Multifrequency Atomic Force Microscopy Research Articles

Eigenmodes of a quartz tuning fork and their application to photoinduced force microscopy

We examine the mechanical eigenmodes of a quartz tuning fork (QTF) for the purpose of facilitat- ing its use as a probe for multi-frequency atomic force microscopy (AFM). We perform simulations based on the three-dimensional finite element method (FEM) and compare the observed motions of the beams with experimentally measured resonance frequencies of two QTF systems. The com- parison enabled us to assign the first seven asymmetric eigenmodes of the QTF. We also find that a modified version of single beam theory can be used to guide the assignment of mechanical eigen- modes of QTFs. The usefulness of the QTF for multi-frequency AFM measurements is demonstrated through photo-induced force microscopy (PiFM) measurements. By using the QTF in different con- figurations, we show that the vectorial components of the photo-induced force can be independently assessed, and that lateral forces can be probed in true non-contact mode.

Sub-nanometre mapping of the aquaporin-water interface using multifrequency atomic force microscopy.

Aquaporins are integral membrane proteins that regulate the transport of water and small molecules in and out of the cell. In eye lens tissue, circulation of water, ions and metabolites is ensured by a microcirculation system in which aquaporin-0 (AQP0) plays a central role. AQP0 allows water to flow beyond the diffusion limit through lens membranes. AQP0 naturally arranges in a square lattice. The malfunction of AQP0 is related to numerous diseases such as cataracts. Despite considerable research into its structure, function and dynamics, the interface between the protein and the surrounding liquid and the effect of the lattice arrangement on the behaviour of water at the interface with the membrane are still not fully understood. Here we use a multifrequency atomic force microscopy (AFM) approach to map both the liquid at the interface with AQP0 and the protein itself with sub-nanometer resolution. Imaging using the fundamental eigenmode of the AFM cantilever probes mainly the interfacial water at the surface of the membrane. The results highlight a well-defined region that surrounds AQP0 tetramers and where water exhibits a higher affinity for the protein. Imaging in the second eigenmode is dominated by the mechanical response of the protein and provides sub-molecular details of the protein surface and the sub-surface structure. The relationship between modes and harmonics is also examined.

High-Bandwidth Demodulation in MF-AFM: A Kalman Filtering Approach

Emerging multifrequency atomic force microscopy (MF-AFM) methods rely on coherent demodulation of the cantilever deflection signal at multiple frequencies. These measurements are needed in order to close the z -axis feedback loop and to acquire complementary information on the tip–sample interaction. While the common method is to use a lock-in amplifier capable of recovering low-level signals from noisy backgrounds, its performance is ultimately bounded by the bandwidth of low-pass filters. In light of the demand for constantly increasing imaging speeds while providing multifrequency flexibility, we propose to estimate the in-phase and quadrature components with a linear time-varying Kalman filter. The chosen representation allows for an efficient high-bandwidth implementation on a field programmable gate array. Tracking bandwidth and noise performance are verified experimentally, and trimodal AFM results on a two-component polymer sample highlight the applicability of the proposed method for MF-AFM.

Design and analysis of higher harmonic cantilever based on finite element analysis

Recently, the developing multi-frequency atomic force microscopy, not only can characterize more physical properties of samples with a remarkable spatial resolution, but also detect non-linear force with time-resolved. Its basic principle is that multiple vibrating frequencies of micro cantilever probe is motivated and detected, which is closely related to higher harmonics or eigenmodes of micro cantilever. In order to realize this new technology, it is very important and necessary to design special micro cantilever. Generally, silicon cantilever and quartz cantilever are widely used in traditional AFM. For rectangular silicon cantilever, the ratio of the second order eigenmode and basic frequency is 6.27, and for quartz tuning micro-cantilever, it also isn’t an integral value, so it is almost impossible to study the MF-AFM using the conventional cantilevers directly. Based on the resonant amplification effect, in this article, we discussed the corresponding eigenvibration of traditional rectangular silicon micro-cantilever and quartz tuning micro-cantilever by the method of changing the mass distribution of micro cantilever, namely changing its geometric size and shape. Finally we designed some special cantilevers, which the ratio of second mode frequency and basic frequency are all integer times by theoretical calculation and Finite Element Analysis, including some discussions between flexural resonant and basic frequency.

