基于LSTM的矩形纳米光栅AFM图像复原方法

原子力显微镜(AFM)利用探针与待测物之间的交互作用力进行成像,通过获取矩形纳米光栅计量标准器具的高分辨率成像得到相关的几何量参数并进行标定,实现从标准计量器具到工作计量器具的量值传递。在AFM扫描过程中,由于针尖的影响作用,使得扫描所获图像是探针和样品共同作用的结果,而不是样品形貌的真实描述。针对这一现象,本文提出了一种基于长短期记忆网络(LSTM)的AFM图像复原方法,该方法对通过膨胀法获得的仿真图像各扫描行进行训练,进而获得适用于矩形纳米光栅AFM图像复原模型。实验结果表明,针对线宽20 nm,高40 nm的矩形纳米光栅,经过该方法复原后光栅线宽的相对误差为7.40%,相较于传统的复原方法进一步提高了测量准确度。     

Computational models of a nano probe tip for static behaviors

It is difficult to predict the measurement bias arising from the compliance of the atomic force microscope (AFM) probe. The issue becomes particularly important in this situation where nanometer uncertainties are sought for measurements with dimensional probes composed of flexible carbon nanotubes mounted on AFM cantilevers. We have developed a finite element model for simulating the mechanical behavior of AFM cantilevers with carbon nanotubes attached. Spring constants of both the nanotube and cantilever in two directions are calculated using the finite element method with known Young's moduli of both silicon and multiwall nanotube as input data. Compliance of the nanotube-attached AFM probe tip may be calculated from the set of spring constants. This paper presents static models that together provide a basis to estimate uncertainties in linewidth measurement using nanotubes. In particular, the interaction between a multiwall nanotube tip and a silicon sample is modeled using the Lennard-Jones theory. Snap-in and snap-out of the probe tip in a scanning mode are calculated by integrating the compliance of the probe and the sample-tip interacting force model. Cantilever and probe tip deflections and points of contact are derived for both horizontal scanning of a plateau and vertically scanning of a wall. The finite element method and the Lennard-Jones model provide a means to analyze the interaction of the probe and sample and measurement uncertainty, including actual deflection and the gap between the probe tip and the measured sample surface.     

Study of the rheological properties and the finishing behavior of abrasive gels in abrasive flow machining

Abrasive flow machining (AFM) is an effective method to finish the smooth surface in the complex holes. Abrasive media are key elements which dominate the polished results in AFM. But it is hard to develop the machining model of these abrasive gels because of its complicated mechanism. In this research, a non-Newtonian flow is used to set up the abrasive mechanism of the abrasive media in AFM. Power law is a main equation of the non-Newtonian flow to describe the motion of the abrasive media. Viscosities vs. shear rates of different abrasive gels are used to establish the power law in CFD-ACE⁺ software first. And the working parameters of AFM were applied as input to study the properties of the abrasive gels in AFM. Finally, the relationships between the simulations and the experiments were found. And the abrasive mechanism of the abrasive gels was set up in AFM. The simulated results show that the abrasive gel with high viscosity can entirely deform in the complex hole than the abrasive gel with low viscosity. And the abrasive gel with high viscosity generates a larger shear force than the abrasive gel with low viscosity in the same area. Moreover, the strain rate is seriously changed when the abrasive gel cross over the narrow cross-section of the complex hole. It also means that abrasive gel will produce large finish force in that area. And these results indeed consist with the experiments in AFM.     

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each 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.     

Quantitative measurement of mRNA at different loci within an individual living cell

Asymmetric localizations of cellular proteins and mRNAs are important for cell functions such as division, differentiation and development. The localization of specific mRNA generates cell polarity by controlling the translation sites of specific proteins and thereby restricting their locations to appropriate cellular regions. We have previously reported a novel method based on atomic force microscopy (AFM) for examining gene expression in a single living cell without killing or destroying it. An AFM tip was inserted into a living cell to extract mRNAs, which were analyzed after multiplication by RT-PCR and quantitative PCR. By applying this method, in this study we performed quantitative measurement of mRNA at different loci within individual living cells.     

AFM悬臂定位系统中光干涉误差及减小方法研究

光杠杆法是原子力显微镜（AFM）悬臂定位的主要方法。由于悬臂自身的尺寸和材料特性、检测光路系统等因素制约，悬臂弯曲测量时存在光泄露。被试样表面反射的部分泄露光与悬臂反射光产生干涉，在探针一试样接近曲线中产生光干涉误差。基于轻触模式AFM，分析了光干涉误差的产生原因，并对其引起的AFM测量误差进行了数学分析和仿真、提出了减小光干涉误差的方法。实验结果和理论分析表明，为了进一步提高AFM的测量精度，有必要克服定位系统中的光干涉误差。     

Quantification of the lateral detachment force for bacterial cells using atomic force microscope and centrifugation

