Multifrequency AFM: from origins to convergence

Heterodyne High-Harmonic Electrostatic Force Microscopy with Improved Spatial Resolution for Nanoscale Identification of Metallic/Semiconducting Carbon Nanotubes

There are two main types of carbon nanotubes (CNTs): metallic and semiconducting. Naturally grown CNTs are randomly distributed, posing challenges in distinguishing between the two types. Here, a novel approach for nanoscale high-resolution imaging and identification of CNTs was introduced by incorporating the heterodyne technique into high-harmonic electrostatic force microscopy (HH-EFM) on an atomic force microscopy (AFM) platform. In the developed heterodyne HH-EFM, a more localized high-order gradient of tip-sample nonlinear interaction force is used as signal channels, resulting in an improved spatial resolution, compared to the conventional HH-EFM. Furthermore, the heterodyne HH-EFM also has the capability to visualize material carrier density and assess qualitative carrier transport performance. Our work not only presents a new approach to identifying/exploring electrical properties of low-dimensional nanomaterials but also provides a solution for optimizing resolution in long-range interaction-based functional AFM technologies.

Fast and high-resolution mapping of van der Waals forces of 2D materials interfaces with bimodal AFM

High-spatial resolution mapping of van der Waals forces is relevant in several fields ranging from nanotechnology to colloidal science. The emergence of two-dimensional heterostructures assembled by van der Waals interactions has enhanced the interest of those measurements. Several AFM methods have been developed to measure the adhesion force between an AFM probe and the material of interest. However, a reliable and high-resolution method to measure the Hamaker constant remains elusive. We demonstrate that an atomic force microscope operated in a bimodal configuration enables fast, quantitative, and high-resolution mapping of the Hamaker constant of interfaces. The method is applied to map the Hamaker constant of monolayer, bilayer and multilayer MoS2 surfaces. Those interfaces are characterized with Hamaker constant and spatial resolutions of, respectively, 0.1 eV and 50 nm.

Insights and guidelines to interpret forces and deformations at the nanoscale by using a tapping mode AFM simulator: dForce 2.0

Amplitude modulation (tapping mode) AFM is the most versatile AFM mode for imaging surfaces at the nanoscale in air and liquid environments. However, it remains challenging to estimate the forces and deformations exerted by the tip. We introduce a new simulator environment to predict the values of the observables in tapping mode AFM experiments. The relevant feature of dForce 2.0 is the incorporation of contact mechanics models aimed to describe the properties of ultrathin samples. These models were essential to determine the forces applied on samples such as proteins, self-assembled monolayers, lipid bilayers, and few-layered materials. The simulator incorporates two types of long-range magnetic forces. The simulator is written in an open-source code (Python) and it can be run from a personal computer.

Review: Advanced Atomic Force Microscopy Modes for Biomedical Research

Visualization of biomedical samples in their native environments at the microscopic scale is crucial for studying fundamental principles and discovering biomedical systems with complex interaction. The study of dynamic biological processes requires a microscope system with multiple modalities, high spatial/temporal resolution, large imaging ranges, versatile imaging environments and ideally in-situ manipulation capabilities. Recent development of new Atomic Force Microscopy (AFM) capabilities has made it such a powerful tool for biological and biomedical research. This review introduces novel AFM functionalities including high-speed imaging for dynamic process visualization, mechanobiology with force spectroscopy, molecular species characterization, and AFM nano-manipulation. These capabilities enable many new possibilities for novel scientific research and allow scientists to observe and explore processes at the nanoscale like never before. Selected application examples from recent studies are provided to demonstrate the effectiveness of these AFM techniques.

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

Dynamic atomic force microscopy (AFM) is a key platform that enables topological and nanomechanical characterization of novel materials. This is achieved by linking the nanoscale forces that exist between the AFM tip and the sample to specific mathematical functions through modeling. However, the main challenge in dynamic AFM is to quantify these nanoscale forces without the use of complex models that are routinely used to explain the physics of tip-sample interaction. Here, we make use of machine learning and data science to characterize tip-sample forces purely from experimental data with sub-microsecond resolution. Our machine learning approach is first trained on standard AFM models and then showcased experimentally on a polymer blend of polystyrene (PS) and low density polyethylene (LDPE) sample. Using this algorithm we probe the complex physics of tip-sample contact in polymers, estimate elasticity, and provide insight into energy dissipation during contact. Our study opens a new route in dynamic AFM characterization where machine learning can be combined with experimental methodologies to probe transient processes involved in phase transformation as well as complex chemical and biological phenomena in real-time.