Identification of HIV-1–Based Virus-like Particles by Multifrequency Atomic Force Microscopy

Virus-like particles (VLPs) have become a promising platform for vaccine production. VLPs are formed by structural viral proteins that inherently self-assemble when expressed in a host cell. They represent a highly immunogenic and safe vaccine platform, due to the absence of the viral genome and its high protein density. One of the most important parameters in vaccine production is the quality of the product. A related bottleneck in VLP-based products is the presence of cellular vesicles as a major contaminant in the preparations, which will require the set up of techniques allowing for specific discrimination of VLPs from host vesicular bodies. In this work novel, to our knowledge, multifrequency (MF) atomic force microscopy (AFM) has permitted full structural nanophysical characterization by its access to the virus capsid of the HIV-based VLPs. The assessment of these particles by advanced amplitude modulation-frequency modulation (AM-FM) viscoelastic mapping mode has enhanced the imaging resolution of their nanomechanical properties, opening a new window for the study of the biophysical attributes of VLPs. Finally, the identification and differentiation of HIV-based VLPs from cellular vesicles has been performed under ambient conditions, providing, to our knowledge, novel methodology for the monitoring and quality control of VLPs.

Comparison between power-law rheological parameters of living cells in frequency and time domains measured by atomic force microscopy

We investigated how stress relaxation mapping is quantified compared with the force modulation mapping of confluent epithelial cells using atomic force microscopy (AFM). Using a multi-frequency AFM technique, we estimated the power-law rheological behaviors of cells simultaneously in time and frequency domains. When the power-law exponent α was low (<0.1), the α values were almost the same in time and frequency domains. On the other hand, we found that at the high values (α > 0.1), α in the time domain was underestimated relative to that in the frequency domain, and the difference increased with α, whereas the cell modulus was overestimated in the time domain. These results indicate that power-law rheological parameters estimated by stress relaxation are sensitive to lag time during initial indentation, which is inevitable in time-domain AFM experiments.

Imaging of surface nanobubbles by atomic force microscopy in liquids: Influence of drive frequency on the characterization of ultrasoft matter.

Imaging of soft matter with atomic force microscopy (AFM) is challenging due to tip-induced deformation, which convolutes with the measurement. The challenges are generally more serious in liquid environments due to a severe loss of sensitivity of the vibrating microcantilever to external forces, as well as due to the presence of undesirable mechanical resonances when piezoelectric excitation systems are used. Furthermore, the choice of imaging parameters can have a significant impact on the quality of the results, such that the customary practices used for tuning the cantilever are not always appropriate. Here we explore the influence of the chosen drive frequency on the imaging of ultrasoft matter, using surface gas nanobubbles on gold-coated glass and highly oriented pyrolytic graphite (HOPG) as a test platform. We carry out single- and multifrequency AFM experiments using both the traditional amplitude-peak method and the recently proposed phase-slope-peak method for tuning the cantilever, as well as piezoelectric and photothermal excitation, providing an extensive discussion on the factors governing the level of tip-induced sample deformation and the quality of the phase contrast obtained for each of the methods. The general conclusion is that there is no "one-size-fits-all" approach for tuning the cantilever for low-impact tapping-mode AFM, although rational optimization of the imaging process is generally possible, whereby the choice of the drive frequency plays a prominent role. The physical insight and guidelines provided here can be extremely useful for the gentle imaging of a wide range of biological and other soft materials in liquid environments. Microsc. Res. Tech. 80:41-49, 2017. © 2016 Wiley Periodicals, Inc.

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions.

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip–sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip–sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

Multifrequency Force Microscopy of Helical Protein Assembly on a Virus.

