Analysis of the atomic force microscopy vibration behavior using the Timoshenko theory by multi‐scale method in the air environment

This article deals with the modeling and simulation of the vibration behavior of piezoelectric micro‐cantilever (MC) based on the Timoshenko theory and using multi‐scale (MTS) method in the air environment. In this regard, the results are compared with the previous literature, such as the finite element method and the MTS method. The analysis of the piezoelectric MC vibrating behavior is investigated in a dynamical mode including non‐contact and tapping modes. The dynamics of this system is affected by interferential forces between probe tip and sample surface, such as van der Waals, capillary, and contact forces. According to the results, the forces applied to the probe tip reduce the amplitude and the resonance frequency. The simulation of surface topography in non‐contact mode and tapping for rectangular and wedge‐shaped roughness in the air environment are presented. Various experiments have been conducted in Ara research Company using the atomic force microscopy device in the amplitude mode. In the NSC15 Cantilever, the first natural frequency is derived from the results of the MC simulation based on Timoshenko beam theory, the practical results are 295.85 and 296.12 kHz, and the error rate is 0.09; at higher natural frequencies, the error rate has been increased. The γ _f coefficient is a measure of the nonlinear effects on the system; the effect of the piezoelectric length and width on γ _f coefficient is also investigated.     

Dynamic modeling of oblique non-uniform piezoelectric MC in liquid with various percentages of glycerin in the presence of rough surface

One of the most useful applications of an AFM is imaging of biological particles in a liquid medium. The increase of the topography accuracy in a liquid medium requires accurate dynamic modeling of a Microcantilever (MC). This article investigates the accurate dynamic modeling of the non-uniform AFM piezoelectric MC with rectangular geometry in the amplitude mode in liquid medium for rough surfaces. To increase the accuracy of the modeling, the Modified couple stress (MCS) theory in the liquid medium according to the Timoshenko beam model has been used. Moreover, the differential quadrature (DQ) method has been used for solving equations, because in comparison with the other methods it has a high speed in solving equations and is accurate in the number of fewer elements. In addition, the accurate force modeling has been established by considering the shear forces caused by liquid on the sides of the piezoelectric MC by solving the Navier-Stokes equations, and by considering the hydrodynamic force, squeeze force and applied forces between the sample surface and the MC tip. The results illustrate that utilizing higher vibration modes affect the quality of rough surface topography with the step roughness in the liquid medium and increase the quality of surfaces topography in the tapping mode, especially in the second MC vibration mode. Moreover, it should be noted that the sensitivity of the MC vibration amplitude to the piezoelectric MC angle is higher in comparison with other investigated parameters.     

Comparative study of the conditions required to image live human epithelial and fibroblast cells using atomic force microscopy

Successful imaging of living human cells using atomic force microscopy (AFM) is influenced by many variables including cell culture conditions, cell morphology, surface topography, scan parameters, and cantilever choice. In this study, these variables were investigated while imaging two morphologically distinct human cell lines, namely LL24 (fibroblasts) and NCI H727 (epithelial) cells. The cell types used in this study were found to require different parameter settings to produce images showing the greatest detail. In contact mode, optimal loading forces ranged between 2-2.8 x 10(-9) and 0.1-0.7 x 10(-9) (N) for LL24 and NCI H727 cells respectively. In tapping (AC) mode, images of LL24 cells were obtained using cantilevers with a spring constant of at least 0.32 N/m, while NCI H727 cells required a greater spring constant of at least 0.58 N/m. To obtain tapping mode images, cantilevers needed to be tuned to resonate at higher frequencies than their resonance frequencies to obtain images. For NCI H727 cells, contact mode imaging produced the clearest images. For LL24 cells, contact and tapping mode AFM produced images of comparable quality. Overall, this study shows that cells with different morphologies and surface topography require different scanning approaches and optimal conditions must be determined empirically to achieve images of high quality.     

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.     

