General theory of amplitude-modulation atomic force microscopy

We present a general analytical theory that enables one to determine accurately the unknown tip-sample interactions from the experimental measurement of the amplitude and phase of the oscillating tip in amplitude-modulation atomic force microscopy (AM-AFM). We apply the method to the known Lennard-Jones-type forces and find excellent agreement with the reconstructed results. AM-AFM, widely used in air and liquid, is now not only an imaging tool but also a quantitative force measurement tool.     

Sensing dipole fields at atomic steps with combined scanning tunneling and force microscopy

The electric field of dipoles localized at the atomic steps of metal surfaces due to the Smoluchowski effect were measured from the electrostatic force exerted on the biased tip of a scanning tunneling microscope. By varying the tip-sample bias the contribution of the step dipole was separated from changes in the force due to van der Waals and polarization forces. Combined with electrostatic calculations, the method was used to determine the local dipole moment in steps of different heights on Au(111) and on the twofold surface of an Al-Ni-Co decagonal quasicrystal.     

Measuring viscous dissipative interactions in dynamic force microscopy

The periodic motion of a harmonic pendulum in an arbitrary force field including viscous damping is studied as it pertains to dynamic force microscopy. It is shown that the damping constant as a function of tip-sample distance and thus the dissipative force can be obtained unambiguously by measuring the driving-force amplitude versus displacement of the force sensor. This methodology provides the basis for quantitative force spectroscopy of dissipative interactions.     

Investigating biomolecular recognition at the cell surface using atomic force microscopy

Probing the interaction forces that drive biomolecular recognition on cell surfaces is essential for understanding diverse biological processes. Force spectroscopy has been a widely used dynamic analytical technique, allowing measurement of such interactions at the molecular and cellular level. The capabilities of working under near physiological environments, combined with excellent force and lateral resolution make atomic force microscopy (AFM)-based force spectroscopy a powerful approach to measure biomolecular interaction forces not only on non-biological substrates, but also on soft, dynamic cell surfaces. Over the last few years, AFM-based force spectroscopy has provided biophysical insight into how biomolecules on cell surfaces interact with each other and induce relevant biological processes. In this review, we focus on describing the technique of force spectroscopy using the AFM, specifically in the context of probing cell surfaces. We summarize recent progress in understanding the recognition and interactions between macromolecules that may be found at cell surfaces from a force spectroscopy perspective. We further discuss the challenges and future prospects of the application of this versatile technique.     

Analytical model for nanoscale viscoelastic properties characterization using dynamic nanoindentation

In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.     

Force dependence of transition rates in atomic friction

The lateral forces during stick-slip motion of an atomic force microscope cantilever on highly oriented pyrolytic graphite are measured and analyzed. We identify the regimes where thermally activated interstitial hopping of the cantilever tip proceeds according to a single-step reaction scheme and extract the corresponding force-dependent transition rates directly from the experimental data. We find that such a single-step reaction scenario is valid only at relatively high velocities, while at slower pulling speeds, a more complicated hopping mechanism must be at work. We suggest formation of multiple bonds of the tip-sample contact as a possible candidate for this mechanism.     

Influence of ultrasonic surface acoustic waves. on local friction studied by lateral force microscopy

We studied dynamic friction phenomena introduced by ultrasonic surface acoustic waves using a scanning force microscope in the lateral force mode and a scanning acoustic force microscope. An effect of friction reduction was found when applying surface acoustic waves to the micro-mechanical tip-sample contact. Employing standing acoustic wave fields, the wave amplitude dependent friction variation can be visualized within a microscopic area. At higher wave amplitudes, a regime was found where friction vanishes completely. This behavior is explained by the mechanical diode effect, where the tip's rest position is shifted away from the surface in response to ultrasonic waves.     

Theory of higher harmonics imaging in tapping-mode atomic force microscopy

The periodic impact force induced by tip-sample contact in tapping mode atomic force microscope (AFM) gives rise to non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip--sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip--sample impact force and tip motion. The theoretical analysis and numerical results both show that the time-varying tip--sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip--sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.     

Experimental determination of the viscosity at the nanometer scale on a block copolymer with an oscillating nanotip

: This work is an attempt to investigate viscosities at the nanometer scale. To do so, the tapping mode atomic force microscopy is used on a triblock copolymer exhibiting a well-defined periodic structure at the nanometer scale. Variations of the oscillator amplitude and phase delay as a function of the tip-sample distance are recorded on the glassy and rubbery domains of the copolymer. The experimental data are compared to analytical expressions derived from Stokes law. In the present study, among the different possible expressions of the viscous forces depending on the tip shape and on the experimental length scale, only a force proportional to the indentation depth is able to describe the experimental data. In this particular case, quantitative measurements are possible. Finally, the oscillator is shown to be sensitive to local variations of the viscosity within few nanometers.     

