Multifrequency Atomic Force Microscopy Research Articles

Enhancing higher-order modal response in multifrequency atomic force microscopy with a coupled cantilever system.

Multifrequency atomic force microscopy (AFM) utilizes the multimode operation of cantilevers to achieve rapid high-resolution imaging and extract multiple properties. However, the higher-order modal response of traditional rectangular cantilever is weaker in air, which affects the sensitivity of multifrequency AFM detection. To address this issue, we previously proposed a bridge/cantilever coupled system model to enhance the higher-order modal response of the cantilever. This model is simpler and less costly than other enhancement methods, making it easier to be widely used. However, previous studies were limited to theoretical analysis and preliminary simulations regarding ideal conditions. In this paper, we undertake a more comprehensive investigation of the coupled system, taking into account the influence of probe and excitation surface sizes on the modal response. To facilitate the exploration of the effectiveness and optimal conditions for the coupled system in practical applications, a macroscale experimental platform is established. By conducting finite element analysis and experiments, we compare the performance of the coupled system with that of traditional cantilevers and quantify the enhancement in higher-order modal response. Also, the optimal conditions for the enhancement of macroscale cantilever modal response are explored. Additionally, we also supplement the characteristics of this model, including increasing the modal frequency of the original cantilever and generating additional resonance peaks, demonstrating the significant potential of the coupled system in various fields of AFM.

Light-induced modulation of viscoelastic properties in azobenzene polymers.

Photo-induced isomerization of azobenzene molecules drives mass migrations in azopolymer samples. The resulting macroscopic directional photo-deformation of the material morphology has found many applications in literature, although the fundamental mechanisms behind this mass transfer are still under debate. Hence, it is of paramount importance to find quantitative observables that could drive the community toward a better understanding of this phenomenon. In this regard, azopolymer mechanical properties have been intensively studied, but the lack of a nanoscale technique capable of quantitative viscoelastic measurements has delayed the progress in the field. Here, we use bimodal atomic force microscopy (AFM) as a powerful technique for nanomechanical characterizations of azopolymers. With this multifrequency AFM approach, we map the azopolymer local elasticity and viscosity, with high resolution, after irradiation. We find that, while in the (previously) illuminated region, a general photo-softening is measured; locally, the Young modulus and the viscosity depend upon the inner structuring of the illuminating light spot. We then propose a possible interpretation based on a light-induced expansion plus a local alignment of the polymer chains (directional hole-burning effect), which explains the experimental observations. The possibility to access, in a reliable and quantitative way, both Young modulus and viscosity could trigger new theoretical-numerical investigations on the azopolymer mass migration dynamics since, as we show, both parameters can be considered measurable. Furthermore, our results provide a route for engineering the nanomechanical properties of azopolymers, which could find interesting applications in cell mechanobiology research.

Machine learning assisted multifrequency AFM: Force model prediction

Multifrequency atomic force microscopy (AFM) enhances resolving power, provides extra contrast channels, and is equipped with a formalism to quantify material properties pixel by pixel. On the other hand, multifrequency AFM lacks the ability to extract and examine the profile to validate a given force model while scanning. We propose exploiting data-driven algorithms, i.e., machine learning packages, to predict the optimum force model from the observables of multifrequency AFM pixel by pixel. This approach allows distinguishing between different phenomena and selecting a suitable force model directly from observables. We generate predictive models using simulation data. Finally, the formalism of multifrequency AFM can be employed to analytically recover material properties by inputting the right force model.

Tailored Microcantilever Optimization for Multifrequency Force Microscopy.

