Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments

Abstract

A mathematical model is presented to predict the oscillating dynamics of atomic force microscope cantilevers with nanoscale tips tapping on elastic samples in liquid environments. Theoretical simulations and experiments performed in liquids using low stiffness probes on hard and soft samples reveal that, unlike in air, the second flexural mode of the probe is momentarily excited near times of tip-sample contact. The model also predicts closely the tip amplitude and phase of the tip at different set points.

Compositional Contrast of Biological Materials in Liquids Using the Momentary Excitation of Higher Eigenmodes in Dynamic Atomic Force Microscopy

“…By way of summary, we have shown that the momentary excitation of the second eigenmode is a naturally occurring phenomenon unique to AFM operation using soft cantilevers (k 1 < 1 N=m, Q 1 < 5) in liquids where quality factors are inherently low [10]. This phenomenon is manifest by the enhancement of integer higher harmonics of the drive frequency near the second eigenmode frequency and is quite sensitive to local elasticity when gentle imaging forces (high setpoints) are used.…”

“…In this Letter, we build on recent work [10] to show that the tapping dynamics of soft AFM cantilevers in liquids features a unique nonlinear transient phenomenon-that of momentary excitation of higher eigenmodes which occurs naturally and does not require higher eigenmode frequencies to be integer multiples of the fundamental. We find these vibrations provide an order of magnitude improvement in compositional contrast on soft biological materials in liquids when compared to second harmonic imaging [5], under gentle imaging conditions and without the use of specialized cantilevers or intentional bimodal excitation [12,14].…”

“…The experimental deflection data from the photodiode position detector in an Agilent 5500 AFM system are acquired at 2.5 MHz using National Instruments 5911 boards [15]. The distinct distortions seen in the waveforms when the tip contacts the sample are due to the momentary excitation of the second eigenmode [10]. This momentary excitation enhances specific higher harmonics of the drive frequency that lie in the vicinity of the 2nd eigenmode frequency as seen in Fig.…”

“…The nonlinear tip-sample interaction in dAFM induces cantilever vibrations at higher harmonics of the drive frequency [1,[5][6][7][8][9][10] which can provide compositional contrast [1,[5][6][7]9,[11][12][13]. Under ambient or vacuum conditions, the higher harmonics are very small and need to be enhanced using special cantilevers [12] or bimodal excitation [14].…”

“…week ending 13 FEBRUARY 2009 0031-9007=09=102(6)=060801 (4) 060801-1 Ó 2009 The American Physical Society rectangular microcantilever is used [10]:…”