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

该项目研究了原子力显微镜（AFM）中用于纳米级成像和力传感的新型超灵敏模式的动力学，这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方面的大量应用产生重大影响。在参数共振和非线性共振（亚谐波、超谐波和组合共振）驱动下，对AFM微悬臂梁的连续棒模型在尖端-样品相互作用力作用下的平衡位置进行了系统离散化。利用解析渐近技术研究了离散模型的动力学特性，以适应尖样相互作用力的非光滑性，并对非光滑系统进行了精确的数值模拟。重点是在参数空间中识别对尖端-样品相互作用力最敏感的区域以及与分岔和不稳定动力学相对应的区域。在不同的微悬臂和样品材料上进行了仔细的实验，使用定制的带有双锁相放大器的AFM，允许不同的激励和响应频率，这是参数共振和非线性共振的典型情况。原子力显微镜（Atomic Force Microscope， AFM）以其非凡的测量纳米尺度力的能力，以及以纳米分辨率对原子和分子进行成像和操作的能力，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关键的纳米技术支持工具的灵敏度；然而，在环境条件下，这种灵敏度基本上受到激励性质和共振质量因子（q因子）的限制。对纳米级相互作用力的更高灵敏度可以使AFM揭示材料特性对比，并检测隐藏在背景噪声中的纳米级力。提出的研究旨在通过使用(a)参数共振和(b)非线性共振振荡AFM探针来创建全新的AFM模式，这种共振可以绕过传统AFM系统中当前对灵敏度的限制。在此过程中，这项研究将为AFM在各种应用领域的科学突破打开大门，包括生物分子的成像和光谱、基于探针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的爆炸式增长，有一个快速增长的机构的AFM实验人员没有在动力学训练，很少意识到它的重要性在这个“显微镜”。该项目使用NSF支持的nanoHUB （www.nanohub.org）的现有框架来创建AFM动力学的在线模拟工具，该工具将供全球数百名实验人员和教育工作者使用。这是由计算纳米技术网络（NCN）创建的，是一个由NSF资助的将理论、实验和计算联系起来的项目，是NSF在利用网络基础设施刺激科学研究方面的成功案例之一。这些工具的使用不仅有助于解释AFM数据，减少全球研究生和研究人员的AFM培训时间，而且还可以作为本科和研究生课程中教授扫描探针显微镜基础和高级概念的优秀资源。

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.