Microcantilevers are at the heart of atomic force microscopy (AFM) and play a significant role in AFM-based techniques. Recent advancements in multifrequency AFM require the simultaneous excitation and detection of multiple eigenfrequencies of microcantilevers to assess more data channels to quantify the material properties. However, to achieve higher spatiotemporal resolution there is a need to optimize the structure of microcantilevers. In this study, the architecture of the cantilever with gold nanoparticles using a dip-coating method is modified, aiming to tune the higher eigenmodes of the microcantilever as integer multiples of its fundamental frequency. Through the theoretical methodology and simulative model, that integer harmonics improve the coupling in multifrequency AFM measurements is demonstrated, leading to enhanced image quality and resolution. Furthermore, via the combined theoretical-experimental approach, the interplay between induced mass and stiffness change of the modified cantilever depending on the attached particle location, size, mass, and geometry is found. To validate the results of this predictive model, tapping-mode AFM is utilized and bimodal Amplitude Modulation AFM techniques to examine and quantify the impact of tuning higher-order eigenmodes on the imaging quality of a polystyrene-polymethylmethacrylate (PS-PMMA) block co-polymer assembly deposited on a glass slide and Highly Ordered Pyrolytic Graphite (HOPG).

Adsorbate Formation/Removal and Plasma‐Induced Evolution of Defects in Graphitic Materials

AbstractThe preparation of adsorbate‐free graphene with well‐defined layer numbers is a current challenge in materials and surface science and required to fabricate graphene‐based nanodevices, such as used in nanoelectromechanical systems. One strategy to tailor the layer number is oxygen‐plasma treatment of few‐layer graphene/graphite flakes. However, when graphitic materials are stored in air under ambient conditions, it is almost inevitable that adsorbates deposit on their surfaces. When precisely removing individual graphene layers from graphitic flakes by oxygen‐plasma treatment, the amount and type of adsorbates strongly affect the required plasma‐treatment process and duration. To examine the removal/etching mechanism involved in removing such layers, few‐layer graphene/graphite flakes, with areas of different layer numbers, are stored in ambient air and stepwise exposed to oxygen plasma in a shielded configuration. The flakes are then successively analyzed by multifrequency atomic force microscopy together with Raman spectroscopy, focusing on etching rate, and adsorbate and defect evolution. Combined in‐plane and out‐of‐plane tip–adsorbate–substrate interaction analysis facilitates discrimination of different types of adsorbates (water, polycyclic aromatic hydrocarbons, and linear alkanes) and their formation with time. The results demonstrate the potential regarding the development of an efficient method for cleaning of graphitic surfaces and ablation of individual graphene layers.

Probing power laws in multifrequency AFM

Quantification of conservative forces in multifrequency atomic force microscopy requires solving the general equations of the theory expressed in terms of the virials of interaction. Power law expressions are commonly utilized when dealing with electrostatic, ferroelectric, magnetic, or long range (van der Waals) forces. Here, we discuss long range forces modeled in terms of power laws (n), where the exponent n covers the range n = 2–5, and employ the multifrequency theory to explore the relevant parameter space. Numerical integration of the equations of motion suggest that only a narrow range of operational parameters are available when imaging where the approximations are valid. Albeit these conditions exist, and the corresponding errors can be as low as 10% throughout for all exponents explored.

Cell wall fucosylation in Arabidopsis influences control of leaf water loss and alters stomatal development and mechanical properties.

The Arabidopsis sensitive-to-freezing8 (sfr8) mutant exhibits reduced cell wall (CW) fucose levels and compromised freezing tolerance. To examine whether CW fucosylation also affects the response to desiccation, we tested the effect of leaf excision in sfr8 and the allelic mutant mur1-1. Leaf water loss was strikingly higher than in the wild type in these, but not other, fucosylation mutants. We hypothesized that reduced fucosylation in guard cell (GC) walls might limit stomatal closure through altering mechanical properties. Multifrequency atomic force microscopy (AFM) measurements revealed a reduced elastic modulus (E'), representing reduced stiffness, in sfr8 GC walls. Interestingly, however, we discovered a compensatory mechanism whereby a concomitant reduction in the storage modulus (E'') maintained a wild-type viscoelastic time response (tau) in sfr8. Stomata in intact leaf discs of sfr8 responded normally to a closure stimulus, abscisic acid, suggesting that the time response may relate more to closure properties than stiffness does. sfr8 stomatal pore complexes were larger than those of the wild type, and GCs lacked a fully developed cuticular ledge, both potential contributors to the greater leaf water loss in sfr8. We present data that indicate that fucosylation-dependent dimerization of the CW pectic domain rhamnogalacturonan-II may be essential for normal cuticular ledge development and leaf water retention.