Dynamic analysis of tapping mode atomic force microscope (AFM) for critical dimension measurement

Transient dynamics of tapping mode atomic force microscope (AFM) for critical dimension measurement are analyzed. A simplified nonlinear model of AFM is presented to describe the forced vibration of the micro cantilever-tip system with consideration of both contact and non-contact transient behavior for critical dimension measurement. The governing motion equations of the AFM cantilever system are derived from the developed model. Based on the established dynamic model, motion state of the AFM cantilever system is calculated utilizing the method of averaging with the form of slow flow equations. Further analytical solutions are obtained to reveal the effects of critical parameters on the system dynamic performance. In addition, features of dynamic response of tapping mode AFM in critical dimension measurement are studied, where the effects of equivalent contact stiffness, quality factor and resonance frequency of cantilever on the system dynamic behavior are investigated. Contact behavior between the tip and sample is also analyzed and the frequency drift in contact phase is further explored. Influence of the interaction between the tip and sample on the subsequent non-contact phase is studied with regard to different parameters. The dependence of the minimum amplitude of tip displacement and maximum phase difference on the equivalent contact stiffness, quality factor and resonance frequency are investigated. This study brings further insights into the dynamic characteristics of tapping mode AFM for critical dimension measurement, and thus provides guidelines for the high fidelity tapping mode AFM scanning.     

The effect of surface roughness on the vibration behavior of AFM piezoelectric MC in the vicinity of sample surface in air environment based on MCS theory

Recent developments in the field of piezoelectric materials have led to the increasing use of piezoelectric materials in a variety of Atomic Force Microscopy (AFM). Utilizing piezoelectric layer as a sensor and actuator not only reduces the size of microscope but also enhances the quality of surface topography in Micro and Nano scales. In the current study, the effect of surface roughnesson the vibration behavior of AFM piezoelectric micro cantilever (MC) has been investigated in Micro and Nano scales according to the types of the surface roughness. Furthermore, the micro cantilever modelling has been schemed based on the Modified Couple Stress (MCS) theoryin order to model the vibration amplitude of AFM piezoelectric MC that precisely indicates the measured surface roughness. Besides, according to the various modelling of surface roughness, the effect of roughness radius on the minimum and maximum amplitude of Piezoelectric MC has been studied based on the geometry of roughness in air environment. In this environment, the effect of environmental forces including van der Waals, Capillary and contact forces on the vibration amplitude of MC forms the basis of surface topography which has, also, been studied in this article. Moreover, the present study intends to investigate the effect of surface roughness on the vibrating amplitude of MC in both the Tapping and Non-Contact Modes.     

Coupled lateral bending-torsional vibration sensitivity of atomic force microscope cantilever

We study the influence of the contact stiffness and the ration between cantilever and tip lengths on the resonance frequencies and sensitivities of lateral cantilever modes. We derive expressions to determine both the effective resonance frequency and the mode sensitivity of an atomic force microscope (AFM) rectangular cantilever. Once the contact stiffness is given, the resonance frequency and the sensitivity of the vibration modes can be obtained from the expression. The results show that each mode has a different resonant frequency to variations in contact stiffness and each frequency increased until it eventually reached a constant value at very high contact stiffness. The low-order vibration modes are more sensitive to vibration than the high-order mode when the contact stiffness is low. However, the situation is reversed when the lateral contact stiffness became higher. Furthermore, increasing the ratio of tip length to cantilever length increases the vibration frequency and the sensitivity of AFM cantilever.     

Optimization of adhesion mode atomic force microscopy resolves individual molecules in topography and adhesion.

