A practical model of quartz crystal microbalance (QCM) is presented, which considers both the Gaussian distribution characteristic of mass sensitivity and the influence of electrodes on the mass sensitivity. The equivalent mass sensitivity of 5 MHz and 10 MHz AT-cut QCMs with different sized electrodes were calculated according to this practical model. The equivalent mass sensitivity of this practical model is different from the Sauerbrey’s mass sensitivity, and the error between them increases sharply as the electrode radius decreases. A series of experiments which plate rigid gold film onto QCMs were carried out and the experimental results proved this practical model is more valid and correct rather than the classical Sauerbrey equation. The practical model based on the equivalent mass sensitivity is convenient and accurate in actual measurements.

Mass sensitivity is vital for quartz crystal microbalance (QCM)-based data analysis. The mass sensitivity distribution of QCMs may differ greatly depending on the shapes, thicknesses, sizes, and materials of the metal electrodes. This is not considered by the Sauerbrey equation, and has a large potential to cause errors in QCM-based data analysis. Many previous works have studied the effects of shape, thickness, and size of metal electrodes on mass sensitivity. However, it is necessary to continue to clarify the relationship between the mass sensitivity and the electrode material of the QCM. In this paper, the results of both theoretical calculation and experimental analysis showed that the mass sensitivity of QCMs with gold electrodes is higher than that of the QCMs with silver electrodes, which in turn indicated that the mass sensitivity of QCMs varies with the electrode material. Meanwhile, the results of this study showed that the mass sensitivity of QCMs with different electrode materials is not proportional to the density of the electrode materials. This result suggests that, in order to obtain more accurate results in the practical applications of QCMs, the influence of electrode material on the mass sensitivity of the QCMs must be considered.

Due to the influence of liquid load, the equivalent resistance of in-liquid quartz crystal microbalance (QCM) increases sharply, and the quality factor and resonant frequency decreases. We found that the change in the resonant frequency of in-liquid QCM consisted of two parts: besides the frequency changes due to the mass and viscous load (which could be equivalent to motional inductance), the second part of frequency change was caused by the increase of motional resistance. The theoretical calculation and simulation proved that the increases of QCM motional resistance may indeed cause the decreases of resonant frequency, and revealed that the existence of static capacitance was the root cause of this frequency change. The second part of frequency change (due to the increases of motional resistance) was difficult to measure accurately, and may cause great error for in-liquid QCM applications. A technical method to reduce the interference caused by this effect is presented. The study contributes to the accurate determination of the frequency and amplitude change of in-liquid QCM caused by liquid load, which is significant for the QCM applications in the liquid phase.