Soft, Structured Layers on the Surface of a Quartz Crystal Microbalance (QCM): A Computational Model to Predict Shifts of Frequency and Bandwidth Based on the Lattice-Boltzmann Method

基于晶格玻尔兹曼方法的线性化变体（称为频域晶格玻尔兹曼方法），应开发模拟石英晶体微天平（QCM）在液相中与结构样品接触时的行为的模拟包。虽然该方法适用于任意形状的样品，但这项工作的重点是厚度远低于声波波长的颗粒吸附物（如吸附的球状蛋白质）。要改变的参数之一是覆盖率。要预测的参数是共振频率和共振带宽在谐振器不同泛音上的位移。预测这些参数的分析模型存在于平面层体系中，但不存在于横向非均质样品中。第一步应该是量化被吸附颗粒之间的液体质量对总表观质量的贡献，后者是用（非常简单的）Sauerbrey方程从频移计算出来的。可变大小、形状和方向的颗粒应随机沉积在谐振器表面，这样做的算法应允许聚类。第二步应该是研究颗粒和基材之间接触的有限顺应性的后果。有限顺应性有望增加共振带宽。这种期望需要经过检验，并转化为定量预测。确定反演策略：对于某些具有实际重要性的配置，需要推导出规则，根据实验确定的值作为泛音阶和覆盖率的函数来推断样本的参数（如粒子的平均高度、连杆的刚度或聚类程度）。在项目的后期，还需要改进代码的精度，以获得颗粒表面的力。这一步对于研究大小与声波波长相当的吸附剂是很重要的。对于目前的代码来说，这种层构成了一个技术问题，如果层在声学上很薄，就可以绕过这个问题。具有声波波长数量级厚度的吸附粒子经常显示所谓的耦合共振。耦合共振可以看作是剪切波光谱中的吸附谱线。分子与振动光谱学有着深远的相似之处。特别是，有一个模式分配问题，这意味着耦合共振可以由吸附物体的不同运动模式引起。模式分配问题由拟建作品解决。特别需要说明的是，对于给定的实验实例，耦合共振是由在连杆处施加弯曲应力的摇摆模式引起的，还是由施加切向应力的滑移模式引起的。

Building on a linearized variant of the Lattice Boltzmann Method (termed Frequency-Domain Lattice-Boltzmann Method), a simulation package shall be developed, which models the behavior a quartz crystal microbalance (QCM) in contact with structured samples in the liquid phase. While the method shall be applicable to samples with arbitrary shape, this work shall focus on particulate adsorbates with a thickness much below the wavelength of sound (such adsorbed globular proteins). Among the parameters to be varied is the coverage. The parameters to be predicted are the shifts of resonance frequency and resonance bandwidth on the different overtones of the resonator. Analytical models predicting these parameters exist for planar layer systems, but not for laterally heterogeneous samples. A first step shall be to quantify the contribution of the liquid mass trapped between adsorbed particles to the overall apparent mass, where the latter is calculated from the frequency shift with the (very simple) Sauerbrey equation. Particles of variable size, shape, and orientation shall be randomly deposited on the resonator surface, where the algorithm doing so shall allow for clustering. A second step shall be to study the consequences of a finite compliance of the contact between the particle and the substrate. Finite compliance is expected to increase the resonance bandwidth. This expectation shall be tested and be turned into a quantitative prediction. Strategies for inversion shall be identified: For certain configurations of practical importance, rules shall be derived, which allow to infer parameters of the sample (such as the average height of the particles, the stiffness of link, or the degree of clustering) from the experimentally determined values as a function of overtone order and coverage. Later in the project, the code shall be improved with regard to the accuracy, by which the forces at the particle surfaces are obtained. This step will be important for the study of adsorbates with sizes comparable to the wavelength of sound. For the current code, such layers pose a technical problem, which can be circumvented if the layers are acoustically thin. Adsorbed particles with a thickness of the order of the wavelength of sound often display so-called coupled resonances. Coupled resonances can be viewed as adsorption lines in shear-wave spectroscopy. There is a far-reaching analogy to vibrational spectroscopy on molecules. In particular, there is a mode-assignment problem, meaning that a coupled resonance can be caused by different modes of motion of the adsorbed object. The mode assignment problem shall be solved by the proposed work. In particular, it shall be clarified for a given experimental example, whether the coupled resonance is caused by a rocking mode, which exerting a bending stress at the link, or a slipping mode which exerts a tangential stress.