The force sensor of an atomic force microscope (AFM) is sensitive enough to measure single molecular binding strengths by means of a force-distance curve. In order to combine high-force sensitivity with the spatial resolution of an AFM in topography mode, adhesion mode has been developed. Since this mode generates a force-distance curve for every pixel of an image, the measurement speed in liquid is limited by the viscous drag of the cantilever. We have equipped our adhesion mode AFM with a cantilever that has a low viscous drag in order to reach pixel frequencies of 65 Hz. Optimized filtering techniques combined with an auto-zero circuitry that reduces the drift in the deflection signal, limited high- and low-frequency fluctuations in the height signal to 0.3 nm. This reduction of the height noise, in combination with a thermally stabilized AFM, allowed the visualization of individual molecules on mica with an image quality comparable to tapping mode. The lateral resolution in both the topography and the simultaneously recorded adhesion image are only limited by the size of the tip. Hardware and software position feedback systems allows individual molecules to be followed in time during more than 30 min with scan sizes down to 60 x 60 nm2.     

Attachment of carbon nanotubes to atomic force microscope probes

In atomic force microscopy (AFM) the accuracy of data is often limited by the tip geometry and the effect on this geometry of wear. One way to improve the tip geometry is to attach carbon nanotubes (CNT) to AFM tips. CNTs are ideal because they have a small diameter (typically between 1 and 20nm), high aspect ratio, high strength, good conductivity, and almost no wear. A number of methods for CNT attachment have been proposed and explored including chemical vapour deposition (CVD), dielectrophoresis, arc discharge and mechanical attachment. In this work we will use CVD to deposit nanotubes onto a silicon surface and then investigate improved methods to pick-up and attach CNTs to tapping mode probes. Conventional pick-up methods involve using standard tapping mode or non-contact mode so as to attach only those CNTs that are aligned vertically on the surface. We have developed improved methods to attach CNTs using contact mode and reduced set-point tapping mode imaging. Using these techniques the AFM tip is in contact with a greater number of CNTs and the rate and stability of CNT pick-up is improved. The presence of CNTs on the modified AFM tips was confirmed by high-resolution AFM imaging, analysis of the tips dynamic force curves and scanning electron microscopy (SEM).     

Topography imaging with a heated atomic force microscope cantilever in tapping mode

This article describes tapping mode atomic force microscopy (AFM) using a heated AFM cantilever. The electrical and thermal responses of the cantilever were investigated while the cantilever oscillated in free space or was in intermittent contact with a surface. The cantilever oscillates at its mechanical resonant frequency, 70.36 kHz, which is much faster than its thermal time constant of 300 micros, and so the cantilever operates in thermal steady state. The thermal impedance between the cantilever heater and the sample was measured through the cantilever temperature signal. Topographical imaging was performed on silicon calibration gratings of height 20 and 100 nm. The obtained topography sensitivity is as high as 200 microVnm and the resolution is as good as 0.5 nmHz(1/2), depending on the cantilever power. The cantilever heating power ranges 0-7 mW, which corresponds to a temperature range of 25-700 degrees C. The imaging was performed entirely using the cantilever thermal signal and no laser or other optics was required. As in conventional AFM, the tapping mode operation demonstrated here can suppress imaging artifacts and enable imaging of soft samples.     

Manipulation, dissection, and lithography using modified tapping mode atomic force microscope

A modified tapping mode of the atomic force microscope (AFM) was introduced for manipulation, dissection, and lithography. By sufficiently decreasing the amplitude of AFM tip in the normal tapping mode and adjusting the setpoint, the tip-sample interaction can be efficiently controlled. This modified tapping mode has some characteristics of the AFM contact mode and can be used to manipulate nanoparticles, dissect biomolecules, and make lithographs on various surfaces. This method did not need any additional equipment and it can be applied to any AFM system.     

Novel operation mode for eliminating influence of inclination angle and friction in atomic force microscopy

The accuracy of topography imaging in contact force mode of atomic force microscopy (AFM) depends on the one-to-one corresponding relationship between the cantilever deflection and the tip–sample distance, whereas such a relationship cannot be always achieved in the presence of friction and incline angle of sample surface. Recently, we have developed a novel operation mode in which we keep the van der Waals force as constant instead of the applied normal force, to eliminate the effect of inclination angle and friction on topography imaging in the contact force mode. We have improved our AFM to enable the new operation mode for validation. Comparative experiments have been performed and the results have shown that the effect of friction and inclination angle on topography imaging in contact mode of AFM can be eliminated or at least decreased effectively by working in the new operation mode we present.     

