Analysis of dynamic cantilever behavior in tapping mode atomic force microscopy

Tapping mode atomic force microscopy (AFM) provides phase images in addition to height and amplitude images. Although the behavior of tapping mode AFM has been investigated using mathematical modeling, comprehensive understanding of the behavior of tapping mode AFM still poses a significant challenge to the AFM community, involving issues such as the correct interpretation of the phase images. In this paper, the cantilever's dynamic behavior in tapping mode AFM is studied through a three dimensional finite element method. The cantilever's dynamic displacement responses are firstly obtained via simulation under different tip‐sample separations, and for different tip‐sample interaction forces, such as elastic force, adhesion force, viscosity force, and the van der Waals force, which correspond to the cantilever's action upon various different representative computer‐generated test samples. Simulated results show that the dynamic cantilever displacement response can be divided into three zones: a free vibration zone, a transition zone, and a contact vibration zone. Phase trajectory, phase shift, transition time, pseudo stable amplitude, and frequency changes are then analyzed from the dynamic displacement responses that are obtained. Finally, experiments are carried out on a real AFM system to support the findings of the simulations. Microsc. Res. Tech. 78:935–946, 2015. © 2015 Wiley Periodicals, Inc.     

Atomic force microscopy can be used to mechanically stimulate osteoblasts and evaluate cellular strain distributions

In this study, atomic force microscopy (AFM) was used to mechanically stimulate primary osteoblasts. In response to mechanical force applied by the AFM, the indented cell increased its intracellular calcium concentration. The material properties of the cell could be estimated and the membrane strains calculated. We proceeded to validate this technique experimentally and a 20% error was found between the predicted and the measured diameter of indentation. We also determined the strain distributions within the cell that result from AFM indentation using a simple finite element model. This enabled us to formulate hypotheses as to the mechanism through which cells may sense the applied mechanical strains. Finally, we report the effect of the Poisson ratio and the cell thickness on the strain distributions. Varying the Poisson ratio did not change the order of magnitude of the strains; whereas the cellular thickness dramatically changed the order of magnitude of the cellular strains. We conclude that AFM can be used for controlled mechanical stimulation of osteoblasts and that cellular strain distributions can be computed with a good accuracy when the cell is indented in its highest part.     

Controlling tip–sample interaction forces during a single tap for improved topography and mechanical property imaging of soft materials by AFM

We introduce a method that exploits the “active” nature of the force-sensing integrated readout and active tip (FIRAT), a recently introduced atomic force microscopy (AFM) probe, to control the interaction forces during individual tapping events in tapping mode (TM) AFM. In this method the probe tip is actively retracted if the tip–sample interaction force exceeds a user-specified force threshold during a single tap while the tip is still in contact with the surface. The active tip control (ATC) circuitry designed for this method makes it possible to control the repulsive forces and indentation into soft samples, limiting the repulsive forces during the scan while avoiding instability due to attractive forces. We demonstrate the accurate topographical imaging capability of this method on suitable samples that possess both soft and stiff features.     

Topographic characterization of unworn contact lenses assessed by atomic force microscopy and wavelet transform

This paper analyses the three‐dimensional (3‐D) surface morphology of optic surface of unworn contact lenses (CLs) using atomic force microscopy (AFM) and wavelet transform. Refractive powers of all lens samples were 2.50 diopters. Topographic images were acquired in contact mode in air‐conditioned medium (35% RH, 23°C). Topographic measurements were taken over a 5 µm × 5 µm area with 512 pixel resolution. Resonance frequency of the tip was 65 kHz. The 3‐D surface morphology of CL unworn samples revealed (3‐D) micro‐textured surfaces that can be analyzed using (AFM) and wavelet transform. AFM and wavelet transform are accurate and sensitive tools that may assist CL manufacturers in developing CLs with optimal surface characteristics. Microsc. Res. Tech. 78:1026–1031, 2015. © 2015 Wiley Periodicals, Inc.     

