Quantitative Rheometry of Thin Soft Materials Using the Quartz Crystal Microbalance with Dissipation

In the inertial limit, the resonance frequency of the quartz crystal microbalance (QCM) is related to the coupled mass on the quartz sensor through the Sauerbrey expression that relates the mass to the change in resonance frequency. However, when the thickness of the film is sufficiently large, the relationship becomes more complicated and both the frequency and damping of the crystal resonance must be considered. In this regime, a rheological model of the material must be used to accurately extract the adhered film's thickness, shear modulus, and viscoelastic phase angle from the data. In the present work we examine the suitability of two viscoelastic models, a simple Voigt model ( Physica Scripta 1999, 59, 391-396) and a more realistic power-law model ( Langmuir 2015, 31, 4008-4017), to extract the rheological properties of a thermoresponsive hydrogel film. By changing temperature and initial dry film thickness of the gel, the operation of QCM was traversed from the Sauerbrey limit, where viscous losses do not impact the frequency, through the regime where the QCM response is sensitive to viscoelastic properties. The density-shear modulus and the viscoelastic phase angle from the two models are in good agreement when the shear wavelength ratio, d/λ _n, is in the range of 0.05-0.20, where d is the film thickness and λ _n is the wavelength of the mechanical shear wave at the n^th harmonic. We further provide a framework for estimating the physical properties of soft materials in the megahertz regime by using the physical behavior of polyelectrolyte complexes. This provides the user with an approximate range of allowable film thicknesses for accurate viscoelastic analysis with either model, thus enabling better use of the QCM-D in soft materials research.