Analysis of the Frequency Shift versus Force Gradient of a Dynamic AFM Quartz Tuning Fork Subject to Lennard-Jones Potential Force

A self-sensing and self-actuating quartz tuning fork (QTF) can be used to obtain its frequency shift as function of the tip-sample distance. Once the function of the frequency shift versus force gradient is acquired, the combination of these two functions results in the relationship between the force gradient and the tip-sample distance. Integrating the force gradient once and twice elucidates the values of the interaction force and the interatomic potential, respectively. However, getting the frequency shift as a function of the force gradient requires a physical model which can describe the equations of motion properly. Most papers have adopted the single harmonic oscillator model, but encountered the problem of determining the spring constant. Their methods of finding the spring constant are very controversial in the research community and full of discrepancies. By circumventing the determination of the spring constant, we propose a method which models the prongs and proof mass as elastic bodies. Through the use of Hamilton’s principle, we can obtain the equations of motion of the QTF, which is subject to Lennard-Jones potential force. Solving these equations of motion analytically, we get the relationship between the frequency shift and force gradient.

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Impact of Inter Tine Coupling on the Spring Constant of the Quartz Tuning Fork

2019 IEEE International Conference on Mechatronics and Automation (ICMA) ◽

10.1109/icma.2019.8816492 ◽

2019 ◽

Author(s):

Sajid Parveez ◽

Danish Hussain ◽

Usman Asad

Keyword(s):

Tuning Fork ◽

Quartz Tuning Fork ◽

Spring Constant

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The Coefficient of the Voltage Induced Frequency Shift Measurement on a Quartz Tuning Fork

Sensors ◽

10.3390/s141121941 ◽

2014 ◽

Vol 14 (11) ◽

pp. 21941-21949

Author(s):

Yubin Hou ◽

Qingyou Lu

Keyword(s):

Frequency Shift ◽

Tuning Fork ◽

Quartz Tuning Fork ◽

Shift Measurement

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Spring constant of a tuning-fork sensor for dynamic force microscopy

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.3.90 ◽

2012 ◽

Vol 3 ◽

pp. 809-816 ◽

Cited By ~ 15

Author(s):

Dennis van Vörden ◽

Manfred Lange ◽

Merlin Schmuck ◽

Nico Schmidt ◽

Rolf Möller

Keyword(s):

Tuning Fork ◽

Quartz Tuning Fork ◽

Simple Calculation ◽

Spring Constant ◽

Thermal Excitation ◽

Dynamic Force ◽

Mechanical Measurement ◽

Force Microscopy ◽

Real Geometry ◽

The Difference

We present an overview of experimental and numerical methods to determine the spring constant of a quartz tuning fork in qPlus configuration. The simple calculation for a rectangular cantilever is compared to the values obtained by the analysis of the thermal excitation and by the direct mechanical measurement of the force versus displacement. To elucidate the difference, numerical simulations were performed taking account of the real geometry including the glue that is used to mount the tuning fork.

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Designing an Intelligent Controller for a Molecular Valve

2008 Second International Conference on Integration and Commercialization of Micro and Nanosystems ◽

10.1115/micronano2008-70257 ◽

2008 ◽

Author(s):

Kasra Momeni ◽

Aria Alasty

Keyword(s):

Single Molecule ◽

Fuzzy Controller ◽

Equations Of Motion ◽

The Other ◽

Scanning Tunneling ◽

Lennard Jones Potential ◽

Membership Functions ◽

Jones Potential ◽

Intelligent Controller ◽

Lennard Jones

Too much effort has been done for manipulating individual atoms, using nano-manipulators and Scanning Tunneling Microscopes (STM). On the other hand, characterization and manipulation of nano-flows is of great concern. In the current work a molecular valve has been considered, which is made up of six atoms placed on the circumstance of a circle. A fuzzy controller has been designed for controlling the diameter of this molecular valve. The designed fuzzy controller used singleton fuzzifier, Mamdani inference engine, center average defuzzifier and exponential membership functions. A model based on the classical Molecular Dynamics (MD) is used for modeling the nano-system and passing the states to the fuzzy controller. Then the fuzzy controller sets the actuators positions in order to control the diameter of the molecular valve. It has been shown that the designed controller can control the radius with an appropriate accuracy. Dimensionless equations of motion are used for designing the controller; therefore the designed controller is versatile and applicable to all the cases that the interactions between actuators and molecules can be modeled by Lennard-Jones potential. Using such a controller makes the molecular valve become applicable in the real world which has great applications such as drug delivery and controlling nano-flows with single molecule accuracy.

