Cell Membrane Oscillations under Radiofrequency Electromagnetic Modulation

Cell responses to external radiofrequencies (RF) are a fundamental problem of much scientific research, clinical applications, and even daily lives surrounded by wireless communication hardware. In this work, we report an unexpected observation that the cell membrane can oscillate at the nanometer scale in phase with the external RF radiation from kHz to GHz. By analyzing the oscillation modes, we reveal the mechanism behind the membrane oscillation resonance, membrane blebbing, the resulting cell death, and the selectivity of plasma-based cancer treatment based on the difference in the membrane's natural frequencies among cell lines. Therefore, a selectivity of treatment can be achieved by aiming at the natural frequency of the target cell line to focus the membrane damage on the cancer cells and avoid normal tissues nearby. This gives a promising cancer therapy that is especially effective in the mixing lesion of the cancer cells and normal cells such as glioblastoma where surgical removal is not applicable. Along with these new phenomena, this work provides a general understanding of the cell coupling with RF radiation from the externally stimulated membrane behavior to the cell apoptosis and necrosis.

Optimizing the accuracy of viscoelastic characterization with AFM force-distance experiments in the time and frequency domains

Atomic Force Microscopy (AFM) force-distance (FD) experiments have emerged as an attractive alternative to traditional micro-rheology measurement techniques owing to their versatility of use in materials of a wide range of mechanical properties. Here, we show that the range of time dependent behaviour which can reliably be resolved from the typical method of FD inversion (fitting constitutive FD relations to FD data) is inherently restricted by the experimental parameters: sampling frequency, experiment length, and strain rate. Specifically, we demonstrate that violating these restrictions can result in errors in the values of the parameters of the complex modulus. In the case of complex materials, such as cells, whose behaviour is not specifically understood a priori, the physical sensibility of these parameters cannot be assessed and may lead to falsely attributing a physical phenomenon to an artifact of the violation of these restrictions. We use arguments from information theory to understand the nature of these inconsistencies as well as devise limits on the range of mechanical parameters which can be reliably obtained from FD experiments. The results further demonstrate that the nature of these restrictions depends on the domain (time or frequency) used in the inversion process, with the time domain being far more restrictive than the frequency domain. Finally, we demonstrate how to use these restrictions to better design FD experiments to target specific timescales of a material's behaviour through our analysis of a polydimethylsiloxane (PDMS) polymer sample.

Frequency-dependent nanomechanical profiling for medical diagnosis

Atomic force microscopy (AFM), developed in the early 1980s, has become a powerful characterization tool in micro- and nanoscale science. In the early 1990s, its relevance within biology and medicine research became evident, although its incorporation into healthcare applications remains relatively limited. Here, we briefly explore the reasons for this low level of technological adoption. We also propose a path forward for the incorporation of frequency-dependent nanomechanical measurements into integrated healthcare strategies that link routine AFM measurements with computer analysis, real-time communication with healthcare providers, and medical databases. This approach would be appropriate for diseases such as cancer, lupus, arteriosclerosis and arthritis, among others, which bring about significant mechanical changes in the affected tissues.

Corrosion Resistance of Sulfur-Selenium Alloy Coatings

Despite decades of research, metallic corrosion remains a long-standing challenge in many engineering applications. Specifically, designing a material that can resist corrosion both in abiotic as well as biotic environments remains elusive. Here a lightweight sulfur-selenium (S-Se) alloy is designed with high stiffness and ductility that can serve as an excellent corrosion-resistant coating with protection efficiency of ≈99.9% for steel in a wide range of diverse environments. S-Se coated mild steel shows a corrosion rate that is 6-7 orders of magnitude lower than bare metal in abiotic (simulated seawater and sodium sulfate solution) and biotic (sulfate-reducing bacterial medium) environments. The coating is strongly adhesive, mechanically robust, and demonstrates excellent damage/deformation recovery properties, which provide the added advantage of significantly reducing the probability of a defect being generated and sustained in the coating, thus improving its longevity. The high corrosion resistance of the alloy is attributed in diverse environments to its semicrystalline, nonporous, antimicrobial, and viscoelastic nature with superior mechanical performance, enabling it to successfully block a variety of diffusing species.