Breaking the Fundamental Limitations of Nanoscale Ferroelectric Characterization: Non-Contact Heterodyne Electrostrain Force Microscopy

Perceiving nanoscale ferroelectric phenomena from real space is of great importance for elucidating underlying ferroelectric physics. During the past decades, nanoscale ferroelectric characterization has mainly relied on the Piezoresponse Force Microscopy (PFM) invented in 1992, however, the fundamental limitations of PFM have made the nanoscale ferroelectric studies encounter significant bottlenecks. In this study, a high-resolution non-contact ferroelectric measurement, named Non-Contact Heterodyne Electrostrain Force Microscopy (NC-HEsFM), is introduced. It is demonstrated that NC-HEsFM can operate on multiple eigenmodes to perform ideal high-resolution ferroelectric domain mapping, standard ferroelectric hysteresis loop measurement, and controllable domain manipulation. By using a quartz tuning fork (QTF) sensor, multi-frequency operation, and heterodyne detection schemes, NC-HEsFM achieves a real non-contact yet non-destructive ferroelectric characterization with negligible electrostatic force effect and hence breaks the fundamental limitations of the conventional PFM. It is believed that NC-HEsFM can be extensively used in various ferroelectric or piezoelectric studies with providing substantially improved characterization performance. Meanwhile, the QTF-based force detection makes NC-HEsFM highly compatible for high-vacuum and low-temperature environments, providing ideal conditions for investigating the intrinsic ferroelectric phenomena with the possibility of achieving an atomically resolved ferroelectric characterization.

Discrimination of adhesion and viscoelasticity from nanoscale maps of polymer surfaces using bimodal atomic force microscopy

The simultaneous excitation and measurement of two eigenmodes in bimodal atomic force microscopy (AFM) during sub-micron scale surface imaging augments the number of observables at each pixel of the image compared to the normal tapping mode. However, a comprehensive connection between the bimodal AFM observables and the surface adhesive and viscoelastic properties of polymer samples remains elusive. To address this gap, we first propose an algorithm that systematically accommodates surface forces and linearly viscoelastic three-dimensional deformation computed via Attard's model into the bimodal AFM framework. The proposed algorithm simultaneously satisfies the amplitude reduction formulas for both resonant eigenmodes and enables the rigorous prediction and interpretation of bimodal AFM observables with a first-principles approach. We used the proposed algorithm to predict the dependence of bimodal AFM observables on local adhesion and standard linear solid (SLS) constitutive parameters as well as operating conditions. Secondly, we present an inverse method to quantitatively predict the local adhesion and SLS viscoelastic parameters from bimodal AFM data acquired on a heterogeneous sample. We demonstrate the method experimentally using bimodal AFM on polystyrene-low density polyethylene (PS-LDPE) polymer blend. This inverse method enables the quantitative discrimination of adhesion and viscoelastic properties from bimodal AFM maps of such samples and opens the door for advanced computational interaction models to be used to quantify local nanomechanical properties of adhesive, viscoelastic materials using bimodal AFM.

Quantitative mapping of magnetic properties at the nanoscale with bimodal AFM

We demonstrate that a force microscope operated in a bimodal configuration enables the mapping of magnetic interactions with high quantitative accuracy and high-spatial resolution (∼30 nm). Bimodal AFM operation doubles the number of observables with respect to conventional magnetic force microscopy methods which enables to determine quantitatively in a single processing step several magnetic properties. The theory of bimodal AFM provides analytical expressions for different magnetic force models, in particular those characterized by power-law and exponential distance dependences. Bimodal AFM provides a self-evaluation protocol to test the accuracy of the measurements. The agreement obtained between the experiments and theory for two different magnetic samples support the application of bimodal AFM to map quantitatively long-range magnetic interactions.

Piezoelectric Heterogeneity in Collagen Type I Fibrils Quantitatively Characterized by Piezoresponse Force Microscopy

Piezoelectricity of Type I collagen can provide the stress-generated potential that is considered to be one of the candidate mechanisms to explain bone's adaptation to loading. However, it is still challenging to quantify piezoelectricity because of its heterogeneity and small magnitude. In this study, resonance-enhanced piezoresponse force microscopy (PFM) was utilized to amplify a weak piezoresponse of a single collagen fibril with a carefully calibrated cantilever. The quantitative PFM, combined with a dual-frequency resonance-tracking method, successfully identified the anisotropic and heterogenous nature of the piezoelectric properties in the collagen fibril. The profile of shear piezoelectric coefficient (d₁₅) was obtained to be periodic along the collagen fibril, with a larger value in the gap zone (0.51 pm/V) compared to the value in the overlap zone (0.29 pm/V). Interestingly, this piezoelectric profile corresponds to the periodic profile of mechanical stiffness in a mineralized collagen fibril having a higher stiffness in the gap zone. Considering that apatite crystals are nucleated at the gap zone and subsequently grown along the collagen fibril, the heterogeneous and anisotropic nature of piezoelectric properties highlights the physiological importance of the collagen piezoelectricity in bone mineralization.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

Fast, high-resolution, non-destructive and quantitative characterization methods are needed to develop materials with tailored properties at the nanoscale or to understand the relationship between mechanical properties and cell physiology. This review introduces the state-of-the-art force microscope-based methods to map at high-spatial resolution the elastic and viscoelastic properties of soft materials. The experimental methods are explained in terms of the theories that enable the transformation of observables into material properties. Several applications in materials science, molecular biology and mechanobiology illustrate the scope, impact and potential of nanomechanical mapping methods.

