Theoretical mass sensitivity of Love wave and layer guided acoustic plate mode sensors

Abstract

A model for the mass sensitivity of Love wave and layer guided shear horizontal acoustic plate mode ͑SH-APM͒ sensors is developed by considering the propagation of shear horizontally polarized acoustic waves in a three layer system. A dispersion equation is derived for this three layer system and this is shown to contain the dispersion equation for the two layer system of the substrate and the guiding layer plus a term involving the third layer, which is regarded as a perturbing mass layer. This equation is valid for an arbitrary thickness perturbing mass layer. The perturbation, ⌬ , of the wave speed for the two-layer system by a thin third layer of density, p and thickness ⌬h is shown to be equal to the mass per unit area multiplied by a function dependent only on the properties of the substrate and the guiding layer, and the operating frequency of the sensor. The independence of the function from the properties of the third layer means that the mass sensitivity of the bare, two-layer, sensor operated about any thickness of the guiding layer can be deduced from the slope of the numerically or experimentally determined dispersion curve. Formulas are also derived for a Love wave on an infinite thickness substrate describing the change in mass sensitivity due to a change in frequency. The consequences of the various formulas for mass sensing applications are illustrated using numerical calculations with parameters describing a ͑rigid͒ poly͑methylmethacrylate͒ wave-guiding layer on a finite thickness quartz substrate. These calculations demonstrate that a layer-guided SH-APM can have a mass sensitivity comparable to, or higher, than that of Love waves propagating on the same substrate. The increase in mass sensitivity of the layer guided SH-APMs over previously studied SH-APM sensors is of significance, particularly for liquid sensing applications. The relevance of the dispersion curve to experiments using higher frequencies or frequency hopping and to experiments using thick guiding layers is discussed.

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

“…However, what is particularly important experimentally is that if we can determine the sensitivity function g for any perturbing layer then it is the same function for any other layer. 21 While we have previously noted the importance of this last observation, our present work shows that its relevance is much wider than previously indicated. The function g can be determined using a thin elastic mass layer, but will then be valid whether the device is used for sensing mass deposited from the vapor phase or for sensing liquid ͑or polymer͒ properties.…”

“…͑37͒ appears to be the same as in the case of elastic mass derived in Ref. 21 except for the additional tan x/x type multiplicative factor arising from maintaining a finite thickness, rather than an infinitesimally thin, third layer. If the waveguide layer is simply elastic mass then both the function g and the unperturbed speed v 0 are real and any complex component to ⌬ arises purely from the viscoelasticity of the perturbing layer.…”

“…The first generalization of the previously published model of mass sensitivity 21 is to allow the waveguiding layer itself to become viscoelastic. This viscoelasticity means that the ''bare'' device of the substrate and the waveguiding layer has a complex dispersion curve with a wave velocity that has both real and imaginary parts indicating that both a velocity shift and attenuation occur due to the waveguiding layer.…”

“…͑24͒ in Ref. 21, except we keep the third layer thickness finite and the shear moduli and, hence, velocities of the waveguide and perturbing layers are allowed to be complex. Thus, using a subscript f to represent quantities for the third, perturbing, layer of thickness h, the complex perturbation is…”

“…[19][20][21] This involved extending the theoretical treatment of both Love wave sensors with guiding layers composed of elastic mass to Love waves on finite thickness substrates and of SH-APMs to SH-APMs coated by waveguiding layers. In this previous treatment, higher order Love wave modes were shown to be continuations of the layer-guided SH-APMs and it was shown that significantly enhanced mass sensitivity could be obtained for SHAPMs by the use of a waveguiding layer.…”