High-resolution microscopy techniques have been extensively used to investigate the structure of soft, biological matter at the nanoscale, from very thin membranes to small objects, like viruses. Electron microscopy techniques allow for obtaining extraordinary resolution by averaging signals from multiple identical structures. In contrast, atomic force microscopy (AFM) collects data from single entities. Here, it is possible to finely modulate the interaction with the samples, in order to be sensitive to their top surface, avoiding mechanical deformations. However, most biological surfaces are highly curved, such as fibers or tubes, and ultimate details of their surface are in the vicinity of steep height variations. This limits lateral resolution, even when sharp probes are used. We overcome this problem by using multifrequency force microscopy on a textbook example, the Tobacco Mosaic Virus (TMV). We achieved unprecedented resolution in local maps of amplitude and phase shift of the second excited mode, recorded together with sample topography. Our data, which combine multifrequency imaging and Fourier analysis, confirm the structure deduced from averaging techniques (XRD, cryoEM) for surface features of single virus particles, down to the helical pitch of the coat protein subunits, 2.3 nm. Remarkably, multifrequency AFM images do not require any image postprocessing.

High-bandwidth multimode self-sensing in bimodal atomic force microscopy.

Using standard microelectromechanical system (MEMS) processes to coat a microcantilever with a piezoelectric layer results in a versatile transducer with inherent self-sensing capabilities. For applications in multifrequency atomic force microscopy (MF-AFM), we illustrate that a single piezoelectric layer can be simultaneously used for multimode excitation and detection of the cantilever deflection. This is achieved by a charge sensor with a bandwidth of 10 MHz and dual feedthrough cancellation to recover the resonant modes that are heavily buried in feedthrough originating from the piezoelectric capacitance. The setup enables the omission of the commonly used piezoelectric stack actuator and optical beam deflection sensor, alleviating limitations due to distorted frequency responses and instrumentation cost, respectively. The proposed method benefits from a more than two orders of magnitude increase in deflection to strain sensitivity on the fifth eigenmode leading to a remarkable signal-to-noise ratio. Experimental results using bimodal AFM imaging on a two component polymer sample validate that the self-sensing scheme can therefore be used to provide both the feedback signal, for topography imaging on the fundamental mode, and phase imaging on the higher eigenmode.

Multi-frequency atomic force microscopy

It has always been the goal of atomic force microscopy to improve the spatial resolution, the data acquisition speed and the detection of material properties continuously. At present, the multi-frequency atomic force microscopy, which is a new technology, in recent years is the most possible mean to achieve the goal. Multi-frequency atomic force microscopy, which includes various methods to characterize the samples’ nanoscale properties, drives and/or detects micro-cantilever vibration by using multiple frequency. It can extract the nonlinear signal between tip and sample with a high composition detection sensitivity as well as temporal and spatial imaging resolution. In this paper, we reviews the basic principle of different implementation methods included in the multi-frequency atomic force microscopy, and illustrates them by some cutting-edge applications in high resolution imaging, nanometre mechanics, materials, biological application, etc. In addition, we proposed a special micro-cantilever model of quartz tuning fork that can be used in the multi-frequency atomic force microscopy. Finally, the article looks forward to its future development and applied research.

Multifrequency force microscopy using flexural and torsional modes by photothermal excitation in liquid: atomic resolution imaging of calcite

We introduce a new multifrequency atomic force microscopy (AFM) method which involves the excitation of flexural and torsional eigenmodes of the microcantilever probe in liquid environments. The flexural and torsional deflection signals are mostly decoupled in the majority of commercial AFM setups, so they can be relatively easily recorded and processed. The use of torsional modes provides additional surface information at the atomic scale, with respect to flexural mode imaging alone, although the flexural modes are the only ones capable of ‘true’ atomic resolution imaging. In our experiments, the torsional modes are shown to be particularly sensitive to protruding oxygen surface atoms on the calcite plane. The high lateral resolution capability of the flexural modes, combined with the high sensitivity of the torsional modes to specific surface features in liquid environments, can thus offer the means of observing chemical contrast at the atomic level using purely mechanical measurement AFM techniques, even in the absence of tip functionalization.

