Accurate determination of spring constant of atomic force microscope cantilevers and comparison with other methods

We present calibration results of commercial AFM cantilevers using the KRISS nanoforce calibrator (NFC) that can determine traceably spring constants with an uncertainty better than 1%, along with the results obtained from other four calibration methods: the dimensional method, the cantilever-on-cantilever method, the Sader method, and the thermal noise method. Two types (contact and tapping mode) of beam-shaped AFM cantilevers with nominal spring constants of 0.9 N m⁻¹ and 42 N m⁻¹, respectively, were investigated in this study. Because of its small uncertainty, the NFC method was used to assess the uncertainties of other four methods through comparisons between values obtained from other methods and those from the NFC method for the same cantilever. Results from other methods were generally in good agreement with those from the NFC method within the uncertainties of other methods claimed in other literatures, but values obtained from the Sader method were differed by up to 40% from the NFC values, which is 2 times worse than the known uncertainty.     

Dynamic spring constants for higher flexural modes of cantilever plates with applications to atomic force microscopy

In atomic force microscopy (AFM) a sharp tip fixed close to the free end of a cantilever beam interacts with a surface. The interaction can be described by a point-mass model of an equivalent oscillator with a single spring located at the position of the tip. However, other spring constants have to be used to describe the oscillation behavior correctly if forces are acting on the cantilever over an extended lateral range. A point-mass model is then no longer valid. In the present study we derive expressions for the spring constants of cantilevers that can interact with any part of their plan view area along the beam and for all flexural modes. The equations describe the oscillation behavior in the corresponding mass model and are based on the eigenfrequencies and modal shapes of the free cantilever. The results are of high practical relevance, for example if an AFM is operated in a higher flexural mode, if the tip is not located at the free end of the cantilever beam, or if the external conservative forces affecting cantilever movement are not restricted to a single point. The limitations of the approach are discussed.     

Fast contact-mode atomic force microscopy on biological specimen by model-based control

The dynamic behavior of the piezoelectric tube scanner limits the imaging rate in atomic force microscopy (AFM). In order to compensate for the lateral dynamics of the scanning piezo a model based open-loop controller is implemented into a commercial AFM system. Additionally, our new control strategy employing a model-based two-degrees-of-freedom controller improves the performance in the vertical direction, which is important for high-speed topographical imaging. The combination of both controllers in lateral and vertical direction compensates the three-dimensional dynamics of the AFM system and reduces artifacts that are induced by the systems dynamic behavior at high scan rates. We demonstrate this improvement by comparing the performance of the model-based controlled AFM to the uncompensated and standard PI-controlled system when imaging pUC 18 plasmid DNA in air as well as in a liquid environment.     

原子力显微镜原理与应用技术

本文简述原子力显微镜的工作原理,对比说明敲击模式的优越性,指出针尖-样品卷积效应和假象产生的原因,并例证其应用领域及其测试效果。     

A symmetrical stretching stage for electrical atomic force microscopy

We present a remotely-controlled device for sample stretching, designed for use with atomic force microscopy (AFM) and providing electrical connection to the sample. Such a device enables nanoscale investigation of electrical properties of thin gold films deposited on polydimethylsiloxane (PDMS) substrate as a function of the elongation of the structure. Stretching and releasing is remotely controlled with use of a dc actuator. Moreover, the sample is stretched symmetrically, which gives an opportunity to perform AFM scans in the same site without a time-consuming finding procedure. Electrical connections to the sample are also provided, enabling Kelvin probe force microscopy (KPFM) investigations. Additionally, we present results of AFM imaging using the stretching stage.     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

Spectroscopy and atomic force microscopy of biomass

Scanning probe microscopy has emerged as a powerful approach to a broader understanding of the molecular architecture of cell walls, which may shed light on the challenge of efficient cellulosic ethanol production. We have obtained preliminary images of both Populus and switchgrass samples using atomic force microscopy (AFM). The results show distinctive features that are shared by switchgrass and Populus. These features may be attributable to the lignocellulosic cell wall composition, as the collected images exhibit the characteristic macromolecular globule structures attributable to the lignocellulosic systems. Using both AFM and a single case of mode synthesizing atomic force microscopy (MSAFM) to characterize Populus, we obtained images that clearly show the cell wall structure. The results are of importance in providing a better understanding of the characteristic features of both mature cells as well as developing plant cells. In addition, we present spectroscopic investigation of the same samples.     

