SaM - Quartz as a Sensor • QCM (Quartz Crystal Microbalance)

Memory Card

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Taken a quartz slice in between two “functionalization layer”:

• ==The “functionalization layer” is a special material that can absorb a “special target molecule”, and when it does so it increases its mass==.
  We will model this added layer with an added mass, so an impedance of this value will be added in the ciruit: $Z_M=\Delta m\Rightarrow \frac{Z_M}{k^{2}d}=\frac{\Delta m}{k^{2}d}$Where:
  • $\Delta m$: mass of the “functionalization layer”
  • $K$ : cosntant defined by the geometry of the piezoelectric crystal
  • $d$ : piezoelectric coefficient.
• The rest of the circuit is as before.
  ==This time we cannot the mass of the quartz $\left(Z_m\right)$==, as we have done before.

So we can change the $L_{eq}$ value incorporating $Z_{\Delta M}$:$L_{eq}^{\prime }=L_{eq}+\frac{\Delta m}{K^{2}d}\Rightarrow \{\begin{array}{l}{\omega }_s^{\prime }=\frac{1}{\sqrt{L_{eq}^{\prime }\cdot C_{eq}}}\\ {\omega }_p^{\prime }=\sqrt{\frac{C_E+C_{eq}}{C_E{L}_{eq}^{\prime }{C}_{eq}}}\end{array}$

• So we have a relation between ${\omega }_s^{\prime }$ and $\Delta m$, so as the “functionalization layer” absorbs the target molecule we will se a decrease of ${\omega }_s^{\prime }$.
• The name of this sensor is: QCM (Quartz Crystal Microbalance), and it is based on the concentration of the target species (that gets absorbed by the functionalization layer).