Intermodal coupling spectroscopy of mechanical modes in microcantilevers.

Atomic force microscopy (AFM) is highly regarded as a lens peering into the next discoveries of nanotechnology. Fundamental research in atomic interactions, molecular reactions, and biological cell behaviour are key focal points, demanding a continuous increase in resolution and sensitivity. While renowned fields such as optomechanics have marched towards outstanding signal-to-noise ratios, these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in AFM, starting with the first two flexural modes of cantilevers and asses the impact of an amplified coupling between them. In the following, we expand our investigation to the sea of eigenmodes available in the same structure and find a maximum coupling of 9.38 × 103 Hz/nm between two torsional modes. Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware.

In-plane and out-of-plane interaction analysis of adsorbates on multilayer graphene and graphite by multifrequency atomic force microscopy

Graphene and graphite are generally considered as materials exhibiting friction anisotropy. However, it was demonstrated by friction force microscopy experiments that friction anisotropy most likely originates from adsorbates aligning in well-ordered stripes on graphitic surfaces. In this study, we analyzed the evolution of adsorbates on a few-layer graphene-/graphite-flake on top of a Si/SiO 2 -substrate after different times of storage using a multifrequency force microscopy approach. The method allows for the simultaneous in-plane and out-of-plane sample analysis as well as the discrimination of conservative and dissipative tip-sample interactions directed parallel and perpendicular to the surface and thus offers a myriad of complementary physical information. We found that friction anisotropy was observable at distinct areas of the graphene-/graphite-flake after 14 days of storage when exposed to air, albeit not throughout the whole flake, indicating different types of adsorbates. High-resolution imaging revealed that friction anisotropy occurred not only at positions where stripe-like structures were visible, but also on areas which were completely covered with adsorbates. Additionally, we demonstrated that after removal of the adsorbate material by oxygen-plasma treatment, no friction anisotropy was observable on the graphene-/graphite-flake, corroborating adsorbate driven nature of friction anisotropy on graphitic surfaces. • Combined in-plane and out-of-plane force microscopy for interpretation of ordered adsorbate formation on graphite/graphene. • Discrimination of different types of adsorbates by tip-sample interactions parallel and perpendicular to the surface. • 90° rotation of the graphene/graphite flake revealed that friction anisotropy is only caused by certain types of adsorbates.

A cantilever-based, ultrahigh-vacuum, low-temperature scanning probe instrument for multidimensional scanning force microscopy.

Cantilever-based atomic force microscopy (AFM) performed under ambient conditions has become an important tool to characterize new material systems as well as devices. Current instruments permit robust scanning over large areas, atomic-scale lateral resolution, and the characterization of various sample properties using multifrequency and multimodal AFM operation modes. Research of new quantum materials and devices, however, often requires low temperatures and ultrahigh vacuum (UHV) conditions and, more specifically, AFM instrumentation providing atomic resolution. For this, AFM instrumentation based on a tuning fork force sensor became increasingly popular. In comparison to microfabricated cantilevers, the more macroscopic tuning forks, however, lack sensitivity, which limits the measurement bandwidth. Moreover, multimodal and multifrequency techniques, such as those available in cantilever-based AFM carried out under ambient conditions, are challenging to implement. In this article, we describe a cantilever-based low-temperature UHV AFM setup that allows one to transfer the versatile AFM techniques developed for ambient conditions to UHV and low-temperature conditions. We demonstrate that such a cantilever-based AFM offers experimental flexibility by permitting multimodal or multifrequency operations with superior force derivative sensitivities and bandwidths. Our instrument has a sub-picometer gap stability and can simultaneously map not only vertical and lateral forces with atomic-scale resolution, but also perform rapid overview scans with the tip kept at larger tip–sample distances for robust imaging.

