Jump-to-contact is a commonly observed phenomenon in atomic force microscopy (AFM) measurements. It occurs when the AFM tip approaches the surface of the substrate, and the attractive forces – such as van der Waals forces – between the tip and the surface become sufficiently strong, causing the tip to jump towards the surface suddenly. Here, we investigate how the surface deformation affects the onset of jump-to-contact, and show that jump-to-contact happens prematurely in the deformable case (compared to the rigid case). We formulate this problem for surfaces that respond to external forces linearly and consider both retarded and non-retarded van der Waals forces. The jump-to-contact is investigated with linearly elastic substrates of arbitrary thicknesses. Specifically, we focus on small surface deformation relative to the tip–surface gap and perform a perturbation analysis for thin and thick substrates. Analytical solutions are obtained for the force or distance at which the jump occurs. These results should be useful for characterizing the strength and retardation behavior of van der Waals forces in soft materials and structures.

中文翻译：

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过早跳接与弹性表面接触


跳跃接触是原子力显微镜 （AFM） 测量中常见的现象。当 AFM 针尖接近基板表面时，就会发生这种情况，并且针尖和表面之间的吸引力（例如范德华力）变得足够强，导致针尖突然跳向表面。在这里，我们研究了表面变形如何影响跳跃接触的开始，并表明在可变形情况下（与刚性情况相比），跳跃接触会过早发生。我们为线性响应外力的表面制定这个问题，并同时考虑延迟和非延迟范德华力。使用任意厚度的线性弹性基板研究跳跃接触。具体来说，我们专注于相对于针尖-表面间隙的小表面变形，并对薄和厚基底进行扰动分析。获得跳跃发生的力或距离的解析解。这些结果应该有助于表征软材料和结构中范德华力的强度和延迟行为。