EaStCHEM School of Chemistry, University of St. Andrews, North Haugh, St. Andrews, KY16 9ST, UK.
Ultramicroscopy. 2010 Jun;110(7):801-6. doi: 10.1016/j.ultramic.2010.02.008. Epub 2010 Feb 12.
In atomic force microscopy (AFM) a sharp tip fixed close to the free end of a cantilever beam interacts with a surface. The interaction can be described by a point-mass model of an equivalent oscillator with a single spring located at the position of the tip. However, other spring constants have to be used to describe the oscillation behavior correctly if forces are acting on the cantilever over an extended lateral range. A point-mass model is then no longer valid. In the present study we derive expressions for the spring constants of cantilevers that can interact with any part of their plan view area along the beam and for all flexural modes. The equations describe the oscillation behavior in the corresponding mass model and are based on the eigenfrequencies and modal shapes of the free cantilever. The results are of high practical relevance, for example if an AFM is operated in a higher flexural mode, if the tip is not located at the free end of the cantilever beam, or if the external conservative forces affecting cantilever movement are not restricted to a single point. The limitations of the approach are discussed.
在原子力显微镜（AFM）中，一个固定在悬臂梁自由端附近的尖锐尖端与表面相互作用。可以通过位于尖端位置的等效振荡器的质点模型来描述相互作用，该模型具有单个弹簧。但是，如果力在悬臂梁的扩展横向范围内作用，则必须使用其他弹簧常数来正确描述振荡行为。此时，质点模型不再有效。在本研究中，我们推导出了能够与沿梁的整个平面区域的任何部分相互作用的悬臂梁的弹簧常数的表达式，以及所有挠曲模态的表达式。这些方程描述了相应质量模型中的振荡行为，并且基于自由悬臂梁的本征频率和模态形状。这些结果具有很高的实际意义，例如，如果 AFM 以更高的挠曲模态运行，如果尖端未位于悬臂梁的自由端，或者如果影响悬臂梁运动的外部保守力不限于单点。讨论了该方法的局限性。
