On the measurement of thin liquid overlayers with the quartz-crystal microbalance

We present a simple model that predicts the changes in resonance frequency and dissipation factor for a quartz-crystal microbalance (QCM) when it is coated with a viscous film that may or may not slip on the crystal. In this context, the validity of the Sauerbrey equation (change in resonance frequency α change in applied mass) is discussed. The Sauerbrey equation gives an accurate estimate of the film thickness, tf, only if (i) the film is thin compared to the shear-wave penetration depth, δ, into the liquid, i.e., tf  δ, and (ii) the film does not slide on the QCM electrode (s). We have shown that by measuring both the QCM resonance frequency and the dissipation factor simultaneously, the thickness range over which tf can be measured accurately can be extended to about 2δ for non-slipping films. If the film slips, which we have only observed for molecularly thin films, changes in dissipation factor can be used to calculate the coefficient of friction between the film and the substrate. We also show the usefulness of measuring the dissipation factor of the QCM when studying solid to liquid phase transitions.

Keywords: Quartz-crystal microbalances; Thin liquid films; Q-factor; Theory; Friction; Phase transitions