Chemical resolution at ionic crystal surfaces using dynamic atomic force microscopy with metallic tips

We demonstrate that well prepared and characterized Cr tips can provide atomic resolution on the bulk NaCl(001) surface with dynamic atomic force microscopy in the noncontact regime at relatively large tip-sample separations. At these conditions, the surface chemical structure can be resolved yet tip-surface instabilities are absent. Our calculations demonstrate that chemical identification is unambiguous, because the interaction is always largest above the anions. This conclusion is generally valid for other polar surfaces, and can thus provide a new practical route for straightforward interpretation of atomically resolved images.     

Higher harmonic atomic force microscopy: imaging of biological membranes in liquid

The contribution of higher harmonics to the movement of a dynamic force microscope cantilever interacting with a sample in liquid was investigated. The amplitude of the second harmonic has been found to be an order of magnitude higher in liquid than in air, reflecting an increased sensitivity to local variations in elasticity and interaction geometries. A theoretical model of the tip-sample interactions in liquid was introduced and shown to be consistent with experimental findings. Second harmonic amplitude images were recorded on soft biological samples yielding a lateral resolution of approximately 0.5 nm.     

Evaluation of the contact resonance frequencies in atomic force microscopy as a method for surface characterisation (invited)

The combination of ultrasound with atomic force microscopy (AFM) opens the high lateral resolution of scanning probe techniques in the nanometer range to ultrasonics. One possible method is to observe the resonance frequencies of the AFM sensors under different tip-sample interaction conditions. AFM sensors can be regarded as small flexible beams. Their lowest flexural and torsional resonance frequencies are usually found to be in a range between several kHz and several MHz depending on their exact geometrical shape. When the sensor tip is in a repulsive elastic contact with a sample surface, the local indentation modulus can be determined by the contact resonance technique. Contact resonances in the ultrasonic frequency range can also be used to improve the image contrast in other dynamic techniques as, for example, in the so-called piezo-mode. Here, an alternating electric field is applied between a conducting cantilever and a piezoelectric sample. Via the inverse piezoelectric effect, the sample surface is set into vibration. This excitation is localised around the contact area formed by the sensor tip and the sample surface. We show applications of the contact resonance technique to piezoelectric ceramics.     

Fluctuation-induced electromagnetic interaction of a moving particle with a plane surface

The most general (nonrelativistic) formulas for the force of attraction to the surface and for the drag of a nonrelativistic atom moving parallel to it, as well as for the lateral and normal forces acting on a moving dipole molecule and on a charged particle (in the case of parallel and perpendicular motion), are derived for the first time in the framework of the fluctuational electromagnetic theory. The dependences of these forces on the velocity, temperature, separation, and dielectric properties of the atom and the surface are derived. The effect of the nondissipative resonance interaction between a moving neutral atom and the field of surface plasmons, as well as the possible emergence of a positive (accelerating) force acting on the atom (nanoprobe), is substantiated theoretically. The role of dynamic fluctuational forces and their possible experimental measurement when using the quartz microbalance technique and an atomic-force microscope (in the dynamic mode), as well as during deceleration of atomic beams in open nanotubes, are considered. The correctness of the obtained results is confirmed by their agreement with most of the available theoretical relations derived by other authors.     

Linear and nonlinear approaches towards amplitude modulation atomic force microscopy

Frequency response behavior of microcantilever is analytically and experimentally investigated in amplitude modulation Atomic Force Microscopy (AFM). AFM microcantilever probe is modeled as a continuous beam, and tip-sample interaction force is considered to include both attractive and repulsive force regimes. The developed model is compared with the linear lumped-parameters model that has been extensively used in the literature so far. Experimental measurements are also provided for the frequency response of a typical microcantilever-sample system to demonstrate the advantages of the developed model over the linear formulation. The results indicate that the nonlinear continuous model is more accurate, particularly in the estimation of the saturated amplitude value and frequency zone in which the tip-sample contact happens.     

