### Citations

327 |
The physics of rubber elasticity
- Treloar
- 1958
(Show Context)
Citation Context ...oad-controlled compression of the gelscylinders at a ramp speed of 1 mm/s. For all samples (at leaststhree of each concentration), the shear modulus was determinedsfrom the rubber elasticity equation =-=[35,36]-=-su = G(A − A−2) (7)swhere u is the normal component of the engineering, or nominal,sstress (force per undeformed area); G is the shear modulus; and Asis the deformation ratio (=L /L0, where L and L0 a... |

250 | Surface energy and the contact of elastic solids - Johnson, Kendall, et al. - 1971 |

106 | Force measurements with the atomic force microscope: Technique, interpretation and applications,” - Butt, Cappella, et al. - 2005 |

62 | Determination of elastic moduli of thin layers of soft material using the atomic force microscope,
- Dimitriadis, Horkay, et al.
- 2002
(Show Context)
Citation Context ...iterated in the concluding remarks.sheorysContact Mechanics Models. The classical problem of an elas ic half-space indented by a rigid object was first treated by Hertz n 1881 and Boussinesq in 1885 =-=[18]-=-. Numerous others have con ributed to the theoretical framework, which is widely used in nterpreting the results of indentation tests at all length scales. xact solutions in the form of force-indenta... |

41 |
Measuring the Elastic Properties of Biological Sample with the AFM,”
- Radmacher
- 1997
(Show Context)
Citation Context ... are given in Table 1 for ndenters that are spherical (from the original Hertz theory of ontact between two ellipsoidal bodies and oftentimes referred to s the Hertz equation or model), sharp conical =-=[5,25]-=-, or sharpipped pyramidal [26] in geometry. For typical tapered indenters ith a blunt tip (Fig. 1), the relationship is [25,27,28]s3R tan ¢ 3Rs( ) [ ]{F = ao − m − arcsin1 −sv2 tan ¢ 2 a a3 b a2 − b2s... |

37 | Relative Microelastic Mapping of Living Cells by Atomic Force Microscopy,”
- A-Hassan, Heinz, et al.
- 1998
(Show Context)
Citation Context ... automated, contact point indepen ent technique to generate relative elasticity maps by showing that he relative work of indentation at some force is proportional to he relative measure of stiffness =-=[31]-=-. However, an absolute mea ure of elastic properties requires fitting of force-indentation data o contact mechanics models. Since both F and o are dependent n the contact point, objective approaches ... |

33 |
Analysis of Indentation: Implications for Measuring Mechanical Properties With Atomic Force Microscopy,”
- Costa, Yin
- 1999
(Show Context)
Citation Context ... are given in Table 1 for ndenters that are spherical (from the original Hertz theory of ontact between two ellipsoidal bodies and oftentimes referred to s the Hertz equation or model), sharp conical =-=[5,25]-=-, or sharpipped pyramidal [26] in geometry. For typical tapered indenters ith a blunt tip (Fig. 1), the relationship is [25,27,28]s3R tan ¢ 3Rs( ) [ ]{F = ao − m − arcsin1 −sv2 tan ¢ 2 a a3 b a2 − b2s... |

33 | Comparison of calibration methods for atomic-force microscopy cantilevers”
- Burnham, Chen, et al.
- 2003
(Show Context)
Citation Context ...e compliant canti lever (0.06 N/m nominal spring constant) than the other gelss(0.58 N/m nominal spring constant). The spring constant of eachscantilever was determined using the thermal tune method =-=[38,39]-=-.sThe algorithm outlined previously was used to extract Young’ssmodulus from each dataset.sMultiple force curves for each PVA film were collected usingsthe “force-volume” mode of the AFM. In this auto... |

29 | Microrheology of human lung epithelial cells measured by atomic force microscopy. - 1Alcaraz, Buscemi, et al. - 2003 |