Machine learning to probe modal interaction in dynamic atomic force microscopy

Modal interactions are pervasive effects that commonly emerge in nanomechanical systems. The coupling of vibrating modes can be leveraged in many ways, including to enhance sensing or to disclose complex phenomenologies. In this work we show how machine learning and data-driven approaches could be used to capture intermodal coupling. We employ a quasi-recurrent neural network (QRNN) for identifying mode coupling and verify its applicability on experimental data obtained from tapping mode atomic force microscopy (AFM). Hidden units of the QRNN are monitored to trace fingerprints of modes activation and to quantify their contributions over the global distortion of orbits in the phase space. To demonstrate the broad applicability of the method, the trained model is re-applied over different experiments and on diverse materials. Over a range of tip-sample configurations, dynamic AFM possesses features general enough to be seized by the QRNN and it is not required an ad-hoc re-training for the identification of interacting modes. Our study opens up a route for utilizing established machine learning techniques for rapid recognition of nonlinear complex effect such as internal resonances in nanotechnology. The QRNN analysis is meant to assist AFM sensing operations when exploiting modal interaction to enhance the signal-to-noise ratio of higher harmonics and provide high resolution compositional contrast in multi-frequency AFM applications.

Torsional and lateral eigenmode oscillations for atomic resolution imaging of HOPG in air under ambient conditions

Combined in-plane and out-of-plane multifrequency atomic force microscopy techniques have been demonstrated to be important tools to decipher spatial differences of sample surfaces at the atomic scale. The analysis of physical properties perpendicular to the sample surface is routinely achieved from flexural cantilever oscillations, whereas the interpretation of in-plane sample properties via force microscopy is still challenging. Besides the torsional oscillation, there is the additional option to exploit the lateral oscillation of the cantilever for in-plane surface analysis. In this study, we used different multifrequency force microscopy approaches to attain better understanding of the interactions between a super-sharp tip and an HOPG surface focusing on the discrimination between friction and shear forces. We found that the lateral eigenmode is suitable for the determination of the shear modulus whereas the torsional eigenmode provides information on local friction forces between tip and sample. Based on the results, we propose that the full set of elastic constants of graphite can be determined from combined in-plane and out-of-plane multifrequency atomic force microscopy if ultrasmall amplitudes and high force constants are used.

The Generalized Lyapunov Demodulator: High-Bandwidth, Low-Noise Amplitude and Phase Estimation

Effective demodulation of amplitude and phase is a requirement in a wide array of applications. Recent efforts have increased the demodulation performance, in particular, the Lyapunov demodulator allows bandwidths up to the carrier frequency of the signal. However, being inherently restricted to first-order filtering of the input signal, it is highly sensitive to frequency components outside its passband region. This makes it unsuitable for certain applications such as multifrequency atomic force microscopy (AFM). In this article, the structure of the Lyapunov demodulator is transformed to an equivalent form and generalized by exploiting the internal model principle. The resulting generalized Lyapunov demodulator structure allows for arbitrary filtering order and is easy to implement, requiring only a bandpass filter, a single integrator, and two nonlinear transformations. The generalized Lyapunov demodulator is implemented experimentally on a field-programmable gate array (FPGA). Then it is used for imaging in an AFM and benchmarked against the standard Lyapunov demodulator and the widely used lock-in amplifier. The lock-in amplifier achieves great noise attenuation capabilities and off-mode rejection at low bandwidths, whereas the standard Lyapunov demodulator is shown to be effective at high bandwidths. We demonstrate that the proposed demodulator combines the best from the two state-of-the-art demodulators, demonstrating high bandwidths, large off-mode rejection, and excellent noise attenuation simultaneously.

