Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juan Ines de la Cruz 3, 28049 Madrid, Spain.
Beilstein J Nanotechnol. 2013 Dec 6;4:852-9. doi: 10.3762/bjnano.4.96. eCollection 2013.
The peak forces exerted on soft and rigid samples by a force microscope have been modeled by performing numerical simulations of the tip motion in liquid. The forces are obtained by using two contact mechanics models, Hertz and Tatara. We present a comparison between the numerical simulations and three analytical models for a wide variety of probe and operational parameters. In general, the forces derived from analytical expressions are not in good quantitative agreement with the simulations when the Young modulus and the set-point amplitude are varied. The only exception is the parametrized approximation that matches the results given by Hertz contact mechanics for soft materials and small free amplitudes. We also study the elastic deformation of the sample as a function of the imaging conditions for materials with a Young modulus between 25 MPa and 2 GPa. High lateral resolution images are predicted by using both small free amplitudes (less than 2 nm for soft materials) and high set-point amplitudes.
力显微镜对软质和硬质样品施加的峰值力已经通过对液体内针尖运动进行数值模拟来建模。利用 Hertz 和 Tatara 两种接触力学模型来获得力。我们对各种探针和操作参数的数值模拟和三个分析模型进行了比较。一般来说，当杨氏模量和设定点幅度变化时，解析表达式得出的力与模拟结果没有很好的定量一致性。唯一的例外是参数化近似，它与软材料和小自由幅度下 Hertz 接触力学给出的结果相匹配。我们还研究了杨氏模量在 25 MPa 到 2 GPa 之间的材料的弹性变形作为成像条件的函数。通过使用小的自由幅度（对于软材料小于 2nm）和高的设定点幅度，可以预测出具有高横向分辨率的图像。
