Impedance analysis for the investigation of the behaviors of piezoelectric quartz crystal in the liquid at harmonic resonance

The behaviors of piezoelectric quartz crystal (PQC) at harmonic resonance in viscous liquid have been studied by using impedance analysis. The theoretical equations comprising of the harmonic number (h), fundamental frequency (f0) and the number of sides in contact with liquid (N) have been derived. The effects of h, f0, and N on the change of resonant frequency, Δf, and the motional resistance, R1, for PQC in viscous liquid were discussed. It was shown that the crystal with higher fundamental frequency produced smaller response of R1 at a certain value of (ρLηL)1/2. This reason was that R1 was proportional to f03/2L1, where L1 was the motional inductance in air. It was found that, the responses of Δf and R1 both deviated from their respective linearity with (ρLηL)1/2 when (ρLηL)1/2 is higher than 8.7 g 1/2 cm−3/2 cP1/2. This deviation was explained by the difference of the decay length (δ) in different liquids. The slope of Δf vs. R1 has been suggested to be a qualitative indicator of the (ρLηL) contribution to the total frequency changes. For adsorption of some biological materials on gold, the magnitude order of this contribution to their respective Δf can be given by Au–C16SH/DNA>Au/l-cys>Au/BSA.