Sensor response of superhydrophobic quartz crystal resonators

Abstract

Quartz crystal microbalances are used to sense mass deposition from the gas or liquid phase, to determine the viscosity-density product of a liquid and to extract the shear moduli of polymers. These situations are described by the Sauerbrey equation, the Kanazawa and Gordon equation and by viscoelastic modeling of the full impedance spectrum of a crystal. In all of these cases the fundamental assumption in the theories of the sensor response is that a no-slip boundary condition is valid. For a smooth surface, this may be the case, but recently surfaces have been constructed that use high aspect ratio surface features to amplify the effect of surface chemistry (superhydrophobic surfaces). On these surfaces, droplets are effectively suspended on the tips of the surface features and roll easily. Moreover, recent reports have suggested that the steady flow of a simple Newtonian liquid, such as a water-glycerol mixture, over such a surface effectively occurs over a layer of air and so with greatly reduced drag. In this report, we discuss the effect of superhydrophobic surfaces on quartz crystals and develop an acoustic reflection view of crystal resonance to describe how the acoustic response might be modified. We present data for three types of superhydrophobic surfaces: a) a micro-post based surface, b) a titanium dioxide based surface and c) two silicon dioxide based surfaces. The impedance spectra are analyzed for frequency and dissipation changes in response to immersion in water-glycerol solutions. We compare the results to i) a theory for a quartz crystal in contact with a Newtonian liquid assuming a slip boundary condition, and ii) to an acoustic reflection view of the sensor response. When the slip length is much less than the shear wave penetration depth, the slip boundary condition predicts the frequency response has a response equal to a Kanazawa and Gordon liquid term plus an additional Sauerbrey "rigid" liquid mass; to first order the dissipation is unchanged from the Kanazawa and Gordon value. The data for the surfaces with the shortest micro-posts and for the titanium dioxide based surfaces is consistent with these expectations. We interpret this as due to penetration of the liquid into the surface structure. For the surface with the tallest micro-posts and for one of the silicon dioxide surfaces both frequency decrease and dissipation increase are substantially less than predicted by the Kanazawa and Gordon equation. We interpret this within the acoustic reflection view as due to the presence of an air layer, due to the superhydrophobicity, and its effect on decoupling the response of the crystal.