Analysis of the Mechanical Impedance Spectrum

When the EQCM was fist introduced, the only parameter measured was the frequency of the resonance. The shift of the frequency was interpreted, often erroneously, as the change in mass calculated from Eq. (17.1). In recent years the EQCM has been studied with a frequency-response analyzer, which yields the mechanical impedance spectrum of the system. It turns out that the impedance is a complex number, so that the real and the imaginary parts can be determined separately. An equivalent way of treating the data is to plot the real part of the admittance as a function of frequency. In this way the peak represents the resonance frequency,/, while the width-at half-height, F, represents the imaginary part of the admittance. By combining Eq. (17.6) and 17.7 we find 

It follows that the ratio of width-at-half-height to the shift of the resonance frequency, upon immersion of an EQCM in a fluid, is simply 

Note that immersing the oscillating crystal in a liquid loads it, because energy is transferred to the solution adjacent to the surface of the vibrating crystal. This leads to a lowering of the resonance frequency, just as expected for mass loading. However, the width-at-half-height increases. 

The total shift of frequency shown here can be written as 

It is important to note that determination of the width of the resonance can be critical for the use of the EQCM as a true microbalance. Relating A/ to the change in mass Am employing Eq. (17.1) is only valid if the parameter T is constant in a given composition of the solution and at constant temperature and pressure. In the general case, it may be better to regard the QCM as a quartz crystal microsensor. On the other hand, measurement of both A/ and F can be very useful in more advance analysis of the structure of the metal/electrolyte interface, employing suitable models, which can be tested experimentally. 

---