Unlocking higher harmonics in atomic force microscopy with gentle interactions

Abstract

SummaryIn dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

Identification of HIV-1–Based Virus-like Particles by Multifrequency Atomic Force Microscopy

“…Some studies refer to a strong dependence of the second mode to the Hamaker constant of the material, which should lead to an increased sensitivity of the composition of the surface for this second mode (17,24,25). The differential composition should not significantly affect the contrast of the image, because in these samples the VLPs are stained with uranyl acetate.…”

Periodicity in bimodal atomic force microscopy

“…Mode numbers are bracketed in this work to distinguish them from harmonic number n as done elsewhere. 23,37 The external drive frequencies are x D1 and x D2 ; D1 and D2 stand for drives 1 and 2, respectively. Typically, x D1 % x (1) and x D2 % x (2) .…”

“…18 Still, while attractive for the development of the field, the simultaneous excitation of multiple frequencies at or near the eigenmodes comes at the cost of additional instrumentation, 19 added complexity to cantilever dynamics 20,21 and the requirement of interpreting secondary contrast channels. 7,14,22,23 Furthermore, in order to exploit the potential of bimodal AFM, it is of great interest to understand whether the motion is, or can be forced to be, periodic. Periodic motion in this context implies that there is a fundamental frequency the integer multiples of which constitute the full set of higher frequencies present in the signal.…”

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

“…In frequency modulation-AFM (FM-AFM), the force is usually reconstructed from the resonance frequency shift, which in the small amplitude regime is proportional to the derivative of the force with respect to tip-surface distance. Similarly, it has been recognized that higher harmonics generated by the nonlinear tip-surface interaction (to be distinguished from higher flexural modes of the cantilever) are related to higher derivatives of the force, and thus carry additional information on the interaction [5][6][7][8][9][10][11]. Broad implementation of force spectroscopy by analysing higher harmonics has been nevertheless impeded by the lack of a closed-form expression for the force in terms of measured quantities, namely, the lack of a higher harmonics analogue of the Sader-Jarvis formula for the fundamental harmonic [12,13].…”

“…While the former are measured with reference to zero, the latter are obtained by offsetting large, inherently noisy signals, such as the driving frequency in FM-AFM or oscillation amplitude in AM-AFM. Second, there is evidence [5][6][7][8][9][10][11] that higher harmonics are more sensitive to short-range forces than the fundamental harmonic. This becomes evident when the cantilever oscillation amplitude is small compared with the interaction length.…”