As an ultra-sensitivity sensor, a quartz crystal microbalance (QCM) could be used to quantitatively characterize the relation between QCM parameters and the characteristics of viscoelastic films. When a QCM coated with a viscoelastic thin film is in the gas phase, based on the constructive equation of the quartz crystal and ignoring the capacitance effect, the equivalent Butterworth–Van Dyke (BVD) model of the QCM and the explicit expression for its frequency shift are derived. The “extra mass effect” deduced by the complex modulus is also obtained. It is found that the tendency of the BVD model in this work agrees well with that of Voinova’s model, although both are derived in different ways. Meanwhile, it can be seen that the two above-mentioned models exhibit different characteristics when compared with Sauerbrey’s model and Arnau’s model. The BVD model will help analyze the properties of viscoelastic films in the gas phase.

中文翻译：

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气相应用粘弹性膜加载QCM的BVD模型

作为超灵敏传感器，可以使用石英晶体微量天平（QCM）定量表征QCM参数与粘弹性薄膜特性之间的关系。当涂有粘弹性薄膜的QCM处于气相状态时，基于石英晶体的构造方程，并且忽略电容效应，该QCM的等效Butterworth-Van Dyke（BVD）模型及其频率的明确表示形式移位是派生的。还获得了由复数模量得出的“额外质量效应”。可以发现，尽管这两种方法都是以不同的方式推导的，但是BVD模型在这项工作中的趋势与Voinova模型的趋势非常吻合。同时，可以看出，与Sauerbrey模型和Arnau模型相比，上述两个模型表现出不同的特性。