The additive effect of harmonics on conservative and dissipative interactions

Santos, Sérgio; Gadelrab, Karim; Barcons, Victor; Font, Josep; Stefancich, Marco; Chiesa, Matteo

doi:10.1063/1.4769434

Cited by 11 publications

(23 citation statements)

References 60 publications

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“…66 That is, any errors from (2) are due to the single mode-single frequency 59,64 and/or the small frequency shi 56 approximations only. Furthermore, and while these forces are not discussed in detail in this work, the two conditions above imply that 63,76 …”

Section: This Approximation Is Reasonablementioning

confidence: 94%

“…In particular, no assumptions 59 regarding the nature of dissipative forces are required. This implies that the formalism is robust and recovers the true force even in the presence of complex hysteretic dissipative forces 66,76 that might account for bond formation and rupture, capillary interactions or other relevant interactions. 59 Furthermore, the forces can be reconstructed in a single oscillation cycle.…”

Section: 2150mentioning

confidence: 96%

“…This can potentially lead to high throughput since the topography can be tracked while simultaneously mapping sample's properties via the higher harmonics. 76,77 A main disadvantage of this technique relates to the difficulties in detecting the very small amplitudes of the higher harmonics. Experimentally, the amplitudes are excited by the non-linear tip-sample interaction, 78 i.e.…”

Section: 2150mentioning

confidence: 99%

“…92 That is, a conservative force should be independent of the velocity and, in particular, of the sense of motion and the history of tip-sample trajectories. 59,76,99 The conservative part of the tip-sample force can be termed F c (d) 63,76 and its contribution to E dis should be zero. On the other hand, the energy dissipated per cycle E dis is the work done per cycle by the dissipative forces present in the interaction.…”

Section: 45mentioning

confidence: 99%

“…In all these cases, expression (2) will then recover a value of F c (d) that is either that of the viscous independent path on tip approach only or that lying in between that of tip approach and tip retraction. 66,76 In fact, the condition…”

Section: This Approximation Is Reasonablementioning

confidence: 99%

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Single cycle and transient force measurements in dynamic atomic force microscopy

Gadelrab¹,

Santos²,

Font

et al. 2013

Nanoscale

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The monitoring of the deflection of a micro-cantilever, as the end of a sharp probe mounted at its end, i.e. the tip, interacts with a surface, forms the foundation of atomic force microscopy AFM. In a nutshell, developments in the field are driven by the requirement of obtaining ever increasing throughput and sensitivity, and enhancing the versatility of the instrument to simultaneously map the topography and quantify nanoscale processes and properties. In the most common dynamic mode of operation, the motion of the driven cantilever is monitored at a single point on its longitudinal axis. Here, we show that from this single point a waveform is obtained that contains all the details about conservative and dissipative interactions. Then a formalism that accounts for multiple arbitrary flexural modes is developed for an indirectly driven cantilever. The formalism is shown to allow recovery of the details of the interaction even in the presence of complex and relevant hysteretic forces when the cantilever oscillates in the steady state. In a different approach, we develop a formalism that monitors the wave profile of the cantilever, i.e. the waveform at five different points on its longitudinal axis. With this formalism the interaction can be reconstructed during a single oscillation cycle even in the transient state of oscillation. Finally, we discuss the potential and advantages of the proposed methods and future technical challenges. Other standard and state of the art techniques and methods are also discussed and compared with the ones presented here. This work should also provide insight into the current high throughput-high sensitivity developments dealing with multifrequency dynamic AFM where information is recovered from multiple eigenmodes.

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Section: This Approximation Is Reasonablementioning

confidence: 94%

Section: 2150mentioning

confidence: 96%

Section: 2150mentioning

confidence: 99%

Section: 45mentioning

confidence: 99%

Section: This Approximation Is Reasonablementioning

confidence: 99%

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Single cycle and transient force measurements in dynamic atomic force microscopy

Gadelrab¹,

Santos²,

Font

et al. 2013

Nanoscale

Self Cite

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Mixed frequency excitation of an electrostatically actuated resonator

2015

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they are excited by mixed-frequency signals. This interest has been stimulated by their potential use in such fields as communications (Wong and Nguyen 2004), logic functions (Mahboob et al. 2011(Mahboob et al. , 2013, and atomic microscopy (Garcia and Herruzo 2012). For instance, Mahboob et al. (2011) explored that use in logic gates. In order to display new logic architectures, they employed mechanical oscillators at different frequencies. Using a single resonator, they built a new algorithm to eradicate wiring by means of condensed Boolean logic. They simultaneously executed their logic gates in efforts to provide a parallel logic circuit in a single mechanical resonator. Mahboob et al. (2013) demonstrated parametric coupling between multiple vibrations modes in an electromechanical resonator via a strain inducing piezoelectric pump. This parametric coupling can be useful because it rapidly quenches the vibration of the modes, a reduction that leads to the exchange of the vibration of the modes and of energy. Moreover, their technique helps control the oscillation amplitude and generates high speed. The effect of mixed frequency excitation can be a viable solution in these areas due to mixing frequencies through quadratic electrostatic forces. This method has been found in (Wong and Nguyen 2004; Garcia and Herruzo 2012) to realize down converters, mixers, and filters.Many researchers investigated different ways of mixing signals. Hetch (1977) analyzed the acousto-optic diffraction with multiple waves at different carrier frequencies using a coupled mode formulation. Later, a three-wave mixing technique was used to find nonlinear index for different transparent material (Garcia and Herruzo 2012). Nayfeh and Mook (1979) derived the analytical expression of multi frequency excitation of a system with a quadratic nonlinearity using straightforward expansion and the method of the multiple scales. Elnagarand and EI-Bassiouny (1992) used the method of multiple scales to find the response Abstract We investigate experimentally and theoretically the dynamics of a capacitive resonator under mixed frequency excitation of two AC harmonic signals. The resonator is composed of a proof mass suspended by two cantilever beams. Experimental measurements are conducted using a laser Doppler vibrometer to reveal the interesting dynamics of the system when subjected to two-source excitation. A nonlinear single-degree-of-freedom model is used for the theoretical investigation. The results reveal combination resonances of additive and subtractive type, which are shown to be promising to increase the bandwidth of the resonator near primary resonance frequency. Our results also demonstrate the ability to shift the combination resonances to much lower or much higher frequency ranges. We also demonstrate the dynamic pull-in instability under mixed frequency excitation.

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Dynamic modeling and sensitivity analysis of dAFM in the transient and steady state motions

Payam

2016

Ultramicroscopy

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In this paper, based on the slow time varying function theory, dynamical equations for the amplitude and phase of the dynamic atomic force microscope are derived. Then, the sensitivity of the amplitude and phase to the dissipative and conservative parts of interaction force is investigated. The most advantage of this dynamical model is the ability to simulate and analysis the dynamics behavior of amplitude and phase of the AFM tip motion not only in the steady state but also in the transient regime. Using numerical analysis the transient and steady state behavior of amplitude and phase is studied and the sensitivity of amplitude and phase to the interaction force is analyzed.

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The additive effect of harmonics on conservative and dissipative interactions

Cited by 11 publications

References 60 publications

Single cycle and transient force measurements in dynamic atomic force microscopy

Single cycle and transient force measurements in dynamic atomic force microscopy

Mixed frequency excitation of an electrostatically actuated resonator

Dynamic modeling and sensitivity analysis of dAFM in the transient and steady state motions

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