“…The change in mass on the surface of a QCM is related to the shift in resonance frequency using the Sauerbrey equation [ 69 ], which is written as follows: where Δ m is the change in mass on the surface of the QCM, a is the surface area of the gold-coated region of QCM, ρ q is the density of quartz, µ q is the shear modulus of quartz, f 0 is the resonance frequency of blank QCM, and Δ f is the shift in resonance frequency caused by change in mass. In case of IDE capacitors, the capacitance reactance at drive frequency f using closed-form solution with N number of electrodes ( N > 3) [ 70 , 71 ] is calculated as follows: where C IDE is calculated using where C I and C E are calculated using where L is the length of electrodes, ε 1 is the relative permittivity of the layer coated onto the IDE, ε S is the relative permittivity of the substrate, ε 0 is the relative permittivity of free space, K ( k ) is the complete integral of the first kind with modulus k , , , , , , W is the width of each electrode, and G is the gap between the IDE.…”