Sauerbrey

Sauerbrey refers to a German physicist, Günther Sauerbrey, and the equation named after him that forms the basis of quartz crystal microbalance (QCM) mass sensing. The Sauerbrey equation relates the change in resonant frequency of a quartz crystal to the change in mass loaded onto its surface. For a rigid, uniformly distributed film, the mass change per unit area is proportional to the frequency shift, described in practical form as Δm = - C Δf, where Δm is the added mass per unit area, Δf is the frequency change, and C is the mass sensitivity constant that depends on the crystal’s fundamental frequency and geometry (for a typical 5 MHz crystal, C is about 17.7 ng cm^-2 Hz^-1). The corresponding physical form is Δf = - (2 f0^2 / (A sqrt(ρq μq))) Δm, with f0 the fundamental frequency, A the active area, and ρq and μq the density and shear modulus of quartz.

History and scope: Sauerbrey proposed the relation in 1959, and it has become a foundational tool in QCM. The equation is most accurate for thin, rigid films with no significant viscoelastic losses and good adherence to the sensor. It provides a direct, real-time measure of small mass changes and is widely used to monitor adsorption, film deposition, biosensor analyte binding, and corrosion or surface reactions.

Limitations and extensions: The Sauerbrey relation can fail for soft, viscoelastic, highly hydrated, or thick films where phase differences occur between the film and crystal. In liquids or complex matrices, corrections or alternative models (such as the Kanazawa–Gordon or Voigt-based approaches) are employed to interpret data. Despite limitations, the equation remains a central concept in surface science and sensor technology.