To determine the lateral detachment force for individual bacterial cells, a quantitative method using the contact mode of an atomic force microscope (AFM) was developed in this study. Three key factors for the proposed method, i.e. scan size, scan rate and cantilever choice, were evaluated and optimized. The scan size of 40×40 μm² was optimal for capturing sufficient number of adhered cells in a microscopic field and provide adequate information for cell identification and detachment force measurement. The scan rate affected the measurement results significantly, and was optimized at 40 μm/s considering both force measurement accuracy and experimental efficiency. The hardness of applied cantilevers also influenced force determination. The proposed protocol for cantilever selection is to use those with the lowest spring constant first and then step up to a harder cantilever until all cells are detached. The lateral detachment force of Escherichia coli cells on polished stainless steel and a glass-slide coated with poly-l-lysine were measured as 0.763±0.167 and 0.639±0.136 nN, respectively. The results showed that the established method had good repeatability and sensitivity to various bacteria/substrata combinations. The detachment force quantified by AFM (0.639±0.136 nN) was comparable to that measured by the centrifugation method (1.12 nN).     

Scanning electron microscopy studies of protein-functionalized atomic force microscopy cantilever tips

Protein-functionalized atomic force microscopy (AFM) tips have been used to investigate the interaction of individual ligand-receptor complexes. Herein we present results from scanning electron microscopy (SEM) studies of protein-functionalized AFM cantilever tips. The goals of this study were (1) to examine the surface morphology of protein-coated AFM tips and (2) to determine the stability of the coated tips. Based on SEM images, we found that bovine serum albumin (BSA) in solution spontaneously adsorbed onto the surface of silicon nitride cantilevers, forming a uniform protein layer over the surface. Additional protein layers deposited over the initial BSA-coated surface did not significantly alter the surface morphology. However, we found that avidin-functionalized tips were contaminated with debris after a series of force measurements with biotinylated agarose beads. The bound debris presumably originated from the transfer of material from the agarose bead. This observation is consistent with the observed deterioration of functional activity as measured in ligand-receptor binding force experiments.     

Prototype cantilevers for quantitative lateral force microscopy

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.     

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.     

Imaging streptavidin 2D crystals on biotinylated lipid monolayers at high resolution with the atomic force microscope

Streptavidin crystals were grown on biotinylated lipid monolayers at an air/water interface and transferred onto highly oriented pyrolytic graphite (HOPG). These arrays could be imaged to a resolution below 1 nm using the atomic force microscope. The surface topographs obtained were compared with negative-stain electron microscopy images and the atomic model as determined by X-ray crystallography. The streptavidin tetramer (60 kDa) exposes two free biotin-binding sites to the buffer solution, while two are occupied by linkage to the lipid monolayer. Therefore, the streptavidin 2D crystals can be used as nanoscale matrices for binding biotinylated compounds. Furthermore, this HOPG-based preparation method provides a general novel approach to study the structure of protein arrays assembled on lipid monolayers with the AFM.     

AFM imaging of functionalized double-walled carbon nanotubes

We present a comparative study of several non-covalent approaches to disperse, debundle and non-covalently functionalize double-walled carbon nanotubes (DWNTs). We investigated the ability of bovine serum albumin (BSA), phospholipids grafted onto amine-terminated polyethylene glycol (PL-PEG₂₀₀₀-NH₂), as well as a combination thereof, to coat purified DWNTs. Topographical imaging with the atomic force microscope (AFM) was used to assess the coating of individual DWNTs and the degree of debundling and dispersion. Topographical images showed that functionalized DWNTs are better separated and less aggregated than pristine DWNTs and that the different coating methods differ in their abilities to successfully debundle and disperse DWNTs. Height profiles indicated an increase in the diameter of DWNTs depending on the functionalization method and revealed adsorption of single molecules onto the nanotubes. Biofunctionalization of the DWNT surface was achieved by coating DWNTs with biotinylated BSA, providing for biospecific binding of streptavidin in a simple incubation step. Finally, biotin-BSA-functionalized DWNTs were immobilized on an avidin layer via the specific avidin–biotin interaction.     

Quantitative analysis of the number of antigens immobilized on a glass surface by AFM

To develop force measurements using an atomic force microscope (AFM) in a quantitative manner, it is necessary to estimate the number density of target molecules on a sample surface, and for this, the sensitivity of detection should be known. In this study, the AFM was used as a mechanical detector and an antigen and its antibody were used as a model to evaluate the sensitivity of detection. Antigens were immobilized on a glass surface and number density was estimated by monitoring optical absorbance due to product formation by the reaction of crosslinkers. The concentration of antigen was controlled by mixing control peptides. A microbead was used as a probe and antibodies were immobilized on the bead. AFM force measurements were then made for a range of number densities in the order of 10–10⁶ antigen molecules per square micrometer of surface and were compared to evaluate the sensitivity of detection. Our result establishes the reliability of estimating a number of molecules like receptors on the cell surface, and indicates that the AFM is useful as a mechanical detector with high sensitivity.     

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.     