Improved lateral force calibration based on the angle conversion factor in atomic force microscopy

A novel calibration method is proposed for determining lateral forces in atomic force microscopy (AFM), by introducing an angle conversion factor, which is defined as the ratio of the twist angle of a cantilever to the corresponding lateral signal. This factor greatly simplifies the calibration procedures. Once the angle conversion factor is determined in AFM, the lateral force calibration factors of any rectangular cantilever can be obtained by simple computation without further experiments. To determine the angle conversion factor, this study focuses on the determination of the twist angle of a cantilever during lateral force calibration in AFM. Since the twist angle of a cantilever cannot be directly measured in AFM, the angles are obtained by means of the moment balance equations between a rectangular AFM cantilever and a simple commercially available step grating. To eliminate the effect of the adhesive force, the gradients of the lateral signals and the twist angles as a function of normal force are used in calculating the angle conversion factor. To verify reliability and reproducibility of the method, two step gratings with different heights and two different rectangular cantilevers were used in lateral force calibration in AFM. The results showed good agreement, to within 10%. This method was validated by comparing the coefficient of friction of mica so determined with values in the literature.     

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.     

Investigation of nanoparticles by atomic and lateral force microscopy

Metallic nanoparticles have been produced on vitreous carbon substrates by means of thermal evaporation. From pictures of the particles, made by a high-resolution scanning electron microscope (HRSEM), a semispherical shape is suggested due to the total mass of deposited material. Atomic force microscopy (AFM) has been applied to this sample in order to get direct topographic information. The AFM has been operated with normal and super tips, the latter having a smaller cone angle and radius, thus following more precisely the contours of an object. Simultaneously lateral-force microscopic (LFM) images have been recorded. Major differences between the contents of HRSEM- and AFM-images are considered, emphasizing the important influence of the tips' geometry. Both the AFM and LFM line scans have been compared with and have qualitatively agreed with those calculated under simplifying assumptions.     

Improvement of thermally induced bending of cantilevers used for atomic force microscopy

The microfabricated silicon nitride cantilevers that are used for atomic force microscopy (AFM) are, unfortunately, sensitive thermometers. They bend with ambient temperature changes and those due to laser heating. The bend can result in displacements for the silicon nitride cantilevers of an order several hundred nanometers at the tip of the cantilever. If, however, the silicon nitride cantilevers are treated by removing the metallization and annealing at 500°C for 30 min, these displacements can be reduced by one or two orders of magnitude. Silicon cantilevers have approximately a one order of magnitude smaller drift than silicon nitride cantilevers as received from vendors and are improved less by treatment.     

Improving tapping mode atomic force microscopy with piezoelectric cantilevers

This article summarizes improvements to the speed, simplicity and versatility of tapping mode atomic force microscopy (AFM). Improvements are enabled by a piezoelectric microcantilever with a sharp silicon tip and a thin, low-stress zinc oxide (ZnO) film to both actuate and sense deflection. First, we demonstrate self-sensing tapping mode without laser detection. Similar previous work has been limited by unoptimized probe tips, cantilever thicknesses, and stress in the piezoelectric films. Tests indicate self-sensing amplitude resolution is as good or better than optical detection, with double the sensitivity, using the same type of cantilever. Second, we demonstrate self-oscillating tapping mode AFM. The cantilever's integrated piezoelectric film serves as the frequency-determining component of an oscillator circuit. The circuit oscillates the cantilever near its resonant frequency by applying positive feedback to the film. We present images and force-distance curves using both self-sensing and self-oscillating techniques. Finally, high-speed tapping mode imaging in liquid, where electric components of the cantilever require insulation, is demonstrated. Three cantilever coating schemes are tested. The insulated microactuator is used to simultaneously vibrate and actuate the cantilever over topographical features. Preliminary images in water and saline are presented, including one taken at 75.5 μm/s—a threefold improvement in bandwidth versus conventional piezotube actuators.     

Phase imaging with intermodulation atomic force microscopy

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.     

The effect of deformation on the lateral resolution of atomic force microscopy

A computer model based on the elastic properties of rubber is introduced for the evaluation of the lateral resolution in atomic force microscopy of deformable specimens. The computational results show that, if the full width at half-height can be defined as the lateral resolution, it is continuously improved at greater probe forces, at the expense of a reduced molecular height. In fact, even for a probe that is bigger than the molecule, the real size of the molecule can be 'recovered' at about 25% compression. This result demonstrates that for a better lateral resolution, a greater probe force can be beneficial, provided that the molecule is not moved or damaged and the response remains elastic. Measurements on isolated low-density lipoproteins (LDL) show that with 26% vertical compression, the lateral size measured in atomic force microscopy is only about 72% of the value predicted by a simple convolution, and is only slightly larger (≈ 13%) than the known size of LDL. Therefore, the results on LDL provide a direct support for the conclusions of the computational model.     

