G. Bar

Importance of the indentation depth in tapping-mode atomic force microscopy study of compliant materials

We studied the response of a cantilever tapping on polydimethylsiloxane (PDMS) samples of different crosslink density. It is shown experimentally that the tip deeply penetrates into the compliant PDMS samples. A more compliant material leads to a larger indentation such that at a given set-point ratio the indentation force is nearly constant on samples of different elastic moduli. This confirms the simulations by J. Tamayo and R. Garcia [Appl. Phys. Lett. 71, 2394 (1997)] that phase contrast acquired at constant set point does not depend on the sample’s modulus if other contrast relevant parameters remain identical. PDMS samples of different crosslink density are distinguished in terms of amplitude and phase versus distance measurements if the tip-sample interaction is made substantially large and indentation is taken into account.

Investigation of the stiffness change in, the indentation force and the hydrophobic recovery of plasma-oxidized polydimethylsiloxane surfaces by tapping mode atomic force microscopy

Polydimethylsiloxane (PDMS) samples of different crosslink densities were oxidized in air plasma, and the stiffness change in the oxidized PDMS surface was monitored by performing tapping mode atomic force microscopy (TMAFM) distance-sweep measurements and numerical simulations of the cantilever equation of motion based on a contact mechanics model. The diffusion mechanism of hydrophobic recovery of an oxidized PDMS surface was examined by a combined use of TMAFM distance-sweep and phase imaging experiments. Our work shows that the modulus of the oxidized PDMS surface increases with increasing the oxidation time, and supports the diffusion mechanism of hydrophobic recovery. It is possible to extract information about the indentation force from observed indentation curves and to employ TMAFM for force modulation experiments at high modulation frequency.

Examination of the relationship between phase shift and energy dissipation in tapping mode atomic force microscopy by frequency-sweep and force-probe measurements

Abstract The relationship between phase shift and energy dissipation in tapping mode atomic force microscopy was examined by performing frequency-sweep and force-probe experiments on polydimethylsiloxane (PDMS) samples of different cross-link densities. Phase shift is related to the reduced tip–sample energy dissipation, i.e. the fraction of the maximum energy of a tapping cantilever that is dissipated by the tip–sample interaction. The reduced tip–sample energy dissipation varies linearly with phase shift, and increases continuously as the tip–sample interaction increases. On a compliant polymer such as PDMS the tip–sample interaction dissipates only a small fraction of the power delivered to the tapping cantilever even under hard tapping conditions, so that the vibration of the tapping cantilever is well described in terms of the harmonic approximation.

Description of the frequency dependence of the amplitude and phase angle of a silicon cantilever tapping on a silicon substrate by the harmonic approximation

Abstract The frequency dependence of the amplitude and phase angle of a silicon cantilever tapping on a silicon surface was examined. The amplitude and phase angle curves exhibit hysteresis depending on the driving and set-point amplitudes. The main features of these curves are explained in terms of the harmonic approximation. The frequency shifts determined from the phase curves vary almost linearly as a function of the set-point ratio, in support of the harmonic approximation. The quality factor of a tapping cantilever was estimated from amplitude and phase curves using the harmonic approximation. The quality factor is reduced by the tip–sample interaction, and this reduction is stronger when the interaction is dominated by repulsive forces than by attractive forces.

Effect of tip sharpness on the relative contributions of attractive and repulsive forces in the phase imaging of tapping mode atomic force microscopy

Abstract The way in which the sharpness of a tip affects phase imaging in tapping mode atomic force microscopy was examined by performing experiments on polystyrene and Si surfaces with tips of different sharpness. The dominant tip–sample interaction controlling the cantilever vibration can be made repulsive with a sharp tip, and attractive with a dull tip. When the dominant interaction is either attractive or repulsive, the magnitude of the phase shift (Δ φ ) increases with decreasing set-point ratio r sp = A sp / A 0 , and the Δ φ -vs.- r sp plots are nearly independent of the drive amplitude, A 0 . These observations indicate that the cantilever vibration is affected mainly by the amount of time the tip spends in going through the lower turning point of each oscillation and by the forces whose force derivatives change sharply during this period.

Harmonic responses of a cantilever interacting with elastomers in tapping mode atomic force microscopy

Abstract Frequency-sweep tapping-mode atomic force microscopy experiments were carried out on four elastomers, cis-1,4-butadiene rubber, styrene-co-butadiene rubber, natural rubber and polydimethylsiloxane to examine how well a cantilever tapping on compliant samples is described by the harmonic approximation. The amplitude curves and the phase shifts calculated for these elastomers using the harmonic approximation are in excellent agreement with the experimental values even when the tip–sample interaction is strong. When the overall tip–sample interaction is repulsive, the phase shift varies linearly with the reduced tip–sample energy dissipation because both quantities increase with increasing the tip–sample contact time. The phase shift is affected not only by the reduced tip–sample energy dissipation via the effective quality factor but also by the frequency shift.

Hysteresis in the distance-sweep curves of elastomers and its implications in tapping mode atomic force microscopy

Abstract Distance-sweep tapping mode atomic force microscopy experiments were carried out for a cross-linked elastomer, polydimethylsiloxane (PDMS), and non-cross-linked elastomers, styrene-co-butadiene rubber (SBR) and cis-1,4-butadiene rubber (BR). The amplitude curves, A(Z), recorded for the approach and retraction cycles exhibit a strong hysteresis for SBR and BR, but a negligible hysteresis for PDMS. Nevertheless, the A(Z) curves for the approach and retraction cycles are each well described by the harmonic approximation for a wide region of tip–sample interaction. To examine the probable causes for this observation, the observed A(Z) curves were simulated by numerically solving the equation of motion for a tapping cantilever and by performing dynamical mechanical analysis experiments for SBR and BR. For the non-cross-linked elastomers SBR and BR, the sample vibration induced by the tapping cantilever is somewhat out of phase with the cantilever vibration, and the surface of the vibrating sample rises above the rest surface of the sample, thereby causing the observed hysteresis. In the region of strong tip–sample interaction, the amplitude curve A(Z) is mainly governed by the modulus of the sample, and the tapping cantilever senses the bulk property.

Correlation between frequency-sweep hysteresis and phase imaging instability in tapping mode atomic force microscopy

Abstract Frequency-sweep and phase imaging experiments of tapping mode atomic force microscopy were carried out for patterned self-assembled monolayers of S(CH 2 ) 15 CH 3 and S(CH 2 ) 12 OH groups on a polycrystalline Au substrate. The phase shift values of opposite signs associated with phase imaging instability are shown to be the same as the corresponding ones resulting from frequency-sweep hysteresis.