Institute of Physical Chemistry > Research > Modeling the QCM with the Finite Element Method

Modeling the QCM with the Finite Element Method

When the crystal contacts a liquid or a film, analytic predictions of the frequency shift exist.  These can be inverted in order to derive certain system parameters, such as the film thickness.  For complicated samples (such as spheres or bubbles) there are no such analytical equations.  One can still predict Δf numericaly, using the Finite Element Method.

The frequency shift is proportional to the area-averaged lateral stress, which the sampe exerts onto the crystal surface.  This stress can be computed with models such as the one shown below.  As a side results, one obtains the distribution of pressure and dissipated energy inside the sample.


  • Pomorska, A.; Shchukin, D.; Hammond, R.; Cooper, M. A.; Grundmeier, G.; Johannsmann, D.,
    Positive Frequency Shifts Observed Upon Adsorbing Micron-Sized Solid Objects to a Quartz Crystal Microbalance from the Liquid Phase.
    Analytical Chemistry 2010, 82, (6), 2237-2242.

  • Johannsmann, D.; Reviakine, I.; Richter, R. P., Dissipation in Films of Adsorbed Nanospheres Studied by Quartz Crystal Microbalance (QCM). Analytical Chemistry 2009, 81, (19), 8167-8176.


  • Johannsmann, D.; Reviakine, I.; Rojas, E.; Gallego, M., Effect of Sample Heterogeneity on the Interpretation of QCM(-D) Data: Comparison of Combined Quartz Crystal Microbalance/Atomic Force Microscopy Measurements with Finite Element Method Modeling. Analytical Chemistry 2008, 80, (23), 8891-8899.


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