A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques

Viscoelastic characterization of materials at the micro- and the nanoscale is commonly performed with the aid of force-distance relationships acquired using atomic force microscopy (AFM). The general strategy for existing methods is to fit the observed material behavior to specific viscoelastic models, such as generalized viscoelastic models or power-law rheology models, among others. Here we propose a new method to invert and obtain the viscoelastic properties of a material through the use of the Z-transform, without using a model. We present the rheological viscoelastic relations in their classical derivation and their z-domain correspondence. We illustrate the proposed technique on a model experiment involving a traditional ramp-shaped force-distance AFM curve, demonstrating good agreement between the viscoelastic characteristics extracted from the simulated experiment and the theoretical expectations. We also provide a path for calculating standard viscoelastic responses from the extracted material characteristics. The new technique based on the Z-transform is complementary to previous model-based viscoelastic analyses and can be advantageous with respect to Fourier techniques due to its generality. Additionally, it can handle the unbounded inputs traditionally used to acquire force-distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time.

Correction: Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

[This corrects the article DOI: 10.3762/bjnano.11.77.].

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

Atomic force microscopy (AFM) is a widely use technique to acquire topographical, mechanical, or electromagnetic properties of surfaces, as well as to induce surface modifications at the micrometer and nanometer scale. Viscoelastic materials, examples of which include many polymers and biological materials, are an important class of systems, the mechanical response of which depends on the rate of application of the stresses imparted by the AFM tip. The mechanical response of these materials thus depends strongly on the frequency at which the characterization is performed, so much so that important aspects of behavior may be missed if one chooses an arbitrary characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies observed in their mechanical response and alert the reader about situations where mischaracterization may occur as a result of probing the material at frequency ranges or with probes that preclude observation of its viscoelastic behavior. While we do not offer a solution to the formidable problem of inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force-distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can help inform dynamic AFM characterization.

Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

Atomic force microscopy (AFM) techniques have provided and continue to provide increasingly important insights into surface morphology, mechanics, and other critical material characteristics at the nanoscale. One attractive implementation involves extracting meaningful material properties, which demands physically accurate models specifically designed for AFM experimentation and simulation. The AFM community has pursued the precise quantification and extraction of rate-dependent material properties, in particular, for a significant period of time, attempting to describe the standard viscoelastic response of materials. AFM static force spectroscopy (SFS) is one approach commonly used in pursuit of this goal. It is capable of acquiring rich temporal insight into the behavior of a sample. During AFM-SFS experiments the cantilever base approaches samples with a nearly constant velocity, which is manipulated to investigate different timescales of the mechanical response. This manuscript seeks to build upon our previous work and presents an approach to extracting useful linear viscoelastic information from AFM-SFS experiments. In addition, the basis for selecting and restricting the model parameters for fitting is discussed from the perspective of applying this technique on a practical level. This work begins with a guided discussion that develops a fit function from fundamental laws, continues with conditioning a raw SFS experimental dataset, and concludes with the fit and prediction of viscoelastic response parameters such as storage modulus, loss modulus, loss angle, and compliance. These steps constitute a complete guide to leveraging AFM-SFS data to estimate key material parameters, with a series of detailed insights into both the methodology and supporting analytical choices.

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip-sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip-sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

Acquisition of time-frequency localized mechanical properties of biofilms and single cells with high spatial resolution

Biofilms are a cluster of bacteria embedded in extracellular polymeric substances (EPS) that contain a complex composition of polysaccharides, proteins, and extracellular DNA (eDNA). Desirable mechanical properties of the biofilms are critical for their survival, propagation, and dispersal, and the response of mechanical properties to different treatment conditions also sheds light on biofilm control and eradication in vivo and on engineering surfaces. However, it is challenging yet important to investigate mechanical behaviors of biofilms with a high spatial resolution because biofilms are very heterogeneous. Moreover, biofilms are viscoelastic, and their time-dependent mechanical behavior is difficult to capture. Herein, we develop a powerful technique that combines the high spatial resolution of an atomic force microscope (AFM) with a rigorous history-dependent viscoelastic analysis to deliver highly spatial-localized biofilm properties within a wide time-frequency window. By exploiting the use of static force spectroscopy in combination with an appropriate viscoelastic framework, we highlight the intensive amount of time-dependent information experimentally available that has been largely overlooked. It is shown that this technique provides a detailed nanorheological signature of the biofilms even at the single-cell level. We share the computational routines that would allow any user to perform the analysis from experimental raw data. The detailed localization of mechanical properties in space and in time-frequency domain provides insights into the understanding of biofilm stability, cohesiveness, dispersal, and control.

