Effect of surface film structure on the quartz crystal microbalance response in liquids

The effect of surface roughness and the morphology of nonuniform surface films on a quartz crystal microbalance (QCM) response in liquids has been investigated. Our description of the velocity field in the interfacial region is based on Brinkman's equation, commonly employed in the treatment of a flow through porous media. In this approach one treats the flow of a liquid through a nonuniform surface layer as the flow of a liquid through a porous medium. The morphology of the interfacial layer is characterized by the permeability that depends on the ''porosity'' of the layer. The model proposed here gives a unified approximate description of the QCM response for various scales of roughness. It includes both the effect of viscous dissipation in the interfacial layer and the effect of the liquid mass rigidly coupled to the surface. A relation between the QCM response and the interface geometry has been found. The model discussed here can be used for the treatment of QCM response of rough electrode surfaces, of porous deposited films, and of surface polymer films.