Imaging and measurement of elasticity and friction using the TRmode

Abstract

Torsional and lateral vibrations of atomic force microscope (AFM) cantilevers can be used to measure elastic and frictional properties on a nanoscale. Recently a new dynamic operation mode called Torsional Resonance mode (TRmode) has been introduced. This paper describes the physical base of the TRmode and compares it to related dynamic AFM modes. In the theoretical part the torsional equation of motion of the cantilever beam is analysed. In the experimental part the contrast of images is interpreted based on the equation of motion. The route to quantitative measurements of contact stiffness, elastic moduli and friction is laid out.

Bidirectional quantitative force gradient microscopy

“…It is limited to in-plane measurements. In contrast, torsional resonance mode dSFM [18][19][20] that is sensitive to in-plane forces can be combined with perpendicular modes based on flexural oscillations.…”

“…the average distance of the carbon nanotube end to the sample surface. If we use q and δ as free parameters, the tipʼs real stray field gradient can be fitted with equation (20). Small deviations might be explained by the nonvanishing lateral extension of the nanowire.…”

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“…2,3 The use of torsional resonances 17 and higher flexural modes 18 have been explored for visualizing various surface properties other than topography. The higher flexural modes are also used for oscillating a cantilever with very small amplitude.…”

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“…The differential equation that governs the torsional vibration of a bilayered cantilever can be approximated for a narrow prismatic beam with W>>T c +T a and for small twisting angles, θ, as [18],…”