A direct method to calculate tip–sample forces from frequency shifts in frequency-modulation atomic force microscopy

Frequency modulation atomic force microscopy is a method for imaging the surface of metals, semiconductors and insulators in ultrahigh vacuum with true atomic resolution. The imaging signal in this technique is the frequency shift $\ensuremath{\Delta}f$ of an oscillating cantilever with eigenfrequency ${f}_{0},$ spring constant k and amplitude A, which is subject to tip-sample forces ${F}_{\mathrm{ts}}.$ Here, we present analytical results of $\ensuremath{\Delta}{f(f}_{0},k,A)$ for several basic classes of ${F}_{\mathrm{ts}}.$ With these results, a method to calculate images is derived and demonstrated with an example.

Tip-enhanced Raman scattering (TERS) microscopy attracts increasing attention for visualization and characterization of strain distribution on crystalline samples at a nanoscale due to nano-sized fields localized at a metal tip. However, as the metal tip approaches close to a sample surface, a force acts between the tip and sample, which can induce unwanted perturbation on the local strain of the sample. Analysis and evaluation of intrinsic strains on samples with a high reliability demands a technique to correlate TERS spectra with the tip-sample force. Here, we present a TERS microscope based on a frequency-modulation atomic force microscope (FM-AFM) using a quartz tuning fork (QTF) as a force sensor. By continuously monitoring a shift in the resonance frequency of the QTF during TERS, the tip-sample force can be directly measured in both attractive and repulsive force regions, which is not possible by other AFMs. TERS spectra of single-walled carbon nanotubes (CNTs) were measured simultaneously while changing the tip-sample distance and hence the tip-sample force acting on the CNTs. We found that TERS occurs at the tip-sample distance where the repulsive force dominantly works and mostly decays out in the attractive force region.

Polythiophene molecules adsorbed on a highly oriented pyrolytic graphite surface were studied by combined dynamic scanning tunneling microscopy (STM) and frequency modulation atomic force microscopy (FM-AFM) with a quartz tuning fork sensor operating in Qplus mode and equipped with a Pt/Ir tip. Upon completing a careful sub-angström oscillation amplitude calibration of the probe, experiments were conducted in an ultra high vacuum at room temperature. By selecting the tip/surface distance regulation parameter, one can select the type of simultaneous information obtained in an area. For distance regulation based on the mean tunneling current, dynamic STM images together with maps of tip/surface force gradient were obtained. FM-AFM images with maps of the tunneling current were also acquired when the distance regulation was based on the frequency shift. Comparison between these images reveals interesting features. For example the tip which operates in STM mode with ultra low current (<10 pA) generates different interaction forces above molecules or graphite. Changes in energy dissipation processes as small as tens of millielectronvolts per cycle were recorded when the tip oscillates above the polymer or on the graphite surface. Hence data demonstrates that a stiff piezoelectric tuning fork of several kilonewtons/meters working as an AFM/STM probe with sub-angström amplitude can characterize weakly adsorbed molecules.

True atomic resolution of frequency-modulation atomic force microscopy in liquid is demonstrated. Hexagonal lattice of a cleaved (001) surface of muscovite mica is resolved in water. Nonperiodic structures such as defects and adsorbates are simultaneously imaged with the atomic-scale features of mica surface. The use of small oscillation amplitude (0.16–0.33 nm) of a force sensing cantilever allows us to obtain vertical and lateral resolutions of 2–6 and 300 pm, respectively, even with a low Q factor in water (Q=20–30).

Localization of cesium on montmorillonite surface investigated by frequency modulation atomic force microscopy

Nanocelluloses are attractive for bio‐based materials development due to their renewability, intrinsic properties, and ease of functionalization. However, characterization of nanocelluloses functionalized with small molecules at low grafting densities is challenging. Here, the use of high‐resolution frequency modulation atomic force microscopy (FM‐AFM) to directly visualize the covalent grafting of small molecules is demonstrated for the first time. Using epichlorohydrin as a linker, α‐cyclodextrin, β‐cyclodextrin, and tris(4‐tert‐butylphenyl)methanol are attached to the surface of bacterial nanocellulose. The presence of these groups is verified through spectroscopic measurements, and their covalent attachment is confirmed with FM‐AFM. Furthermore, the retention of cyclodextrin host‐guest activity after surface grafting is also demonstrated. This work represents a novel application of FM‐AFM for the characterization of small molecule‐grafted nanocelluloses, allowing for future development of advanced functionalization strategies.

Mechanical energy stored in an oscillating cantilever in frequency modulation atomic force microscopy (FM-AFM) was dissipated through nonconservative interactions between a sample and a tip on the cantilever. The energy dissipation (D dis) was measured using FM-AFM with a metal-coated tip for a metal-coated Si substrate partly covered with thin mica films. At tip–sample separations where electrostatic force was dominant under a bias voltage, Joule heat was generated owing to the tip oscillation, responsible for D dis. From analysis of D dis and the frequency shift of the cantilever, electric resistance responsible for the Joule heat was estimated to be of the order of GΩ. The great values of the resistance were discussed in the terms of surface scattering of charges moved by the oscillating tip and the dielectric energy loss in the mica films. Measurement of the energy dissipation exhibited potential to probe the local surface electronic properties in non-contact.

In frequency modulation atomic force microscopy (FM-AFM), the average interaction force is detected as the frequency shift of the oscillating cantilever. Therefore, it is desirable to oscillate a cantilever with a small amplitude in order to achieve a high resolution. However, the oscillation may become unstable or the tip may jump into a static contact unless a cantilever with a high spring constant is used. In this study, we used a silicon cantilever with a spring constant as high as 700 N/m, which is far larger than those for conventional FM-AFM. We demonstrated molecular-resolution FM-AFM on lead phthalocyanine thin films with an oscillation amplitude of 2 nm.

