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.     

Spectroscopy of the shear force interaction in scanning near-field optical microscopy

Shear force detection is a common method of tip-sample distance control in scanning near-field optical microscopy. Shear force is the force acting on a laterally oscillating probe tip near a surface. Despite its frequent use, the nature of the interaction between tip and sample surface is a matter of debate. In order to investigate the problem, approach curves, i.e. amplitude and phase of the tip oscillation as a function of the tip-sample distance, are studied in terms of a harmonic oscillator model. The extracted force and damping constants are influenced by the substrate material. The character of the interaction ranges from elastic to dissipative. The interaction range is of atomic dimensions with a sharp onset. Between a metal-coated tip and a Cu sample, a power law for the force-distance curve is observed.     

Topographic effects on adhesive force mapping of stretched DNA molecules by pulsed-force-mode atomic force microscopy

Adhesive interaction between a tip and a sample surface was examined on a microscopic scale by pulsed-force-mode atomic force microscopy (PFM-AFM). The signal measured by monitoring pull-off force is influenced by various factors such as topography, elasticity, electrostatic charges, and adsorbed water on surfaces. Here, we focus on the topographic effects on the adhesive interaction. To clarify the topographic influence, the adhesive force measurement of a stretched DNA molecule with a smaller radius of curvature than that of a tip was carried out at low relative humidity (RH) with an alkanethiol-modified tip. The experimental conditions such as low RH and the use of the alkanethiol-modified tip were required to minimise the influence of water capillary force on hydrated DNA strands. The hydrophobic modification of a substrate surface was also important to minimise the adsorbed water effect. The DNA molecules were stretched on the substrate surfaces by an immobilisation process called a dynamic molecular combing method. The two-component vapour-phase surface modification with an alkylsilane mixed with a silane derivative containing an amino end group enhanced the DNA adsorption due to the electrostatic interaction. The experimental results for the topographic effects on the adhesive force mapping were reproducible.     

Influence of the tip mass on the tip-sample interactions in TM-AFM

This paper focuses on the influences of the tip mass ratio (the ratio of the tip mass to the cantilever mass), on the excitation of higher oscillation eigenmodes and also on the tip-sample interaction forces in tapping mode atomic force microscopy (TM-AFM). A precise model for the cantilever dynamics capable of accurate simulations is essential for the investigation of the tip mass effects on the interaction forces. In the present work, the finite element method (FEM) is used for modeling the AFM cantilever to consider the oscillations of higher eigenmodes oscillations. In addition, molecular dynamics (MD) is used to calculate precise data for the tip-sample force as a function of tip vertical position with respect to the sample. The results demonstrate that in the presence of nonlinear tip-sample interaction forces, the tip mass ratio plays a significant role in the excitations of higher eigenmodes and also in the normal force applied on the surface. Furthermore, it has been shown that the difference between responses of the FEM and point-mass models in different system operational conditions is highly affected by the tip mass ratio.     

Velocity dependent friction laws in contact mode atomic force microscopy

Friction forces in the tip–sample contact govern the dynamics of contact mode atomic force microscopy. In ambient conditions typical contact radii between tip and sample are in the order of a few nanometers. In order to account for the large interaction area the dynamics of contact mode atomic force microscope (AFM) is investigated under the assumption of a multi-asperity contact interface between tip and sample. Thus, the kinetic friction force between tip and sample is the product of the real contact area between both solids and the interfacial shear strength. The velocity strengthening of the lateral force is modeled assuming a logarithmic relationship between shear-strength and velocity. Numerical simulations of the system dynamics with this empirical model show the existence of two different regimes in contact mode AFM: steady sliding and stick–slip where the tip undergoes periodically stiction and kinetic friction. The state of the system depends on the scan velocity as well as on the velocity dependence of the interfacial friction force between tip and sample. Already small viscous damping contributions in the tip–sample contact are sufficient to suppress stick–slip oscillations.     

Microfabrication of a combined AFM-SNOM sensor

The objective of this work is to fabricate a scanning probe sensor that combines the well-established method for atomic force microscopy, employing a micro-machined Si cantilever and integrated tip, with a probe for the optical near field. A photosensitive pn-junction is integrated into the tip for that purpose and an Al coating is applied to the tip. It comprises an aperture of 50-70 nm in diameter at the apex of the tip in order to spatially limit the interaction of the tip to the optical near field of the sample. Characterization of the tip and first results of simultaneously recorded force and photon images are presented.     

