Biomedical Engineering Reference
In-Depth Information
is the density of quartz, m q is the shear modulus of the particular cut of quartz
employed and Dm is the change in mass. Key assumptions in this treatment are
that acoustic energy is confined to the device and film in place on its surface,
and that the acoustic properties of the film are identical to those of quartz.
Given the fact that the film in place under these conditions predicts an
extension of wavelength and, always, a reduction in resonant frequency, the
device has been employed universally as a sensor of added (or lost) mass. This
notion has spawned the ubiquitous term 'quartz crystal microbalance' or
QCM. Unfortunately, this argument has been widely extended to operation of
the device in the liquid phase and has become something of a dogma, especially
in the community of electrochemists. In such a medium, it is a reality that
acoustic energy is transferred to the surrounding liquid resulting in a damped
wave via the effects of bulk phase viscosity (Figure 1.15).
The years have seen numerous attempts at the development of theories for
operation of the TSM in liquids (reviewed in ref. 72). These have included the
influence of liquid density, conductivity, dielectric constant and viscosity, and
interfacial properties such as roughness, slip and stress. A prominent earlier
model was that provided by Kanazawa and Gordon 73 which predicts that the
change resonant frequency will be proportional to the square root of the liquid
viscosity/density product.
Since the introduction of the earlier models, it has now become apparent that
acoustic coupling effects and the phenomenon of interfacial slip at the
liquid-solid interface are important properties which, in part, govern the
response of the device when operated in the liquid phase. 74-76 One particularly
crucial aspect of these phenomena, in sharp contrast to the QCM notion, is that
imposed mass on the device surface can lead to frequency increases under
certain conditions. Just as important, the implied perturbation of acoustic
coupling by interfacial chemistry offers a unique mechanism for biomolecular
detection. This includes the detection of phenomena such as biomolecule
conformational changes.
Experimentally, a number of approaches have been employed to measure the
resonant frequency and other acoustic parameters, in some cases in a static
fashion, and in others, in flowing liquid through a flow-injection configuration.
The most rigorous approach is that provided by what is often termed acoustic
network analysis. In this method the magnitude and phase of impedance of the
sensor are determined at a set of frequencies under resonance conditions.
A network analyzer is employed to record the Butterworth-Van Dyke
equivalent circuit which essentially relates physical properties of the device to
electrical parameters (Figure 1.16). Note that the true measured series
resonance frequency is detected at zero phase angle. Other determined
parameters from the equivalent circuit are the motional resistance, R m , which is
importantly associated with energy dissipation in the system including any
added surface film, inductance, I m and two capacitances, C m and C 0 . The
second approach, which is available on a commercial basis, involves the
measurement of a resonance frequency and an energy dissipation factor, D. 77
The latter parameter provides analogous information to the R m factor
d n 4 t 3 n g | 1
d n 3 .
 
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