Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance

Bandey, Helen; Brown, Mark J.; Cernosek, R.W.; Hillman, A. Robert; Martin, Stephen J.

doi:10.1021/ac9908290

Cited by 98 publications

(99 citation statements)

References 17 publications

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“…Values of G′ and G″ were calculated using the Maple package by fitting experimental impedance (Z) data using [21,22,34,35]:…”

Section: Data Fittingmentioning

confidence: 99%

“…The experimental approach is to use a high frequency acoustic wave device (a thickness shear mode, TSM, resonator [20]) to determine the surface mechanical impedance, from which one can extract the film mechanical behaviour [21]. We parameterize this in terms of the shear modulus (G), expressed as the complex quantity G′ + jG″, where G′ is the storage modulus, G″ is the loss modulus and j indicates the phase relationship.…”

Section: Introductionmentioning

confidence: 99%

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The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling

Mohamoud

Hillman

2007

Electrochimica Acta

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Acoustic admittance measurements at thickness shear mode resonators were used to determine shear moduli for polyaniline films during their potentiodynamic electrodeposition and subsequent redox cycling in aqueous background electrolyte. Data were acquired for films doped with perchlorate, sulphate or chloride anion. For all media, film shear moduli increased progressively with film thickness, from values consistent with a diffuse fluid-like layer to values typical of a viscoelastic material. At any given thickness, both the storage and loss moduli were largest in perchlorate medium; values in chloride and sulphate media were similar to each other, but smaller than in perchlorate. These measures of polymer dynamics are consistent with a previous classification of polyaniline film behaviour, in which perchlorate-doped films are viewed as compact while chlorideand sulphate-doped films are viewed as more open. In monomer-free background electrolyte solution, both film shear modulus components for all anions increased modestly upon film oxidation. Despite some hysteresis on the timescale of slow scan voltammetry, these variations were chemically reversible. Based on measurements involving deposition from chloride medium and transfer to sulphate medium, film shear moduli respond promptly to changes in dopant identity; this is consistent with rapid redox-driven exchange of anions with the bathing electrolyte.

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“…Values of G′ and G″ were calculated using the Maple package by fitting experimental impedance (Z) data using [21,22,34,35]:…”

Section: Data Fittingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling

Mohamoud

Hillman

2007

Electrochimica Acta

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“…The concept of liquid entrainment enables the Kanazawa and Gordon frequency shift to be written in terms of a frequency dependent interfacial mass loading layer of thickness 8, i.e. Af n lf n =-fpi8l{jd s p s ) Modelling of the TSM response to mass loading layers has developed well beyond the simple Sauerbrey and the Kanazawa and Gordon equations and the frequency and damping response of a quartz crystal to single or multiple viscoelastic layers, which contain the rigid mass and Newtonian liquid limits, can now be calculated [7][8][9][10]. However, these original equations still provide an important conceptual reference for how solid and liquid properties, and changes in operating frequency, influence acoustic wave response.…”

Section: Introductionmentioning

confidence: 99%

Generalized concept of shear horizontal acoustic plate mode and Love wave sensors

McHale

2003

Meas. Sci. Technol.

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An approach to mass and liquid sensitivity for both the phase velocity and insertion loss of shear mode acoustic wave sensors based on the dispersion equations for layered systems is outlined; the approach is sufficiently general to allow for viscoelastic guiding layers. An equation for the phase velocity and insertion loss sensitivities is given which depends on the slope of the complex phase velocity dispersion curves. This equation contains the equivalent of the Sauerbrey and Kanazawa equations for loading of a quartz crystal microbalance by rigid mass and Newtonian liquids, respectively, and also describes surface loading by viscoelastic layers. The theoretical approach can be applied to a four-layer system, with any of the four layers being viscoelastic, so that mass deposition from a liquid can also be modelled. The theoretical dispersion equation based approach to layer-guided shear horizontal acoustic wave modes on finite substrates presented in this work, provides a unified view of Love wave and shear horizontal acoustic plate mode (SH-APM) devices, which have been generally regarded as distinct in sensor research. It is argued that SH-APMs with guiding layers possessing shear acoustic speeds lower than that of the substrate and Love waves are two branches of solution of the same dispersion equation. The layer guided SH-APMs have a phase velocity higher than that of the substrate and the Love waves a phase velocity lower than that of the substrate. Higher order Love wave modes are continuations of the layer guided SH-APMs. The generalized concept of SH-APMs and Love waves provides a basis for understanding the change in sensitivity with higher frequency operation and the relationship between multiple modes in Love wave sensors. It also explains why a relatively thick layer of a high loss polymer can be used as a waveguide layer and so extends the range of materials that can be considered experimentally. Moreover, it is predicted that a new type of sensor, a layer-guided SH-APM sensor, can be constructed in a manner analogous to a Love wave device. The sensitivity of such a device is predicted to approach that of a Love wave sensor whilst retaining the advantage of the SH-APM of using the face opposite the one possessing the transducers as the sensing surface.

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“…Indeed, it is similar in origin to the idea of a shear wave resonance known in work with QCMs. 24,25 A close comparison of Eq. ͑36͒ in the thin layer mass loading limit with acoustic impedance models for QCMs shows that the tan x term in Eq.…”

Section: B Numerical Results For Phase Speed and Insertion Lossmentioning

confidence: 70%

Theoretical mass, liquid, and polymer sensitivity of acoustic wave sensors with viscoelastic guiding layers

McHale

Newton

Martin

2003

Journal of Applied Physics

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The theoretical sensitivity of Love wave and layer-guided shear horizontal acoustic plate mode ͑SH-APM͒ sensors for viscoelastic guiding layers and general loading by viscoelastic materials is developed. A dispersion equation previously derived for a system of three rigidly coupled elastic mass layers is modified so that the second and third layers can be viscoelastic. The inclusion of viscoelasticity into the second, wave guiding layer, introduces a damping term, in addition to a phase velocity shift, into the response of the acoustic wave system. Both the waveguiding layer and the third, perturbing layer, are modeled using a Maxwell model of viscoelasticity. The model therefore includes the limits of loading of both nonguided shear horizontal surface acoustic wave and acoustic plate mode ͑APM͒ sensors, in addition to Love wave and layer-guided SH-APM sensors, by rigidly coupled elastic mass and by Newtonian liquids. The three-layer model is extended to include a viscoelastic fourth layer of arbitrary thickness and so enable mass deposition onto an immersed Love wave or layer-guided SH-APM sensor to be described. A relationship between the change in the complex velocity and the slope of the complex dispersion curve is derived and the similarity to the mass and liquid sensor response of quartz crystal microbalances is discussed. Numerical calculations are presented for the case of a Love wave device in vacuum with a viscoelastic waveguiding layer. It is shown that, while a particular polymer relaxation time may be chosen such that the effect of viscoelasticity on the real part of the phase speed is relatively small, it may nonetheless induce a large insertion loss. The potential or the use of insertion loss as a sensor parameter is discussed.

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Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance

Cited by 98 publications

References 17 publications

The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling

The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling

Generalized concept of shear horizontal acoustic plate mode and Love wave sensors

Theoretical mass, liquid, and polymer sensitivity of acoustic wave sensors with viscoelastic guiding layers

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