Observer Design for Topography Estimation in Atomic Force Microscopy Using Neural and Fuzzy Networks

In this study, a novel artificial intelligence-based approach is presented to directly estimate the surface topography. To this aim, performance of different artificial intelligence-based techniques, including the multi-layer perceptron neural, radial basis function neural, and adaptive neural fuzzy inference system networks, in estimation of the sample topography is investigated. The results demonstrate that among the designed observers, the multi-layer perceptron method can estimate surface characteristics with higher accuracy than the other methods. In the classical imaging techniques, the scanning speed of atomic force microscope is restricted due to the time required by the oscillating tip to reach the steady state motion while the closed-loop controller tries to maintain the tip vibration amplitude at a set-point value. To address this issue, we have proposed an innovative imaging technique that not only eliminates the need to a closed-loop controller but also estimates the surface topography very quick and accurate compared to the conventional imaging method. Also, the proposed technique is capable of simultaneous estimation of the topography, Hamaker parameter, and the tip-sample interaction force.

Euler-Bernoulli theory accurately predicts atomic force microscope cantilever shape during non-equilibrium snap-to-contact motion

We prove that the Euler-Bernoulli elastic beam theory can be reliably used to describe the dynamics of an atomic force microscope cantilever during the far from equilibrium snap-to-contact event. In conventional atomic force microscope operation, force-separation curves are obtained by post-processing voltage versus time traces produced by measuring one point on the cantilever close to the hanging end. In this article, we assess the validity of the Euler-Bernoulli equation during the snap-to-contact event. The assessment is based on a direct comparison between experiment and theory. The experiment uses Doppler vibrometry to measure displacement versus time for many points along the long axis of the cantilever. The theoretical algorithm is based on a solution of the Euler-Bernoulli equation to obtain the full shape of the cantilever as a function of time. The algorithm uses as boundary conditions, experimentally obtained information only near the hanging end of the cantilever. The solution is obtained in a manner that takes into account non-equilibrium motion. Within experimental error, the theory agrees with experiment indicating that the Euler-Bernoulli theory is appropriate to predict the cantilever kinematics during snap-to-contact. Since forces on the tip can be obtained from the instantaneous shape of the cantilever, this work should allow for computation of tip-sample forces during the snap-to-contact event from a conventional force-distance measured input.

Rapid discrimination of chemically distinctive surface terminations in 2D material based heterostructures by direct van der Waals identification

We demonstrate that surfaces presenting heterogeneous and atomically flat domains can be directly and rapidly discriminated via robust intensive quantifiables by exploiting one-pass noninvasive methods in standard atomic force microscopy (AFM), single ∼2 min passes, or direct force reconstruction, i.e., ∼10³ force profiles (∼10 min collection time), allowing data collection, interpretation, and presentation in under 20 min, including experimental AFM preparation and excluding only sample fabrication, in situ and without extra experimental or time load. We employ a misfit SnTiS₃ compound as a model system. Such heterostructures can be exploited as multifunctional surface systems and provide multiple support sites with distinguishable chemical, mechanical, or opto-electronic distinct properties. In short, they provide an ideal model system to exemplify how current AFM methods can significantly support material discovery across fields.

WiFi-controlled portable atomic force microscope

This article proposes to develop a WiFi-controlled portable atomic force microscope (AFM). The AFM consists of a horizontal probe, controlling circuits, digital to analog (D/A) and analog to digital (A/D) interfaces, a microcomputer (Raspberry Pi, RPi), and a laptop. The proposed AFM uses a pocket-size power supply to drive the controlling circuits, the D/A and A/D interfaces, as well as the RPi that constructs network hotspots and generates scanning signals. With special design and integration of the whole system, both of the AFM probe and electronic controlling system are portable. At a distance of 50 m from the proposed AFM, experiments in the constant height mode and the constant force mode are conducted to evaluate its performance. The results show that this WiFi-controlled AFM has a maximum scan range of 3.6 × 3.6 μm² with nanometer order resolution. Meanwhile, it achieves satisfactory image contrast, stability, and repeatability. Compared with conventional AFMs, the AFM proposed in this paper no longer relies on commercial AC mains supply or high-voltage DC power supply, and realizes WiFi-controlled AFM scanning and imaging in 50 m or farther without wire or network cable connection to a laptop or a desktop computer. Given credits to these features, WiFi-controlled AFMs are expected to own a wider range of application, especially in isolated environments, outdoor researches, or even fieldwork investigations.

