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.
After the advent of the quartz crystal microbalance (QCM) technology, various QCM-based sensing systems have got certain applications in many science and technology fields and resulted in dramatic progress in these fields. The core advantage of QCM is its high mass sensitivity which leads to high accuracy and low detection limit. For a QCM, the mass sensitivity is determined by the diameter and thickness of the electrode to a certain extent when the frequency of the quartz wafer is already determined. Theoretical approximate calculation reveals that there is an optimum electrode diameter corresponding to the maximum sensitivity. This is different from the traditional opinion that the smaller the electrode, the higher the mass sensitivity. A plating experiment was carried out using 28 QCMs with different electrode diameters, and the experimental results verified the existence of the optimum diameter. This study is helpful to obtain higher mass sensitivity by optimizing electrode parameters.
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.
The nonuniformity of QCMs' mass sensitivity distribution is a disadvantage to practical applications. Through theoretical calculations, we found that common ring electrode QCMs could obtain approximately uniform sensitivity distribution by carefully selecting the inner and outer diameters and mass loading factor of the electrode. A series of experiments were carried out using 10 MHz ring electrode QCMs with an inner diameter of 2 mm, an outer diameter of 5 mm, and a loading factor R of 0.0044. The experimental results proved that its mass sensitivity distribution is approximately uniform. This special designed ring electrode QCMs is suitable and convenient for highly accurate measurements.
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