Kennedy Scott J, Cole Daniel G, Clark Robert L
Department of Mechanical Engineering and Materials Science, Center for Biologically Inspired Materials and Material Systems, Duke University, Durham, North Carolina 27708, USA.
Rev Sci Instrum. 2009 Dec;80(12):125103. doi: 10.1063/1.3263907.
This work presents a method for force calibration of rectangular atomic force microscopy (AFM) microcantilevers under heavy fluid loading. Theoretical modeling of the thermal response of microcantilevers is discussed including a fluid-structure interaction model of the cantilever-fluid system that incorporates the results of the fluctuation-dissipation theorem. This model is curve fit to the measured thermal response of a cantilever in de-ionized water and a cost function is used to quantify the difference between the theoretical model and measured data. The curve fit is performed in a way that restricts the search space to parameters that reflect heavy fluid loading conditions. The resulting fitting parameters are used to calibrate the cantilever. For comparison, cantilevers are calibrated using Sader's method in air and the thermal noise method in both air and water. For a set of eight cantilevers ranging in stiffness from 0.050 to 5.8 N/m, the maximum difference between Sader's calibration performed in air and the new method performed in water was 9.4%. A set of three cantilevers that violate the aspect ratio assumption associated with the fluid loading model (length-to-width ratios less than 3.5) ranged in stiffness from 0.85 to 4.7 N/m and yielded differences as high as 17.8%.
这项工作提出了一种在重流体负载下对矩形原子力显微镜（AFM）微悬臂梁进行力校准的方法。讨论了微悬臂梁热响应的理论建模，包括结合了涨落耗散定理结果的悬臂梁 - 流体系统的流固相互作用模型。该模型与在去离子水中测量的悬臂梁热响应进行曲线拟合，并使用成本函数来量化理论模型与测量数据之间的差异。曲线拟合以将搜索空间限制在反映重流体负载条件的参数的方式进行。所得的拟合参数用于校准悬臂梁。为作比较，在空气中使用萨德方法以及在空气和水中使用热噪声方法对悬臂梁进行校准。对于一组刚度范围从0.050到5.8 N/m的八个悬臂梁，在空气中进行的萨德校准与在水中进行的新方法之间的最大差异为9.4%。一组违反与流体负载模型相关的纵横比假设（长宽比小于3.5）的三个悬臂梁，刚度范围从0.85到4.7 N/m，差异高达17.8%。