Temperature-dependent imaging of living cells by AFM

Characterization of lateral organization of plasma membranes is a prerequisite to the understanding of membrane structure-function relationships in living cells. Lipid-lipid and lipid-protein interactions are responsible for the existence of various membrane microdomains involved in cell signalization and in numerous pathologies. Developing approaches for characterizing microdomains associate identification tools like recognition imaging with high-resolution topographical imaging. Membrane properties are markedly dependent on temperature. However, mesoscopic scale topographical information of cell surface in a temperature range covering most of cell biology experimentation is still lacking. In this work we have examined the possibility of imaging the temperature-dependent behavior of eukaryotic cells by atomic force microscopy (AFM). Our results establish that the surface of living CV1 kidney cells can be imaged by AFM, between 5 and 37 degrees C, both in contact and tapping modes. These first temperature-dependent data show that large cell structures appeared essentially stable at a microscopic scale. On the other hand, as shown by contact mode AFM, the surface was highly dynamic at a mesoscopic scale, with marked changes in apparent topography, friction, and deflection signals. When keeping the scanning conditions constant, a progressive loss in the image contrast was however observed, using tapping mode, on decreasing the temperature.     

FEM analysis of the vibrational motion of oblique piezoelectric microcantilever in the vicinity of a sample surface in liquid

This article examines an oblique Microcantilever (MC) with an extended piezoelectric layer in liquid. The study of hydrodynamic force in MC which has been floated in viscous fluid is considered as paramount importance. To model the Vibrational motion, the Hamilton's principle has been used. For this purpose, the Vibrational motion equation has been modeled by considering the continuous beam based on the Euler–Bernoulli beam theory in liquid. Furthermore, using the Galerkin method and the Newmark algorithm, the differential equations of the MC has been solved. In this modeling, the inter-atomic forces between the MC tip and the sample surface have been considered in addition to the hydrodynamic and squeeze forces. The simulation results illustrate a reduction in the sensitivity of the vibrational motion under the effect of the squeeze force during the angularization of the MC. Moreover, the results illustrate that by reducing the MC distance from the sample surface, the Vibration amplitude decreases due to the increase in the fluid squeeze force. At the end, it has been shown that the time delay in sample surface topography in liquid substantially decreases in comparison with the air.     

Polysaccharide properties probed with atomic force microscopy

In recent years, polysaccharides have been extensively studied using atomic force microscopy (AFM). Owing to its high lateral and vertical resolutions and ability to measure interaction forces in liquids at pico‐ or nano‐Newton level, the AFM is an excellent tool for characterizing biopolymers. The first imaging studies showed the morphology of polysaccharides, but gradually more quantitative image analysis techniques were developed as the AFM grew easier to use in aqueous liquids and in non‐contact modes. Recently, AFM has been used to stretch polysaccharides and characterize their physicochemical properties by application of appropriate polymer stretching models, using a technique called single‐molecule force spectroscopy. From application of such models as the wormlike chain, freely jointed chain, extensible‐freely jointed chain, etc., properties such as the contour length, persistence length and segment elasticity or spring constant can be calculated for polysaccharides. The adhesion between polysaccharides and surfaces has been quantified with AFM, and this application is particularly useful for studying polysaccharides on microbial and other types of cells, because their adhesion is controlled by biopolymer characteristics. This review presents a synthesis of the theory and techniques currently in use to probe the physicochemical properties of polysaccharides with AFM.     

