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.