In QCM (Quartz Crystal microbalance) and QCM-D (Quartz Crystal Microbalance with Dissipation Monitoring) measurements, the quartz crystal can be excited at different resonance harmonics. These include the fundamental frequency and higher overtones. But why does this matter? Are multiple harmonics really needed, and what extra information do they provide?
The short answer is that multiple harmonics make it easier to interpret what is happening at the sensor surface. They provide additional information about how the measured layer responds at different frequencies, which is especially important when analyzing soft, hydrated, or viscoelastic films. In QCM-D, multi-harmonic data are also important for viscoelastic modeling, where several measured variables are needed to extract parameters such as thickness and mechanical properties of surface adhering layers.
A QCM crystal behaves like a mechanical oscillator. Similar to a guitar string, it can be excited to resonate at several different harmonics, labeled with the harmonic number, n.
The lowest resonance frequency is called the fundamental frequency, where n = 1. Higher harmonics are often referred to as overtones. In other words, a harmonic can be either the fundamental or an overtone, while an overtone specifically means a harmonic above the fundamental.
Most QCM and QCM-D sensors use AT-cut quartz crystals. “AT-cut” refers to the angle at which the quartz crystal is cut relative to the crystallographic axes. This cut gives the sensor stable thickness-shear oscillation properties suitable for surface-sensitive measurements.
For AT-cut QCM crystals oscillating in thickness-shear mode, only the odd harmonics can be excited electrically, i.e. n = 1, 3, 5, etc. For example, if the fundamental frequency is 5 MHz, the odd overtones resonate at odd multiples of that frequency, i.e. 5, MHz, 15 MHz, 25 Mhz, etc.
Figure 1. Schematic illustration of the cross section of an AT-cut crystal resonating in the thickness shear mode. Left: the fundamental mode, n = 1. Right: the third harmonic, n = 3.
QCM measurements can be performed at one or several harmonics. Some QCM instruments measure at a single harmonic, meaning that the crystal is excited and monitored at one resonance frequency. This may be the fundamental frequency or one overtone. Other instruments perform multi-harmonic QCM measurements, where the crystal is excited and monitored at several resonance frequencies. The number of harmonics measured can vary between instruments. QSense QCM-D instruments use up to seven harmonics, n = 1–13, with a 5 MHz fundamental frequency. This means the sensor can be measured at 5, 15, 25, 35, 45, 55, and 65 MHz. This multi-harmonic capability is valuable because each harmonic provides a different view of the same surface-bound layer or interfacial process.
The main benefit of measuring multiple harmonics is that each harmonic provides information about how the system responds at a specific resonance frequency. In a QCM-D experiment, the surface-bound material is effectively probed at different oscillation frequencies. If the layer responds in the same way at different harmonics, this can support one type of interpretation. If the harmonic responses differ, this can reveal additional information about the layer’s structure, softness, viscoelasticity, or non-rigid behavior.
This is particularly important when studying for example:
For thin and rigid films, the different harmonics may behave similarly after normalization. For softer or more complex layers, the harmonic responses may spread apart, indicating that the layer does not behave as a simple rigid mass.
Measuring only one harmonic can provide useful information, but it gives only one perspective on the system. Measuring several harmonics provides a richer dataset and improves confidence in the interpretation. A useful analogy is the difference between a black-and-white photograph and a color photograph. A black-and-white image can show the shape of an object, but it does not reveal all the information that a color image provides. Even if the object is truly black and white, you can only confirm that by seeing the color information. Similarly, a single harmonic can show that something is happening at the surface. Multiple harmonics can help reveal more about what kind of layer is forming and whether the response is consistent with a rigid film, a viscoelastic film, or a more complex interfacial structure. This is why multi-harmonic data are useful not only for quantification, but also for assessing whether a chosen interpretation or model is appropriate.
Multiple harmonics are especially important for viscoelastic modeling. In QCM-D analysis, viscoelastic modeling can be used when the layer is not thin and rigid enough for a simple rigid-film interpretation. This is often the case for soft, hydrated, or viscoelastic films. To model such layers, several unknown parameters need to be fitted, such as film thickness, viscosity, shear modulus and the frequency dependence of the viscosity and shear modulus To fit these unknown parameters, the model needs enough measured input variables. In QCM-D, the measured variables include both resonance frequency, f, and dissipation, D.
When frequency and dissipation are measured at several harmonics, the number of input variables increases. For example, measuring f and D at three harmonics provides six measured variables. In theory, this may be enough to fit five unknown parameters if the measurement is perfect and the model describes the system perfectly. In practice, measurements contain noise, and real systems are rarely described perfectly by a mathematical model. For that reason, it is wise to use as many measured input variables as possible and evaluate how well the model fits the data.
