Accessing Time-Varying Forces on the Vibrating Tip of the Dynamic Atomic Force Microscope to Map Material Composition

In dynamic atomic force microscopes the primary physical quantities being measured are the amplitude/phase or amplitude/frequency of the vibrating force probe. Topographic images with spatial resolutions down to the atomic scale can be obtained by mapping these measurements across the sample surface under feedback control. During the imaging process the vibrating tip is observing tip–sample interaction potentials (force–distance relationships) at every point on the surface. The interaction potential is a superposition of shortand long-distance interactions of various origins determined by the material compositions of the tip, sample, and the medium of imaging. In principle, measurement of tip–sample interaction potential should allow determination and mapping of material composition of the sample. However, a single measurement of amplitude/phase or amplitude/frequency in dynamic atomic force microscopes is not enough to characterize a complicated tip–sample interaction potential. Recent developments in the understanding of dynamics of the vibrating force probe (cantilever), together with specially designed cantilevers that utilize torsional vibrations in addition to conventional vertical vibrations, enable the recovery of tip–sample interaction potentials at a timescale less than a millisecond. Here, with theory and experiments, we discuss how these cantilevers recover the information about the tip–sample interaction forces and give an example of compositional mapping on a polymeric material system.