Non-optical bimorph-based tapping-mode force sensing method for scanning near-field optical microscopy

A non‐optical bimorph‐based tapping‐mode force sensing method for tip–sample distance control in scanning near‐field optical microscopy is developed. Tapping‐mode force sensing is accomplished by use of a suitable piezoelectric bimorph cantilever, attaching an optical fibre tip to the extremity of the cantilever free end and fixing the guiding portion of the fibre to a stationary part near the tip to decouple it from the cantilever. This method is mainly characterized by the use of a bimorph, which carries out simultaneous excitation and detection of mechanical vibration at its resonance frequency owing to piezoelectric and anti‐piezoelectric effects, resulting in simplicity, compactness, ease of implementation and lack of parasitic optical background. In conjugation with a commercially available SPM controller, tapping‐mode images of various samples, such as gratings, human breast adenocarcinoma cells, red blood cells and a close‐packed layer of 220‐nm polystyrene spheres, have been obtained. Furthermore, topographic and near‐field optical images of a layer of polystyrene spheres have also been taken simultaneously. The results suggest that the tapping‐mode set‐up described here is reliable and sensitive, and shows promise for biological applications.     

Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe

The resonant frequency and sensitivity of flexural vibration for an atomic force microscope (AFM) cantilever with a sidewall probe have been analyzed. 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. The results show that a sidewall scanning AFM is more sensitive when the contact stiffness is lower and that the first mode is the most sensitive. However, the high-order modes become more sensitive than the low-order modes as the contact stiffness increases. The resonance frequency of an AFM cantilever is low when contact stiffness is small. However, the frequency rapidly increases as contact stiffness increases. In addition, it can be found that the effects of the vertical extension on the sensitivity and the resonant frequency of an AFM cantilever are significant. Decreasing the length of vertical extension can increase the resonance frequency and sensitivity of mode 1 when the contact stiffness is small. However, the situation is reverse when the contact stiffness becomes large.     

金刚石车削工件表面轮廓的仿真与分析

对振动情况下加工的工件表面的三维形貌进行了仿真 ,并从理论上对工件表面形貌的径向、周向与刀具螺旋轨迹方向的截面轮廓进行了分析。结果表明 :不同的截面轮廓分别载有不同的表面特征信息 ,利用这些特征有助于对刀具与工件间的相对振动进行辨识。采用有关文献中的试验数据对仿真结果进行了验证     

Sensitivity and resonant frequency of an AFM with sidewall and top-surface probes for both flexural and torsional modes

The resonant frequencies and flexural sensitivities of an atomic force microscope (AFM) with assembled cantilever probe (ACP) are studied. This ACP comprises a horizontal cantilever, a vertical extension and two tips located at the free ends of the cantilever and the extension, which makes the AFM capable of simultaneous topography at top surface and sidewalls of microstructures especially microgears, which consequently leads to a time-saving swift scanning process. In this work, the effects of the sample surface contact stiffness and the geometrical parameters such as the ratio of the vertical extension length to the horizontal cantilever length and the distance of the vertical extension from clamped end of the horizontal cantilever on both flexural and torsional resonant frequencies and sensitivities are assessed. These geometrical effects are illustrated in some figures. The results show that the low-order vibration modes are more sensitive for low values of the contact stiffness, but the situation is reversed for high values.     

Origin of phase shift in atomic force microscopic investigation of the surface morphology of NR/NBR blend film

Atomic force microscopy (AFM) was used to study the morphology and surface properties of NR/NBR blend. Blends at 1/3, 1/1 and 3/1 weight ratios were prepared in benzene and formed film by casting. AFM phase images of these blends in tapping mode displayed islands in the sea morphology or matrix-dispersed structures. For blend 1/3, NR formed dispersed phase while in blends 1/1 and 3/1 phase inversion was observed. NR showed higher phase shift angle in AFM phase imaging for all blends. This circumstance was governed by adhesion energy hysteresis between the device tip and the rubber surface rather than surface stiffness of the materials, as proved by force distance measurements in the AFM contact mode.