粘弹性薄膜吸附的QCM传感器响应模型研究及验证
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摘要
石英晶体微天平（QCM）是一种超灵敏的质量型传感器，可以检测到纳克量级（10-9g）的微质量变化。它具有快速实时、在线跟踪、单次检测成本低廉、可以给出定量分析结果等诸多优点，是实现农产品农药残留、食品安全、重金属污染、大气污染、水质分析、医学诊疗检测等高精密检测分析的新技术、新方向，近几年成为了生化检测分析领域的研究热点。
在经典的QCM的数据分析响应模型中， Sauerbrey模型只适用于气相刚性膜均匀吸附应用；Kanasawa模型只适用于液相纯粘性液体应用，并且它只能把未知液体的密度和粘度的乘积项当做一个参数来处理。QCM-D响应模型通过QCM的频率变化和能量耗散变化建立方程组来分析粘弹性介质吸附现象。但是，该模型需要已知溶液的密度、粘度等信息，在应用上有一定的局限性。同时，QCM-D响应模型中能量耗散变化的获得是采用瞬时测量法以脉冲激励的方式让QCM传感器振荡，然后测量其衰减时间（一般是在10-6秒量级）计算得到。这种方法容易受到外界的微小干扰而影响分析结果的准确度。
本文在传输线理论和声波理论的基础上，推导了不同介质吸附下QCM传感器响应模型的显性表示式，揭示了QCM传感器的频率变化以及耗散因子变化与所吸附的介质特性之间的关系。进而通过验证，定量分析和评估了多种材料的特性。本文主要工作和创新点包括：
1．应用传输线理论以及负载声波阻抗理论，推导了QCM传感器在空载条件下的BVD (Butterworth-Van Dyke)等效电路模型，并与基于经典本构方程得到的等效电路进行了比较，验证了该推导方法的正确性。在此基础上详细推导了气相弹性介质吸附的Sauerbrey模型、液相粘性介质吸附的Kanasawa模型以及Martin模型，进一步验证了该推导方法的有效性。
2．对于粘弹性介质，目前QCM传感器的数据分析还存在着一定的缺陷和不足，为了解决这一问题，本文采用一种简单的方法准确推导了响应分析模型。同时，本文还结合该模型提出了一种稳态测量方法，从频率测量的角度，应用频率与耗散因子的转换关系，精确得到耗散因子，提高了QCM传感器的数据分析的准确度。
3．分别从气相和液相的应用角度，推导了单层粘弹性薄膜吸附的QCM传感器响应模型，给出了明确的显性表达式，得到了与QCM-D模型完全一样的结论：气相条件下，粘弹性薄膜的粘弹性模量会引入“额外质量”效应；液相条件下，粘弹性薄膜的粘弹性模量会引入“遗失质量”效应。实验事实证明，本文推导的响应模型对粘弹性薄膜特性分析具有一定指导意义，同时为QCM生化分析领域的深入研究提供了量化的分析方法和科学依据。
4．深入分析了溶液特性对QCM传感器的影响因素，针对生化溶液特性的分析，尤其是未知密度、粘度的溶液分析，本文推导了一种新的模型，并提出了一种新的检测方法。传统的方法需要同时测量QCM传感器的输出频率和等效电阻等参量，然后建立方程组求解。而本文提出的新方法，只需要测量QCM传感器输出的频率信息便可以直接计算出未知溶液的密度、粘度等相关信息。大大简化了测试过程，提高了测试的精度。
Quartz Crystal Microbalance (QCM) is an ultrasensitive mass sensing device andcan be used to detect tiny mass change at the precision of nanogram(109g). It hasmany advantages, e.g. results can be shown realtime and traced online, cost isinexpensive on average, and quantitative analysis results can be given as well. It alsoholds great potential and can be widely used to high precise measurement and analysisfields, such as the detection or evaluation of agricultural pesticide residues, food safety,heavy metal pollution, air pollution, water quality, medical diagnosis and treatment, etc.and it has been a hotspot in the field of biochemical detection and analysis.
Among the widely-accepted models of QCM, the Sauerbrey Model can only beapplied to the gas phase, while the Kanasawa Model to the liquid phase. The KanasawaModel multiplies the viscosity and elasticity of the liquid together as one inseparableterm. The QCM-D Model was derived based on fluid mechanics and the theory of theVoigt, in which the quation sets are conducted to explore the viscoelastic mediumadsorption phenomenon. However, the model requires certain information about thesolution, such as the density and the viscosity, which causes certain limitation inapplication. Additionally, to get the energy dissipation change in the Voigt model,instantaneous measurement method are applied, the QCM sensor is excitated tooscillation with an impulse, and then the decay time (usually in10-6seconds) isrecorded. This approach is vulnerable to the tiny perturbation, which affects theaccuracy of analysis results greatly.
