Abstract
Here we introduce the intermittent contact mode (or tapping mode) which is the mode that is used most frequently at ambient conditions.
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Notes
- 1.
The phase \(\phi (A/A_\mathrm {free})\) can be obtained numerically from (2.32) and (2.35). If this result is plotted in Fig. 14.3 it is indistinguishable on top of the curve obtained from (14.5). Alternatively (2.32) and (2.35) can be rearranged analytically leading to (14.5) in a very good approximation.
- 2.
If we approximate the tip-sample force by \(F_\mathrm {ts} = - k' z\) (harmonic oscillator), \(\left\langle F_\mathrm {ts} \cdot z \right\rangle = - 1/2\,k' A^2\) results (cf. (16.10)). Inserting this into (14.13) and remembering that according to (14.5) \(A/A_\mathrm {free} = - \sin {\phi }\), the following expression for the phase is obtained \(\tan {\phi } = k/(k' Q_\mathrm {cant})\), which corresponds to expression (13.20) obtained for the harmonic oscillator.
- 3.
Correspondingly, the left “ear” also occurs on the high-frequency side of the resonance curve.
- 4.
Here we used the dependence \(\phi (A/A_\mathrm {free})\) while in an experiment the \(\phi (d)\) is obtained. However, the two dependences can be converted into each other using the (measured) A(d) dependence.
- 5.
There are also other reasons for the switch between different oscillation sates. For instance, the presence of a valley in the surface topography can enhance the attractive forces (larger regions of the tip will feel the attractive interaction) and thus change the force-distance behavior locally, resulting in a switch to the other branch of the oscillation state.
- 6.
Since \(0>\phi > -180^{\circ }\), \(\left\langle P_\mathrm {drive} \right\rangle \) is positive.
- 7.
- 8.
\(\left\langle F_\mathrm {ts} \cdot \dot{z}(t)\right\rangle \) is negative, as power is dissipated from the system to the environment.
- 9.
The even/odd force contributions with respect to the time \(\Delta t > 0\) relative to the time of the lower turnaround point \(t_0+T/2\) are \(F_\mathrm {ts}^\mathrm {even/odd}(d+z(t_0+T/2-\Delta t)) =1/2 \left( F_\mathrm {ts}(d+z(t_0+T/2-\Delta t)) \pm F_\mathrm {ts}(d+z(t_0+T/2+\Delta t)) \right) = 1/2 \left( F_\mathrm {ts}^\mathrm {approach}(d+z) \pm F_\mathrm {ts}^\mathrm {retract}(d+z) \right) \). If \(\Delta t \rightarrow - \Delta t\), \(F_\mathrm {ts}^\mathrm {even} \rightarrow F_\mathrm {ts}^\mathrm {even}\), while \(F_\mathrm {ts}^\mathrm {odd} \rightarrow - F_\mathrm {ts}^\mathrm {odd}\).
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Voigtländer, B. (2019). Intermittent Contact Mode/Tapping Mode. In: Atomic Force Microscopy. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-13654-3_14
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