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

在格子Boltzmann方法的线性化变体(称为频域格子-Boltzmann方法)的基础上，将开发一个模拟程序包，对石英晶体微天平(QCM)与液体中结构样品接触的行为进行模拟。虽然该方法适用于任意形状的样品，但这项工作应侧重于厚度远低于声波波长的颗粒吸附物(这种吸附的球状蛋白)。在要改变的参数中，覆盖率是不同的。要预测的参数是谐振器不同泛音上的共振频率和共振带宽的偏移。预测这些参数的分析模型存在于平面层系统，但不适用于横向非均质样品。第一步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。不同大小、形状和取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集。第二步是研究颗粒与衬底之间接触的有限柔度的后果。有限顺应性有望增加共振带宽。这一预期应该得到检验，并转化为定量预测。应确定反转策略：对于具有实际重要性的某些构型，应导出规则，这些规则允许从作为泛音顺序和覆盖的函数的实验确定的值中推断样本的参数(例如粒子的平均高度、链接的刚度或聚集度)。在本项目的后期，规范将在获得颗粒表面的力的精度方面进行改进。这一步对于研究大小与声波波长相当的吸附物将是重要的。对于当前的代码，这样的层构成了一个技术问题，如果这些层非常薄，就可以绕过这个问题。厚度在声波波长数量级的被吸附粒子通常表现出所谓的耦合共振。在剪切波谱中，耦合共振可以看作是吸收线。分子的振动光谱学有一个影响深远的类比。具体地说，存在模式分配问题，这意味着耦合共振可能由被吸附物体的不同运动模式引起。模式分配问题将通过拟议的工作来解决。特别是，对于给定的实验例子，应明确耦合共振是由在杆件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.