Quantitative force and dissipation measurements in liquids using piezo-excited atomic forcemicroscopy: a unifying theory

Abstract

The use of a piezoelectric element (acoustic excitation) to vibrate the base ofmicrocantilevers is a popular method for dynamic atomic force microscopy. In air orvacuum, the base motion is so small (relative to tip motion) that it can be neglected.However, in liquid environments the base motion can be large and cannot be neglected. Yetit cannot be directly observed in most AFMs. Therefore, in liquids, quantitativeforce and energy dissipation spectroscopy with acoustic AFM relies on theoreticalformulae and models to estimate the magnitude of the base motion. However,such formulae can be inaccurate due to several effects. For example, a significantcomponent of the piezo excitation does not mechanically excite the cantileverbut rather transmits acoustic waves through the surrounding liquid, which inturn indirectly excites the cantilever. Moreover, resonances of the piezo, chip andholder can obscure the true cantilever dynamics even in well-designed liquid cells.Although some groups have tried to overcome these limitations (either by theorymodification or better design of piezos and liquid cells), it is generally accepted thatacoustic excitation is unsuitable for quantitative force and dissipation spectroscopyin liquids. In this paper the authors present a careful study of the base motionand excitation forces and propose a method by which quantitative analysis isin fact possible, thus opening this popular method for quantitative force anddissipation spectroscopy using dynamic AFM in liquids. This method is validated byexperiments in water on mica using a scanning laser Doppler vibrometer, which canmeasure the actual base motion. Finally, the method is demonstrated by usingsmall-amplitude dynamic AFM to extract the force gradients and dissipation onsolvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.