Viscoelastic property mapping with contact resonance force microscopy

Probing the Mechanical Properties of 2D Materials via Atomic-Force-Microscopy-Based Modulated Nanoindentation

As the field of low-dimensional materials (1D or 2D) grows and more complex and intriguing structures are continuing to be found, there is an emerging need for techniques to characterize the nanoscale mechanical properties of all kinds of 1D/2D materials, in particular in their most practical state: sitting on an underlying substrate. While traditional nanoindentation techniques cannot accurately determine the transverse Young's modulus at the necessary scale without large indentations depths and effects to and from the substrate, herein an atomic-force-microscopy-based modulated nanomechanical measurement technique with Angstrom-level resolution (MoNI/ÅI) is presented. This technique enables non-destructive measurements of the out-of-plane elasticity of ultra-thin materials with resolution sufficient to eliminate any contributions from the substrate. This method is used to elucidate the multi-layer stiffness dependence of graphene deposited via chemical vapor deposition and discover a peak transverse modulus in two-layer graphene. While MoNI/ÅI has been used toward great findings in the recent past, here all aspects of the implementation of the technique as well as the unique challenges in performing measurements at such small resolutions are encompassed.

Nanoscale Rheology: Dynamic Mechanical Analysis over a Broad and Continuous Frequency Range Using Photothermal Actuation Atomic Force Microscopy

Polymeric materials are widely used in industries ranging from automotive to biomedical. Their mechanical properties play a crucial role in their application and function and arise from the nanoscale structures and interactions of their constitutive polymer molecules. Polymeric materials behave viscoelastically, i.e., their mechanical responses depend on the time scale of the measurements; quantifying these time-dependent rheological properties at the nanoscale is relevant to develop, for example, accurate models and simulations of those materials, which are needed for advanced industrial applications. In this paper, an atomic force microscopy (AFM) method based on the photothermal actuation of an AFM cantilever is developed to quantify the nanoscale loss tangent, storage modulus, and loss modulus of polymeric materials. The method is then validated on styrene-butadiene rubber (SBR), demonstrating the method's ability to quantify nanoscale viscoelasticity over a continuous frequency range up to 5 orders of magnitude (0.2-20,200 Hz). Furthermore, this method is combined with AFM viscoelastic mapping obtained with amplitude modulation-frequency modulation (AM-FM) AFM, enabling the extension of viscoelastic quantification over an even broader frequency range and demonstrating that the novel technique synergizes with preexisting AFM techniques for quantitative measurement of viscoelastic properties. The method presented here introduces a way to characterize the viscoelasticity of polymeric materials and soft and biological matter in general at the nanoscale for any application.

Probing Relative Humidity Impact on Biological Protein Bovine Serum Albumin and Bovine Submaxillary Gland Mucin by Using Contact Resonance Atomic Force Microscopy

In biomaterials, a substantial amount of research has been placed on the mechanical properties of biomolecules and their interactions with body fluids. Bovine serum albumin (BSA) is a widely studied model protein, while bovine submaxillary gland mucin (BSM) is another cow-derived protein frequently employed in research. Films were examined with contact resonance atomic force microscopy (CR-AFM), and the results showed that the mechanical characteristics of the films were affected by the relative humidity. We quantitatively analyze the viscoelasticity of these proteins after they have been subjected to humidity by measuring the resonance frequency and quality factor. The findings indicate that prolonged humidity exposure has a different effect on the mechanical properties of BSA and BSM films. The results show that after exposure to humidity, the resonance peaks of BSA shift to the left, indicating stiffness, while those of BSM shift to the right, indicating hydration. Moreover, BSM's hydration is caused by relative humidity, leading to a constant increase in resonance frequency and material softness. Contrarily, BSA showed a decrease in contact resonance frequency due to ongoing strain-induced deformation, indicating increased material stiffness. The findings have significance for the design and development of biomaterials for a variety of applications, such as the delivery of drugs, the engineering of tissue, and the development of biosensors. Our research demonstrates that CR-AFM has the potential to become a non-invasive and sensitive method that can be used to characterize the mechanical characteristics of biomolecules and their interactions with bodily fluids.

In-depth atomic force microscopy investigation of nanoscale mechanical properties of Pāua nacre

Over millions of years, nature has created complex hierarchical structures with exceptional mechanical properties. The nacre of various seashells is an example of such structures, which is formed out of a mainly inorganic mineral with organic material inclusions in a layered arrangement. Due to its high impact-resisting mechanical properties, these structures have been widely investigated and mimicked in artificial nacre-type composite materials. The artificial creation of nacre analogues for future applications requires an accurate understanding of their mechanical properties on the length scale of the nanoscale composite components. Here, we present an in-depth AFM study of the mechanical properties of Pāua nacre (Haliotis iris, 'rainbow abalone') and quantify the elastic modulus as well as related energy scales of both its main nanoscale constituents. We use AFM-based nano-indentation compared to standard micro/nano-indentation, which enables the direct determination of the mechanical properties of the biopolymer layer in nacre, including plastic and elastic energies during indentation. By combining three different AFM-based mechanical characterization methods we affirm the quantitativeness of our mechanical measurements and show that the organic layers have about half the elastic modulus of the inorganic aragonite regions. The obtained results reveal the detailed mechanical properties of the hierarchical structure of nacre and provide a strategy for accurately testing nanoscale mechanical properties of advanced composite materials.

