Accessing Viscoelasticity of PDMS at MHz Frequencies: Physically Intuitive Continuum Mechanics Model for QCM Able to Treat Film Resonance Region

Quartz crystal microbalance (QCM) is increasingly applied as a MHz-rheometer to measure viscoelastic properties of films beyond the simple Sauerbrey equation relating frequency shifts to mass loading of the crystal. For films, the range of harmonics available is often limited by needing higher harmonics to access where frequency shifts become sensitive to the film’s viscoelasticity, while avoiding the film resonance region where shifts and dissipation become large. Film resonance corresponds to the harmonics that form standing acoustic waves in the film. Most QCM modeling applies simplifications assuming small resonance shifts, like the small load approximation, which are not valid under film resonance. This limits the range of film thicknesses whose viscoelasticity can be accurately measured, especially for rubbery films where film resonance occurs at lower harmonics. We present a physically intuitive continuum mechanics model with no small frequency-shift approximations that can numerically treat film resonance, accessing a wider range of film thicknesses. Fits for polydimethylsiloxane (PDMS) films, including film resonance conditions, give shear modulus values in good agreement with interpolated literature values from kHz and GHz frequencies.