28 | On the Influence of Molecular Forces on the Deformation of an Elastic Sphere and Its Sticking to a Rigid Plane,” - Muller, Yuschenko, et al. - 1980 |

24 |
Robust strategies for automated AFM force curve analysis—I. Non-adhesive indentation of soft, inhomogeneous materials.
- Lin, Dimitriadis, et al.
- 2007
(Show Context)
Citation Context ...ly applied force. When signifi cant adhesive forces exist between the contacting solids, theysmust be accounted for. Adhesive contact mechanics models willsbe discussed in a separate paper (Part II) =-=[29]-=-.sBasic Approaches to Extracting Elastic Properties FromsAFM Data. Indentation is performed by moving the cantilever insthe direction perpendicular to the sample surface, z, between asstarting positio... |

22 |
Measuring the elastic properties of living cells by the atomic force microscope
- Radmacher
(Show Context)
Citation Context ... to be successful in eliminating the need for subjective user input (e.g., specifying an estimate of the contact point based on visual inspection [19] or specifying the range of the noncontact region =-=[11]-=-) or capable of accurately processing diverse populations of curves. We have compiled a collection of complementary strate gies that addresses the known issues in the analysis of AFM force curves, an... |

17 | Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy.
- Stolz, Raiteri, et al.
- 2004
(Show Context)
Citation Context ...ata. In lieu of the flawed approach of pproximating the tip as either a sphere or a sharp cone, some esearchers generate calibration curves by combining nanoinden ation with macroscopic test methods =-=[15]-=-. The alternative ap roach introduced in Appendix B makes use of sharp tip models or dealing with blunt indenters and complements the strategies in ur algorithm. Applied in reverse order, the techniq... |

17 | Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Langmuir - Touhami, Nysten, et al. - 2003 |

16 |
Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. Phys Rev E Stat Nonlin Soft Matter Phys.
- Rico, Roca-Cusachs, et al.
- 2005
(Show Context)
Citation Context ... and oftentimes referred to s the Hertz equation or model), sharp conical [5,25], or sharpipped pyramidal [26] in geometry. For typical tapered indenters ith a blunt tip (Fig. 1), the relationship is =-=[25,27,28]-=-s3R tan ¢ 3Rs( ) [ ]{F = ao − m − arcsin1 −sv2 tan ¢ 2 a a3 b a2 − b2s2 − b2)1/2− + (a m + (2a)[ ]} here 2¢ is the tip angle, b is the radius at which the tapered ides transition into a spherical tip ... |

15 |
Imaging of lactic acid bacteria with AFM - elasticity and adhesion maps and their relationship to biological and structural data
- Schaer-Zammaretti, Ubbink
(Show Context)
Citation Context ...the cantilever tip is used as a nanoindenter, the AFM issell suited for probing the local elasticity of small, very soft, andsnhomogeneous samples. It has been used to study the elasticity ofsacteria =-=[8]-=-, cells [9–12], endothelia [13], articular cartilages14–16], and bony tissue [17]. However, despite its advantagessver more conventional testing methodologies, data processingsssues hinder the consist... |

15 |
Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy
- Mathur, Collinsworth, et al.
- 2001
(Show Context)
Citation Context ...a nanoindenter, the AFM issell suited for probing the local elasticity of small, very soft, andsnhomogeneous samples. It has been used to study the elasticity ofsacteria [8], cells [9–12], endothelia =-=[13]-=-, articular cartilages14–16], and bony tissue [17]. However, despite its advantagessver more conventional testing methodologies, data processingsssues hinder the consistency of elasticity measurements... |

14 | Elasticity and Adhesion Force Mapping Reveals Real-Time Clustering of Growth Factor Receptors and Associated Changes in Local Cellular Rheo logical Properties,” Biophys - Almqvist, Bhatia, et al. - 2004 |

