Viscoelastic acoustic response of layered polymer films at fluid-solid interfaces: Continuum mechanics approach

We have derived the general solution of a wave equation describing the dyna mics of two-layer viscoelastic polymer materials of arbitrary thickness dep osited on solid (quartz) surfaces in a fluid environment. Within the Voight model of viscoelastic element, we calculate the acoustic response of the s ystem to an applied shear stress, i.e. we find the shift of the quartz gene rator resonance frequency and of the dissipation factor, and show that it s trongly depends on the viscous loading of the adsorbed layers and on the sh ear storage and loss moduli of the overlayers. These results can readily be applied to quartz crystal acoustical measurements of the viscoelasticity o f polymers which conserve their shape under the shear deformations and do n ot flow, and layered structures such as protein films adsorbed from solutio n onto the surface of self-assembled monolayers.