We have derived the general solution of a wave equation describing thedynamics of two-layere viscoelastic polymer materials of arbitrary thicknessdeposited on solid (quartz) surfaces in a fluid environment. Within the Voightmodel of viscoelastic element, we calculate the acoustic response of the systemto an applied shear stress, i.e. we find the shift of the quartz generatorresonance frequency and of the dissipation factor, and show that it stronglydepends on the viscous loading of the adsorbed layers and on the shear storageand loss moduli of the overlayers. These results can readily be applied toquartz crystal acoustical measurements of the viscoelasticity of polymers,which conserve their shape under the shear deformations and do not flow, andlayered structures such as protein films adsorbed from solution onto thesurface of self-assembled monolayres.
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