Nonlinear vibrations of atomic force microscope probes in Hertzian contact

2001 ◽  
Author(s):  
B. Wei
Keyword(s):  
Atomic Force Microscope ◽  
Nonlinear Vibrations ◽  
Hertzian Contact ◽  
Atomic Force

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.

scholarly journals Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion

2018 ◽  
Vol 241 ◽  
pp. 01004
Author(s):  
Sara Baghdadi ◽  
Faouzi Lakrad ◽  
Mohamed Belhaq
Keyword(s):  
Atomic Force Microscope ◽  
Nonlinear Vibrations ◽  
Linear Mass ◽  
Tapping Mode ◽  
Operating Modes ◽  
Slow Manifolds ◽  
Atomic Force ◽  
Saddle Node ◽  
Base Displacement ◽  
Mass Spring

In the present work, we study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Derjaguin-Muller-Toporov forces and subject to imposed slow harmonic base displacement. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. Then, the charts of behaviors of the different operating modes of the AFM are determined. The dynamic saddle-node bifurcations of the contact and the noncontact invariant slow manifolds are found to be responsible for the occurrence of the tapping mode.

Characterization of photosystem II with the atomic-force microscope

1992 ◽  
Vol 50 (2) ◽  
pp. 1146-1147
Author(s):  
Kathleen M. Marr ◽  
Mary K. Lyon
Keyword(s):  
Photosystem Ii ◽  
Atomic Force Microscope ◽  
Three Dimensional ◽  
Biologically Active ◽  
Atomic Force ◽  
Freeze Etching ◽  
Image Averaging ◽  
Oxygen Evolving ◽  
Averaging Techniques

Photosystem II (PSII) is different from all other reaction centers in that it splits water to evolve oxygen and hydrogen ions. This unique ability to evolve oxygen is partly due to three oxygen evolving polypeptides (OEPs) associated with the PSII complex. Freeze etching on grana derived insideout membranes revealed that the OEPs contribute to the observed tetrameric nature of the PSIl particle; when the OEPs are removed, a distinct dimer emerges. Thus, the surface of the PSII complex changes dramatically upon removal of these polypeptides. The atomic force microscope (AFM) is ideal for examining surface topography. The instrument provides a topographical view of individual PSII complexes, giving relatively high resolution three-dimensional information without image averaging techniques. In addition, the use of a fluid cell allows a biologically active sample to be maintained under fully hydrated and physiologically buffered conditions. The OEPs associated with PSII may be sequentially removed, thereby changing the surface of the complex by one polypeptide at a time.

Imaging polymers, proteins and dna in aqueous solutions with the atomic force microscope

1989 ◽  
Vol 47 ◽  
pp. 32-33
Author(s):  
S.A.C. Gould ◽  
B. Drake ◽  
C.B. Prater ◽  
A.L. Weisenhorn ◽  
S.M. Lindsay ◽  
...  
Keyword(s):  
Amino Acids ◽  
Dna Sequencing ◽  
Aqueous Solutions ◽  
Atomic Force Microscope ◽  
Piezoelectric Crystal ◽  
Atomic Force ◽  
Structure Of Molecules ◽  
Optical Lever

The atomic force microscope (AFM) is an instrument that can be used to image many samples of interest in biology and medicine. Images of polymerized amino acids, polyalanine and polyphenylalanine demonstrate the potential of the AFM for revealing the structure of molecules. Images of the protein fibrinogen which agree with TEM images demonstrate that the AFM can provide topographical data on larger molecules. Finally, images of DNA suggest the AFM may soon provide an easier and faster technique for DNA sequencing.The AFM consists of a microfabricated SiO2 triangular shaped cantilever with a diamond tip affixed at the elbow to act as a probe. The sample is mounted on a electronically driven piezoelectric crystal. It is then placed in contact with the tip and scanned. The topography of the surface causes minute deflections in the 100 μm long cantilever which are detected using an optical lever.

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