Exploring the static acoustic force sensitivity using AFM micro-cantilever under single- and bimodal-frequency excitation

Yilmaz, Cagri; Şahin, Ramazan; Topal, Eyüp Sabri

doi:10.1088/1361-6501/ac0eb1

Cited by 8 publications

(3 citation statements)

References 33 publications

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“…The effective mass is determined by utilizing Hollomonʼs power law stress-strain equation considering the fundamental eigenmode (i = 1) [49].…”

Section: A Multi-modal Nonlinear Dynamic Modelmentioning

confidence: 99%

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

Yilmaz

2024

Eng. Res. Express

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In this current work, a new nonlinear dynamic model based on the forced Van der Pol oscillator is introduced to demonstrate the time-domain sensitivities of the micro-cantilever to the varying properties of the surrounding fluids. Effects of diverse multi-frequency excitations on the hydrodynamically forced displacements are investigated for the Glycerol-water solutions with different concentrations. Driving forces at the eigenmode frequencies are applied simultaneously to actuate the micro-cantilever in multi-modal operations. The hydrodynamic force induces notable variations in the observables of high-frequency steady-state vibrations. To illustrate, the frequency of the displacements decreases with increasing dynamic viscosity and density of the fluids (among 55% and 85% Glycerol-water solutions) in bimodal- and trimodal-frequency excitations. Essentially, the observable responses are often used to distinguish the surrounding fluids in which the micro-cantilever operates. In addition, steady-state observables are achieved at only particular eigenmodes in single- and multi-frequency operations. It is highlighted that the periodic oscillations are obtained for the first and second eigenmodes with the highest value of forced Van der Pol parameter (μ =1030). Clearly, higher eigenmodes require different values of the nonlinearity parameter to acquire periodic vibrations in multi-modal operations. In general, achieving steady-state observables is substantially critical in quantifying sensitivity to varying fluid properties. For instance, the vibration frequency of around 7.33 MHz and amplitude of around 0.03 pm are obtained at the first eigenmode for 75% Glycerol-water solution in tetra-modal operations. Note that femtometer amplitudes of deflections can be measured using quantum-enhanced AFM techniques. The frequency responses obtained in this work are compared with the measured ones in the literature and the results show satisfactory agreements. Therefore, a novel multi-modal nonlinear dynamic model enables to quantify observable sensitivity to micro-rheological properties at higher eigenmodes of the micro-cantilever.

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“…The effective mass is determined by utilizing Hollomonʼs power law stress-strain equation considering the fundamental eigenmode (i = 1) [49].…”

Section: A Multi-modal Nonlinear Dynamic Modelmentioning

confidence: 99%

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

Yilmaz

2024

Eng. Res. Express

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“…Dissipated power and virial per cycle for ith mode in single-and bimodal-frequency excitations are calculated using the analytical expressions ((Equation (12)) and (equation ( 13))) respectively [8].…”

Section: = ( )mentioning

confidence: 99%

“…Following works mentioned below deal with actuation of the micro-cantilever with acoustic forces and detection of acoustic emission. In our earlier work, static acoustic force sensitivity is investigated by using resonant AFM micro-cantilever under monomodal and bimodal operations [8]. In addition, a novel photo-acoustic excitation technique is implemented for effective non-contact actuation of micro-cantilever [9].…”

Section: Introductionmentioning

confidence: 99%

Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Yilmaz¹,

Şahin²,

Topal³

2021

Eng. Res. Express

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We present a detailed analysis on measurement sensitivity of dynamic acoustic forces via numerical simulation of the micro-cantilever responses. The rectangular micro-cantilever is regarded as a point mass in the dynamic model of forced and damped harmonic oscillator. We use single- and bimodal-frequency excitation schemes for actuation of the micro-cantilever in the presence of dynamic acoustic forces. In bimodal-frequency excitation scheme, the micro-cantilever is excited at its first two eigenmode frequencies simultaneously as opposed to single-frequency excitation. First, we numerically obtain micro-cantilever deflections by solving the equations of Motions (EOMs) constructed for the first two eigenmodes. Then, we determine oscillation amplitude and phase shift as a function of acoustic force strength within different frequency regions. Moreover, we relate amplitude and phase shift to virial and energy dissipation in order to explore the interaction between flexural modes in multifrequency excitation. The simulation results point out that bimodal-frequency excitation improves the measurement sensitivity of dynamic acoustic forces at particular frequencies. Herein, simultaneous application of driving forces enables higher sensitivities of observables and energy quantities as acoustic force frequencies become around the eigenmode frequencies. For our case, we obtain the highest phase shift (∼178°) for the acoustic force strength of 100 pN at the frequency of around 307.2 kHz. Therefore, this method can be easily adapted to improve measurement sensitivity of dynamic acoustic forces in a wider frequency window.

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Utilizing a forced Van der Pol-Rayleigh-Helmholtz oscillator under heptamodal-frequency operations in Casimir force measurement

Yilmaz

2024

Indian J Phys

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In this paper, Casimir force sensitivity is investigated by utilizing a micro-cantilever under the driving forces in heptamodal operations. A novel forced Van der Pol-Rayleigh-Helmholtz nonlinear oscillator model is developed to describe the nonlinear dynamics of the micro-cantilever which is subject to the excitation and Casimir forces simultaneously. Demonstrating the effectiveness of the heptamodal operations, single- and tetramodal-frequency excitation schemes are also applied separately to resonate the micro-cantilever at the fundamental and higher eigenmodes. The oscillation observables of the externally driven micro-cantilever are determined in the presence of the Casimir forces in the separation distance range of 200–800 nm. Remarkable variations in amplitude ratio, phase shift, and frequency shift for different effective masses of the micro-cantilever are explored for the higher eigenmodes. In the current work, the AFM micro-cantilever exhibits the amplitude response of 0.82 nm to Casimir force at the fourth eigenmode for the separation distance ranging between 200 and 300 nm. The stable frequency shifts ranging between 103 and 106 Hz are also observed at the first four eigenmodes for larger separation distances (above around 500 nm). Moreover, the maximum phase shift response of around 150 degrees at the sixth eigenmode is achieved using heptamodal-frequency excitation of the lightest micro-cantilever (3.6 × 10−12 kg) at the separation distance of 200 nm. Thus, implementing heptamodal-frequency excitation schemes has considerable potential to improve the phase shift sensitivity to Casimir forces when compared with other excitation schemes. Additionally, the parameters of the nonlinear oscillator significantly determine the patterns of the time-domain sensitivities to the external forces. Correspondingly, displacements of the micro-cantilever under the driving and Casimir forces at different eigenmodes are obtained to investigate diverse system nonlinearities. Furthermore, the virial and dissipated power are also determined for different effective masses of the micro-cantilever to explain the energy dissipation process in the measurement of Casimir forces. Therefore, in the present work, the observable responses and energy quantities for particular system nonlinearities are introduced to be utilized for nanometrological applications.

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Exploring the static acoustic force sensitivity using AFM micro-cantilever under single- and bimodal-frequency excitation

Cited by 8 publications

References 33 publications

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Utilizing a forced Van der Pol-Rayleigh-Helmholtz oscillator under heptamodal-frequency operations in Casimir force measurement

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