Sensitivity of viscoelastic characterization in multi-harmonic atomic force microscopy.

Quantifying the nanomechanical properties of soft-matter using multi-frequency atomic force microscopy (AFM) is crucial for studying the performance of polymers, ultra-thin coatings, and biological systems. Such characterization processes often make use of cantilever's spectral components to discern nanomechanical properties within a multi-parameter optimization problem. This could inadvertently lead to an over-determined parameter estimation with no clear relation between the identified parameters and their influence on the experimental data. In this work, we explore the sensitivity of viscoelastic characterization in polymeric samples to the experimental observables of multi-frequency intermodulation AFM. By performing simulations and experiments we show that surface viscoelasticity has negligible effect on the experimental data and can lead to inconsistent and often non-physical identified parameters. Our analysis reveals that this lack of influence of the surface parameters relates to a vanishing gradient and non-convexity while minimizing the objective function. By removing the surface dependency from the model, we show that the characterization of bulk properties can be achieved with ease and without any ambiguity. Our work sheds light on the sensitivity issues that can be faced when optimizing for a large number of parameters and observables in AFM operation, and calls for the development of new viscoelastic models at the nanoscale and improved computational methodologies for nanoscale mapping of viscoelasticity using AFM.

Chemical bond imaging using torsional and flexural higher eigenmodes of qPlus sensors.

Non-contact atomic force microscopy (AFM) with CO-functionalized tips allows visualization of the chemical structure of adsorbed molecules and identify individual inter- and intramolecular bonds. This technique enables in-depth studies of on-surface reactions and self-assembly processes. Herein, we analyze the suitability of qPlus sensors, which are commonly used for such studies, for the application of modern multifrequency AFM techniques. Two different qPlus sensors were tested for submolecular resolution imaging via actuating torsional and flexural higher eigenmodes and via bimodal AFM. The torsional eigenmode of one of our sensors is perfectly suited for performing lateral force microscopy (LFM) with single bond resolution. The obtained LFM images agree well with images from the literature, which were scanned with customized qPlus sensors that were specifically designed for LFM. The advantage of using a torsional eigenmode is that the same molecule can be imaged either with a vertically or laterally oscillating tip without replacing the sensor simply by actuating a different eigenmode. Submolecular resolution is also achieved by actuating the 2nd flexural eigenmode of our second sensor. In this case, we observe particular contrast features that only appear in the AFM images of the 2nd flexural eigenmode but not for the fundamental eigenmode. With complementary laser Doppler vibrometry measurements and AFM simulations we can rationalize that these contrast features are caused by a diagonal (i.e. in-phase vertical and lateral) oscillation of the AFM tip.

Hydration Dynamics and the Future of Small-Amplitude AFM Imaging in Air.

Here, we discuss the effects that the dynamics of the hydration layer and other variables, such as the tip radius, have on the availability of imaging regimes in dynamic AFM—including multifrequency AFM. Since small amplitudes are required for high-resolution imaging, we focus on these cases. It is possible to fully immerse a sharp tip under the hydration layer and image with amplitudes similar to or smaller than the height of the hydration layer, i.e., ~1 nm. When mica or HOPG surfaces are only cleaved, molecules adhere to their surfaces, and reaching a thermodynamically stable state for imaging might take hours. During these first hours, different possibilities for imaging emerge and change, implying that these conditions must be considered and reported when imaging.

