Nonlinear Dynamics of Microcantilevers Interacting with Nanostructures: New Paradigms for Ultrasensitive Atomic Force Microscopy

本项目研究原子力显微镜(AFM)中用于纳米尺度成像和力传感的新的超灵敏模式的动力学，这些模式可能会对其在纳米技术、材料科学、生物学、凝聚态物理和数据存储技术中的重要应用产生重大影响。在针尖-样品相互作用力的作用下，系统地离散了参数共振和非线性共振(亚谐、超谐和组合)作用下AFM微悬臂梁的连续杆模型的平衡位置。利用(1)用于适应尖端-样品相互作用力的非光滑的解析渐近技术和(2)非光滑系统的精确数值模拟，研究了离散化模型的动力学。重点是识别参数空间中对尖端-样品相互作用力最敏感的区域，以及对应于分叉和不稳定动力学的区域。在不同的微悬臂梁和样品材料上进行了仔细的实验，使用定制的带有双锁定放大器的AFM，允许不同的激励和响应频率，这是参数和非线性共振的典型情况。原子力显微镜(AFM)以其测量纳米尺度的力以及以纳米分辨率成像和操纵原子和分子的非凡能力，已经成为纳米技术最重要的工具之一。世界各地正在努力提高这一纳米技术关键使能工具的灵敏度；然而，在环境条件下，这种灵敏度从根本上受到激励的性质和共振的品质因数(Q因数)的限制。对纳米级相互作用力的更高敏感度可以使AFM揭示材料性质的对比度，并检测原本隐藏在背景噪音中的纳米级力。这项拟议的研究旨在通过使用(A)参数共振和(B)非线性共振来振荡AFM探针来创建全新的AFM模式，该共振可以绕过传统AFM系统中对灵敏度的当前限制。通过这样做，这项研究可以为各种AFM应用打开科学突破的大门，包括生物分子的成像和光谱、基于探测器的数据存储以及纳米材料的合成和表征。鉴于AFM在世界各地的大学校园和研究实验室中的爆炸性增长，有越来越多的AFM实验者没有接受过动力学方面的培训，几乎没有意识到它在这个“显微镜”中的重要性。该项目使用美国国家科学基金会支持的NanHUB(www.nanhub.org)的现有框架来创建AFM动力学的在线模拟工具，全世界数百名实验者和教育工作者都可以使用这些工具。这是由计算纳米技术网络(NCN)创建的一项由NSF资助的倡议，将理论、实验和计算联系在一起，这是NSF在使用网络基础设施刺激科学研究方面的成功故事之一。这些工具的使用不仅有望帮助解释AFM数据，减少世界各地研究生和研究人员的AFM培训时间，而且还是在本科生和研究生课堂上教授扫描探针显微镜的基本和高级概念的极好资源。

This project investigates the dynamics of new ultrasensitive modes for nanoscale imaging and force sensing in the Atomic Force Microscope (AFM) that could impact significantly its considerable applications in nanotechnology, material science, biology, condensed matter physics, and data storage technology. Continuous rod models of AFM microcantilevers driven at parametric and nonlinear resonances (sub-, superharmonic and combination) are systematically discretized about their equilibrium position under the action of tip-sample interaction forces. The dynamics of the discretized model are studied using (1) analytical asymptotic techniques to accommodate non-smoothness of tip-sample interaction forces, and (2) accurate numerical simulations for non-smooth systems. A focus is placed on identifying regions in parameter space with greatest sensitivity to tip-sample interaction forces as well as regions corresponding to bifurcations and unstable dynamics. Careful experiments are performed on different microcantilevers and sample materials with a custom built AFM with dual lock-in amplifiers that allow for different excitation and response frequencies, a typical situation for parametric and nonlinear resonance. The Atomic Force Microscope (AFM) has become one of the most important tools for nanotechnology with its remarkable ability to measure nanoscale forces and image and manipulate atoms and molecules with nanometer resolution. Efforts are ongoing around the world to improve the sensitivity of this key enabling tool for nanotechnology; however, under ambient conditions this sensitivity is fundamentally limited by the nature of excitation and the quality factor (Q-factor) of the resonance. Greater sensitivity to nanoscale interaction forces could enable the AFM to reveal material property contrast and detect nanoscale forces that are otherwise hidden in background noise. The proposed research aims to create entirely new AFM modes by oscillating the AFM probes using (a) parametric and (b) nonlinear resonances that could bypass the current limits on sensitivity in conventional AFM systems. In doing so, the research could open the door to scientific breakthroughs in diverse AFM applications including the imaging and spectroscopy of biological molecules, probe-based data storage, and synthesis and characterization of nanomaterials. Given the explosion of AFM's in University campuses and research labs around the world, there is a rapidly growing body of AFM experimentalists who are not trained in dynamics and little realize its importance in this "microscope". The project uses the existing framework of the NSF supported nanoHUB (www.nanohub.org) to create online simulation tools for AFM dynamics that would be accessible to hundreds of experimentalists and educators worldwide. Created by the Network for Computational Nanotechnology (NCN), this is a NSF-funded initiative connecting theory, experiment, and computation one of NSF's success stories in the use of cyberinfrastructure to spur scientific research. Not only is the use of these tools expected to aid the interpretation of AFM data and reduce AFM training time for graduate students and researchers worldwide, it also serves as an excellent resource for teaching fundamental and advanced concepts of scanning probe microscopy in both undergraduate and graduate classes.