12 |
Regular Pyramid Punch Problem
- Bilodeau
- 1992
(Show Context)
Citation Context ...rs that are spherical (from the original Hertz theory of ontact between two ellipsoidal bodies and oftentimes referred to s the Hertz equation or model), sharp conical [5,25], or sharpipped pyramidal =-=[26]-=- in geometry. For typical tapered indenters ith a blunt tip (Fig. 1), the relationship is [25,27,28]s3R tan ¢ 3Rs( ) [ ]{F = ao − m − arcsin1 −sv2 tan ¢ 2 a a3 b a2 − b2s2 − b2)1/2− + (a m + (2a)[ ]} ... |

12 | Atomic force microscope tip deconvolution using calibration arrays. - Markiewicz, Goh - 1995 |

12 | Colloidal gold particles as an incompressible atomic force microscope imaging standard for assessing the compressibility of biomolecules - Vesenka, Manne, et al. - 1993 |

10 | Molecular recognition imaging and force spectroscopy of single biomolecules Acc. - Kienberger, Ebner, et al. - 2006 |

10 | Using the adhesive interaction between atomic force microscopy tips and polymer surfaces to measure the elastic modulus of compliant samples," - Sun, Akhremitchev, et al. - 2004 |

6 | Atomic Force Microscopy Investigation of the Dependence of Cellular Elastic Moduli on Glutaraldehyde Fixation - Hutter, Chen, et al. - 2005 |

3 |
On Atomic Force Microscopy and the Constitutive Behavior of Living Cells
- Na, Sun, et al.
- 2004
(Show Context)
Citation Context ... and oftentimes referred to s the Hertz equation or model), sharp conical [5,25], or sharpipped pyramidal [26] in geometry. For typical tapered indenters ith a blunt tip (Fig. 1), the relationship is =-=[25,27,28]-=-s3R tan ¢ 3Rs( ) [ ]{F = ao − m − arcsin1 −sv2 tan ¢ 2 a a3 b a2 − b2s2 − b2)1/2− + (a m + (2a)[ ]} here 2¢ is the tip angle, b is the radius at which the tapered ides transition into a spherical tip ... |

3 | Polystyrene Latex Particles as a Size Cali bration for the Atomic Force Microscope - Li, Lindsay - 1991 |

2 | Imaging Proteins With Atomic Force Microscopy: An Overview - Silva - 2005 |

2 | Strategies and Results of Atomic Force - Simon, Durrieu - 2006 |

2 |
Extracting Mechanical Properties of Cells/ Biomaterials Using the Atomic Force Microscope
- Kolambkar
- 2004
(Show Context)
Citation Context ...ulus E as the fitting parameters. This approachscan be considered the semi-constrained counterpart to the visualsinspection method and is likewise prone to error when noise levelssare high.sKolambkar =-=[19]-=- formulated a more rigorous unconstrained ap proach by evaluating the error associated with assuming an incor rect contact point. He expanded the resulting force-indentationsrelation in a power seri... |

2 |
Measuring the Elastic
- Domke, Radmacher
- 1998
(Show Context)
Citation Context ...ion [18]. The pointwise calculations of E will tend toward a constant value that issdependent on the chosen contact point. Typically, Poisson’s ratiosis assumed to be 0.5 for soft, gel-like materials =-=[5,20,30]-=-. To avoidsuncertainties about the compressibility of the sample, some re searchers define an elastic constant incorporating the terms E ands(1−v2), thereby combining the linear elastic and compressi... |

2 |
Elasticity of Swollen Polyvinyl
- Horkay, Nagy
- 1980
(Show Context)
Citation Context ...H was adjusted by HCl. To createssamples of increasing stiffness, the PVA concentration was in creased while maintaining a constant crosslink density (one unitsof GDA per 100 units of vinyl alcohol) =-=[34]-=-. Gel cylinders andsthick layers (2 mmsto>1 cm) with final PVA concentrations ofs3%, 6%, 9%, and 12% (w/w) were cast in molds (1 cm diam ands1 cm high) and 35 mm Petri dishes, respectively. All sample... |