Functionalization of polyacrylamide for nanotrapping positively charged biomolecules

Engineering new materials which are capable of trapping biomolecules in nanoscale quantities, is crucial in order to achieve earlier diagnostics in different diseases. This article demonstrates that using free radical copolymerization, polyacrylamide can be successfully functionalized with specific synthons for nanotrapping positively charged molecules, such as numerous proteins, through electrostatic interactions due to their negative charge. Specifically, two functional random copolymers, acrylamide/acrylic acid (1) and acrylamide/acrylic acid/N-(pyridin-4-yl-methyl)acrylamide (2), whose negative net charges differ in their water solutions, were synthetized and their ability to trap positively charged proteins was studied using myoglobin as a proof-of-concept example. In aqueous solutions, copolymer 1, whose net charge for a 100 chain fragment (Q_{pH 6}/M) is −1.323 × 10⁻³, interacted with myoglobin forming a stable monodisperse nanosuspension. In contrast, copolymer 2, whose value of Q_{pH 6}/M equals −0.361 × 10⁻³, was not able to form stable particles with myoglobin. Nevertheless, thin films of both copolymers were grown using a dewetting process, which exhibited nanoscale cavities capable of trapping different amounts of myoglobin, as demonstrated by bimodal AFM imaging. The simple procedures used to build protein traps make this engineering approach promising for the development of new materials for biomedical applications where trapping biomolecules is required.

Engineering new materials which are capable of trapping biomolecules in nanoscale quantities, is crucial in order to achieve earlier diagnostics in different diseases.

Thermoelectric stack sample cooling modification of a commercial atomic force microscopy

Enabling temperature dependent experiments in Atomic Force Microscopy is of great interest to study materials and surface properties at the nanoscale. By studying Curie temperature of multiferroic materials, temperature dependent phase transitions on crystalline structures or resistive switching phenomena are only a few examples of applications. We present an equipment capable of cooling samples using a thermoelectric cooling stage down to -61.4 °C in a 15 × 15 mm² sample plate. The equipment uses a four-unit thermoelectric stack to achieve maximum temperature range, with low electrical and mechanical noise. The equipment is installed into a Keysight 5500LS Atomic Force Microscopy maintaining its compatibility with all Electrical and Mechanical modes of operation. We study the contribution of the liquid cooling pump vibration into the cantilever static deflection noise and the temperature dependence of the cantilever deflection. A La_0.7Sr_0.3MnO_3-y thin film sample is used to demonstrate the performance of the equipment and its usability by analyzing the resistive switching phenomena associated with this oxide perovskite.

Fast, High Resolution, and Wide Modulus Range Nanomechanical Mapping with Bimodal Tapping Mode

Tapping mode atomic force microscopy (AFM), also known as amplitude modulated (AM) or AC mode, is a proven, reliable, and gentle imaging mode with widespread applications. Over the several decades that tapping mode has been in use, quantification of tip-sample mechanical properties such as stiffness has remained elusive. Bimodal tapping mode keeps the advantages of single-frequency tapping mode while extending the technique by driving and measuring an additional resonant mode of the cantilever. The simultaneously measured observables of this additional resonance provide the additional information necessary to extract quantitative nanomechanical information about the tip-sample mechanics. Specifically, driving the higher cantilever resonance in a frequency modulated (FM) mode allows direct measurement of the tip-sample interaction stiffness and, with appropriate modeling, the set point-independent local elastic modulus. Here we discuss the advantages of bimodal tapping, coined AM-FM imaging, for modulus mapping. Results are presented for samples over a wide modulus range, from a compliant gel (∼100 MPa) to stiff materials (∼100 GPa), with the same type of cantilever. We also show high-resolution (subnanometer) stiffness mapping of individual molecules in semicrystalline polymers and of DNA in fluid. Combined with the ability to remain quantitative even at line scan rates of nearly 40 Hz, the results demonstrate the versatility of AM-FM imaging for nanomechanical characterization in a wide range of applications.

Mapping Elastic Properties of Heterogeneous Materials in Liquid with Angstrom-Scale Resolution

Fast quantitative mapping of mechanical properties with nanoscale spatial resolution represents one of the major goals of force microscopy. This goal becomes more challenging when the characterization needs to be accomplished with subnanometer resolution in a native environment that involves liquid solutions. Here we demonstrate that bimodal atomic force microscopy enables the accurate measurement of the elastic modulus of surfaces in liquid with a spatial resolution of 3 Å. The Young's modulus can be determined with a relative error below 5% over a 5 orders of magnitude range (1 MPa to 100 GPa). This range includes a large variety of materials from proteins to metal-organic frameworks. Numerical simulations validate the accuracy of the method. About 30 s is needed for a Young's modulus map with subnanometer spatial resolution.