質量附著於石英晶體微天平之頻率飄移研究

Abstract

石英晶體微天平(Quartz Crystal Microbalance, QCM)的發展由來已久，其主要應用在生物醫療檢測上，是用來偵測附著在QCM上的微小質量變化，在有質量附著在QCM上時，QCM的共振頻率會因為質量的附著而有所飄移，而共振頻率的飄移對QCM的幾何形狀與附著質量的多寡以及材料性質的不同而有所不同。本篇論文，將對質量附著面積與頻率飄移的簡易公式 ，使用有限元素軟體建立不同質量附著各種平台高度的QCM模型，藉由得到頻率飄移曲線，來曲線擬合求得待定係數α 與 β，以及將α 與 β根據不同平台高度製成表格，用線性內插的方式求得其他平台高度下α、β，可用於預測在該種高度下時的質量附著面積。同時亦將推導雙電極QCM的頻率飄移公式，將使用與單電極QCM的方法，來建立待定係數表格以及預測個別電極上的質量附著面積。 本文的目標在於建立與平台高度相關的參數表格，可供在設計不同平台高度下時也可用此表格來預測質量附著面積。其預測質量附著面積的應用面在於，QCM在偵測上只能量到頻率變化，無法知道待測物的濃度，如果利用此種方法來預測附著面積，進一步可以推得當時所要偵測的待測物的濃度。

Quartz Crystal Microbalance (QCM) has been a commercialized bio-sensor in recent years. Its application is to detect resonant frequency shift of QCM, which dependent on geometrical shapes of QCM and material properties of loading masses, so that mirror in the change of tiny masses cohered on the electrode surfaces. In this paper, at first, we will proceed a verification of the analytic procedure: a relation between the resonant frequency shift and attached mass area will be introduced, , where α and β are undetermined coefficients. Then, by means of curve fitting approach, two significant coefficients, α and β, are capable of being determined together with the finite element model of different mesa-shaped QCMs. With a series of α and β being tabulated, the prediction of mass area attached on the electrode surfaces will be performed through linear interpolation of α and β. Afterward, extending to the preceding analytic theorem of mesa-shaped QCM, mesa-shaped multichannel QCM will be derived and acquired. Following the analogous procedure before, the prediction of mass area attached on the two electrode surfaces will be still verified and executed. Therefore, the objective on this paper is intent to provide the effective predicted approach for mesa-shaped multichannel QCM, and be beneficial to manipulations of relevant experiments.