A simple comparison is fitting a straight line. It is always possible to draw a straight line through two measured points, but to be confident that the system truly follows a linear trend, you need more data points and need to see whether they fall along the same line. The same principle applies to QCM-D modeling: more harmonics provide more constraints and make it easier to assess whether the model gives a meaningful description of the measured layer.
Multiple harmonics are especially valuable when the layer at the sensor surface is not a simple rigid film. They are particularly important when studying:
Soft and hydrated films: Soft and hydrated films often do not move as a perfectly rigid mass with the sensor. Multiple harmonics can reveal whether the layer response depends on oscillation frequency, which is important for identifying viscoelastic behavior.
Biomolecular and polymer layers: Proteins, polymers, hydrogels, brushes, and multilayers can change conformation, swell, collapse, or reorganize during an experiment. Multi-harmonic data help distinguish these structural changes from simple mass uptake or loss.
Lipid and surfactant layers: Lipid vesicles, supported lipid bilayers, and surfactant layers can form structures with very different mechanical properties. Multiple harmonics help reveal whether the layer is compact and rigid or soft and dissipative.
Film formation, degradation, and removal: During build-up or removal of surface-bound layers, the material may change both in mass and mechanical properties. Measuring multiple harmonics helps follow these changes more reliably over time.
Electrochemical and energy-related interfaces: In EQCM-D applications, electrode interfaces may form, dissolve, swell, or restructure during changes in potential or electrolyte composition. Multi-harmonic QCM-D data can help characterize not only mass changes, but also changes in the mechanical properties of interfacial films.
In practical QCM-D analysis, multiple harmonics can be used in several ways.
Compare normalized frequency shifts
For rigid films, normalized frequency shifts from different harmonics often overlap or follow similar trends. If the harmonics do not overlap, this may indicate that the layer is not behaving as a simple rigid film.
Compare dissipation responses
Dissipation measured at several harmonics helps reveal whether the layer is soft, viscoelastic, or changing structure during the measurement.
Look for overtone spreading
Spreading between harmonics can indicate viscoelastic behavior, layer non-uniformity, or more complex coupling between the surface-bound layer and the oscillating sensor.
Use multiple harmonics for modeling
When viscoelastic modeling is needed, frequency and dissipation data from several harmonics provide the input needed to estimate thickness and mechanical properties.
Check whether the model fits the data
Multiple harmonics also help assess whether a chosen model is appropriate. If the model cannot describe the responses across several harmonics, the model or assumptions may need to be reconsidered.
Assuming one harmonic is always enough: A single harmonic can show that a surface interaction occurs, but it may not provide enough information to determine whether the layer is rigid, soft, hydrated, or viscoelastic.
Ignoring harmonic spreading: If responses from different harmonics separate or behave differently, this is important information. It may indicate that a simple rigid-film interpretation is not sufficient.
Using viscoelastic models with too little input data: Viscoelastic models contain several unknown parameters. Using data from too few harmonics can reduce confidence in the extracted thickness and mechanical properties.
Treating the model as more certain than the data allow: Even with multiple harmonics, modeling depends on assumptions. The best interpretation comes from combining good data quality, multiple harmonics, dissipation information, and an appropriate model.
Comparing only final values: The time-resolved harmonic responses can reveal how a layer forms, rearranges, swells, collapses, or is removed. Looking only at final values can miss important information about the process.
Multiple harmonics provide important information in QCM-D measurements. Each harmonic probes the system at a different resonance frequency, making it possible to assess whether a surface-bound layer behaves consistently across harmonics or shows frequency-dependent behavior. This information helps interpret QCM-D data, identify when a simple rigid-film model may be sufficient, and determine when viscoelastic modeling is needed. For soft, hydrated, or mechanically complex layers, multiple harmonics are especially important because they provide the measured input needed to extract thickness and mechanical properties with greater confidence. To maximize the information extracted from QCM-D data, and to enable reliable viscoelastic film analysis, multi-harmonic measurements are essential. For modeling of a single layer, information on frequency and dissipation from at least two harmonics is needed, which means that overtone measurements are necessary for adequate data analysis.
Download the overview to learn more about the working principles of QCM and QCM-D, how the techniques differ, and why frequency, dissipation, and multiple harmonics are important for surface analysis.
Malin graduated in engineering physics in 2006, where her research focused on the QCM-D technology. Since then, she has been scrutinizing the how’s and why’s of the world in general, and the world of QCM-D in particular.