Visible-Light-Responsive Photocatalyst of Graphitic Carbon Nitride for Pathogenic Biofilm Control

Pathogenic biofilms raise significant health and economic concerns, because these bacteria are persistent and can lead to long-term infections in vivo and surface contamination in healthcare and industrial facilities or devices. Compared with conventional antimicrobial strategies, photocatalysis holds promise for biofilm control because of its broad-spectrum effectiveness under ambient conditions, low cost, easy operation, and reduced maintenance. In this study, we investigated the performance and mechanism of Staphylococcus epidermidis biofilm control and eradication on the surface of an innovative photocatalyst, graphitic carbon nitride (g-C₃N₄), under visible-light irradiation, which overcame the need for ultraviolet light for many current photocatalysts (e.g., titanium dioxide (TiO₂)). Optical coherence tomography and confocal laser scanning microscopy (CLSM) suggested that g-C₃N₄ coupons inhibited biofilm development and eradicated mature biofilms under the irradiation of white light-emitting diodes. Biofilm inactivation was observed occurring from the surface toward the center of the biofilms, suggesting that the diffusion of reactive species into the biofilms played a key role. By taking advantage of scanning electron microscopy, CLSM, and atomic force microscopy for biofilm morphology, composition, and mechanical property characterization, we demonstrated that photocatalysis destroyed the integrated and cohesive structure of biofilms and facilitated biofilm eradication by removing the extracellular polymeric substances. Moreover, reactive oxygen species generated during g-C₃N₄ photocatalysis were quantified via reactions with radical probes and ¹O₂ was believed to be responsible for biofilm control and removal. Our work highlights the promise of using g-C₃N₄ for a broad range of antimicrobial applications, especially for the eradication of persistent biofilms under visible-light irradiation, including photodynamic therapy, environmental remediation, food-industry applications, and self-cleaning surface development.

Theory of Single-Impact Atomic Force Spectroscopy in liquids with material contrast

Scanning probe microscopy has enabled nanoscale mapping of mechanical properties in important technological materials, such as tissues, biomaterials, polymers, nanointerfaces of composite materials, to name only a few. To improve and widen the measurement of nanoscale mechanical properties, a number of methods have been proposed to overcome the widely used force-displacement mode, that is inherently slow and limited to a quasi-static regime, mainly using multiple sinusoidal excitations of the sample base or of the cantilever. Here, a different approach is put forward. It exploits the unique capabilities of the wavelet transform analysis to harness the information encoded in a short duration spectroscopy experiment. It is based on an impulsive excitation of the cantilever and a single impact of the tip with the sample. It performs well in highly damped environments, which are often seen as problematic in other standard dynamic methods. Our results are very promising in terms of viscoelastic property discrimination. Their potential is oriented (but not limited) to samples that demand imaging in liquid native environments and also to highly vulnerable samples whose compositional mapping cannot be obtained through standard tapping imaging techniques.

Artifacts in time-resolved Kelvin probe force microscopy

Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g., light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due to frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Finally, guidelines for avoiding such artifacts are given.

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

In this short paper we explore the use of higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy (AFM) for the small-indentation imaging of soft viscoelastic materials. In viscoelastic materials, whose response depends on the deformation rate, the tip-sample forces generated as a result of sample deformation increase as the tip velocity increases. Since the eigenfrequencies in a cantilever increase with eigenmode order, and since higher oscillation frequencies lead to higher tip velocities for a given amplitude (in viscoelastic materials), the sample indentation can in some cases be reduced by using higher eigenmodes of the cantilever. This effect competes with the lower sensitivity of higher eigenmodes, due to their larger force constant, which for elastic materials leads to greater indentation for similar amplitudes, compared with lower eigenmodes. We offer a short theoretical discussion of the key underlying concepts, along with numerical simulations and experiments to illustrate a simple recipe for imaging soft viscoelastic matter with reduced indentation.

High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation

Bioinspired design has been central in the development of hierarchical nanocomposites. Particularly, the nacre-mimetic brick-and-mortar structure has shown excellent mechanical properties, as well as gas-barrier properties and optical transparency. Along with these intrinsic properties, the layered structure has also been utilized in sensing devices. Here we extend the multifunctionality of nacre-mimetics by designing an optically transparent and electron conductive coating based on PEDOT:PSS and nanoclays Laponite RD and Cloisite Na+. We carry out extensive characterization of the nanocomposite using transmittance spectra (transparency), conductive atomic force microscopy (conductivity), contact-resonance force microscopy (mechanical properties), and SEM combined with a variety of stress-strain AFM experiments and AFM numerical simulations (internal structure). We further study the nanoclay's response to the application of pressure with multifrequency AFM and conductive AFM, whereby increases and decreases in conductivity can occur for the Laponite RD composites. We offer a possible mechanism to explain the changes in conductivity by modeling the coating as a 1-dimensional multibarrier potential for electron transport, and show that conductivity can change when the separation between the barriers changes under the application of pressure, and that the direction of the change depends on the energy of the electrons. We did not observe changes in conductivity under the application of pressure with AFM for the Cloisite Na+ nanocomposite, which has a large platelet size compared with the AFM probe diameter. No pressure-induced changes in conductivity were observed in the clay-free polymer either.

