Figure 1

FIGURE CAPTIONS

Figure 1. Schematic illustration of three distance-dependent regimes of interaction between an

oscillating cantilever/tip and a sample surface. Dashed horizontal line segments denote distance

intervals explored by the tip in each regime, at three values of mean distance (vertical dashed

lines). The interaction regimes are labeled free oscillation (no interaction, bottom), non-contact

(attraction dominant, middle), and intermittent contact (repulsion dominant, top).

Figure 2. (a) Frequency dependence of cantilever amplitude (top panel) and phase (bottom panel)

under free oscillation. Solid circles denote experimental data on PVA at discrete driving

frequencies. Solid curves are fitted response functions using the damped, sinusoidally-driven

oscillator model. Three data points corresponding to drive frequencies below (F-), at (F0) and above

(F+) free resonance are designated with large circles and vertical bars. Left and right-shifted phase

curves (dashed lines) correspond schematically to dominant attractive and repulsive force

gradients, respectively. (b) Dependence of phase on mean tip-sample distance during approach at

drive frequencies (top panel) corresponding to the data points in (a), and in sample approach versus

withdrawal (bottom panel). Decreasing (increasing) phase signals correspond to left (right) shifts in

frequency response as illustrated in (a), plus dampening effects (resonance broadening).

(a) (b)

Figure 2

Figure 3

Figure 3. Amplitude (top) and phase (bottom) data on a PVA film as a function of mean

distance during approach, driving the cantilever at the free resonance. Nominal non-contact and

intermittent contact regimes are separated by jump discontinuities. The amplitude measurement

was calibrated to yield unity slope in intermittent contact; extrapolating a linear fit to zero

amplitude determined the zero of the mean distance scale.

Figure 4. (a) Representative height/phase images (left/right) of an ultrathin PVA film. Brighter

regions correspond to higher surface elevation or phase. The top image pair is 20x20 microns in

dimension; at bottom is a 5x5-micron zoom of the square sub-region designated in the top

image. Three types of surface region are labeled in the lower phase image. The set point

amplitude was 90% of the free oscillation amplitude of 25 nm. The driving frequency was 250

kHz below free resonance. (b) Representative amplitude and phase data as a function of mean

distance during approach towards Regions #1-3 as indicated. The horizontal scale was

referenced to the abrupt phase change from free oscillation to the nominal non-contact regime.

The set point amplitude of 1.65 V, for acquiring the images in (a), is indicated with a horizontal

line. Dashed vertical lines intercept the corresponding phase values, as designated to the right of

each. For comparison, phase values corresponding to a constant mean distance of 21 nm are

designated to the left. Two-dimensional rendering of the raw phase data at a selected Z value is

shown in the inset.

Height Phase(a) (b)

3

1

2

1 m

Figure 4

(a)

(b)

Figure 5

Figure 5. (a) Representative amplitude hysteresis during approach-withdrawal cycles on

Regions #1-3. Approach (withdrawal) data correspond to thin (thick) lines. The horizontal and

vertical scales apply to the data acquired on Region 1. The zero of Z displacement is the position

of nearest sample approach. The amplitude reduction triggering reversal from approach to

withdrawal is indicated with a downward-pointing arrow at left. Data sets for Regions 2 and 3

are shifted for clarity. (b) Histograms of integrated amplitude hysteresis on Regions #1-3. The

hysteresis values are normalized to the peak position for Region #1. Two-dimensional rendering

is shown in the inset, darker regions corresponding to greater integrated hysteresis.

Figure 6. Comparison of data acquired while driving at (F0) and 300 Hz below (F-) the free

resonance frequency. The free resonance amplitude was 25 nm and the set point amplitude for

imaging was 95% of the free oscillation amplitude at each driving frequency. (a) Representative

distance dependence of amplitude (top) and phase (bottom) on Region #1 during approach.

Horizontal lines denote the set point amplitudes; dashed vertical lines intercept the

corresponding phase values. (b) Height/phase images (left/right) corresponding to driving

conditions F0 (upper images) and F- (lower images), with Regions #1-3 indicated in the lower

phase image. Histograms of both phase images are shown at bottom. Upper (solid circles) and

lower (open circles) histograms correspond to driving frequencies F0 and F-, respectively.

Contributions from Regions #1-3 are indicated for driving at F-.

(a) (b)

Figure 6