The Role of Longitudinal Waves in Quartz Crystal Microbalance Applications in Liquids

Zuxuan Lin, Michael D. Ward

Research output: Contribution to journalArticlepeer-review


The generation of shear waves in liquids by the quartz crystal microbalance (QCM) is evident from the influence of liquid properties on the QCM frequency and electrical characteristics. With the exception of a few reports, contributions from longitudinal waves that arise from nonuniform velocity profiles along the shear direction or nonideal contributions from crystal longitudinal and flexure modes have been largely ignored. The presence of these longitudinal components is demonstrated by the influence of a glass plate, fixed parallel to the QCM surface at a remote distance, on the QCM resonant frequency and electrical impedance characteristics. In agreement with a previous report, these effects can be observed even when the glass plate is positioned > 1 cm away from the QCM, substantially longer than the shear wave decay length. Longitudinal standing waves are evident from the periodicity of the resonant frequency, inductance, capacitance, and resistance as the distance between the QCM and the glass plate. The wavelength of the standing waves agrees with that expected for the resonant frequency of the QCM and the fluid medium. The amplitude of the standing waves depends strongly upon the quartz crystal contour, as evident from extremely large frequency excursions observed for plano-convex crystals in which energy trapping in the center of the resonator is greater than that for piano-piano crystals. Impedance analysis indicates that the frequency excursions are primarily a consequence of changes in the capacitance of the quartz crystals that result from a decrease in the compliance of the quartz resonator due to pressure exerted by the longitudinal waves. Standing waves resulting from reflection from the fluid-air interface are also observed, although the amplitude of the standing waves is smaller than the amplitude observed with the glass reflector plate owing to the larger reflection coefficient for the latter. However, the frequency excursions that result from small changes in the height of the fluid-air interface are substantial relative to frequency changes measured in typical QCM experiments. These results demonstrate that it is important to design QCM experiments to avoid contributions from longitudinal waves.

Original languageEnglish (US)
Pages (from-to)685-693
Number of pages9
JournalAnalytical Chemistry
Issue number4
StatePublished - 1995

ASJC Scopus subject areas

  • Analytical Chemistry


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