applications 7 , biochemical applications 8 and with polymer layers 9 , although in this latter case the response of the crystal is more complicated than when operated solely in a liquid [10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Layer guided shear horizontally polarized acoustic plate modes

McHale

Newton

Martin

2002

The theoretical basis describing Love waves propagating on a finite thickness substrate covered by a finite thickness solid layer having a lower shear acoustic speed is considered. A generalized dispersion equation is derived for shear horizontally polarized acoustic waves in this system. Two types of solutions to the dispersion equation, both satisfying stress free boundary conditions at the free surfaces, are shown to exist.The first type of solution has a displacement that decays with depth into the substrate whilst the second does not. Analytical approximations to the solutions for a thin solid guiding layer show that these solutions can be considered as generalizations of Love waves and resonant shear horizontally polarized acoustic plate modes (SH-APM), respectively. Numerical solutions to the dispersion equation are developed and the spectrum of modes for thick guiding layers is examined with particular reference to sensor applications. As expected, increasing the thickness of the guiding layer leads to multiple Love wave modes. However, each of these Love wave modes is found to possess a set of shear horizontally polarized acoustic plate modes. As the guiding layer thickness is increased the Love wave speed decreases until at approximately v l /4f , where v l is the shear acoustic speed of the layer and f is the frequency, a sharp transition occurs in the Love wave speed from a value close to the shear acoustic speed of the substrate, v s , to one close to the shear acoustic speed of the layer, v l . A similar pattern is observed for the layer guided SH-APM's with an increase in the guiding layer thickness resulting in a sharp transition in the speed of the SH-APM towards a value close to that of the next lower SH-APM. It is shown that the appearance of the second Love wave mode is a result of a continuation of the lowest SH-APM associated with the previous Love wave mode. A physical interpretation is developed for the Love waves on the finite substrate and for the layer guided SH-APM's and from this interpretation it is suggested that layer guided SH-APM sensors could provide significantly enhanced mass sensitivity.

“…This surface acoustic impedance summarizes the overall acoustic load acting on the acoustic device and can be applied to single and multilayer arrangements 10 . With some approximations, this model can be translated into equivalent circuit models used in electrical engineering [11][12][13] . The imaginary part of the impedance gives the frequency shift and the real part gives the damping.…”

Section: Introductionmentioning

confidence: 99%

Influence of viscoelasticity and interfacial slip on acoustic wave sensors

McHale

Lücklum

Newton

et al. 2000

100

Acoustic wave devices with shear horizontal displacements, such as quartz crystal microbalances (QCM) and shear horizontally polarised surface acoustic wave (SH-SAW) devices provide sensitive probes of changes at solid-solid and solid-liquid interfaces.Increasingly the surfaces of acoustic wave devices are being chemically or physically modified to alter surface adhesion or coated with one or more layers to amplify their response to any change of mass or material properties. In this work, we describe a model that provides a unified view of the modification in the shear motion in acoustic wave systems by multiple finite thickness loadings of viscoelastic fluids. This model encompasses QCM and other classes of acoustic wave devices based on a shear motion of the substrate surface and is also valid whether the coating film has a liquid or solid character. As a specific example, the transition of a coating from liquid to solid is modelled using a single relaxation time Maxwell model. The correspondence between parameters from this physical model and parameters from alternative acoustic impedance models is given explicitly. The characteristic changes in QCM frequency and attenuation as a function of thickness are illustrated for a single layer device as the coating is varied from liquid-like to that of an amorphous solid. Results for a double layer structure are given explicitly and the extension of the physical model to multiple layers is described. An advantage of this physical approach to modelling the response of acoustic wave devices to multilayer films is that it provides a basis for considering how interfacial slip boundary conditions might be incorporated into the acoustic impedance used within circuit models of acoustic wave devices. Explicit results are derived for interfacial slip occurring at the substrate-layer 1 interface using a single real slip parameter, s, which has inverse dimensions of impedance. In terms of acoustic impedance, such interfacial slip acts as a single-loop negative feedback. It is suggested that these results can also be viewed as arising from a double-layer model with an infinitesimally thin slip layer which gives rise to a modified acoustic load of the second layer. Finally, the difficulties with defining appropriate slip boundary conditions between any two successive layers in a multilayer device are outlined from a physical point of view.