基于最佳加窗啁啾的软材料时间分辨力学谱
Time-Resolved Mechanical Spectroscopy of Soft Materials via Optimally Windowed Chirps
摘要：
结合时间和频率分辨率测量软材料的体动力学行为的能力有助于提高我们的微观结构动力学和宏观力学响应之间的联系的基本理解。当前最先进的技术通常受限于时域和频域中的分辨率之间的折衷，这主要是由于使用了未被设计用于快速时间演变系统（诸如经历凝胶化、固化或自修复的材料）的基本输入信号。在这项工作中，我们开发了一个优化的和强大的激励信号的时间分辨力学光谱通过引入联合频率和振幅调制的指数啁啾。受蝙蝠和海豚的生物声纳信号的启发，我们优化了信号轮廓，以最大限度地提高信噪比，同时通过精心设计的啁啾包络调制来最大限度地减少频谱泄漏。结合实验和数值研究表明，存在一个最佳范围的窗口配置文件，最大限度地减少相对于标准的单频扫描方法的错误。最小误差由仪器的本底噪声设定，这表明最佳加窗线性调频信号的准确度与标准频率扫描可实现的准确度直接相当，而对于可比的频谱内容，采集时间可以减少多达两个数量级。最后，我们证明了这种优化的信号提供时间和频率分辨的流变数据的能力，通过研究快速凝胶化过程中的酸诱导蛋白质凝胶。使用最佳窗口啁啾能够对经历快速突变的各种软材料进行强大的流变表征，并有可能成为不同学科研究人员的宝贵工具。
英文摘要：
The ability to measure the bulk dynamic behavior of soft materials with combined time- and frequency-resolution is instrumental for improving our fundamental understanding of connections between the microstructural dynamics and the macroscopic mechanical response. Current state-of-the-art techniques are often limited by a compromise between resolution in the time and frequency domain, mainly due to the use of elementary input signals that have not been designed for fast time-evolving systems such as materials undergoing gelation, curing or self-healing. In this work, we develop an optimized and robust excitation signal for time-resolved mechanical spectroscopy through the introduction of joint frequency- and amplitude-modulated exponential chirps. Inspired by the biosonar signals of bats and dolphins, we optimize the signal profile to maximize the signal-to-noise ratio while minimizing spectral leakage with a carefully-designed modulation of the envelope of the chirp. A combined experimental and numerical investigation reveals that there exists an optimal range of window profiles that minimizes the error with respect to standard single frequency sweep methods. The minimum error is set by the noise floor of the instrument, suggesting that the accuracy of an optimally windowed chirp signal is directly comparable to that achievable with a standard frequency sweep, while the acquisition time can be reduced by up to two orders of magnitude, for comparable spectral content. Finally, we demonstrate the ability of this optimized signal to provide time- and frequency-resolved rheometric data by studying the fast gelation process of an acid-induced protein gel. The use of optimally windowed chirps enables a robust rheological characterization of a wide range of soft materials undergoing rapid mutation and has the potential to become an invaluable tool for researchers across different disciplines.
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