A dynamic model of the jump-to phenomenon during AFM analysis

The measurement of the physical properties of surfaces on the nanoscale is a long-standing problem, and the atomic force microscope (AFM) has enabled the investigation of surface energies and mechanical properties over a range of length scales. The ability to measure these properties for softer materials presents a challenge when interpreting data obtained from such measurements, in particular because of the dynamics of the compliant AFM microcantilever. This work attempts to better understand the interaction between an AFM tip and samples of varying elastic modulus, in the presence of attractive van der Waals forces. A theoretical model is presented in which the dynamics of the approach of an atomic force microscope cantilever tip toward a surface, prior to and during the van der Waals-induced jump-to phenomenon, are included. The cantilever mechanics incorporates the motion of the air through which the cantilever moves, the acceleration, inertia, and torque of the cantilever, and the squeezing of the fluid between the cantilever tip and the surface, leading to elastohydrodynamic lubrication and deformation of the substrate. Simulations of the cantilever approach are compared to measurements performed using an atomic force microscope, and the effect of cantilever drive velocity is investigated. Cantilevers presenting (1) spherical colloid probe tips and (2) pyramidal tips are employed, and substrates exhibiting Young's moduli of 3 MPa, 500 MPa, and 75 GPa are measured. The analysis presented could be extended to enhance understanding of dynamic phenomena in micro/nanoelectromechanical systems such as resonators and microrheometers, particularly those which contain soft materials and also where surface interactions are important.