Data analysis of interaction forces measured with the atomic force microscope

The force-distance cycle mode of the atomic force microscope (AFM) allows for detection of interaction forces between the AFM-tip and a substrate (probe). This can either be a direct tip-sample interaction or an interaction between molecules coupled to the tip and probe, respectively. The interaction forces are typically in the range of a few pN to some hundred pN. In this article we describe algorithms for the analysis of force-distance cycles, to quantify interaction forces between tip and probe. Both, the direct tip-probe interaction as well as the interaction between specifically bound molecules are analyzed. The molecules bound to tip and probe have to be either long and flexible or have to be bound via a flexible cross linker. The algorithms are exemplified on direct tip-probe interactions and on unbinding events of cadherins which are bound via PEG-spacers to the AFM-tip and to the probe.     

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.     

压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的干涉效应

运用弹性复势方法,研究纵向剪切和面内电场共同作用下无限半平面压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的电弹干涉效应,得到该问题复势函数的封闭形式解答,并由此导出广义应力场、裂纹尖端的广义应力强度因子以及作用在螺型位错上的位错力.算例结果表明:增大材料压电常数会相应增大位错力、位错对裂纹尖端的屏蔽和反屏蔽效应;增大位错离裂纹尖端的距离,位错力会相应减小;变化φ(偶极子臂与x轴正半轴夹角)值会出现一个改变位错偶极子对应力强度因子作用方向的临界值.     

Adhesive interaction measured between AFM probe and lung epithelial type II cells

The toxicity of inhaled nanoparticles entering the body through the lung is thought to be initially defined by the electrostatic and adhesive interaction of the particles with lung's wall. Here, we investigated the first step of the interaction of nanoparticles with lung epithelial cells using atomic force microscope (AFM) as a force apparatus. Nanoparticles were modeled by the apex of the AFM tip and the forces of interaction between the tip and the cell analyzed over time. The adhesive force and work of adhesion strongly increased for the first 100s of contact and then leveled out. During this time, the tip was penetrating deeply into the cell. It first crossed a stiff region of the cell and then entered a much more compliant cell region. The work of adhesion and its progression over time were not dependent on the load with which the tip was brought into contact with the cell. We conclude that the initial thermodynamic aspects and the time course of the uptake of nanoparticles by lung epithelial cells can be studied using our experimental approach. It is discussed how the potential health threat posed by nanoparticles of different size and surface characteristics can be evaluated using the method presented.     

Mapping and control of atomic force on Si(1 1 1)square root(3) x square root(3)-Ag surface using noncontact atomic force microscope

We demonstrated the possibility of measuring the three-dimensional force-related map with true atomic resolution between an Si tip and Si(1 1 1)square root(3) x square root(3)-Ag sample surface by measuring the tip-sample distance dependence of noncontact atomic force microscope (NC-AFM) image, i.e. atomically resolved atomic force spectroscopy. Furthermore, we demonstrated the possibility of controlling the interaction force between the atom on the tip apex and a sample atom of Si(1 1 1)square root(3) x square root(3)-Ag surface on an atomic scale by placing an Ag atom on the Si tip apex instead of Si atom.     

Development of eddy current microscopy for high resolution electrical conductivity imaging using atomic force microscopy

We present a high resolution electrical conductivity imaging technique based on the principles of eddy current and atomic force microscopy (AFM). An electromagnetic coil is used to generate eddy currents in an electrically conducting material. The eddy currents generated in the conducting sample are detected and measured with a magnetic tip attached to a flexible cantilever of an AFM. The eddy current generation and its interaction with the magnetic tip cantilever are theoretically modeled using monopole approximation. The model is used to estimate the eddy current force between the magnetic tip and the electrically conducting sample. The theoretical model is also used to choose a magnetic tip-cantilever system with appropriate magnetic field and spring constant to facilitate the design of a high resolution electrical conductivity imaging system. The force between the tip and the sample due to eddy currents is measured as a function of the separation distance and compared to the model in a single crystal copper. Images of electrical conductivity variations in a polycrystalline dual phase titanium alloy (Ti-6Al-4V) sample are obtained by scanning the magnetic tip-cantilever held at a standoff distance from the sample surface. The contrast in the image is explained based on the electrical conductivity and eddy current force between the magnetic tip and the sample. The spatial resolution of the eddy current imaging system is determined by imaging carbon nanofibers in a polymer matrix. The advantages, limitations, and applications of the technique are discussed.     