Based on the theory of transmission line and acoustic theory, explicit expressionsof response Models of a QCM sensor with different contacting media are derived.Relations among the frequency shift of the QCM sensor as well as the change ofdissipation factor and the characteristics of thin film adsorption are also revealed in thispaper. Characteristics of several materials are analyzed and evaluated quantitatively byexperiments as well. The innovation works in this paper mainly include:
1. Based on the transmission theory and load acoustic impedance theory, the BVD(Butterworth-Van Dyke) equivalent circuit of an unloaded QCM sensor is derived. Thecorrectness of the method is verified by making comparison to the classic constitutiveequation. The Sauerbrey Model, the Kanasawa Model and the Martin Model are deduced in detail with the method, which proves the validity of these models.
2. As for viscoelastic medium, current data analysis method of the QCM sensor hascertain deficiency. To solve the problem, this paper conducted response modelaccurately in a simple way. At the same time, a new method of steady statemeasurement is given based on the model. By applying the transforming relationshipbetween the frequency and the dissipation factor, the new method enables to acquire thedissipation factor accurately, from the perspective of frequency measurement. The newway improved the accuracy of the data analysis of the QCM sensor.
3. Respectively from the perspective of the gas phase and the liquid phase, thispaper derived the response model of the QCM sensor with single viscoelastic thin filmabsorbed, providing certain explicit expression. The conclusion drawn in this paper isexactly same to the QCM-D Model: in gas phase, the extra mass effect is introduced bythe viscoelastic modulus of viscoelastic thin film, while in liquid phase, missing masseffect is introduced by the viscoelastic modulus of viscoelastic thin film. It is revealedby experiments that the response model conducted in this paper has certain guidingsignificance to the analysis of viscoelastic thin film characteristics. It provides ananalysis method and a scientific basis of QCM for further research in the field ofbiochemistry.
4. Influencing factors of the QCM sensors caused by the properties of solutions areexplored in depth. A new model and a new detection method are presented to makeanalysis on biochemistry solutions, especially for the solution with its density andviscosity unknown. Common methods work with the output frequency and theequivalent impedance measured simultaneously, establishing equation sets to be solved.Only the information of the QCM frequency is adopted by the method introduced, andthe density and the viscosity can be seperated directly. The process of measurement isgreatly simplified and the accuracy is improved at the same time.
在经典的QCM的数据分析响应模型中， Sauerbrey模型只适用于气相刚性膜均匀吸附应用；Kanasawa模型只适用于液相纯粘性液体应用，并且它只能把未知液体的密度和粘度的乘积项当做一个参数来处理。QCM-D响应模型通过QCM的频率变化和能量耗散变化建立方程组来分析粘弹性介质吸附现象。但是，该模型需要已知溶液的密度、粘度等信息，在应用上有一定的局限性。同时，QCM-D响应模型中能量耗散变化的获得是采用瞬时测量法以脉冲激励的方式让QCM传感器振荡，然后测量其衰减时间（一般是在10-6秒量级）计算得到。这种方法容易受到外界的微小干扰而影响分析结果的准确度。
本文在传输线理论和声波理论的基础上，推导了不同介质吸附下QCM传感器响应模型的显性表示式，揭示了QCM传感器的频率变化以及耗散因子变化与所吸附的介质特性之间的关系。进而通过验证，定量分析和评估了多种材料的特性。本文主要工作和创新点包括：
1．应用传输线理论以及负载声波阻抗理论，推导了QCM传感器在空载条件下的BVD (Butterworth-Van Dyke)等效电路模型，并与基于经典本构方程得到的等效电路进行了比较，验证了该推导方法的正确性。在此基础上详细推导了气相弹性介质吸附的Sauerbrey模型、液相粘性介质吸附的Kanasawa模型以及Martin模型，进一步验证了该推导方法的有效性。
2．对于粘弹性介质，目前QCM传感器的数据分析还存在着一定的缺陷和不足，为了解决这一问题，本文采用一种简单的方法准确推导了响应分析模型。同时，本文还结合该模型提出了一种稳态测量方法，从频率测量的角度，应用频率与耗散因子的转换关系，精确得到耗散因子，提高了QCM传感器的数据分析的准确度。
3．分别从气相和液相的应用角度，推导了单层粘弹性薄膜吸附的QCM传感器响应模型，给出了明确的显性表达式，得到了与QCM-D模型完全一样的结论：气相条件下，粘弹性薄膜的粘弹性模量会引入“额外质量”效应；液相条件下，粘弹性薄膜的粘弹性模量会引入“遗失质量”效应。实验事实证明，本文推导的响应模型对粘弹性薄膜特性分析具有一定指导意义，同时为QCM生化分析领域的深入研究提供了量化的分析方法和科学依据。
4．深入分析了溶液特性对QCM传感器的影响因素，针对生化溶液特性的分析，尤其是未知密度、粘度的溶液分析，本文推导了一种新的模型，并提出了一种新的检测方法。传统的方法需要同时测量QCM传感器的输出频率和等效电阻等参量，然后建立方程组求解。而本文提出的新方法，只需要测量QCM传感器输出的频率信息便可以直接计算出未知溶液的密度、粘度等相关信息。大大简化了测试过程，提高了测试的精度。
