Supplementary data
It is well known that the dynamic and static deflection of a cantilever are not the same [20].
However, due to the finite spot-size of the laser this effect is averaged out for small cantilevers.
To test this we measured the static and dynamic deflection for cantilevers of various lengths.

Normalised Sensitivity

1.1

1.0

0.9

100

200300

cantilever length [µm]Figure 1 The normalized static (blue) and dynamic (red) deflection sensitivity for various
cantilevers with a different length. The arrow denotes the length of the cantilevers typically usedfor the experiments described in this paper.

In order to compare our data we fitted the extracted interaction stiffness with a decaying cosinefunction (which is known to describe the oscillatory solvation forces for weakly interaction
liquids like OMCTS very well).

kint [N/m]

10-1
0

2

4

6

8

tip surface distance [nm]Fig. 2 The extracted interaction stiffness kint fitted with a decaying cosine function to find theamplitude of the stiffness Kint.

To test whether the Reynolds squeeze-out damping under the cantilever changes as we approachthe surface, we measure the APD curves over a larger distance. Since the amplitude and phase
response of cantilever remain constant over this distance, we know that the Reynolds damping
under the cantilever does not change (to a measurable extent).

0.15

00.10
-90
0.05

0.00
0Amplitude

5101520

Phase [deg]Amplitude [nm]Phase-180

tip surface distance [nm]Fig.3 The Amplitude and Phase response of the cantilever over tens of nanometers (ωres/2π = 42kHz, Au-coated Si cantilever, ω/ω0 = 0.75). Note that, apart from the oscillations close to thesurface, the amplitude and phase response is constant.

In our experiments the biggest contribution to the total error comes from the uncertainty in thecalibration constants. These uncertainties are mostly affecting the results on resonance. Note thaton resonance the error in the phase is significant and can cause cross-coupling between theconservative and dissipative interaction forces.

A / Amax

1.0

0.5

0.0020406080

frequency [kHz]ϕ [deg]0-90-180020406080

frequency [kHz]Fig. 4 The effect of an error of 5% in both Q (2.85+5%, red vs blue) and ωres/2π (42 kHz+5%,green vs. blue) on the amplitude (a) and phase (b) response spectra of an acoustically driven
cantilever using deflection detection.

Nevertheless, for acoustically driven cantilevers using deflection detection, the sensitivity to tipsample interactions is approximately equal for low frequencies (15 kHz) and close to resonance(42 kHz). Fig. 5 shows the effect of an increasing interaction damping on the amplitude and phase
response. Although the response in the amplitude is less for lower frequencies the response in thephase larger. For the effect of a change in interaction stiffness (an even more pronounced effect)
we refer to ref. [15].

(a)1.0A / Amax

γint +
0.50.00(b)20406080
frequency [kHz]1000ϕ [deg]γint +-90-1800

2040
60
80
100
frequency [kHz]Fig. 5 The effect of a linearly increasing interaction damping (from 0 to 5 10-6 kg/s in steps of 0.5

10-6 kg/s) on the amplitude (a) and phase (b) response of an acoustically driven AFM cantileverusing deflection detection (ωres/2π = 42 kHz, Q = 2.85).