Premature jump-to-contact with elastic surfaces

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.