Analysis and modification of defective surface aggregates on PCDTBT:PCBM solar cell blends using combined Kelvin probe, conductive and bimodal atomic force microscopy

Organic photovoltaic systems comprising donor polymers and acceptor fullerene derivatives are attractive for inexpensive energy harvesting. Extensive research on polymer solar cells has provided insight into the factors governing device-level efficiency and stability. However, the detailed investigation of nanoscale structures is still challenging. Here we demonstrate the analysis and modification of unidentified surface aggregates. The aggregates are characterized electrically by Kelvin probe force microscopy and conductive atomic force microscopy (C-AFM), whereby the correlation between local electrical potential and current confirms a defective charge transport. Bimodal AFM modification confirms that the aggregates exist on top of the solar cell structure, and is used to remove them and to reveal the underlying active layer. The systematic analysis of the surface aggregates suggests that the structure consists of PCBM molecules.

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

We explore the contact problem of a flat-end indenter penetrating intermittently a generalized viscoelastic surface, containing multiple characteristic times. This problem is especially relevant for nanoprobing of viscoelastic surfaces with the highly popular tapping-mode AFM imaging technique. By focusing on the material perspective and employing a rigorous rheological approach, we deliver analytical closed-form solutions that provide physical insight into the viscoelastic sources of repulsive forces, tip-sample dissipation and virial of the interaction. We also offer a systematic comparison to the well-established standard harmonic excitation, which is the case relevant for dynamic mechanical analysis (DMA) and for AFM techniques where tip-sample sinusoidal interaction is permanent. This comparison highlights the substantial complexity added by the intermittent-contact nature of the interaction, which precludes the derivation of straightforward equations as is the case for the well-known harmonic excitations. The derivations offered have been thoroughly validated through numerical simulations. Despite the complexities inherent to the intermittent-contact nature of the technique, the analytical findings highlight the potential feasibility of extracting meaningful viscoelastic properties with this imaging method.

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.

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 using flexural and torsional modes by photothermal excitation in liquid: atomic resolution imaging of calcite (1014)

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 (1014) 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.

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

This paper introduces a quasi-3-dimensional (Q3D) viscoelastic model and software tool for use in atomic force microscopy (AFM) simulations. The model is based on a 2-dimensional array of standard linear solid (SLS) model elements. The well-known 1-dimensional SLS model is a textbook example in viscoelastic theory but is relatively new in AFM simulation. It is the simplest model that offers a qualitatively correct description of the most fundamental viscoelastic behaviors, namely stress relaxation and creep. However, this simple model does not reflect the correct curvature in the repulsive portion of the force curve, so its application in the quantitative interpretation of AFM experiments is relatively limited. In the proposed Q3D model the use of an array of SLS elements leads to force curves that have the typical upward curvature in the repulsive region, while still offering a very low computational cost. Furthermore, the use of a multidimensional model allows for the study of AFM tips having non-ideal geometries, which can be extremely useful in practice. Examples of typical force curves are provided for single- and multifrequency tapping-mode imaging, for both of which the force curves exhibit the expected features. Finally, a software tool to simulate amplitude and phase spectroscopy curves is provided, which can be easily modified to implement other controls schemes in order to aid in the interpretation of AFM experiments.

Optimization of the excitation frequency for high probe sensitivity in single-eigenmode and bimodal tapping-mode AFM

The cantilever excitation frequency and tip free oscillation amplitude are two critical imaging parameters in amplitude-modulation atomic force microscopy (AM-AFM, often referred to as tapping-mode AFM). In general, the excitation frequency is selected to be 'near' the measured resonance frequency of the probe, but there is no established systematic approach for making that choice. In this work we show that the choice of excitation frequency can play a very significant role in the characterization of viscoelastic materials, even when considering small deviations with respect to the resonance frequency. Additionally, we offer an analytical expression, verified through experiments and numerical simulations, which offers guidance for selecting the drive frequency that maximizes probe sensitivity. Our approach is illustrated experimentally through single-eigenmode and bimodal AFM measurements performed on spin-coated Nafion(®) proton exchange thin films. We find that very often, the phase contrast channel is optimized by selecting an excitation frequency that is not necessarily at or near the free resonance frequency.

