Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory

2010 ◽  
Vol 88 (5) ◽  
pp. 333-348 ◽  
Author(s):  
Ali Sadeghi ◽  
Hassan Zohoor
Keyword(s):  
Atomic Force Microscope ◽  
Timoshenko Beam ◽  
Frequency Ratio ◽  
Contact Stiffness ◽  
Sample Surface ◽  
Hertzian Contact ◽  
Nonlinear Frequency ◽  
Lateral Contact ◽  
Atomic Force ◽  
Contact Position

The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip–sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact stiffness, the frequency ratio increases for the first mode, but for the second mode, the situation is reversed. The nonlinear-frequency to linear-frequency ratio increases by increasing the Timoshenko beam parameter, but decreases by increasing the contact position for constant amplitude for the first and second modes. For the first mode, the frequency ratio decreases by increasing both of the lateral contact stiffness and the tip height, but increases by increasing the angle α between the cantilever and sample surface.

A fresh insight into the non-linear vibration of double-tapered atomic force microscope cantilevers by considering the Hertzian contact theory

2010 ◽  
Vol 225 (1) ◽  
pp. 233-247 ◽  
Author(s):  
A Sadeghi ◽  
H Zohoor
Keyword(s):  
Atomic Force Microscope ◽  
Timoshenko Beam ◽  
Frequency Ratio ◽  
Contact Stiffness ◽  
Sample Surface ◽  
Hertzian Contact ◽  
Linear Frequency ◽  
Atomic Force ◽  
Non Linear ◽  
Contact Position

The non-linear flexural vibration for a double-tapered atomic force microscope cantilever has been investigated by using the Timoshenko beam theory. In this article, the normal and tangential tip—sample interaction forces are found from the Hertzian contact model, and the effects of the contact position, normal and lateral contact stiffness, height of the tip, thickness of the beam, angle between the cantilever and the sample surface, and breadth and height taper ratios on the non-linear frequency to linear frequency ratio have been studied. The differential quadrature method is employed to solve the non-linear differential equations of motion. The results show that the softening behaviour is seen for all cases. The non-linear frequency to linear frequency ratio increases by increasing the Timoshenko beam parameter and breadth and height taper ratios, but decreases by increasing the contact position for the first and second modes. For the first vibrational mode, the non-linear frequency to linear frequency ratio increases by increasing the height of the tip and the angle α between the cantilever and sample surface. By increasing the normal contact stiffness, the frequency ratio increases for the first mode.

Increasing the Image Contrast of Atomic Force Microscope by Using Improved Rectangular Micro Cantilever

2011 ◽  
Vol 110-116 ◽  
pp. 4888-4892
Author(s):  
Ali Sadeghi
Keyword(s):  
Atomic Force Microscope ◽  
Contact Stiffness ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Sample Surface ◽  
Limited Range ◽  
Image Contrast ◽  
Atomic Force ◽  
Afm Cantilever ◽  
Micro Cantilever

The resonant frequency of flexural vibrations for an atomic force microscope (AFM) cantilever has been investigated using the Euler-Bernoulli beam theory. The results show that for flexural vibration the frequency is sensitive to the contact position, the first frequency is sensitive only to the lower contact stiffness, but high order modes are sensitive in a larger range of contact stiffness. By increasing the height H, for a limited range of contact stiffness the sensitivity to the contact stiffness increases. This sensitivity controls the image contrast, or image quality. Furthermore, by increasing the angle between the cantilever and sample surface, the frequency decreases.

scholarly journals Измерения контактной жесткости в атомно-силовом микроскопе

2020 ◽  
Vol 90 (11) ◽  
pp. 1951
Author(s):  
А.В. Анкудинов ◽  
М.М. Халисов
Keyword(s):  
Atomic Force Microscope ◽  
Analytical Model ◽  
Contact Interaction ◽  
Relative Position ◽  
Mechanical Characteristics ◽  
Contact Stiffness ◽  
Sample Surface ◽  
Atomic Force ◽  
Imaging Mode ◽  
Cantilever Probe

A method is proposed for increasing the accuracy of nanomechanical measurements in an atomic force microscope. To describe the contact interaction of the cantilever with the sample, an analytical model was used that takes into account the following factors: the cantilever probe sticks to the sample surface or slides along it, the geometric and mechanical characteristics of the sample and cantilever, and their relative position. Under the assumption of sliding, a filter was developed to correct the signals of contact stiffness and deformation measured on a sample with a developed relief. The use of the filter is illustrated in images obtained in an atomic force microscope with an imaging mode based on point-by-point registration of the force quasistatic interaction of the cantilever probe with the sample.

Characterization of Multi-Phase and Multi-Component Polymer Systems Using the Atomic Force Microscope

1999 ◽  
Vol 5 (S2) ◽  
pp. 962-963
Author(s):  
M. VanLandingham ◽  
X. Gu ◽  
D. Raghavan ◽  
T. Nguyen
Keyword(s):  
Energy Dissipation ◽  
Atomic Force Microscope ◽  
Mechanical Response ◽  
Sample Surface ◽  
Phase Changes ◽  
Phase Imaging ◽  
Polymer Systems ◽  
Atomic Force ◽  
Phase Images ◽  
Multi Phase

Recent advances have been made on two fronts regarding the capability of the atomic force microscope (AFM) to characterize the mechanical response of polymers. Phase imaging with the AFM has emerged as a powerful technique, providing contrast enhancement of topographic features in some cases and, in other cases, revealing heterogeneities in the polymer microstructure that are not apparent from the topographic image. The enhanced contrast provided by phase images often allows for identification of different material constituents. However, while the phase changes of the oscillating probe are associated with energy dissipation between the probe tip and the sample surface, the relationship between this energy dissipation and the sample properties is not well understood.As the popularity of phase imaging has grown, the capability of the AFM to measure nanoscale indentation response of polymers has also been explored. Both techniques are ideal for the evaluation of multi-phase and multi-component polymer systems.

scholarly journals Generalized Hertz model for bimodal nanomechanical mapping

2016 ◽  
Vol 7 ◽  
pp. 970-982 ◽  
Author(s):  
Aleksander Labuda ◽  
Marta Kocuń ◽  
Waiman Meinhold ◽  
Deron Walters ◽  
Roger Proksch
Keyword(s):  
Contact Mechanics ◽  
Small Amplitude ◽  
Sample Surface ◽  
Hertzian Contact ◽  
Modes Of Operation ◽  
Hertz Model ◽  
Force Microscopy ◽  
Atomic Force ◽  
Resonant Modes ◽  
Shape And Size

Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface.

Nonlinear Vibrations in Contact Atomic Force Microscopy

2003 ◽  
Author(s):  
Joseph A. Turner
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Contact Stiffness ◽  
Vibration Response ◽  
Hertzian Contact ◽  
Force Microscopy ◽  
Softening Behavior ◽  
Atomic Force ◽  
Frequency Relation ◽  
Frequency Curves

The nonlinear vibration response of an atomic force microscope cantilever in contact with a vibrating sample is investigated. The tip-sample contact is modeled using Hertzian contact mechanics. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. The primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. The modal sensitivity to nonlinearity is the result of the nonlinearity being restricted to a single position. The mode shape greatly affects the degree to which the nonlinearity influences the frequency response. The Hertzian restriction is then loosened slightly such that variations in nonlinear contact stiffness are examined. These results depend on the linear contact stiffness and mode number as well. The nonlinear vibration response is expected to provide new insight on the nonlinear tip mechanics present in these systems.

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