Digital light processing in a hybrid atomic force microscope: In Situ, nanoscale characterization of the printing process

Stereolithography (SLA) and digital light processing (DLP) are powerful additive manufacturing techniques that address a wide range of applications including regenerative medicine, prototyping, and manufacturing. Unfortunately, these printing processes introduce micrometer-scale anisotropic inhomogeneities due to the resin absorptivity, diffusivity, reaction kinetics, and swelling during the requisite photoexposure. Previously, it has not been possible to characterize high-resolution mechanical heterogeneity as it develops during the printing process. By combining DLP 3D printing with atomic force microscopy in a hybrid instrument, heterogeneity of a single, in situ printed voxel is characterized. Here, we describe the instrument and demonstrate three modalities for characterizing voxels during and after printing. Sensing Modality I maps the mechanical properties of just-printed, resin-immersed voxels, providing the framework to study the relationships between voxel sizes, print exposure parameters, and voxel-voxel interactions. Modality II captures the nanometric, in situ working curve and is the first demonstration of in situ cure depth measurement. Modality III dynamically senses local rheological changes in the resin by monitoring the viscoelastic damping coefficient of the resin during patterning. Overall, this instrument equips researchers with a tool to develop rich insight into resin development, process optimization, and fundamental printing limits.

Modeling of eccentric nanoneedle in trolling-mode atomic force microscope

Limitations on installation of a standard TR-AFM nanoneedle can have unpredictable effects on dynamics of system. Therefore, it is crucial to pay close attention to the position and geometry of mounted nanoneedle when deriving the mathematical model. During TR-AFM fabrication process, the nanoneedle may not always deposit precisely at the middle of AFM tip, which would result in coupled bending-torsion modes in the dynamical operation of system. In this paper, we investigate the effect of eccentric nanoneedle in dynamic response of TR-AFM. To address this issue, a continuous mathematical model is developed. This model accounts for eccentric nanoneedle which can address the couplings in nonlinear vibration. Hamilton's principle is used to derive equations of motion and then assumed mode method (AMM) is utilized. This model is capable of simulating the cantilever dynamics under complicated nanoneedle tip-sample interactions. Displacements of different components of system for various eccentricity are determined. It is found that nanoneedle eccentricity has noticeable effects on microbeam torsion angle and out of plane nanoneedle tip displacement.

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.

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

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

Nonlinear Phase Imaging of Gold Nanoparticles Embedded in Organic Thin Films

The phase detection in the dynamic mode of the atomic force microscopes is a known technique for mapping nanoscale surface heterogeneities. We present here an additional functionality of this technique, which allows high-resolution imaging of embedded inorganic nanoparticles with diameter and interparticle distances of a few nanometers. The method is based on a highly nonlinear tip-sample interaction occurring markedly above the nanoparticles, giving thus a high phase contrast between zones with and without nanoparticles. A relationship between the tip-sample interaction strength and the phase signal is established in experiments and from calculations conducted with the model developed by Haviland et al. [ Soft Matter 2016 , 12 , 619 ], which is based on solving a combined equation of motion for both the cantilever and surface while taking into account the time-varying interaction forces. The nonlinear phase behavior at the origin of the subnanometer spatial resolution is found by numerical analyses to be the result of a local mechanical stiffening of the zone containing nanoparticles, which is enhanced by 2 orders of magnitude or more.

Contact Resonance Atomic Force Microscopy Using Long, Massive Tips

In this work, we present a new theoretical model for use in contact resonance atomic force microscopy. This model incorporates the effects of a long, massive sensing tip and is especially useful to interpret operation in the so-called trolling mode. The model is based on traditional Euler-Bernoulli beam theory, whereby the effect of the tip as well as of the sample in contact, modeled as an elastic substrate, are captured by appropriate boundary conditions. A novel interpretation of the flexural and torsional modes of vibration of the cantilever, when not in contact with the sample, is used to estimate the inertia properties of the long, massive tip. Using this information, sample elastic properties are then estimated from the in-contact resonance frequencies of the system. The predictive capability of the proposed model is verified via finite element analysis. Different combinations of cantilever geometry, tip geometry, and sample stiffness are investigated. The model's accurate predictive ranges are discussed and shown to outperform those of other popular models currently used in contact resonance atomic force microscopy.

