INFICON PLO-10i Phase Lock Oscillator - Manual (Page 52)

PLO-10 PHASE LOCK OSCILLATOR
THEORY OF OPERATION 8-4
8.4 LIQUID MEASUREMENTS
QCMs have been used as gas-phase mass detectors with lossless films for many years.
However, only recently has their applications been extended to liquids and with
viscoelastic deposits. In these cases, both frequency and series resonance resistance ∗ of
the quartz crystal are important to completely characterize the material and/or the liquid
in contact with the crystal electrode. The development of QCM systems for use in liquids
opened a new world of applications, including electrochemistry and micro-rheology.
More recent developments have focused on tailoring electrode surface chemistry (i.e.
specialized polymer coatings) so that these devices can be applied as discriminating mass
detectors for many applications including: specific gas detection, environmental
monitoring, biosensing and basic surface-molecule interaction studies.
When the QCM comes in contact with a liquid, there is a decrease in frequency that is
dependent upon the viscosity and density of the liquid. Kanazawa’s solution for the
change in resonant frequency of the crystal due to liquid loading is shown in Equation 7.
Equation 7
q q
L L
q
f f
ρ µ π
ρ η
⋅ ⋅
⋅
− = ∆
2
3
Where:
f
q
= Resonant frequency of unloaded crystal in Hz.
ρ
q
= Density of quartz = 2.648×103 kg/m 3 .
q
µ = shear modulus of quartz = 2.947×10 10 Pa
L
ρ = density of the liquid in contact with the electrode in kg/m 3 ,
L
η = viscosity of the liquid in contact with the electrode in N · Sec/m 2
Liquid loading also dampens the resonant oscillation of the crystal causing an increase in
series resonance resistance, R, of the crystal. ∆f and ∆R measurements are both routinely
used as independent indicators of mass loading and viscosity at the crystal-liquid
interface of the QCM resonator during chemical and electrochemical depositions in
solution 23 .
A Butterworth-Van Dyke equivalent circuit model (Figure 18) was applied to derive a
linear relationship between the change in series resonance resistance, ∆R, of the crystal
and
L L
ρ η ⋅ under liquid loading. Using the relations in this study the change in
resistance, ∆R, can be put in the form:
Equation 8
( )
( )
2
26
3
2
3
32
2
e A f
f R
q r
q q
⋅ ⋅ ⋅ ⋅
⋅ ⋅
⋅ ∆ = ∆
ρ
µ ρ π
∗ See Section 8.6 for a detail discussion.