Energy transfer between eigenmodes in multimodal atomic force microscopy

We present experimental and computational investigations of tetramodal and pentamodal atomic force microscopy (AFM), respectively, whereby the first four or five flexural eigenmodes of the cantilever are simultaneously excited externally. This leads to six to eight additional observables in the form of amplitude and phase signals, with respect to the monomodal amplitude modulation method. We convert these additional observables into three or four dissipation and virial expressions, and show that these quantities can provide enhanced contrast that would otherwise remain hidden in the original observables. We also show that the complexity of the multimodal impact leads to significant energy transfer between the active eigenmodes, such that the dissipated power for individual eigenmodes may be positive or negative, while the total dissipated power remains positive. These results suggest that the contrast of individual eigenmodes in multifrequency AFM should be not be considered in isolation and that it may be possible to use different eigenfrequencies to probe sample properties that respond to different relaxation times.

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

This paper presents computational simulations of single-mode and bimodal atomic force microscopy (AFM) with particular focus on the viscoelastic interactions occurring during tip-sample impact. The surface is modeled by using a standard linear solid model, which is the simplest system that can reproduce creep compliance and stress relaxation, which are fundamental behaviors exhibited by viscoelastic surfaces. The relaxation of the surface in combination with the complexities of bimodal tip-sample impacts gives rise to unique dynamic behaviors that have important consequences with regards to the acquisition of quantitative relationships between the sample properties and the AFM observables. The physics of the tip-sample interactions and its effect on the observables are illustrated and discussed, and a brief research outlook on viscoelasticity measurement with intermittent-contact AFM is provided.

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case

This paper presents experiments on Nafion(®) proton exchange membranes and numerical simulations illustrating the trade-offs between the optimization of compositional contrast and the modulation of tip indentation depth in bimodal atomic force microscopy (AFM). We focus on the original bimodal AFM method, which uses amplitude modulation to acquire the topography through the first cantilever eigenmode, and drives a higher eigenmode in open-loop to perform compositional mapping. This method is attractive due to its relative simplicity, robustness and commercial availability. We show that this technique offers the capability to modulate tip indentation depth, in addition to providing sample topography and material property contrast, although there are important competing effects between the optimization of sensitivity and the control of indentation depth, both of which strongly influence the contrast quality. Furthermore, we demonstrate that the two eigenmodes can be highly coupled in practice, especially when highly repulsive imaging conditions are used. Finally, we also offer a comparison with a previously reported trimodal AFM method, where the above competing effects are minimized.

Challenges and complexities of multifrequency atomic force microscopy in liquid environments

This paper illustrates through numerical simulation the complexities encountered in high-damping AFM imaging, as in liquid enviroments, within the specific context of multifrequency atomic force microscopy (AFM). The focus is primarily on (i) the amplitude and phase relaxation of driven higher eigenmodes between successive tip-sample impacts, (ii) the momentary excitation of non-driven higher eigenmodes and (iii) base excitation artifacts. The results and discussion are mostly applicable to the cases where higher eigenmodes are driven in open loop and frequency modulation within bimodal schemes, but some concepts are also applicable to other types of multifrequency operations and to single-eigenmode amplitude and frequency modulation methods.

Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies

The resonance frequency, amplitude, and phase response of the first two eigenmodes of two contact-resonance atomic force microscopy (CR-AFM) configurations, which differ in the method used to excite the system (cantilever base vs sample excitation), are analyzed in this work. Similarities and differences in the observables of the cantilever dynamics, as well as the different effect of the tip-sample contact properties on those observables in each configuration are discussed. Finally, the expected accuracy of CR-AFM using phase-locked loop detection is investigated and quantification of the typical errors incurred during measurements is provided.

Nanoscale mechanics by tomographic contact resonance atomic force microscopy

We report on quantifiable depth-dependent contact resonance AFM (CR-AFM) measurements over polystyrene-polypropylene (PS-PP) blends to detail surface and sub-surface features in terms of elastic modulus and mechanical dissipation. The depth-dependences of the measured parameters were analyzed to generate cross-sectional images of tomographic reconstructions. Through a suitable normalization of the measured contact stiffness and indentation depth, the depth-dependence of the contact stiffness was analyzed by linear fits to obtain the elastic moduli of the materials probed. Besides elastic moduli, the contributions of adhesive forces (short-range versus long-range) to contact on each material were determined without a priori assumptions. The adhesion analysis was complemented by an unambiguous identification of distinct viscous responses during adhesion and in-contact deformation from the dissipated power during indentation.