Analysis of simulated scanning of atomic-scale silicon surface by atomic force microscopy

This study constructs a contact-mode atomic force microscopy (AFM) simulation measurement model with constant force mode to simulate and analyze the outline scanning measurement by AFM. The simulation method is that when the probe passes the surface of sample, the action force of the atom of sample received by the atom of the probe can be calculated by using Morse potential. Through calculation, the equivalent force on the cantilever of probe can be acquired. By using the deflection angle equation for the cantilever of probe developed and inferred by this study, the deflection angle of receiving action force can be calculated. On the measurement point, as the deflection angle reaches a fixed deflection angle, the scan height of this simulation model can be acquired. By scanning in the right order, the scan curve of the simulation model can be obtained. By using this simulation measurement model, this study simulates and analyzes the scanning of atomic-scale surface outline. Meanwhile, focusing on the tip radii of different probes, the concept of sensitivity analysis is employed to investigate the effects of the tip radius of probe on the atomic-scale surface outline. As a result, it is found from the simulation on the atomic-scale surface that within the simulation scope of this study, when the tip radius of probe is greater than 12 nm, the effects of single atom on the scan curve of AFM can be better decreased or eliminated.     

Comparison of different aminofunctionalization strategies for attachment of single antibodies to AFM cantilevers

Atomic force microscopy (AFM) has developed into a key technique for elucidation of biological systems on the single molecular level. In particular, molecular recognition force microscopy has proven to be a powerful tool for the investigation of biological interactions under near physiological conditions. For this purpose, ligands are tethered to AFM tips and the interaction forces with cognate receptors on the sample surface are measured with pico-Newton accuracy. In the first step of tip functionalization, amino groups are typically introduced on the initially inert AFM tip. Several methods have been developed to reproducibly adjust the desired low density of amino groups on the tip surface, i.e. esterification with ethanolamine, gas-phase silanization with aminopropyl-triethoxysilane (APTES), or treatment with aminophenyl-trimethoxysilane (APhS) in toluene solution. In the present study, the usefulness of these methods for attachments of antibodies to AFM tips was characterized by a standardized test system, in which biotinylated IgG was bound to the tip and a dense monolayer of avidin on mica served as test sample. All three methods of aminofunctionalization were found fully satisfactory for attachment of single antibodies to AFM tips, only in a parallel macroscopic assay on silicon nitride chips a minor difference was found in that APTES appeared to yield a slightly lower surface density of amino groups.     

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.     

The comparison between force volume and peakforce quantitative nanomechanical mode of atomic force microscope in detecting cell's mechanical properties

Atomic force microscope (AFM) has been widely used in the biological field owing to its high sensitivity (subnanonewton), high spatial resolution (nanometer), and adaptability to physiological environments. Nowadays, force volume (FV) and peakforce quantitative nanomechanical (QNM) are two distinct modes of AFM used in biomechanical research. However, numerous studies have revealed an extremely confusing phenomenon that FV mode has a significant difference with QNM in determining the mechanical properties of the same samples. In this article, for the case of human benign prostatic hyperplasia cells (BPH) and two cancerous prostate cells with different grades of malignancy (PC3 and DU145), the differences were compared between FV and QNM modes in detecting mechanical properties. The results show measured Young's modulus of the same cells in FV mode was much lower than that obtained by QNM mode. Combining experimental results with working principles of two modes, it is indicated that surface adhesion is highly suspected to be a critical factor resulting in the measurement difference between two modes. To further confirm this conjecture, various weight ratios of polydimethylsiloxane (PDMS) were assessed by two modes, respectively. The results show that the difference of Young's modulus measured by two modes increases with the surface adhesion of PDMS, confirming that adhesion is one of the significant elements that lead to the measurement difference between FV and QNM modes.     

Imaging and Measuring the Molecular Force of Lymphoma Pathological Cells Using Atomic Force Microscopy

Atomic force microscopy (AFM) provides a new technology to visualize the cellular topography and quantify the molecular interactions at nanometer spatial resolution. In this work, AFM was used to image the cellular topography and measure the molecular force of pathological cells from B‐cell lymphoma patients. After the fluorescence staining, cancer cells were recognized by their special morphological features and then the detailed topography was visualized by AFM imaging. The AFM images showed that cancer cells were much rougher than healthy cells. CD20 is a surface marker of B cells and rituximab is a monoclonal antibody against CD20. To measure the CD20‐rituximab interaction forces, the polyethylene glycol (PEG) linker was used to link rituximab onto the AFM tip and the verification experiments of the functionalized probe indicated that rituximab molecules were successfully linked onto the AFM tip. The CD20‐rituximab interaction forces were measured on about 20 pathological cells and the force measurement results indicated the CD20‐rituximab binding forces were mainly in the range of 110–120 pN and 130–140 pN. These results can improve our understanding of the topography and molecular force of lymphoma pathological cells. SCANNING 35:40‐46, 2013. © 2012 Wiley Periodicals, Inc.