Université de Lyon, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS, 46 allée d'Italie, F-69007, Lyon, France.
Nanotechnology. 2013 Jun 7;24(22):225504. doi: 10.1088/0957-4484/24/22/225504. Epub 2013 May 3.
The functionalization of an atomic force microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response? And more importantly for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques?In this paper, the influence of the colloidal mass loading on the eigenmode shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without beads attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode is almost unchanged by mass loading. However the oscillation behavior of higher resonances presents a marked difference: with a particle glued at its extremity, the nodes of the modes are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and inertial moment of the load in an Euler-Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.
原子力显微镜（AFM）悬臂的胶体微球功能化是一种广泛使用的技术，当探针和样品之间的几何形状必须控制时，特别是在力谱学中。但是，仍然存在一些问题：粘在悬臂末端的微球如何影响其机械响应？更重要的是，对于定量测量，我们仍然可以用传统技术确定 AFM 探针的刚度吗？在本文中，通过测量带有和不带有胶体质量负载的矩形 AFM 微悬臂的热噪声，研究了胶体质量负载对本征模态形状和共振频率的影响。实验是在基于差分干涉的自制超灵敏 AFM 上进行的。干涉仪的聚焦光束在不同位置探测悬臂，并且在没有外部激励的情况下，确定模式的空间形状直到第五共振。结果清楚地表明，第一本征模式几乎不受质量负载的影响。然而，较高共振的振荡行为呈现出明显的差异：在其末端粘附有颗粒时，模式的节点向悬臂的自由端移动。这些结果与考虑负载的质量和惯性矩的 Euler-Bernoulli 框架中的分析模型进行了比较，其中明确地制定了本征模态的归一化，以便能够对每个模式的热噪声幅度进行定量预测。实验结果与分析模型之间的良好一致性得到了证明，从而可以对探针刚度进行清洁校准。
