Elastic and Viscoelastic Films on a SAW Device

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (pfc) contributed by the film — the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAW-induced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment. 

The mechanical properties of a linear, isotropic material can be specified by a bulk modulus, K, and a shear modulus, G. For an ideal elastic solid, these moduli are real-valued. For real solids undergoing sinusoidal deformation, these are best represented as complex quantities [49] K = K jA and G = G -I- jG . The real parts of K and G represent the component of stress in-phase with strain, giving rise to energy storage in the film (consequently K and G are referred to as storage moduli) the imaginary parts represent the component of stress 90° out of phase with strain, giving rise to power dissipation in the film (thus, K and G are called loss moduli). 

The regime of film operation can be determined from the ratio R of cross-film to in-plane gradients induced by the SAW [50]  

Example 3.7 For a film on a 100-A //z ST-quartz SAW device, what film thickness h marks the transition from acoustically thin to thick for (a) a glassy polymer film with G = 10 0 dynelcm, and (h) a rubbery polymer film with G = 10 dynelcm Assume P = 1 /cw G G, andA = 1.9. 

Strain Mode Dtspkuiement Gradient Modulus Definition Modulus El (in terms (in terms of X, fi) K, G)  

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