(Invited) Multi-Frequency Atomic Force Microscopy for Nanoscale Infrared Spectroscopy

The emergence of tools at the forefront of advanced atomic force microscopy (AFM) holds great potential to bolster our fundamental understanding of heterogeneous and dynamic systems at the nanoscale, of prime interest for material science, chemistry and life sciences. Developments using multi-frequency AFM provide more sensitive detection and a wider frequency span to explore the morphology, mechanical and chemical properties of the sample volume. However how these performances compare to more conventional modes is not well established.Here, we will present the implementation of multifrequency AFM nanoscale infrared imaging and spectroscopy. We will first discuss how the nonlinear nature of the tip-sample interaction in AFM can be used as a sensitive channel to access infrared (IR) fingerprints of materials at the nanoscale. We will compare the IR signatures obtained with conventional nanoscale IR spectroscopy, both on homogeneous and heterogeneous materials. In doing so, we will estimate the volume probed as a function of the data acquisition parameters and materials properties. Finally, we will illustrate how the high sensitivity and spatial resolution of nanoscale IR spectroscopy provide new insights in the molecular arrangements of complex systems, especially when guided by macro- and micro-scale studies.

Simultaneous Deconvolution of In‐Plane and Out‐of‐Plane Forces of HOPG at the Atomic Scale under Ambient Conditions by Multifrequency Atomic Force Microscopy

AbstractMultifrequency atomic force microscopy (AFM) is shown to be an excellent tool for imaging crystal structures at atomic resolution in different spatial directions. However, determining the forces between single atoms remains challenging, particularly in air under ambient conditions. Developed here is a trimodal AFM approach that simultaneously acquires torsional and flexural frequency‐shift images and spectroscopic data to transfer these observables into in‐plane and out‐of‐plane forces between single bonds of highly oriented pyrolytic graphite (HOPG) at atomic resolution in air under ambient conditions based on the Fourier method. It is found that the cantilever mean deflection is an excellent indicator to understand that strong attractive interactions between the tip and the surface of HOPG in dynamic AFM imply a local lift of the topmost carbon layer when using higher eigenmodes for the topographical feedback. Cross‐talk between torsional and flexural‐oscillation modes is shown to be negligible. Interestingly, significant differences are observed in the in‐plane forces depending on the orientation of the carbon bonds relative to the direction of torsional oscillation.

Enhancing higher-order eigenmodes of AFM using bridge/cantilever coupled system

The wide application of multi-frequency atomic force microscopy (AFM) places higher demands on the higher-order modes response of the cantilever. The response of the higher modes however is generally weaker than that of the fundamental mode in air. Researchers have proposed many methods, most of which involve cantilever modification, to enhance higher-order eigenmodes response. These previous results are proved to be effective, but the microfabrication is expensive. In this article, we propose a novel model based on bridge/cantilever coupled system to enhance the higher-order modes response of AFM cantilever. The segmented beam model provides a new thinking to explain the appearance of undesired peaks in mode analysis of cantilever. Through theoretical analysis and simulation, we find that higher resonance modes are enhanced by tuning the bridge to match the high resonances of the single clamped cantilever. The length, thickness of the coupled system and the location of excitation can affect the enhancement. In summary, this model provides a new way to improve higher mode response for multi-frequency and other high bandwidth applications of AFM.

Nanoscale Wetting of Single Viruses.

The epidemic spread of many viral infections is mediated by the environmental conditions and influenced by the ambient humidity. Single virus particles have been mainly visualized by atomic force microscopy (AFM) in liquid conditions, where the effect of the relative humidity on virus topography and surface cannot be systematically assessed. In this work, we employed multi-frequency AFM, simultaneously with standard topography imaging, to study the nanoscale wetting of individual Tobacco Mosaic virions (TMV) from ambient relative humidity to water condensation (RH > 100%). We recorded amplitude and phase vs. distance curves (APD curves) on top of single virions at various RH and converted them into force vs. distance curves. The high sensitivity of multifrequency AFM to visualize condensed water and sub-micrometer droplets, filling gaps between individual TMV particles at RH > 100%, is demonstrated. Dynamic force spectroscopy allows detecting a thin water layer of thickness ~1 nm, adsorbed on the outer surface of single TMV particles at RH < 60%.