Korayem Moharam Habibnejad, Saraie Maniya B, Saraee Mahdieh B
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran.
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran.
Ultramicroscopy. 2017 Apr;175:9-24. doi: 10.1016/j.ultramic.2017.01.004. Epub 2017 Jan 13.
An important challenge when using an atomic force microscope (AFM) is to be able to control the force exerted by the AFM for performing various tasks. Nevertheless, the exerted force is proportional to the deflection of the AFM cantilever, which itself is affected by a cantilever's stiffness coefficient. Many papers have been published so far on the methods of obtaining the stiffness coefficients of AFM cantilevers in 2D; however, a comprehensive model is yet to be presented on 3D cantilever motion. The discrepancies between the equations of the 2D and 3D analysis are due to the number and direction of forces and moments that are applied to a cantilever. Moreover, in the 3D analysis, contrary to the 2D analysis, due to the interaction between the forces and moments applied on a cantilever, its stiffness values cannot be separately expressed for each direction; and instead, a stiffness matrix should be used to correctly derive the relevant equations. In this paper, 3D stiffness coefficient matrices have been obtained for three common cantilever geometries including the rectangular, V-shape and dagger-shape cantilevers. The obtained equations are validated by two methods. In the first approach, the Finite Element Method is combined with the cantilever deflection values computed by using the obtained stiffness matrices. In the second approach, by reducing the problem's parameters, the forces applied on a cantilever along different directions are compared with each other in 2D and 3D cases. Then the 3D manipulation of a stiff nanoparticle is modeled and simulated by using the stiffness matrices obtained for the three cantilever geometries. The obtained results indicate that during the manipulation process, the dagger-shaped and rectangular cantilevers exert the maximum and minimum amounts of forces on the stiff nanoparticle, respectively. Also, by examining the effects of different probe tip geometries, it is realized that a probe tip of cylindrical geometry exerts the smallest force on a biological nanoparticle. Therefore, the rectangular cantilever is a more suitable geometry for preventing the exertion of excessive force and the possible damage of such nanoparticle.
使用原子力显微镜（AFM）时的一个重要挑战是能够控制AFM施加的力以执行各种任务。然而，施加的力与AFM悬臂的挠度成正比，而悬臂的挠度本身又受悬臂刚度系数的影响。到目前为止，已经发表了许多关于在二维中获取AFM悬臂刚度系数方法的论文；然而，尚未有关于三维悬臂运动的综合模型。二维和三维分析方程之间的差异是由于施加在悬臂上的力和力矩的数量和方向不同。此外，在三维分析中，与二维分析不同，由于施加在悬臂上的力和力矩之间的相互作用，其刚度值不能针对每个方向单独表示；相反，应该使用刚度矩阵来正确推导相关方程。在本文中，已经获得了三种常见悬臂几何形状（包括矩形、V形和匕首形悬臂）的三维刚度系数矩阵。通过两种方法对得到的方程进行了验证。在第一种方法中，将有限元方法与使用得到的刚度矩阵计算出的悬臂挠度值相结合。在第二种方法中，通过减少问题的参数，比较二维和三维情况下沿不同方向施加在悬臂上的力。然后，使用为三种悬臂几何形状获得的刚度矩阵对刚性纳米颗粒的三维操纵进行建模和模拟。获得的结果表明，在操纵过程中，匕首形和矩形悬臂分别对刚性纳米颗粒施加最大和最小的力。此外，通过研究不同探针尖端几何形状的影响，发现圆柱形几何形状的探针尖端对生物纳米颗粒施加的力最小。因此，矩形悬臂是一种更合适的几何形状，可防止施加过大的力以及避免此类纳米颗粒可能受到的损坏。