Multi-frequency tapping-mode atomic force microscopy beyond three eigenmodes in ambient air

We present an exploratory study of multimodal tapping-mode atomic force microscopy driving more than three cantilever eigenmodes. We present tetramodal (4-eigenmode) imaging experiments conducted on a thin polytetrafluoroethylene (PTFE) film and computational simulations of pentamodal (5-eigenmode) cantilever dynamics and spectroscopy, focusing on the case of large amplitude ratios between the fundamental eigenmode and the higher eigenmodes. We discuss the dynamic complexities of the tip response in time and frequency space, as well as the average amplitude and phase response. We also illustrate typical images and spectroscopy curves and provide a very brief description of the observed contrast. Overall, our findings are promising in that they help to open the door to increasing sophistication and greater versatility in multi-frequency AFM through the incorporation of a larger number of driven eigenmodes, and in highlighting specific future research opportunities.

Modeling viscoelasticity through spring-dashpot models in intermittent-contact atomic force microscopy

We examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring-dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force-distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip-sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip-sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work).

Amplitude modulation dynamic force microscopy imaging in liquids with atomic resolution: comparison of phase contrasts in single and dual mode operation

We present a systematic analysis of the atomic-scale imaging capabilities for mineral surfaces in a liquid environment in single and dual mode amplitude modulation dynamic force microscopy. To study the difference in sensitivity between the first and second eigenmode phase signals we investigate the observed atomic-scale contrasts of the mica-water interface under varying imaging conditions. For this purpose, we systematically change the main imaging parameters including the setpoint amplitude of the imaging feedback, the free oscillation amplitudes of the first and second flexural eigenmodes, and their ratio. This allows for an in-depth analysis of the sensitivities of the first and second eigenmode phase signals to draw conclusions regarding the underlying physical mechanisms and the interpretation of the contrast in the multi-frequency technique.

Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case

We present an overview of the bimodal amplitude-frequency-modulation (AM-FM) imaging mode of atomic force microscopy (AFM), whereby the fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in which the higher eigenmode is driven with constant frequency and constant excitation amplitude. General as well as particular characteristics of the different driving schemes are highlighted from theoretical and experimental points of view, revealing the advantages and disadvantages of each. This study provides information and guidelines that can be useful in selecting the most appropriate operation mode to characterize different samples in the most efficient and reliable way.

Directed patterning of the self-assembled silk-elastin-like nanofibers using a nanomechanical stimulus

We investigate the effects of the frequency and density of a nanomechanical stimulus on nucleation and growth of silk-elastin-like protein polymer (SELP) nanofibers. Repetitive tappings are crucial to create nucleation areas and a potential molecular level mechanism was proposed. Using this technique mechanically guided nanofiber patterns were successfully created.

Towards 4-dimensional atomic force spectroscopy using the spectral inversion method

We introduce a novel and potentially powerful, yet relatively simple extension of the spectral inversion method, which offers the possibility of carrying out 4-dimensional (4D) atomic force spectroscopy. With the extended spectral inversion method it is theoretically possible to measure the tip-sample forces as a function of the three Cartesian coordinates in the scanning volume (x, y and z) and the vertical velocity of the tip, through a single 2-dimensional (2D) surface scan. Although signal-to-noise ratio limitations can currently prevent the accurate experimental implementation of the 4D method, and the extraction of rate-dependent material properties from the force maps is a formidable challenge, the spectral inversion method is a promising approach due to its dynamic nature, robustness, relative simplicity and previous successes.

Nanoscale interfacial friction and adhesion on supported versus suspended monolayer and multilayer graphene

Using atomic force microscopy (AFM), supported by semicontinuum numerical simulations, we determine the effect of tip-subsurface van der Waals interactions on nanoscale friction and adhesion for suspended and silicon dioxide supported graphene of varying thickness. While pull-off force measurements reveal no layer number dependence for supported graphene, suspended graphene exhibits an increase in pull-off force with thickness. Further, at low applied loads, friction increases with increasing number of layers for suspended graphene, in contrast to reported trends for supported graphene. We attribute these results to a competition between local forces that determine the deformation of the surface layer, the profile of the membrane as a whole, and van der Waals forces between the AFM tip and subsurface layers. We find that friction on supported monolayer graphene can be fit using generalized continuum mechanics models, from which we extract the work of adhesion and interfacial shear strength. In addition, we show that tip-sample adhesive forces depend on interactions with subsurface material and increase in the presence of a supporting substrate or additional graphene layers.

