2.3.5 Approach-retraction curves

Consider a cantilever oscillations near a sample surface. As shown in chapter 2.2.1, the tip-sample interaction potential has a characteristic appearance depicted in Fig. 1. As the cantilever touches the sample and deforms its surface, the force of elastic repulsion prevails. At the tip-sample separation on the order of a few tens of angstrom, the intermolecular interaction called the Van der Waals force predominates.

Fig. 1. Typical appearance of the tip-sample interaction potential.

As shown in chapter 2.3.4, the presence of external force dependent on spatial coordinates, gives rise to the change in resonance properties of the cantilever-sample oscillating system.

Change in the oscillations phase:     ,

(1)

change in the oscillations amplitude:     ,

(2)

change in the resonant frequency:     ,

(3)

where - cantilever stiffness, – oscillating system Q-factor, – cantilever oscillations amplitude in the absence of external force.

Thus, measuring dependence of the oscillations resonant frequency, phase or amplitude on the tip-sample separation, one can render the derivative appearance and, in some cases, the interaction force itself. The corresponding experimental curves are called the approach curves (Fig. 2).