Surface defects characterization with frequency and force modulation atomic force microscopy using molecular dynamics simulations

This paper is devoted to the characterization of the surface defects using a recently developed AFM technique called frequency and force modulation AFM (FFM–AFM). The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including single-atom vacancy and impurities. In order to examine the behavior of the above system on different transition metals, the molecular dynamics (MD) simulation with Sutton–Chen (SC) inter-atomic potential is used. In this study, an online imaging simulation of the probe and sample is performed, and the effects of the horizontal scan speed, the effective frequency set-point, the cantilever stiffness, the tip-sample rest position and the cantilever quality factor on the resulting images are investigated. Using a proposed optimum controlling scheme for the excitation force amplitude, the cantilever horizontal speed can be increased.     

Nanomanipulation using only mechanical energy

We present the first computational study targeting the nanomanipulation capability of dynamic surface force microscopy. Using a very simple but challenging model, an antisite defect on a III-V(110) surface, we show how the defect can be manipulated in both the attractive and the repulsive modes and identify the role of the tip-sample interaction: either lowering the barriers or pushing the system over a high stress state using exclusively the mechanical energy stored in the oscillating cantilever. Our study also sheds light on other key issues, such as chemical resolution, explaining why vacancies are the only defects imaged in topography, and dissipation contrast formation, identifying a physical mechanism to explain the intriguing small shift between topographical and damping images.     

Ultrasonic resonance regulated near-field scanning optical microscope and laser induced near-field optical-force interaction

We have developed a novel sample-tip regulation for a near-field optical microscope: an ultrasonic resonance regulation method. The regulation range is from 0 to 50 nm. It shows not only stability, simplicity in construction, but also versatility in vacuum, magnetic field, and low temperature environments. The main advantage of this technique is that it is a non-optical detecting scheme, which is very important for near-field spectroscopy. Such construction can also be used as a force microscope to study the topography of insulating samples. The laser light induced force interaction in the near-field range has been observed for the first time, showing that aided by laser radiation, the shear force between sample and tip can be changed depending on the type of sample. This can be interpreted as the light induced optical tip-sample interaction of light pressure effect. The van der Waals dispersion energy and the optical binding energy induced by laser beam between dielectric tip and samples play important role. The effect confirms a theoretical prediction. This new technique and phenomenon will add new aspects to near-field optics.     

Upper bound for the magnetic force gradient in graphite

In this work we investigate possible ferromagnetic order on the graphite surface by using magnetic force microscopy (MFM). Our data show that the tip-sample interaction along the steps is independent of an external magnetic field. Moreover, by combining kelvin probe force microscopy and MFM, we are able to separate the electrostatic and magnetic interactions along the steps obtaining an upper bound for the magnetic force gradient of 16 μN/m. Our experiments suggest the absence of ferromagnetic signal in graphite at room temperature.     

On the contribution of circumferential resonance modes in acoustic radiation force experienced by cylindrical shells

A body insonified by a constant (time-varying) intensity sound field is known to experience a steady (oscillatory) force that is called the steady-state (dynamic) acoustic radiation force. Using the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of a resonance field and a background (non-resonance) component, we show that the radiation force acting on a cylindrical shell may be synthesized as a composition of three components: background part, resonance part and their interaction. The background component reveals the pure geometrical reflection effects and illustrates a regular behavior with respect to frequency, while the others demonstrate a singular behavior near the resonance frequencies. The results illustrate that the resonance effects associated to partial waves can be isolated by the subtraction of the background component from the total (steady-state or dynamic) radiation force function (i.e., residue component). In the case of steady-state radiation force, the components are exerted on the body as static forces. For the case of oscillatory amplitude excitation, the components are exerted at the modulation frequency with frequency-dependant phase shifts. The results demonstrate the dominant contribution of the non-resonance component of dynamic radiation force at high frequencies with respect to the residue component, which offers the potential application of ultrasound stimulated vibro-acoustic spectroscopy technique in low frequency resonance spectroscopy purposes. Furthermore, the proposed formulation may be useful essentially due to its intrinsic value in physical acoustics. In addition, it may unveil the contribution of resonance modes in the dynamic radiation force experienced by the cylindrical objects and its underlying physics.     

The Colloidal Probe Technique and its Application to Adhesion Force Measurements

Knowledge of the interaction forces between colloidal particles and surfaces is a precondition for understanding the stability of dispersed systems and adhesion phenomena. One of the methods available for direct measurement of surface forces is the atomic force microscope (AFM). Based on this method the so called “colloidal probe technique” was developed more than 10 years ago. Using a micron‐sized particle glued to the end of an AFM cantilever as the force sensor, this technique is predestined for the study of colloidal interactions. In this review we describe the colloidal probe technique and give an overview of its application in the field of adhesion forces.