Multifrequency imaging in the intermittent contact mode of atomic force microscopy: beyond phase imaging

The cantilever dynamics in single-frequency scanning probe microscopy (SPM) are undefined due to having only two output variables, which leads to poorly understood image contrast. To address this shortcoming, generalized phase imaging scanning probe microscopy (GP-SPM), based on broad band detection and multi-eigenmode operation, is developed and demonstrated on diamond nanoparticles with different functionalization layers. It is shown that rich information on tip-surface interactions can be acquired by separating the response amplitude, instant resonance frequency, and quality factor. The obtained data allow high-resolution imaging even in the ambient environment. By tuning the strength of tip-surface interaction, different surface functionalizations can be discerned.

Characterization of surface stiffness and probe-sample dissipation using the band excitation method of atomic force microscopy: a numerical analysis

Recently Jesse and co-workers introduced the band excitation atomic force microscopy (BE-AFM) method (Jesse et al 2007 Nanotechnology 18 435503), in which the cantilever probe is excited in a continuum frequency band in order to measure its response at all frequencies in the band. Analysis of the cantilever response using the damped harmonic oscillator model provides information on the stiffness and level of dissipation at the tip-sample junction as the sample is scanned. Since its introduction, this method has been used in magnetic, electromechanical, thermal and molecular unfolding applications, among others, and has given rise to a new family of scanning probe microscopy techniques. Additionally, the concept is applicable to any field in which measurement of the frequency response of harmonic oscillators is relevant. In this paper we present an analytical and numerical analysis of the excitation signals used in BE-AFM, as well as of the cantilever response under different conditions. Our analysis is performed within the context of viscoelastic characterization. We discuss subtleties in the cantilever dynamics, provide guidelines for implementing the method effectively and illustrate the use of simulation in interpreting the results.

On mapping subangstrom electron clouds with force microscopy

In 2004 Hembacher et al. (Science 2004, 305, 380-383) reported simultaneous higher-harmonics atomic force mocroscopy (AFM)/scanning tunneling microscopy (STM) images acquired while scanning a graphite surface with a tungsten tip. They interpreted the observed subatomic features in the AFM images as the signature of lobes of increased electron density at the tungsten tip apex. Although these intriguing images have stirred controversy, an in-depth theoretical feasibility study has not yet been produced. Here we report on the development of a method for simulating higher harmonics AFM images and its application to the same system. Our calculations suggest that four lobes of increased electron density are expected to be present at a W(001) tip apex atom and that the corresponding higher harmonics AFM images of graphite can exhibit 4-fold symmetry features. Despite these promising results, open questions remain since the calculated amplitudes of the higher harmonics generated by the short-range forces are on the order of hundredths of picometers, leading to very small corrugations in the theoretical images. Additionally, the complex, intermittent nature of the tip-sample interaction, which causes constant readjustment of the tip and sample orbitals as the tip approaches and retracts from the surface, prevents a direct quantitative connection between the electron density and the AFM image features.

Nanomechanical stimulus accelerates and directs the self-assembly of silk-elastin-like nanofibers

One-dimensional nanostructures are ideal building blocks for functional nanoscale assembly. Peptide-based nanofibers have great potential in building smart hierarchical structures due to their tunable structures at the single residue level and their ability to reconfigure themselves in response to environmental stimuli. We observed that pre-adsorbed silk-elastin-based protein polymers self-assemble into nanofibers through conformational changes on a mica substrate. Furthermore, we demonstrate that the rate of self-assembly was significantly enhanced by applying a nanomechanical stimulus using atomic force microscopy. The orientation of the newly grown nanofibers was mostly perpendicular to the scanning direction, implying that the new fiber assembly was locally activated with directional control. Our method provides a novel way to prepare nanofiber patterned substrates using a bottom-up approach.

Numerical analysis of dynamic force spectroscopy using the torsional harmonic cantilever

A spectral analysis method has been recently introduced by Stark et al (2002 Proc. Natl Acad. Sci. USA 99 8473-8) and implemented by Sahin et al (2007 Nat. Nanotechnol. 2 507-14) using a T-shaped cantilever design, the torsional harmonic cantilever (THC), which is capable of performing simultaneous tapping-mode atomic force microscopy imaging and force spectroscopy. Here we report on numerical simulations of the THC system using a simple dual-mass flexural-torsional model, which is applied in combination with Fourier data processing software to illustrate the spectroscopy process for quality factors corresponding to liquid, air and vacuum environments. We also illustrate the acquisition of enhanced topographical images and deformed surface contours under the application of uniform forces, and compare the results to those obtained with a previously reported linear dual-spring-mass model.