Quartz Crystal Microbalance (QCM) is an ultrasensitive mass sensing device andcan be used to detect tiny mass change at the precision of nanogram(109g). It hasmany advantages, e.g. results can be shown realtime and traced online, cost isinexpensive on average, and quantitative analysis results can be given as well. It alsoholds great potential and can be widely used to high precise measurement and analysisfields, such as the detection or evaluation of agricultural pesticide residues, food safety,heavy metal pollution, air pollution, water quality, medical diagnosis and treatment, etc.and it has been a hotspot in the field of biochemical detection and analysis.
Among the widely-accepted models of QCM, the Sauerbrey Model can only beapplied to the gas phase, while the Kanasawa Model to the liquid phase. The KanasawaModel multiplies the viscosity and elasticity of the liquid together as one inseparableterm. The QCM-D Model was derived based on fluid mechanics and the theory of theVoigt, in which the quation sets are conducted to explore the viscoelastic mediumadsorption phenomenon. However, the model requires certain information about thesolution, such as the density and the viscosity, which causes certain limitation inapplication. Additionally, to get the energy dissipation change in the Voigt model,instantaneous measurement method are applied, the QCM sensor is excitated tooscillation with an impulse, and then the decay time (usually in10-6seconds) isrecorded. This approach is vulnerable to the tiny perturbation, which affects theaccuracy of analysis results greatly.
Based on the theory of transmission line and acoustic theory, explicit expressionsof response Models of a QCM sensor with different contacting media are derived.Relations among the frequency shift of the QCM sensor as well as the change ofdissipation factor and the characteristics of thin film adsorption are also revealed in thispaper. Characteristics of several materials are analyzed and evaluated quantitatively byexperiments as well. The innovation works in this paper mainly include:
1. Based on the transmission theory and load acoustic impedance theory, the BVD(Butterworth-Van Dyke) equivalent circuit of an unloaded QCM sensor is derived. Thecorrectness of the method is verified by making comparison to the classic constitutiveequation. The Sauerbrey Model, the Kanasawa Model and the Martin Model are deduced in detail with the method, which proves the validity of these models.
2. As for viscoelastic medium, current data analysis method of the QCM sensor hascertain deficiency. To solve the problem, this paper conducted response modelaccurately in a simple way. At the same time, a new method of steady statemeasurement is given based on the model. By applying the transforming relationshipbetween the frequency and the dissipation factor, the new method enables to acquire thedissipation factor accurately, from the perspective of frequency measurement. The newway improved the accuracy of the data analysis of the QCM sensor.
3. Respectively from the perspective of the gas phase and the liquid phase, thispaper derived the response model of the QCM sensor with single viscoelastic thin filmabsorbed, providing certain explicit expression. The conclusion drawn in this paper isexactly same to the QCM-D Model: in gas phase, the extra mass effect is introduced bythe viscoelastic modulus of viscoelastic thin film, while in liquid phase, missing masseffect is introduced by the viscoelastic modulus of viscoelastic thin film. It is revealedby experiments that the response model conducted in this paper has certain guidingsignificance to the analysis of viscoelastic thin film characteristics. It provides ananalysis method and a scientific basis of QCM for further research in the field ofbiochemistry.
4. Influencing factors of the QCM sensors caused by the properties of solutions areexplored in depth. A new model and a new detection method are presented to makeanalysis on biochemistry solutions, especially for the solution with its density andviscosity unknown. Common methods work with the output frequency and theequivalent impedance measured simultaneously, establishing equation sets to be solved.Only the information of the QCM frequency is adopted by the method introduced, andthe density and the viscosity can be seperated directly. The process of measurement isgreatly simplified and the accuracy is improved at the same time.
引文
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