General scaling law for stiffness measurement of small bodies with applications to the atomic force microscope

Sader, John E.; Pacífico, Jessica; Green, Christopher P.; Mulvaney, Paul

doi:10.1063/1.1935133

Cited by 71 publications

(88 citation statements)

References 19 publications

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“…Fit a Lorentzian function around the peak to automatically calculate the spring constant by the software. Some useful resources for the theory of the thermal noise method are given in references [27][28][29][30] .…”

Section: 12mentioning

confidence: 99%

Atomic Force Microscopy Imaging and Force Spectroscopy of Supported Lipid Bilayers

Unsay

Cosentino

García‐Sáez

2015

JoVE

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Atomic force microscopy (AFM) is a versatile, high-resolution imaging technique that allows visualization of biological membranes. It has sufficient magnification to examine membrane substructures and even individual molecules. AFM can act as a force probe to measure interactions and mechanical properties of membranes. Supported lipid bilayers are conventionally used as membrane models in AFM studies. In this protocol, we demonstrate how to prepare supported bilayers and characterize their structure and mechanical properties using AFM. These include bilayer thickness and breakthrough force.The information provided by AFM imaging and force spectroscopy help define mechanical and chemical properties of membranes. These properties play an important role in cellular processes such as maintaining cell hemostasis from environmental stress, bringing membrane proteins together, and stabilizing protein complexes. Video LinkThe video component of this article can be found at

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Section: 12mentioning

confidence: 99%

Atomic Force Microscopy Imaging and Force Spectroscopy of Supported Lipid Bilayers

Unsay

Cosentino

García‐Sáez

2015

JoVE

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“…25 to enable measurement of the spring constant of any elastic body, including AFM cantilevers of arbitrary geometry -this shall be referred to as the "general method." The general method relies on knowledge of the hydrodynamic function 28 for a cantilever of arbitrary shape -a protocol for its determination was also presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Sader

Sanelli

Adamson

et al. 2012

Review of Scientific Instruments

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245

229

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Compact metal probes: A solution for atomic force microscopy based tip-enhanced Raman spectroscopy Rev. Sci. Instrum. 83, 123708 (2012) Note: Radiofrequency scanning probe microscopy using vertically oriented cantilevers Rev. Sci. Instrum. 83, 126103 (2012) Switching spectroscopic measurement of surface potentials on ferroelectric surfaces via an open-loop Kelvin probe force microscopy method Appl. Phys. Lett. 101, 242906 (2012) Enhanced quality factors and force sensitivity by attaching magnetic beads to cantilevers for atomic force microscopy in liquid J. Appl. Phys. 112, 114324 (2012) Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues Rev. Sci. Instrum. 83, 121101 (2012) Additional information on Rev. Sci. Instrum. The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro-and nanomechanical systems in general.

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“…In its original form, the method was formulated for cantilevers of rectangular geometry [15]. This was subsequently generalised to accommodate cantilevers of arbitrary geometry [16] -the hydrodynamic function defines a universal dimensionless function for a particular cantilever type, i.e., plan view geometry; see Section II of Ref. [11].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…With knowledge of this hydrodynamic function for a given geometry, the spring constant of a cantilever is evaluated from measurement of its resonant frequency and quality factor in air. A number of approaches have been formulated to determine this hydrodynamic function [11,16].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

A virtual instrument to standardise the calibration of atomic force microscope cantilevers

Sader

Borgani

Gibson

et al. 2016

Review of Scientific Instruments

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135

105

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Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This is performed without reference to a global standard, which hinders robust comparison of force measurements reported by different laboratories. In this article, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others -standardising AFM force measurements -and simultaneously enabling noninvasive calibration of AFM cantilevers of any geometry. This global calibration initiative requires no additional instrumentation or data processing on the part of the user. It utilises a single website where users upload currently available data. A proof-of-principle demonstration of this initiative is presented using measured data from five independent laboratories across three countries, which also allows for an assessment of current calibration.

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General scaling law for stiffness measurement of small bodies with applications to the atomic force microscope

Cited by 71 publications

References 19 publications

Atomic Force Microscopy Imaging and Force Spectroscopy of Supported Lipid Bilayers

Atomic Force Microscopy Imaging and Force Spectroscopy of Supported Lipid Bilayers

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

A virtual instrument to standardise the calibration of atomic force microscope cantilevers

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