Single Biomolecule Imaging with Frequency and Force Modulation in Tapping-Mode Atomic Force Microscopy

A new intermittent-contact atomic force microscopy (AFM) mode (frequency and force modulation AFM, FFM-AFM) has been recently proposed to characterize soft samples. This method uses excitation force frequency and amplitude modulation to eliminate bistability and reduce the tip-sample forces. This letter describes theoretical modeling of FFM-AFM applied to a single bacteriorhodopsin molecule on a substrate, showing that its cross section can be measured without damage, in contrast to conventional tapping-mode AFM. Speculations are made regarding nonideal conditions and the ability of FFM-AFM to perform quantitative nanoelasticity measurements.

Scanning tunneling microscopy of ethylated Si(111) surfaces prepared by a chlorination/alkylation process

Scanning tunneling microscopy (STM) and computational modeling have been used to study the structure of ethyl-terminated Si(111) surfaces. The ethyl-terminated surface was prepared by treating the H-terminated Si(111) surface with PCl5 to form a Cl-terminated Si(111) surface with subsequent exposure to C(2)H(5)MgCl in tetrahydrofuran to produce an alkylated Si(111) surface. The STM data at 77 K revealed local, close-packed, and relatively ordered regions with a nearest-neighbor spacing of 0.38 nm as well as disordered regions. The average spot density corresponded to approximately 85% of the density of Si atop sites on an unreconstructed Si(111) surface. Molecular dynamics simulations of a Si(111) surface randomly populated with ethyl groups to a total coverage of approximately 80% confirmed that the ethyl-terminated Si(111) surface, in theory, can assume reasonable packing arrangements to accommodate such a high surface coverage, which could be produced by an exoergic surface functionalization route such as the two-step chlorination/alkylation process. Hence, it is possible to consistently interpret the STM data within a model suggested by recent X-ray photoelectron spectroscopic data and infrared absorption data, which indicate that the two-step halogenation/alkylation method can provide a relatively high coverage of ethyl groups on Si(111) surfaces.

Quantum Mechanics Calculations of the Thermodynamically Controlled Coverage and Structure of Alkyl Monolayers on Si(111) Surfaces

The heat of formation, Delta E, for silicon (111) surfaces terminated with increasing densities of the alkyl groups CH3- (methyl), C2H5- (ethyl), (CH3)2CH- (isopropyl), (CH3)3C- (tert-butyl), CH3(CH2)5- (hexyl), CH3(CH2)7- (octyl), and C6H5- (phenyl) was calculated using quantum mechanics (QM) methods, with unalkylated sites being H-terminated. The free energy, Delta G, for the formation of both Si-C and Si-H bonds from Si-Cl model compounds was also calculated using QM, with four separate Si-H formation mechanisms proposed, to give overall Delta G(S) values for the formation of alkylated Si(111) surfaces through a two step chlorination/alkylation method. The data are in good agreement with measurements of the packing densities for alkylated surfaces formed through this technique, for Si-H free energies of formation, Delta G(H), corresponding to a reaction mechanism including the elimination of two H atoms and the formation of a C=C double bond in either unreacted alkyl Grignard groups or tetrahydrofuran solvent.

Theoretical Investigation of the Structure and Coverage of the Si(111)−OCH3 Surface

The surface structure, strain energy, and charge profile of the methoxylated Si(111) surface, Si(111)-OCH3, has been studied using quantum mechanics, and the results are compared to those obtained previously for Si(111)-CH3 and Si(111)-C2H5. The calculations indicate that 100% coverage is feasible for Si(111)-OCH3 (similar to the methylated surface), as compared to only approximately 80% coverage for the ethylated surface. These differences can be understood in terms of nearest-neighbor steric and electrostatic interactions. Enthalpy and free energy calculations indicate that the formation of the Si(111)-OCH3 surface from Si(111)-H and methanol is favorable at 300 K. The calculations have also indicated the conditions under which stacking faults can emerge on Si(111)-OCH3, and such conditions are contrasted with the behavior of Si(111)-CH3 and Si(111)-CH2CH3 surfaces, for which stacking faults are calculated to be energetically feasible when etch pits with sufficiently long edges are present on the surface.