Electrochemical quartz crystal microbalance

The EQCM sensitivity factor K can be calculated by combing the electrochemical cell measured charge density and QCM measured frequency shift.[6] The sensitivity factor is only valid when the mass change on the electrode is homogenous.[6] Otherwise, K is taken as the average sensitivity factor of the EQCM.[6]

${\displaystyle \Delta f=-({\frac {2f_{o}^{2}}{S\surd (\mu \rho )}})\Delta m=-K\Delta m}$[6]

where ${\displaystyle \Delta f}$ is the measured frequency shift (${\displaystyle Hz}$), S is the quartz crystal active area (${\displaystyle cm^{2}}$), ρ is the density of quartz crystal, ${\displaystyle \mu }$ is the quartz crystal shear modulus and ${\displaystyle f_{o}}$ is the fundamental quartz crystal frequency. K is the intrinsic sensitivity factor of the EQCM.[6]

In a certain electrolyte solution, a metal film will deposited on the working electrode, which is the QCM sensor surface of QCM.[6]

${\displaystyle M^{z+}+ze^{-}\longrightarrow M}$[6]

The charge density (${\displaystyle {\frac {\Delta Q}{C}}\cdot cm^{-2}}$) is involved in the electro-reduction of metal ions at a constant current ${\displaystyle I}$, in a period of time ${\displaystyle \Delta T}$ (${\displaystyle \Delta Q=I\Delta t}$).[6]

The active areal mass density is calculated by

${\displaystyle \Delta m={\frac {A_{m}}{zF}}\Delta Q}$[6]

where ${\displaystyle A_{m}}$ is the atomic weight of deposited metal, z is the electrovalency, and F is the Faraday constant.[6]

The experimental sensitivity of the EQCM is calculated by combing ${\displaystyle \Delta m}$ and ${\displaystyle \Delta f}$.[6]

${\displaystyle K=-{\frac {zF}{A_{m}}}{\frac {\Delta f}{\Delta Q}}}$[6]