Comparison of Optical and Acoustic Reflectometry

It is instructive to compare Eq. 78 with the corresponding equation apphed in the context of SPR spectroscopy. For the shift of the couphng angle, 9c, we have [17,100,101]  

Evidently, the fact that the acoustic contrast is much higher than the optical contrast is beneficial for sensing. The advantage which the QCM has over the competing optical techniques is most strongly felt for dilute adsorbates. The QCM responds very sensitively to these because—pictorially speaking— a few polymer strands suffice to turn the film into a solid-like object. 

The term in brackets in Eq. 77 is a viscoelastic correction to the Sauerbrey equation. The viscoelastic correction is independent of film thickness in a li-qiud environment. This is in contrast to films in air or vacuum, where the viscoelastic correction scales as the square of the mass (Eq. 72). In air, the film surface is stress-free. The film only shears under its own inertia and in the hmit of vanishing film thickness, the shear strain goes to zero. As a conse- 

In most cases, the viscoelastic correction cannot be directly extracted from the frequency shift because the mass, mf, is not known independently. The frequency shift contains the product of the mass and the real part of the term in brackets in Eq. 77. The two contributions cannot be disentangled. Note, however, that the mass can be eliminated by considering the ratio of the shift in half-band-half-width, A F, and the negative frequency shift, - Af (the D/f ratio , where the D stands for dissipation). One has  

In the following, we assume that the liquid is Newtonian with a density, p q, and a viscosity, rj. The acoustic impedance then is  

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