Rhodamine-doped nanoporous polymer films as high-performance anti-reflection coatings and optical filters.

We demonstrate a simple and robust procedure for the fabrication of rhodamine-doped nanoporous poly(methyl methacrylate) (PMMA) films, whose optical properties, such as anti-reflection, fluorescence and absorption can be tailored to specific applications. By exploiting phase separation of a binary polymer blend (PMMA and polystyrene), we fabricated foam-like nanoporous films that could be easily and cost-effectively integrated into the fabrication process of optical components. We link film morphology, studied by multifrequency atomic force microscopy (AFM), to the effective refractive index of the films for use as anti-reflection coatings. The film's morphology leads to superior broadband anti-reflection performance compared with homogeneous films. For applications involving optical filters and spectral conversion layers (e.g., for photovoltaic applications), we doped the films with the fluorescent molecule rhodamine, whereby simple variations in the fabrication process enabled us to prepare rhodamine-doped nanoporous PMMA with tunable fluorescence and absorption, without losing the anti-reflective properties. The above combination of optical properties makes the films attractive for a wide range of applications.

A Kalman Filter for Amplitude Estimation in High-Speed Dynamic Mode Atomic Force Microscopy

A fundamental challenge in dynamic mode atomic force microscopy (AFM) is the estimation of the cantilever oscillation amplitude from the deflection signal, which might be distorted by noise and/or high-frequency components. When the cantilever is excited at resonance, its deflection is typically obtained via narrow-band demodulation using a lock-in amplifier (LIA). However, the bandwidth of this measurement technique is ultimately bounded by the low-pass filter, which must be employed after demodulation to attenuate the component at twice the carrier frequency. Furthermore, to measure the amplitude of multiple frequency components, such as higher eigenmodes and/or higher harmonics in multifrequency AFM, multiple LIAs must be employed. In this paper, the authors propose the estimation of amplitude and phase using a linear time-varying Kalman filter that is easily extended to multiple frequencies. Experimental results are obtained using square-modulated sine waves and closed-loop AFM scans, verifying the performance of the proposed Kalman filter.

Design and optimization of a harmonic probe with step cross section in multifrequency atomic force microscopy.

In multifrequency atomic force microscopy (AFM), probe's characteristic of assigning resonance frequencies to integer harmonics results in a remarkable improvement of detection sensitivity at specific harmonic components. The selection criterion of harmonic order is based on its amplitude's sensitivity on material properties, e.g., elasticity. Previous studies on designing harmonic probe are unable to provide a large design capability along with maintaining the structural integrity. Herein, we propose a harmonic probe with step cross section, in which it has variable width in top and bottom steps, while the middle step in cross section is kept constant. Higher order resonance frequencies are tailored to be integer times of fundamental resonance frequency. The probe design is implemented within a structural optimization framework. The optimally designed probe is micromachined using focused ion beam milling technique, and then measured with an AFM. The measurement results agree well with our resonance frequency assignment requirement.

Selective enhancement of individual cantilever high resonance modes

Multifrequency atomic force microscopy (AFM) in liquid media where several eigenmodes or harmonics are simultaneously excited is improving the performance of the scanning probe techniques in biological studies. As a consequence, an important effort is being made to search for a reliable, efficient and strong cantilever high mode excitation method that operates in liquids. In this work we present (theoretical and experimentally) a technique for improving the efficiency of the most common excitation methods currently used in AFM operated in liquids: photothermal, torque (MAC Mode™) and magnetostriction. By etching specific areas of the cantilever coating, the oscillation amplitude (both flexural and torsional) of each specific eigenmode increases, leading to an improvement in signal to noise ratio of the multifrequency techniques. As an alternative, increment in high mode oscillation amplitude is also obtained by Ga+ ion implantation in the specific areas of the magnetic material.

