Numerical Analysis of the Tapping Atomic Force Microscopy on a Viscoelastic Sample

2014 ◽  
Author(s):  
Ben Carmichael ◽  
Gary Frey ◽  
S. Nima Mahmoodi
Keyword(s):  
Numerical Analysis ◽  
Time History ◽  
Equation Of Motion ◽  
Viscous Effects ◽  
Force Microscopy ◽  
Forcing Function ◽  
Atomic Force ◽  
Cantilevered Beam ◽  
Soft Samples ◽  
The Galerkin Method

Mechanical characterization of thin samples is now routine due to the prominence of the Atomic Force Microscope. Advances in amplitude modulation techniques have allowed for accurate measurement of a sample’s elastic properties by interpreting the changes in the vibration of a cantilevered beam in intermittent contact. However, the nonlinearities associated with contact complicate attempts to find an accurate time-history for the beam. Furthermore, the inclusion of viscous effects, common to soft samples, puts an explicit solution even farther from reach. A numerical method is proposed that analyzes the time-history and frequency response of a microcantilever beam with a viscoelastic end-condition. The mathematics can be simplified by incorporating the viscoelastic end-condition into the equation of motion directly by modeling it as a distributed load. A forcing function can then be derived from the Standard Linear Solid model of viscoelasticity and implemented in the non-conservative work term of Hamilton’s principle. The Galerkin method can separate the resulting nonlinear equation of motion into time and space components. Performing a numerical analysis of the time factor equation provide the beam’s response over time. The results demonstrate the distinctive effects of viscoelasticity and periodic contact on the beam’s motion and provide the framework for the determination of viscous properties using dynamic techniques.

Phase Contrast Imaging in Atomic Force Microscopy

1997 ◽  
Vol 3 (S2) ◽  
pp. 1275-1276
Author(s):  
Sergei Magonov
Keyword(s):  
Atomic Force Microscopy ◽  
Phase Contrast ◽  
Phase Changes ◽  
Phase Imaging ◽  
Phase Detection ◽  
Contrast Imaging ◽  
Force Microscopy ◽  
Atomic Force ◽  
Resonance Frequencies ◽  
Soft Samples

Phase detection in TappingMode™ enhances capabilities of Atomic Force Microscopy (AFM) for soft samples (polymers and biological materials). Changes of amplitude and phase changes of a fast oscillating probe are caused by tip-sample force interactions. Height images reflect the amplitude changes, and in most cases they present a sample topography. Phase images show local differences between phases of free-oscillating probe and of probe interacting with a sample surface. These differences are related to the change of the resonance frequency of the probe either by attractive or repulsive tip-sample forces. Therefore phase detection helps to choose attractive or repulsive force regime for surface imaging and to minimize tip-sample force. For heterogeneous materials the phase imaging allows to distinguish individual components and to visualize their distribution due to differences in phase contrast. This is typically achieved in moderate tapping, when set-point amplitude, Asp, is about half of the amplitude of free-oscillating cantilever, Ao. In contrast, light tapping with Asp close to Ao is best suited for recording a true topography of the topmost surface layer of soft samples. Examples of phase imaging of polymers obtained with a scanning probe microscope Nanoscope® IIIa (Digital Instruments). Si probes (225 μk long, resonance frequencies 150-200 kHz) were used.

Correction of Microrheological Measurements of Soft Samples with Atomic Force Microscopy for the Hydrodynamic Drag on the Cantilever

Langmuir ◽  
2002 ◽  
Vol 18 (3) ◽  
pp. 716-721 ◽  
Author(s):  
J. Alcaraz ◽  
L. Buscemi ◽  
M. Puig-de-Morales ◽  
J. Colchero ◽  
A. Baró ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Hydrodynamic Drag ◽  
Force Microscopy ◽  
Atomic Force ◽  
Soft Samples

Atomic Force Microscopy of Soft Samples: Gelatin and Living Cells

1998 ◽  
pp. 178-193 ◽  
Author(s):  
Jan Domke ◽  
Christian Rotsch ◽  
Paul K. Hansma ◽  
Ken Jacobson ◽  
Manfred Radmacher
Keyword(s):  
Atomic Force Microscopy ◽  
Living Cells ◽  
Force Microscopy ◽  
Atomic Force ◽  
Soft Samples

Numerical analysis of fractional dynamical behavior of Atomic Force Microscopy

2021 ◽  
Author(s):  
Mauricio A. Ribeiro ◽  
Angelo M. Tusset ◽  
Wagner B. Lenz ◽  
Ilham Kirrou ◽  
Jose M. Balthazar
Keyword(s):  
Atomic Force Microscopy ◽  
Numerical Analysis ◽  
Dynamical Behavior ◽  
Force Microscopy ◽  
Atomic Force

Measuring Viscoelasticity of Soft Samples Using Atomic Force Microscopy

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
S. Tripathy ◽  
E. J. Berger
Keyword(s):  
Atomic Force Microscopy ◽  
Soft Tissues ◽  
Relaxation Times ◽  
Indentation Test ◽  
Strain History ◽  
Force Microscopy ◽  
Afm Indentation ◽  
Atomic Force ◽  
Dependent Part ◽  
Soft Samples

Relaxation indentation experiments using atomic force microscopy (AFM) are used to obtain viscoelastic material properties of soft samples. The quasilinear viscoelastic (QLV) model formulated by Fung (1972, “Stress Strain History Relations of Soft Tissues in Simple Elongation,” in Biomechanics, Its Foundation and Objectives, Prentice-Hall, Englewood Cliffs, NJ, pp. 181–207) for uniaxial compression data was modified for the indentation test data in this study. Hertz contact mechanics was used for the instantaneous deformation, and a reduced relaxation function based on continuous spectrum is used for the time-dependent part in the model. The modified QLV indentation model presents a novel method to obtain viscoelastic properties from indentation data independent of relaxation times of the test. The major objective of the present study is to develop the QLV indentation model and implement the model on AFM indentation data for 1% agarose gel and a viscoelastic polymer using spherical indenter.

scholarly journals Исследование структуры объемного гетероперехода в полимерных солнечных элементах с помощью комбинации ультрамикротомирования и атомно-силовой микроскопии

2018 ◽  
Vol 52 (1) ◽  
pp. 110
Author(s):  
А.М. Алексеев ◽  
A. Ал-Афееф ◽  
Г.Д. Хедли ◽  
С.С. Харинцев ◽  
А.Е. Ефимов ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Solar Cells ◽  
Organic Solar Cells ◽  
Polymer Solar Cells ◽  
Structural Investigations ◽  
Photoactive Layer ◽  
Force Microscopy ◽  
Atomic Force ◽  
Bulk Structure ◽  
Soft Samples

AbstractA method for visualization via atomic-force microscopy of the internal structure of photoactive layers of polymer solar cells using an ultramicrotome for photoactive layer cutting is proposed and applied. The method creates an opportunity to take advantage of atomic-force microscopy in structural investigations of the bulk of soft samples. Such advantages of atomic-force microscopy include a high contrast and the ability to measure various surface properties at nanometer resolution. Using the proposed method, samples of the photoactive layer of polymer solar cells based on a mixture of PTB7 polythiophene and PC_71BM fullerene derivatives are studied. The disclosed details of the bulk structure of this mixture allow us to draw additional conclusions about the effect of morphology on the efficiency of organic solar cells.

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