Analysis of Indentation: Implications for Measuring Mechanical Properties With Atomic Force Microscopy

1999 ◽  
Vol 121 (5) ◽  
pp. 462-471 ◽  
Author(s):  
K. D. Costa ◽  
F. C. P. Yin
Keyword(s):  
Indentation Depth ◽  
Constitutive Law ◽  
Elastic Materials ◽  
Force Microscopy ◽  
Linear Elastic ◽  
Afm Indentation ◽  
Atomic Force ◽  
Afm Probe ◽  
Nonlinear Elastic ◽  
Indenter Geometry

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law—a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

A discussion regarding the application of the Hertz contact theory on biological samples in AFM nanoindentation experiments

2020 ◽  
Vol 12 ◽  
Author(s):  
S.V. Kontomaris ◽  
A. Stylianou ◽  
K.S. Nikita ◽  
A. Malamou
Keyword(s):  
Young’S Modulus ◽  
Biological Samples ◽  
Indentation Depth ◽  
Young's Modulus ◽  
Contact Theory ◽  
Hertz Model ◽  
Force Microscopy ◽  
Linear Elastic ◽  
Atomic Force ◽  
New Equation

: Atomic Force Microscopy (AFM) Nanoindentation procedure regarding biological samples poses significant challenges with respect to the accuracy of the provided results. These challenges are related to the inhomogeneity of biological samples, various uncertainties in experimental methods and certain approximations regarding the theoretical analysis. The most commonly used theoretical model for data processing at the linear elastic regime regarding biological samples is the Hertz model. This paper focuses on the investigation of the resulting errors of the basic equation of the Hertz theory that depend on the ratio, indentation depth/indenter’s radius regarding the Young’s modulus calculation. Several examples in the literature that do not take into account the value of the ratio indentation depth/indenter’s radius are reported and the related errors are presented and discussed. In addition, an extended new equation is derived which takes into account the influence of the aforementioned ratio on the calculation of the Young’s modulus and can be easily used for calculations. Moreover, a rational explanation, regarding the extended differences of the Young’s modulus calculations using the same experimental results when these are processed using the Hertz model and the Oliver & Pharr analysis (which is the general model that applies for any axisymmetric indenter) is provided. In conclusion, the derived equation is further combined with equations which take into account the shape of the sample in order to provide a complete and reliable theoretical tool which can be generally applied in order to reduce the errors produced by the current methodology.

Force-Strain Curves Of Microcapsules With Atomic Force Microscopy

2004 ◽  
Vol 838 ◽  
Author(s):  
Eli Lansey ◽  
Fredy R. Zypman
Keyword(s):  
Atomic Force Microscopy ◽  
Indentation Depth ◽  
Point Of View ◽  
Classical Elasticity ◽  
Force Microscopy ◽  
Afm Indentation ◽  
Atomic Force ◽  
Atomic Interactions ◽  
Linear Effects ◽  
Classical Elasticity Theory

ABSTRACTWe develop an algorithm to measure elastic properties of microcapsules with Atomic Force Microscopy (AFM). The AFM is used as an indenter and presses down on a spherical microcapsule. We study the system from an atomic point of view (considering interactions between the atoms in the system via Equivalent Crystal Theory) and calculate the force produced by the system to balance the external AFM force. We plot this force as a function of the indentation depth, and from that curve we extract the interatomic parameters of ECT that are related with elastic constants. Our calculations model measurements of force-strain curves including non-linear effects. This is relevant as classical elasticity theory breaks down in the AFM indentation regime, when atomic interactions must be considered explicitly.

A Validation Study of the Repeatability and Accuracy of Atomic Force Microscopy Indentation Using Polyacrylamide Gels and Colloidal Probes

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Donghee Lee ◽  
Sangjin Ryu
Keyword(s):  
Atomic Force Microscopy ◽  
Elastic Materials ◽  
Time Intervals ◽  
Indentation Method ◽  
Force Microscopy ◽  
Afm Indentation ◽  
Atomic Force ◽  
Comparable Accuracy ◽  
Soft Biological Materials ◽  
Colloidal Probes