2 |
Microelectromechanical System Device for Calibration of Atomic Force Mi croscope Cantilever Spring Constants Between 0.01 and 4
- Cumpson, Hedley, et al.
- 2004
(Show Context)
Citation Context ... In the interest of achieving consistency and accuracy in bsolute measurements of elastic properties, it is necessary to uti ize the calibration methods available for determining cantilever tiffness =-=[38,39,48,49]-=- and tip geometry [50–53].sAlthough the strategies discussed here have been applied to ontact mechanics models dealing with the indentation of an infi ite half-space, they are readily applicable to m... |

2 | Silicon Structures for in Situ Characterization of Atomic Force Microscope Probe Geometry - Jarausch, Stark, et al. - 1996 |

1 | Sample Prepa ration Procedures for Biological Atomic Force Microscopy - Kirat, Burton, et al. - 2005 |

1 |
Measuring the Microelastic Properties
- Tao, Lindsay, et al.
- 1992
(Show Context)
Citation Context ...the local elasticity of small, very soft, andsnhomogeneous samples. It has been used to study the elasticity ofsacteria [8], cells [9–12], endothelia [13], articular cartilages14–16], and bony tissue =-=[17]-=-. However, despite its advantagessver more conventional testing methodologies, data processingsssues hinder the consistency of elasticity measurements on softsiological tissues and preclude the use of... |

1 |
Morphology and Transverse Stiff ness of Drosophila Myofibrils Measured by Atomic Force Microscopy,” Bio phys
- Nyland, Maughan
- 2000
(Show Context)
Citation Context ...ion [18]. The pointwise calculations of E will tend toward a constant value that issdependent on the chosen contact point. Typically, Poisson’s ratiosis assumed to be 0.5 for soft, gel-like materials =-=[5,20,30]-=-. To avoidsuncertainties about the compressibility of the sample, some re searchers define an elastic constant incorporating the terms E ands(1−v2), thereby combining the linear elastic and compressi... |

1 |
Introduction to Polymer Viscoelas ticity
- Aklonis, MacKnight
- 1983
(Show Context)
Citation Context ...oad-controlled compression of the gelscylinders at a ramp speed of 1 mm/s. For all samples (at leaststhree of each concentration), the shear modulus was determinedsfrom the rubber elasticity equation =-=[35,36]-=-su = G(A − A−2) (7)swhere u is the normal component of the engineering, or nominal,sstress (force per undeformed area); G is the shear modulus; and Asis the deformation ratio (=L /L0, where L and L0 a... |

1 |
Calibration of Atomic-Force Micro scope Tips
- Hutter, Bechhoefer
- 1993
(Show Context)
Citation Context ...e compliant canti lever (0.06 N/m nominal spring constant) than the other gelss(0.58 N/m nominal spring constant). The spring constant of eachscantilever was determined using the thermal tune method =-=[38,39]-=-.sThe algorithm outlined previously was used to extract Young’ssmodulus from each dataset.sMultiple force curves for each PVA film were collected usingsthe “force-volume” mode of the AFM. In this auto... |

1 | Accurate Height and Volume - Jiao, Schaffer - 2004 |

1 | Dimensional and Me chanical Dynamics of Active and Stable Edges in Motile Fibroblasts Investi gated by Using Atomic Force Microscopy - Rotsch, Jacobson, et al. - 1999 |

1 |
A Method for Deter mining the Spring Constant of Cantilevers for Atomic Force Microscopy,” Meas
- Torii, Sasaki, et al.
- 1996
(Show Context)
Citation Context ... In the interest of achieving consistency and accuracy in bsolute measurements of elastic properties, it is necessary to uti ize the calibration methods available for determining cantilever tiffness =-=[38,39,48,49]-=- and tip geometry [50–53].sAlthough the strategies discussed here have been applied to ontact mechanics models dealing with the indentation of an infi ite half-space, they are readily applicable to m... |