The QCM is an acoustic technology, i.e. it measures changes of sound. The sound is typically in the MHz regime, however, and not detectable by the human ear.
The core of the technology is the oscillating unit - a thin quartz crystal disk, which has electrodes deposited on each side. Via an applied voltage, the crystal can be excited to resonance, and the resonance frequency is related to the thickness (mass) of the disk. If the thickness changes, so will the resonance frequency, f. By monitoring changes of the resonance frequency, Δf, it is possible to detect small changes of the crystal thickness (mass). The measurement makes it possible to detect nanoscale mass changes such as adsorption or binding of molecules to the surface, which will be detected as mass increase, whereas mass decrease will indicate mass removal, for example via molecular desorption or etching of the surface.
In addition to measuring Δf, which is measured by all QCM.:s, QCM-D measures an additional parameter, the dissipation, ΔD. The dissipation gives information about the energy losses in the system and are particularly useful in the study of soft layers, where this information is used for quantification of the layer properties.
Piezoelectricity - a key phenomenon for QCM-technology
As mentioned above, the core of QCM technology is the sensor which reveals mass changes via changes of its resonance frequency. A key quality of the sensor for this excitation to be possible is that it is made of a piezoelectric material. Piezoelectricity is a phenomenon that couples the electrical and the mechanical state of a material. This means that when the material is mechanically deformed, its faces will be charged, and vice versa - i.e. when the material is exerted to an electric field, the material will be deformed. Typically, QCM sensors are made of quartz, but other piezoelectric materials could be used as well.
The Sauerbrey equation - converting frequency change to mass change
The relation between frequency and mass, which enables the detection of molecule-surface interactions, was first identified by Günther Sauerbrey in 1959 and resulted in the so-called Sauerbrey relation.
The equation states that there is a linear relation between frequency change and mass change according to
where C, the so-called mass sensitivity constant, is a constant related to the properties of quartz and n=1, 3, 5… is the number of the harmonic used.
For the Sauerbrey equation to be valid, the layer on the sensor must be thin, rigid and firmly attached to the crystal surface. When hydrated systems are studied, for example polymers or biomolecules in liquid, the conditions are often not fulfilled and Sauerbrey relation will underestimate the mass. In this situation, there are other ways to quantify the layer properties, for example via so-called viscoelastic modelling.
The Dissipation - enabling analysis of viscoelastic layers
QCM-D measures changes of both frequency, f, and dissipation, D. The D-value gives information about the energy loss in the system, and reveals how soft, or viscoelastic the layer at the surface is. This means that the D-value will reveal whether the layer is rigid, and if the Sauerbrey equation can be used for the quantification or not. In situations where the Sauerbrey equation cannot be used, the D-value contributes with valuable information to be used as input in the quantification model and to extract mass, thickness and viscoelastic properties.
A parameter that is often discussed in the context of QCM is the mass sensitivity, C, in the Sauerbrey equation, (eq 1). This constant, which is often referred to as the ‘sensitivity’, says how many ng of material per cm2 of the sensor that is needed to shift the resonance frequency 1 Hz, i.e. the smaller the C, the higher the mass sensitivity. The value depends purely on the fundamental resonant frequency of the crystal, and is defined as
where υq is the shear wave velocity in quartz, ρq is the density of the quartz plate, and f0 is the fundamental resonant frequency. It is noted in eq. 2 that the higher the fundamental mode, the higher the theoretical mass sensitivity. As an example, the theoretical mass sensitivity of a 5MHz crystal is 17.7 ng/(cm2∙Hz) and that of a 10MHz crystal is and 4.4 ng/(cm2∙Hz).
The importance of the overtones
QCM is an acoustic technology, and like an acoustic instrument, the QCM crystal can be excited to resonate at several different harmonics, n. For AT-cut QCM crystals, which oscillate in the thickness shear mode, only the odd harmonics, n = 1, 3, 5,…. are possible to excite. The lowest resonance frequency, n = 1, is called the fundamental, and n = 3, 5, 7 etc are overtones to the fundamental. As an example, if the fundamental frequency is 5HMz, then available overtone resonances would be 15 MHz, 25 MHz, 35 MHz etc.
Each harmonic measured will contribute with unique information about the system under study and be useful when interpreting the QCM data. Additionally, information from multiple overtones is also key when performing viscoelastic modeling - the model contains several unknown parameters, and at least the same number of measured variables are needed to feed into the model.