The elasticity of soft biological materials is a critical property to understand their biomechanical behaviors. Atomic force microscopy (AFM) indentation method has been widely employed to measure the Young's modulus (E) of such materials. Although the accuracy of the method has been recently evaluated based on comparisons with macroscale E measurements, the repeatability of the method has yet to be validated for rigorous biomechanical studies of soft elastic materials. We tested the AFM indentation method using colloidal probes and polyacrylamide (PAAM) gels of E < 20 kPa as a model soft elastic material after having identified optimal trigger force and probe speed. AFM indentations repeated with time intervals show that the method is well repeatable when performed carefully. Compared with the rheometric method and the confocal microscopy indentation method, the AFM indentation method is evaluated to have comparable accuracy and better precision, although these elasticity measurements appear to rely on the compositions of PAAM gels and the length scale of measurement. Therefore, we have confirmed that the AFM indentation method can reliably measure the elasticity of soft elastic materials.

scholarly journals Magnetic Driven Two-Finger Micro-Hand with Soft Magnetic End-Effector for Force-Controlled Stable Manipulation in Microscale

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 410
Author(s):  
Dan Liu ◽  
Xiaoming Liu ◽  
Pengyun Li ◽  
Xiaoqing Tang ◽  
Masaru Kojima ◽  
...  
Keyword(s):  
Magnetic Force ◽  
Force Feedback ◽  
Soft Magnetic ◽  
End Effector ◽  
Force Microscopy ◽  
System A ◽  
Atomic Force ◽  
Afm Probe ◽  
End Effectors ◽  
Fixed End

In recent years, micromanipulators have provided the ability to interact with micro-objects in industrial and biomedical fields. However, traditional manipulators still encounter challenges in gaining the force feedback at the micro-scale. In this paper, we present a micronewton force-controlled two-finger microhand with a soft magnetic end-effector for stable grasping. In this system, a homemade electromagnet was used as the driving device to execute micro-objects manipulation. There were two soft end-effectors with diameters of 300 μm. One was a fixed end-effector that was only made of hydrogel, and the other one was a magnetic end-effector that contained a uniform mixture of polydimethylsiloxane (PDMS) and paramagnetic particles. The magnetic force on the soft magnetic end-effector was calibrated using an atomic force microscopy (AFM) probe. The performance tests demonstrated that the magnetically driven soft microhand had a grasping range of 0–260 μm, which allowed a clamping force with a resolution of 0.48 μN. The stable grasping capability of the magnetically driven soft microhand was validated by grasping different sized microbeads, transport under different velocities, and assembly of microbeads. The proposed system enables force-controlled manipulation, and we believe it has great potential in biological and industrial micromanipulation.

scholarly journals Simultaneous acquisition of current and lateral force signals during AFM for characterising the piezoelectric and triboelectric effects of ZnO nanorods

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yijun Yang ◽  
Kwanlae Kim
Keyword(s):  
Linear Regression Analysis ◽  
Zno Nanorods ◽  
Lateral Force ◽  
Mechanical Force ◽  
Force Microscopy ◽  
Atomic Force ◽  
Simultaneous Acquisition ◽  
Afm Probe ◽  
Triboelectric Effect ◽  
Conversion Efficiencies

AbstractAtomic force microscopy (AFM) is central to investigating the piezoelectric potentials of one-dimensional nanomaterials. The AFM probe is used to deflect individual piezoelectric nanorods and to measure the resultant current. However, the torsion data of AFM probes have not been exploited to elucidate the relationship between the applied mechanical force and resultant current. In this study, the effect of the size of ZnO nanorods on the efficiency of conversion of the applied mechanical force into current was investigated by simultaneously acquiring the conductive AFM and lateral force microscopy signals. The conversion efficiency was calculated based on linear regression analysis of the scatter plot of the data. This method is suitable for determining the conversion efficiencies of all types of freestanding piezoelectric nanomaterials grown under different conditions. A pixel-wise comparison of the current and lateral force images elucidated the mechanism of current generation from dense arrays of ZnO nanorods. The current signals generated from the ZnO nanorods by the AFM probe originated from the piezoelectric and triboelectric effects. The current signals contributed by the triboelectric effect were alleviated by using an AFM probe with a smaller spring constant and reducing the normal force.

