Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

“Unexpected” frequency behavior in QCM-D: When can frequency increase with increased adhered mass?



Christopher C. White, Wiener Clinton, Robert A. Weiss, Vogt D. Bryan


For the qualitative interpretation of quartz crystal microbalance (QCM) data, a decrease in frequency is generally indicative of increased coupled mass to the quartz sensor. The frequency to mass relationship is generally assumed valid without limitation. However, Kanazawa and Melroy (IBM Journal of Research and Development, 1993, 37, 2,157-171), White and Schrag (Journal of Chemical Physics, 1999, 111, 24,11192-11206), and Voinova et al. (Physica Scripta, 1999, 59, 291-296) have predicted non-monotonic frequency dependence on adhered mass in their theoretical QCM models. An inversion of the relationship from a decrease in frequency with an increase in mass to an increase in frequency with an increased mass can occur. This inversion occurs when the coupled layer is both very lossy (viscous dissipation of energy) and relatively thick in these models. QCM with dissipation (QCM-D) enables quantification of the lossy character of the attached layer to compare model predictions to experimental data. Highly swollen, physically crosslinked thermally responsive hydrogels provide highly lossy films as a platform to test the models. Using simultaneous QCM-D and spectroscopic ellipsometry (SE) measurements, the thickness of the hydrogel film is known from SE and can be directly compared to the change in thickness from the modeled frequency change. The frequency decreases as the thickness increases as expected for sufficiently thin films (sub 30 nm) and low swelling ratios. For thicker films near the edge of the operating range of the crystal sensor there is a reversal in this relationship and frequency increases as the thickness increases prior to total dampening of the quartz. Application of the standard Q-Tools fitting software used with QCM-D results in thickness predictions within 10% of that measured by SE in this regime where the frequency increases for the higher overtones.
Soft Matter


Quartz Crystal Microbalance, Viscoelasticity, Modeling, Sauerbrey


White, C. , Clinton, W. , Weiss, R. and Bryan, V. (2018), “Unexpected” frequency behavior in QCM-D: When can frequency increase with increased adhered mass?, Soft Matter, [online], (Accessed April 22, 2024)
Created February 23, 2018, Updated November 10, 2018