Mapping power-law rheology of living cells using multi-frequency force modulation atomic force microscopy

We present multi-frequency force modulation atomic force microscopy (AFM) for mapping the complex shear modulus G* of living cells as a function of frequency over the range of 50–500 Hz in the same measurement time as the single-frequency force modulation measurement. The AFM technique enables us to reconstruct image maps of rheological parameters, which exhibit a frequency-dependent power-law behavior with respect to G*. These quantitative rheological measurements reveal a large spatial variation in G* in this frequency range for single cells. Moreover, we find that the reconstructed images of the power-law rheological parameters are much different from those obtained in force-curve or single-frequency force modulation measurements. This indicates that the former provide information about intracellular mechanical structures of the cells that are usually not resolved with the conventional force measurement methods.

Design and Evaluation of Torsional Probes for Multifrequency Atomic Force Microscopy

Multifrequency atomic force microscopy is a powerful nanoscale imaging and characterization technique that involves excitation of the atomic force microscope (AFM) probe and measurement of its response at multiple frequencies. This paper reports the design, fabrication, and evaluation of AFM probes with a specified set of torsional eigen-frequencies that facilitate enhancement of sensitivity in multifrequency AFM. A general approach is proposed to design the probes, which includes the design of their generic geometry, adoption of a simple lumped-parameter model, guidelines for determination of the initial dimensions, and an iterative scheme to obtain a probe with the specified eigen-frequencies. The proposed approach is employed to design a harmonic probe wherein the second and the third eigen-frequencies are the corresponding harmonics of the first eigen-frequency. The probe is subsequently fabricated and evaluated. The experimentally evaluated eigen-frequencies and associated mode shapes are shown to closely match the theoretical results. Finally, a simulation study is performed to demonstrate significant improvements in sensitivity to the second- and the third-harmonic spectral components of the tip-sample interaction force with the harmonic probe compared to that of a conventional probe.

A variable-width harmonic probe for multifrequency atomic force microscopy

In multifrequency atomic force microscopy (AFM) to simultaneously measure topography and material properties of specimens, it is highly desirable that the higher order resonance frequencies of the cantilever probe are assigned to be integer harmonics of the excitation frequency. The harmonic resonances are essential for significant enhancement of the probe's response at the specified harmonic frequencies. In this letter, a structural optimization technique is employed to design cantilever probes so that the ratios between one or more higher order resonance frequencies and the fundamental natural frequency are ensured to be equal to specified integers and, in the meantime, that the fundamental natural frequency is maximized. Width profile of the cantilever probe is the design variable in optimization. Thereafter, the probes were prepared by modifying a commercial probe through the focused ion beam (FIB) milling. The resonance frequencies of the FIB fabricated probes were measured with an AFM. Results of the measurement show that the optimal design of probe is as effective as design prediction.

Bimodal frequency-modulated atomic force microscopy with small cantilevers.

Small cantilevers with ultra-high resonant frequencies (1-3 MHz) have paved the way for high-speed atomic force microscopy. However, their potential for multi-frequency atomic force microscopy is unexplored. Because small cantilevers have small spring constants but large resonant frequencies, they are well-suited for the characterisation of delicate specimens with high imaging rates. We demonstrate their imaging capabilities in a bimodal frequency modulation mode in constant excitation on semi-crystalline polypropylene. The first two flexural modes of the cantilever were simultaneously excited. The detected frequency shift of the first eigenmode was held constant for topographical feedback, whereas the second eigenmode frequency shift was used to map the local properties of the specimen. High-resolution images were acquired depicting crystalline lamellae of approximately 12 nm in width. Additionally, dynamic force curves revealed that the contrast originated from different interaction forces between the tip and the distinct polymer regions. The technique uses gentle forces during scanning and quantified the elastic moduli Eam = 300 MPa and Ecr = 600 MPa on amorphous and crystalline regions, respectively. Thus, multimode measurements with small cantilevers allow one to map material properties on the nanoscale at high resolutions and increase the force sensitivity compared with standard cantilevers.