日本精工SAP400原子力显微镜性能的改进

日本精工公司(SEIKO)生产的原子力显微镜的功能多、性能好,国内已经有近百台的拥有量。它的信号放大、处理主要由锁相放大器完成。但其内部的锁相放大器灵敏度不够高,外加一台高性能、高灵敏度的锁相放大器,可大大提高其性能。用美国斯坦福公司产的SR830锁相放大器对本实验室的日本SEIKO公司SPA400原子力显微镜进行性能改进,可使其性能有很大提高。     

Multifrequency high-speed phase-modulation atomic force microscopy in liquids

We have developed a new technique, called multifrequency high-speed phase-modulation atomic force microscopy (PM-AFM) in constant-amplitude (CA) mode based on the simultaneous excitation of the first two flexural modes of a cantilever. By performing a theoretical investigation, we have found that this technique enables the simultaneous imaging of the surface topography, energy dissipation and elasticity (nonlinear mapping) of materials. We experimentally demonstrated high-speed imaging at a scan speed of 5 frames/s for a polystyrene (PS) and polyisobutylene (PIB) polymer-blend thin-film surface in water.     

Climbing the steps of viral atomic force microscopy: visualization of Dengue virus particles

In recent years, the application of atomic force microscopy (AFM) to biological systems has highlighted the potential of this technology. AFM provides insights into studies of biological structures and interactions and can also identify and characterize a large panel of pathogens, including viruses. The Flaviviridae family contains a number of viruses that are important human and animal pathogens. Among them, Dengue virus causes epidemics with fatal outcomes mainly in the tropics. In this study, Dengue virus is visualized for the first time using the in air AFM technique. Images were obtained from a potassium-tartrate gradient-purified virus. This study enhances the application of AFM as a novel tool for the visualization and characterization of virus particles. Because flavivirus members are closely related, studies of the morphologic structure of the Dengue virus can reveal strategies that may be useful to identify and study other important viruses in the family, including the West Nile virus.     

原子力显微镜矩形测力臂弹性系数计算方法研究

原子力显微镜测力臂弹性系数的准确性直接影响其测量精度,是仪器标定的一个重要指标。分别运用理论计算方法、动态计算方法和静态计算方法计算原子力显微镜测力臂弹性系数。以矩形测力臂为例,对其进行灵敏度分析,找出影响测力臂弹性系数的参数。分别选取矩形测力臂原始参数值及参数上下极限值,构成3组实验数据。利用上述3种计算方法,分别计算出3组不同参数值的矩形测力臂的弹性系数,然后对这3种计算方法计算所得的弹性系数进行分析并和生产商给出的名义值进行比较,所得结果为原子力显微镜矩形测力臂弹性系数的精确计算提供参考。     

Time-lapse imaging of In Vitro myogenesis using atomic force microscopy

Myoblast therapy relies on the integration of skeletal muscle stem cells into distinct muscular compartments for the prevention of clinical conditions such as heart failure, or bladder dysfunction. Understanding the fundamentals of myogenesis is hence crucial for the success of these potential medical therapies. In this report, we followed the rearrangement of the surface membrane structure and the actin cytoskeletal organization in C2C12 myoblasts at different stages of myogenesis using atomic force microscopy (AFM) and confocal laser scanning microscopy (CLSM). AFM imaging of living myoblasts undergoing fusion unveiled that within minutes of making cell–cell contact, membrane tubules appear that unite the myoblasts and increase in girth as fusion proceeds. CLSM identified these membrane tubules as built on scaffolds of actin filaments that nucleate at points of contact between fusing myoblasts. In contrast, similarly behaving membrane tubules are absent during cytokinesis. The results from our study in combination with recent findings in literature further expand the understanding of the biochemical and membrane structural rearrangements involved in the two fundamental cellular processes of division and fusion.     

Molecular dynamics of DNA and nucleosomes in solution studied by fast-scanning atomic force microscopy

Nucleosome is a fundamental structural unit of chromatin, and the exposure from or occlusion into chromatin of genomic DNA is closely related to the regulation of gene expression. In this study, we analyzed the molecular dynamics of poly-nucleosomal arrays in solution by fast-scanning atomic force microscopy (AFM) to obtain a visual glimpse of nucleosome dynamics on chromatin fiber at single molecule level. The influence of the high-speed scanning probe on nucleosome dynamics can be neglected since bending elastic energy of DNA molecule showed similar probability distributions at different scan rates. In the sequential images of poly-nucleosomal arrays, the sliding of the nucleosome core particle and the dissociation of histone particle were visualized. The sliding showed limited fluctuation within ∼50 nm along the DNA strand. The histone dissociation occurs by at least two distinct ways: a dissociation of histone octamer or sequential dissociations of tetramers. These observations help us to develop the molecular mechanisms of nucleosome dynamics and also demonstrate the ability of fast-scanning AFM for the analysis of dynamic protein–DNA interaction in sub-seconds time scale.