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Virial Coefficients of Modified Lennard-Jones Potential

Ukrainian Journal of Physics ◽

10.15407/ujpe59.02.0172 ◽

2014 ◽

Vol 59 (2) ◽

pp. 172-178 ◽

Cited By ~ 10

Author(s):

Ushcats M.V. Ushcats M.V. ◽

Keyword(s):

Virial Coefficients ◽

Lennard Jones Potential ◽

Jones Potential ◽

Lennard Jones

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Development and Comparative Analysis of Electrochemically Etched Tungsten Tips for Quartz Tuning Fork Sensor

Micromachines ◽

10.3390/mi12030286 ◽

2021 ◽

Vol 12 (3) ◽

pp. 286

Author(s):

Ashfaq Ali ◽

Naveed Ullah ◽

Asim Ahmad Riaz ◽

Muhammad Zeeshan Zahir ◽

Zuhaib Ali Khan ◽

...

Keyword(s):

Tuning Fork ◽

Mechanical Stability ◽

Electrochemical Etching ◽

Research Work ◽

Cone Angle ◽

Quartz Tuning Fork ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

High Quality ◽

Scanning Electron

Quartz Tuning Fork (QTF) based sensors are used for Scanning Probe Microscopes (SPM), in particular for near-field scanning optical microscopy. Highly sharp Tungsten (W) tips with larger cone angles and less tip diameter are critical for SPM instead of platinum and iridium (Pt/Ir) tips due to their high-quality factor, conductivity, mechanical stability, durability and production at low cost. Tungsten is chosen for its ease of electrochemical etching, yielding high-aspect ratio, sharp tips with tens of nanometer end diameters, while using simple etching circuits and basic electrolyte chemistry. Moreover, the resolution of the SPM images is observed to be associated with the cone angle of the SPM tip, therefore Atomic-Resolution Imaging is obtained with greater cone angles. Here, the goal is to chemically etch W to the smallest possible tip apex diameters. Tips with greater cone angles are produced by the custom etching procedures, which have proved superior in producing high quality tips. Though various methods are developed for the electrochemical etching of W wire, with a range of applications from scanning tunneling microscopy (SPM) to electron sources of scanning electron microscopes, but the basic chemical etching methods need to be optimized for reproducibility, controlling cone angle and tip sharpness that causes problems for the end users. In this research work, comprehensive experiments are carried out for the production of tips from 0.4 mm tungsten wire by three different electrochemical etching techniques, that is, Alternating Current (AC) etching, Meniscus etching and Direct Current (DC) etching. Consequently, sharp and high cone angle tips are obtained with required properties where the results of the W etching are analyzed, with optical microscope, and then with field emission scanning electron microscopy (FE-SEM). Similarly, effects of varying applied voltages and concentration of NaOH solution with comparison among the produced tips are investigated by measuring their cone angle and tip diameter. Moreover, oxidation and impurities, that is, removal of contamination and etching parameters are also studied in this research work. A method has been tested to minimize the oxidation on the surface and the tips were characterized with scanning electron microscope (SEM).

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Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

International Journal of Molecular Sciences ◽

10.3390/ijms22115914 ◽

2021 ◽

Vol 22 (11) ◽

pp. 5914

Author(s):

Mengsheng Zha ◽

Nan Wang ◽

Chaoyang Zhang ◽

Zheng Wang

Keyword(s):

Single Cell ◽

Loss Function ◽

Gaussian Function ◽

Three Dimensional ◽

Lennard Jones Potential ◽

Jones Potential ◽

Cubic Lattice ◽

Lennard Jones ◽

3D Fish ◽

Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

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