QCM in the Gas Phase

Oscillation of the crystal is due to the AC electric field applied across the crystal from metal electrodes. Typical electric fields are quite low, 10-20 V cm-1. The electrodes are deposited directly on the quartz crystal (Fig. 4.4) although, in principle, a noncontact activation of the crystal is also possible. 

There are two modes excited by the AC field, longitudinal and transverse. For crystals in the 100-300 pm thickness range, only the transverse standing wave needs to be considered (Janshoff et al 2000). The actual lateral displacement of a point on the crystal surface (and therefore the mass sensitivity) is the Gaussian function of the radial distance from the center of the electrode (Fig. 4.5). It also depends on the amplitude of the applied electric field and ranges from few nm/V in water to tens of nm/V in air or in vacuum. 

The direction of the displacement comes from the periodic boundary condition of the solution of the wave equation. It is normal to the flat of the crystal 

Another level of complexity must be considered the oscillations in the z-direction. For chemical sensing, we need to impart the selectivity by depositing an additional selective layer on top of the smaller of the two electrodes. Therefore, on a quartz crystal that is used for chemical sensing, we have at least three interfaces one between the quartz and the metal, a second one between the metal and the selective layer, and the third between the selective layer and the sample (Fig. 4.4b). 

At each interface, reflection and refraction of the acoustic energy occur similar to the reflection and refraction of light at the boundary between two materials of different optical densities (see Chapter 9). 

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