Error analysis and regression mode of the V‐grooved sample in the atomic force microscope simulation measurement mode by the molecular mechanics

Based on the molecular mechanics, this study uses the two‐body potential energy function to construct a trapezoidal cantilever nano‐scale simulation measurement model of contact mode atomic force microscopy (AFM) under the constant force mode to simulate the measurement the nano‐scale V‐grooved standard sample. We investigate the error of offset distance of the cross‐section profile when using the probes with different trapezoidal cantilever probe tip radii (9.5, 8.5, and 7.5 Å) to scan the peak of the V‐grooved standard sample being reduced to one‐tenth (1/10) of its size, and use the offset error to inversely find out the regression equation. We analyze how the tip apex as well as the profile of the tip edge oblique angle and the oblique edge angle affects the offset distance. Furthermore, a probe with a larger radius of 9.5 nm is used to simulate and measure the offset error of scan curve, and acquire the regression equation. By the conversion proportion coefficient of size (ω), and revising the size‐reduced regression equation during the small size scale, a revised regression equation of a larger size scale can be acquired. The error is then reduced, further enhancing the accuracy of the AFM scanning and measurement. SCANNING 31: 147–159, 2009. © 2009 Wiley Periodicals, Inc.     

Lateral force microscopy of multiwalled carbon nanotubes

Carbon nanotubes are usually imaged with the atomic force microscope (AFM) in non-contact mode. However, in many applications, such as mechanical manipulation or elasticity measurements, contact mode is used. The forces affecting the nanotube are then considerable and not fully understood. In this work lateral forces were measured during contact mode imaging with an AFM across a carbon nanotube. We found that, qualitatively, both magnitude and sign of the lateral forces to the AFM tip were independent of scan direction and can be concluded to arise from the tip slipping on the round edges of the nanotube. The dependence on the normal force applied to the tip and on the ratio between nanotube diameter and tip radius was studied. We show that for small values of this ratio, the lateral force signal can be explained with a simple geometrical model.     

An edge reversal method for precision measurement of cutting edge radius of single point diamond tools

A method, which is referred to as the edge reversal method, is proposed for precision measurement of the cutting edge radius of single point diamond tools. An indentation mark of the cutting edge which replicates the cutting edge geometry is firstly made on a soft metal substrate surface. The cutting edge of the diamond tool and its indentation mark, which is regarded as the reversal cutting edge, are then measured by utilizing an atomic force microscopy (AFM), respectively. The cutting edge radius can be accurately evaluated through removing the influence of the AFM probe tip radius, which is comparable to the cutting edge radius, based on the two measured data without characterization of the AFM probe tip radius. The results of measurement experiments and uncertainty analysis are presented to demonstrate the feasibility of the proposed method.     

Indentation modulus and hardness of viscoelastic thin films by atomic force microscopy: A case study

We propose a nanoindentation technique based on atomic force microscopy (AFM) that allows one to deduce both indentation modulus and hardness of viscoelastic materials from the force versus penetration depth dependence, obtained by recording the AFM cantilever deflection as a function of the sample vertical displacement when the tip is pressed against (loading phase) and then removed from (unloading phase) the surface of the sample. Reliable quantitative measurements of both indentation modulus and hardness of the investigated sample are obtained by calibrating the technique through a set of different polymeric samples, used as reference materials, whose mechanical properties have been previously determined by standard indentation tests. By analyzing the dependence of the cantilever deflection versus time, the proposed technique allows one to evaluate and correct the effect of viscoelastic properties of the investigated materials, by adapting a post-experiment data processing procedure well-established for standard depth sensing indentation tests. The technique is described in the case of the measurement of indentation modulus and hardness of a thin film of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate), deposited by chronoamperometry on an indium tin oxide (ITO) substrate.     

Quantitative measurement of indentation hardness and modulus of compliant materials by atomic force microscopy

An atomic force microscopy (AFM) based technique is proposed for the characterization of both indentation modulus and hardness of compliant materials. A standard AFM tip is used as an indenter to record force versus indentation curves analogous to those obtained in standard indentation tests. In order to overcome the lack of information about the apex geometry, the proposed technique requires calibration using a set of reference samples whose mechanical properties have been previously characterized by means of an independent technique, such as standard indentation. Due to the selected reference samples, the technique has been demonstrated to allow reliable measurements of indentation modulus and hardness in the range of 0.3-4.0 GPa and 15-250 MPa, respectively.     

A new automatic contact point detection algorithm for AFM force curves

A new method for estimating the contact point in AFM force curves, based on a local regression algorithm, is presented. The main advantage of this method is that can be easily implemented as a computer algorithm and used for a fully automatic detection of the contact points in the approach force curves on living cells. The estimated contact points have been compared to those obtained by other published methods, which were applied either for materials with an elastic response to indentation forces or for experiments at high loading rates. We have found that the differences in the values of the contact points estimated with three different methods were not statistically significant and thus the algorithm is reliable. Also, we test the convenience of the algorithm for batch‐processing by computing the contact points of a force curve map of 625 (25×25) curves. Microsc. Res. Tech. 76:870–876, 2013. © 2013 Wiley Periodicals, Inc.     

Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine

This paper describes the surface profile measurement of a XY-grid workpiece with sinusoidal microstructures using an atomic force microscope (AFM) on a diamond turning machine. The sinusoidal micro-structures, which are fabricated on an aluminum plate by fast tool servo-assisted diamond turning, are a superposition of periodic sine-waves along the X- and Y-directions (wavelength (XY): 150 μm, amplitude (Z): 0.25 μm). A linear encoder with a resolution of 0.5 nm is integrated into the AFM-head for accurate measurement of the Z-directional profile height in the presence of noise associated with the diamond turning machine. The spindle and the X-slide of the machine are employed to spirally scan the AFM-head over the sinusoidal grid workpiece. Experiments fabricating and measuring the sinusoidal grid workpiece are carried out after accurate alignment of the AFM cantilever tip with the spindle centerline.     

A compact CCD‐monitored atomic force microscope with optical vision and improved performances

A novel CCD‐monitored atomic force microscope (AFM) with optical vision and improved performances has been developed. Compact optical paths are specifically devised for both tip‐sample microscopic monitoring and cantilever's deflection detecting with minimized volume and optimal light‐amplifying ratio. The ingeniously designed AFM probe with such optical paths enables quick and safe tip‐sample approaching, convenient and effective tip‐sample positioning, and high quality image scanning. An image stitching method is also developed to build a wider‐range AFM image under monitoring. Experiments show that this AFM system can offer real‐time optical vision for tip‐sample monitoring with wide visual field and/or high lateral optical resolution by simply switching the objective; meanwhile, it has the elegant performances of nanometer resolution, high stability, and high scan speed. Furthermore, it is capable of conducting wider‐range image measurement while keeping nanometer resolution. Microsc. Res. Tech. 76:931–935, 2013. © 2013 Wiley Periodicals, Inc.     

Atomic force microscope tip cleaning by using gratings as micro‐washboards

The sharpness of atomic force microscope (AFM) tips is essential for acquiring high quality AFM images. However, AFM tips would easily get contaminated during scanning and storage at ambient condition, which influences image resolution and causes image distortion. Replacing the probe frequently is a solution, but uneconomical. To solve this problem, several tip cleaning methods have been proposed but there is space for further improvement. Therefore, this article developed a method of tip cleaning by using a one‐dimensional grating (600 lines/mm) as a micro‐washboard to “wash” contaminated tips. We demonstrate that the contaminants can be scrubbed away by rapidly scanning such micro‐washboard against the tip in the aids of Z‐dithering (10–20 Hz) exerted on the washboard. This method is highly efficient and proved to be superior to traditional ones. Experiments show that AFM images acquired with “washed” tips have higher resolution and less distortion compared with images acquired using contaminated tips, even comparable to those scanned by new ones. Microsc. Res. Tech. 76:1131–1134, 2013. © 2013 Wiley Periodicals, Inc.     

Study of the sensitivity and resonant frequency of the torsional modes of an AFM cantilever with a sidewall probe based on a nonlocal elasticity theory

A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed‐form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small‐scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory. Microsc. Res. Tech. 78:408–415, 2015. © 2015 Wiley Periodicals, Inc.     

Measuring biomaterials mechanics with atomic force microscopy. 1. Influence of the loading rate and applied force (pyramidal tips)

Atomic force microscopy (AFM) is today an established tool in imaging and determination of mechanical properties of biomaterials. Due to their complex organization, those materials show intricate properties such as viscoelasticity. Therefore, one has to consider that the loading rate at which the sample is probed will lead to different mechanical response (properties). In this work, we studied the dependence of the mechanical properties of endothelial cells on the loading rate using AFM in force spectroscopy mode. We employed a sharp, four‐sided pyramidal indenter and loading rates ranging from 0.5 to 20 μm/s. In addition, by variation of the load (applied forces from 100 to 10,000 pN), the dependence of the cell properties on indentation depth could be determined. We then showed that the mechanical response of endothelial cells depends nonlinearly on the loading rate and follows a weak power‐law. In addition, regions of different viscous response at varying indentation depth could be determined. Based on the results we obtained, a general route map for AFM users for design of cell mechanics experiments was described.     