Effects of higher oscillation modes on TM-AFM measurements

The finite element method and molecular dynamics simulations are used for modeling the AFM microcantilever dynamics and the tip-sample interaction forces, respectively. Molecular dynamics simulations are conducted to calculate the tip-sample force data as a function of tip height at different lateral positions of the tip with respect to the sample. The results demonstrate that in the presence of nonlinear interaction forces, higher eigenmodes of the microcantilever are excited and play a significant role in the tip and sample elastic deformations. Using comparisons between the results of FEM and lumped models, how some aspects of the system behavior can be hidden when the point-mass model is used is illustrated.     

Chemical force microscopy of microcontact-printed self-assembled monolayers by pulsed-force-mode atomic force microscopy

A novel chemically sensitive imaging mode based on adhesive force detection by previously developed pulsed-force-mode atomic force microscopy (PFM-AFM) is presented. PFM-AFM enables simultaneous imaging of surface topography and adhesive force between tip and sample surfaces. Since the adhesive forces are directly related to interaction between chemical functional groups on tip and sample surfaces, we combined the adhesive force mapping by PFM-AFM with chemically modified tips to accomplish imaging of a sample surface with chemical sensitivity. The adhesive force mapping by PFM-AFM both in air and pure water with CH3- and COOH-modified tips clearly discriminated the chemical functional groups on the patterned self-assembled monolayers (SAMs) consisting of COOH- and CH3-terminated regions prepared by microcontact printing (microCP). These results indicate that the adhesive force mapping by PFM-AFM can be used to image distribution of different chemical functional groups on a sample surface. The discrimination mechanism based upon adhesive forces measured by PFM-AFM was compared with that based upon friction forces measured by friction force microscopy. The former is related to observed difference in interactions between tip and sample surfaces when the different interfaces are detached, while the latter depends on difference in periodic corrugated interfacial potentials due to Pauli repulsive forces between the outermost functional groups facing each other and also difference in shear moduli of elasticities between different SAMs.     

Lateral force microscopy profiles for amorphous potentials

In this work, the lateral force profiles of the scanning force microscope tip on an amorphous surface were simulated with the use of an independent oscillator model. The correlation between the lateral force profiles and the surface potential were studied as a function of the tip-surface normal force and relative scanning velocity. It is shown that the microscope resolution is governed by the quotient between the average potential interaction energy and the average elastic energy stored before the jumps. We show that there is an optimal velocity with which the scanning tip better senses the surface potential and we present its scaling laws.     

Analysis of force curves obtained on the live cell membrane using chemically modified AFM probes

Force curves were obtained on the live cell surface using an atomic force microscope mounted with a modified tip with the bifunctional covalent crosslinker, disuccinimidyl suberate, which forms a covalent bond with amino-bearing molecules on the cell surface. A ramp delay time of 1.0 s was introduced before the start of the retraction regime of the force curve to increase the stationary reaction time between the crosslinkers on the tip and the amino groups on the cell surface. While live cell surface responses to forced contact with a non-functionalized tip rarely showed evidence of tip–cell interaction, those obtained with modified tips gave clear indication of prolonged adhesion which was terminated by a single step release of the tip to its neutral position. Under the given experimental conditions of this work, 58% of a total of 198 force curves gave only one jump and 70% of those with one jump gave the final rupture force of 4.5±0.22 nN. The result emphasized the uniqueness of the observed mechanical response of the cell surface when probed with chemically modified tips.     

Inverse estimation of the tapered probe-sample shear force of scanning near-field optical microscope

In this paper, the conjugate gradient method of minimization with an adjoint equation is successfully applied to solve the inverse problem in estimating the shear force between the tapered probe and sample during the scanning process of scanning near-field optical microscope (SNOM). While knowing the available deflection at the tapered probe tip, the determination of the interaction shear force is regarded as an inverse vibration problem. In the estimating processes, no prior information on the functional form of the unknown quantity is required. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements of deflection at the tapered probe tip. Numerical results show that good estimations on the interaction shear force can be obtained for all the test cases considered in this study.     

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.     

High-sensitivity detection of proteins using gel electrophoresis and atomic force microscopy

We have developed a method to detect specific proteins with a high sensitivity using a gel electrophoresis method and force measurement of atomic force microscopy (AFM). Biotinylated proteins were separated by electrophoresis and fixed with cross-linking chemicals on the gel, followed by direct force measurement between the biotinylated proteins on the gel and a streptavidin-modified tip of an AFM cantilever. We were able to achieve a high enough sensitivity to detect the picogram order of the biotinylated proteins by evaluating the frequency of the interaction force larger than 100 pN in the force profile, which corresponds to the rupture force of interaction between streptavidin and biotin.