Material Property Characterization of Costal Cartilage Using AFM Indentation

2009 ◽  
Author(s):  
S. Tripathy ◽  
E. J. Berger
Keyword(s):  
Material Characterization ◽  
Costal Cartilage ◽  
Indentation Modulus ◽  
Hertz Contact ◽  
Force Microscopy ◽  
Afm Indentation ◽  
Atomic Force ◽  
Macro Scale ◽  
Property Characterization

Costal cartilage is one of the load bearing tissues of the rib cage. Literature on the material characterization of the costal cartilage is limited. Atomic force microscopy has been extremely successful in characterizing the elastic properties of articular cartilage, but no studies have been published on costal cartilage. In this study AFM indentations on human costal cartilage were performed and compared with macro scale indentation data. Spherical beaded tips of three sizes were used for the AFM indentations. The Hertz contact model for spherical indenter was used to analyze the data and obtain the Young’s modulus. The costal cartilage was found to be almost linearly elastic till 600 nm of indentation depth. It was also found that the modulus values decreased with the distance from the junction. The modulus values from macro indentations were found to be 2-fold larger than the AFM indentation modulus.

scholarly journals LIM-Nebulette Reinforces Podocyte Structural Integrity by Linking Actin and Vimentin Filaments

2020 ◽  
Vol 31 (10) ◽  
pp. 2372-2391 ◽  
Author(s):  
Xuhua Ge ◽  
Tao Zhang ◽  
Xiaoxia Yu ◽  
Alecia N. Muwonge ◽  
Nanditha Anandakrishnan ◽  
...  
Keyword(s):  
Structural Integrity ◽  
Rho Gtpase ◽  
Focal Adhesions ◽  
Super Resolution ◽  
Actin Binding ◽  
Puromycin Aminonucleoside ◽  
Force Microscopy ◽  
Afm Indentation ◽  
Atomic Force ◽  
Key Aspects

BackgroundMaintenance of the intricate interdigitating morphology of podocytes is crucial for glomerular filtration. One of the key aspects of specialized podocyte morphology is the segregation and organization of distinct cytoskeletal filaments into different subcellular components, for which the exact mechanisms remain poorly understood.MethodsCells from rats, mice, and humans were used to describe the cytoskeletal configuration underlying podocyte structure. Screening the time-dependent proteomic changes in the rat puromycin aminonucleoside–induced nephropathy model correlated the actin-binding protein LIM-nebulette strongly with glomerular function. Single-cell RNA sequencing and immunogold labeling were used to determine Nebl expression specificity in podocytes. Automated high-content imaging, super-resolution microscopy, atomic force microscopy (AFM), live-cell imaging of calcium, and measurement of motility and adhesion dynamics characterized the physiologic role of LIM-nebulette in podocytes.ResultsNebl knockout mice have increased susceptibility to adriamycin-induced nephropathy and display morphologic, cytoskeletal, and focal adhesion abnormalities with altered calcium dynamics, motility, and Rho GTPase activity. LIM-nebulette expression is decreased in diabetic nephropathy and FSGS patients at both the transcript and protein level. In mice, rats, and humans, LIM-nebulette expression is localized to primary, secondary, and tertiary processes of podocytes, where it colocalizes with focal adhesions as well as with vimentin fibers. LIM-nebulette shRNA knockdown in immortalized human podocytes leads to dysregulation of vimentin filament organization and reduced cellular elasticity as measured by AFM indentation.ConclusionsLIM-nebulette is a multifunctional cytoskeletal protein that is critical in the maintenance of podocyte structural integrity through active reorganization of focal adhesions, the actin cytoskeleton, and intermediate filaments.

Quantitative mechanical analysis of indentations on layered, soft elastic materials

Soft Matter ◽  
2019 ◽  
Vol 15 (8) ◽  
pp. 1776-1784 ◽  
Author(s):  
Bryant L. Doss ◽  
Kiarash Rahmani Eliato ◽  
Keng-hui Lin ◽  
Robert Ros
Keyword(s):  
Atomic Force Microscopy ◽  
Elastic Modulus ◽  
Cell Mechanics ◽  
Biological Samples ◽  
Mechanical Analysis ◽  
Elastic Materials ◽  
Mechanical Heterogeneity ◽  
Popular Method ◽  
Force Microscopy ◽  
Atomic Force

Atomic force microscopy (AFM) is becoming an increasingly popular method for studying cell mechanics, however the existing analysis tools for determining the elastic modulus from indentation experiments are unable to quantitatively account for mechanical heterogeneity commonly found in biological samples.

Sign in / Sign up

Export Citation Format

Share Document