Tribological Properties of Self-Assembled Monolayers and Their Substrates Under Various Humid Environments

Using friction force microscopy (FFM) under controlled environments, we have systematically investigated the humidity effect on the frictional properties of two important classes of self-assembled monolayers (SAMs), i.e., N-octadecyltrimethoxysilane (OTE, CH₃(CH₂)₁₇Si(OCH₃)₃) on SiO₂(OTE/SiO₂), and N-alkanethiols on Au(111), together with their respective substrates. Experimental results show that both OTE and alkylthiol SAMs can decrease the friction force between a Si₃N₄ atomic force microscope (AFM) tip and substrates. The nearly humidity-independent friction of the two kinds of SAMs indicates that these SAMs are ideal lubricants in applications of micro-electro-mechanical systems (MEMS) under different environments. The humidity dependence—as the humidity increases, the friction first increases and then decreases—of the two substrates, SiO₂ and Au(111), can be explained by the adsorption of water. The decrease in the friction at high humidity is attributed to the low viscosity in the multilayers of water, while the increase in the friction at low humidity can be explained by the high viscosity between the water monolayer and the surfaces (AFM tip and sample), possibly due to the confinement effects. The effect of modification of the AFM tip with alkanethiol molecules on the humidity dependence of Au(111) friction has also been investigated.     

Molecular dynamics study of dynamic contact and separation between tip and disk surface

Molecular dynamics simulations were performed to study contact and separation between tip and lubricants on disk surface. The effects of contact indentation depth, indentation velocity, separation velocity, adhesive energy, lubricant molecular structure and lubricating film thickness on interacting force were analyzed. The results indicate that the tip force exerted by lubricants is velocity-dependent. The tip force increases with increasing indentation velocity and separation force reduces with increasing separation velocity. The damping of branched molecule and thick lubricating film is high. The high adhesive energy of tip material can produce high separation force which reduces bouncing vibration.     

Membrane deformation of living glial cells using atomic force microscopy

Using atomic force microscopy (AFM) it has been possible to detect actin filaments that are beneath the cell membrane of living cells despite the fact that the AFM tip is applied to the surface of the cell. To determine whether the AFM tip actually penetrates or deforms the cell membrane we determined whether an intracellularly trapped fluorescent indicator was lost from cells during AFM. Using epi-fluorescence illumination to monitor the presence of fluo-3 in the cell, we found that AFM did not cause dye leakage from the cell. Further, force–distance curves indicated that standard tips did not penetrate the membrane while sharper Supertips^TM did. In addition, the physiology of cells was found to be unaffected by AFM with standard tips since volume regulatory signal transduction mechanisms were intact in such studies. Thus, traditional AFM tips deform the cell membrane in order to reveal the presence of subcellular structures.     

Estimations of work hardening exponents of engineering metals using residual indentation profiles of nano-indentation

This study was designed to predict work hardening exponent n of materials from AFM (atomic force microscope) observations of residual indentation impression in sharp indentations. FE simulations of nano-indentation were performed to 140 combinations to each parameter (elastic modulus E, yield stress σ _y , work hardening exponent n, and Poisson’s ratio gv) expressing elastic-plastic behaviors of universal engineering metals. Using the results from FE simulations and dimensional analysis, dimensionless functions were established to correlate residual indentation profiles with the work hardening exponent. This function was examined with nano-indentation, tensile test, and AFM observations after indentation for two materials (Al6061-T6 and copper).     

Fabrication of various tip-size AFM probes for evaluating single-molecular retraction force between actin and anti-actin

The authors fabricated a probe tip with various sizes and examined the size dependency of the probe tip on the distribution of retraction forces between actin and anti-actin. Probe tips of various sizes were fabricated by two-photon polymerization methods on a micro cantilever of an atomic force microscope (AFM). The authors succeeded in fabricating a spherical tip having a smooth surface and the tip size varied between φ 0.8 and 5.5 μm. Anti-actin was immobilized on the fabricated probe tips and force curves were measured against an actin-immobilized mica substrate by AFM to analyze the retraction forces. The histograms of retraction forces showed that the single-molecular retraction force between actin and anti-actin was ca. 350–400 pN. It was observed that the average retraction forces for each tip size correlated with the square of the tip radius.