Organic molecule crystalline materials have been widely utilized for various applications. Controlling their crystallization and morphology is important for improving their performance and functionality. We have been investigating fundamental mechanisms of the crystal growth process of organic molecules from the viewpoint of hydration structure formed at an interface between a crystal surface and a solution. In this review, we introduce our recent studies on comparison of hydration structure between organic crystal polymorphs and between organic crystal planes measured by frequency modulation atomic force microscopy combined with three-dimensional atomic force microscopy, discussing the relationship of hydration structure with crystal growth process.

Structural Biology (SB) techniques are particularly successful in solving virus structures. Taking advantage of the symmetries, a heavy averaging on the data of a large number of specimens, results in an accurate determination of the structure of the sample. However, these techniques do not provide true single molecule information of viruses in physiological conditions. To answer many fundamental questions about the quickly expanding physical virology it is important to develop techniques with the capability to reach nanometer scale resolution on both structure and physical properties of individual molecules in physiological conditions. Atomic force microscopy (AFM) fulfills these requirements providing images of individual virus particles under physiological conditions, along with the characterization of a variety of properties including local adhesion and elasticity. Using conventional AFM modes is easy to obtain molecular resolved images on flat samples, such as the purple membrane, or large viruses as the Giant Mimivirus. On the contrary, small virus particles (25–50 nm) cannot be easily imaged. In this work we present Frequency Modulation atomic force microscopy (FM-AFM) working in physiological conditions as an accurate and powerful technique to study virus particles. Our interpretation of the so called “dissipation channel” in terms of mechanical properties allows us to provide maps where the local stiffness of the virus particles are resolved with nanometer resolution. FM-AFM can be considered as a non invasive technique since, as we demonstrate in our experiments, we are able to sense forces down to 20 pN. The methodology reported here is of general interest since it can be applied to a large number of biological samples. In particular, the importance of mechanical interactions is a hot topic in different aspects of biotechnology ranging from protein folding to stem cells differentiation where conventional AFM modes are already being used.

Atomic Force Microscopy (AFM) has excellent potential ability for quantitative electrostatic measurements of surface potential and dielectric permittivity of materials with nanoscale resolution. Implementation of this ability, however, requires overcoming several challenges. The first task is developing an accurate computational model for electrostatic tip-sample interaction; the second - efficient instrumentation and a control system that supports the measurements. An analytical model of nanoscale tip-sample capacitance on thin dielectric films was introduced (Gomila, Toset, and Fumagalli, 2008). This model allows describing the electrostatic tip-sample interaction force in a form suitable for the AFM dynamic control model (Belikov, Magonov, 2009). This dynamic model contains integrals over the tip-sample forces that can be presented in a closed form for the Gomila-Toset-Fumagalli analytical model. These results allow for developing very efficient electrostatic AFM computational model. As for the second task (instrumentation and control), the above mentioned AFM dynamic model with (amplitude-phase) state variables can be used for the control system design that combines mechanical Amplitude Modulation mode and consequent electrical modulation of the mechanical phase cosine. The cosine is monitored by lock-in amplifiers at the electrical modulation frequency, and twice that frequency; surface potential and dielectric permittivity of the sample can then be mapped. This paper presents the model derivation, description of instrumentation and control schematics, and their implementation on NT-MDT microscopes. Results are illustrated with practical measurements on different materials.

Surface charge distributions on biological molecules in aqueous solutions are essential for the interactions between biomolecules, such as DNA condensation, antibody–antigen interactions, and enzyme reactions. There has been a significant demand for a molecular-scale charge density measurement technique for better understanding such interactions. In this paper, we present the local electric double layer (EDL) force measurements on DNA molecules in aqueous solutions using frequency modulation atomic force microscopy (FM-AFM) with a three-dimensional force mapping technique. The EDL forces measured in a 100 mM KCl solution well agreed with the theoretical EDL forces calculated using reasonable parameters, suggesting that FM-AFM can be used for molecular-scale quantitative charge density measurements on biological molecules especially in a highly concentrated electrolyte.

The crystal growth and dissolution processes of a fluorite (CaF2) crystal have attracted much attention due to the importance in the industrial, environmental, and medical applications. While previous studies clarified nanoscale processes at the fluorite–water interface, atomic-scale origins of the processes have yet to be understood. In this study, we have investigated atomic-scale processes at the fluorite–water interface by frequency modulation atomic force microscopy (FM-AFM). We performed atomic-resolution imaging of a fluorite(111) surface in water (pH = 2 and 6.5), saturated solution (pH = 2 and 6), and supersaturated solution (pH = 6, σ = 10 and 100). Based on the results, we present three major findings. First, atomic-scale roughening of the crystal surface takes place at low pH due to the proton adsorption. Second, surface adsorbates with a subnanometer-scale height are formed on the crystal surface at high pH. They are most likely to be calcium hydroxo complexes physisorbed on the crystal surfa...

Surface processing of a rubrene single crystal immersed in ionic liquids is valuable for further development of low voltage transistors operated by an electric double layer. We performed a precise and clean surface processing based on the tip-induced dissolution of rubrene molecules at the ionic liquid/rubrene single crystal interfaces by using frequency modulation atomic force microscopy. Molecular resolution imaging revealed that the tip-induced dissolution proceeded via metastable low density states derived from the anisotropic intermolecular interactions within the crystal structure.

Submolecular-Scale Imaging of α-Helices and C-Terminal Domains of Tubulins by Frequency Modulation Atomic Force Microscopy in Liquid