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

Dynamic atomic force microscopy (AFM) was employed to spatially map the elastic modulus of highly oriented pyrolytic graphite (HOPG), specifically by using force modulation microscopy (FMM) and contact resonance (CR) AFM. In both of these techniques, a variation in the amplitude signal was observed when scanning over an uncovered step edge of HOPG. In comparison, no variation in the amplitude signal was observed when scanning over a covered step on the same surface. These observations qualitatively indicate that there is a variation in the elastic modulus over uncovered steps and no variation over covered ones. The quantitative results of the elastic modulus required the use of FMM, while the CR mode better highlighted areas of reduced elastic modulus (although it was difficult to convert the data into a quantifiable modulus). In the FMM measurements, single atomic steps of graphene with uncovered step edges showed a decrease in the elastic modulus of approximately 0.5%, which is compared with no change in the elastic modulus for covered steps. The analysis of the experimental data taken under varying normal loads and with several different tips showed that the elastic modulus determination was unaffected by these parameters.

Å-Indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures

During conventional nanoindentation measurements, the indentation depths are usually larger than 1-10 nm, which hinders the ability to study ultra-thin films (<10 nm) and supported atomically thin two-dimensional (2D) materials. Here, we discuss the development of modulated Å-indentation to achieve sub-Å indentations depths during force-indentation measurements while also imaging materials with nanoscale resolution. Modulated nanoindentation (MoNI) was originally invented to measure the radial elasticity of multi-walled nanotubes. Now, by using extremely small amplitude oscillations (<<1 Å) at high frequency, and stiff cantilevers, we show how modulated nano/Å-indentation (MoNI/ÅI) enables non-destructive measurements of the contact stiffness and indentation modulus of ultra-thin ultra-stiff films, including CVD diamond films (~1000 GPa stiffness), as well as the transverse modulus of 2D materials. Our analysis demonstrates that in presence of a standard laboratory noise floor, the signal to noise ratio of MoNI/ÅI implemented with a commercial atomic force microscope (AFM) is such that a dynamic range of 80 dB -- achievable with commercial Lock-in amplifiers -- is sufficient to observe superior indentation curves, having indentation depths as small as 0.3 Å, resolution in indentation <0.05 Å, and in normal load <0.5 nN. Being implemented on a standard AFM, this method has the potential for a broad applicability.

Monitoring Fast, Voxel-Scale Cure Kinetics via Sample-Coupled-Resonance Photorheology

Photopolymerizable materials are the focus of extensive research across a variety of fields ranging from additive manufacturing to regenerative medicine. However, poorly understood material mechanical and rheological properties during polymerization at the relevant exposure powers and single-voxel length-scales limit advancements in part performance and throughput. Here, a novel atomic force microscopy (AFM) technique, sample-coupled-resonance photorheology (SCRPR), to locally characterize the mechano-rheological properties of photopolymerized materials on the relevant reaction kinetic timescales, is demonstrated. By coupling an AFM tip to a photopolymer and exposing the coupled region to a laser, two fundamental photopolymerization phenomena: (1) timescales of photopolymerization at high laser power and (2) reciprocity between photodose and material properties are studied. The ability to capture rapid kinetic changes occurring during polymerization with SCRPR is demonstrated. It is found that reciprocity is only valid for a finite range of exposure powers in the verification material and polymerization is highly localized in a low-diffusion system. After polymerization, in situ imaging of a single polymerized voxel is performed using material-appropriate topographic and nanomechanical modalities of the AFM while still in the as-printed environment.

Towards nanoscale electrical measurements in liquid by advanced KPFM techniques: a review

Fundamental mechanisms of energy storage, corrosion, sensing, and multiple biological functionalities are directly coupled to electrical processes and ionic dynamics at solid-liquid interfaces. In many cases, these processes are spatially inhomogeneous taking place at grain boundaries, step edges, point defects, ion channels, etc and possess complex time and voltage dependent dynamics. This necessitates time-resolved and real-space probing of these phenomena. In this review, we discuss the applications of force-sensitive voltage modulated scanning probe microscopy (SPM) for probing electrical phenomena at solid-liquid interfaces. We first describe the working principles behind electrostatic and Kelvin probe force microscopies (EFM & KPFM) at the gas-solid interface, review the state of the art in advanced KPFM methods and developments to (i) overcome limitations of classical KPFM, (ii) expand the information accessible from KPFM, and (iii) extend KPFM operation to liquid environments. We briefly discuss the theoretical framework of electrical double layer (EDL) forces and dynamics, the implications and breakdown of classical EDL models for highly charged interfaces or under high ion concentrations, and describe recent modifications of the classical EDL theory relevant for understanding nanoscale electrical measurements at the solid-liquid interface. We further review the latest achievements in mapping surface charge, dielectric constants, and electrodynamic and electrochemical processes in liquids. Finally, we outline the key challenges and opportunities that exist in the field of nanoscale electrical measurements in liquid as well as providing a roadmap for the future development of liquid KPFM.

On the effect of local sample slope during modulus measurements by contact-resonance atomic force microscopy

Contact-resonance atomic force microscopy (CR-AFM) is of great interest and very valuable for a deeper understanding of the mechanics of biological materials with moduli of at least a few GPa. However, sample surfaces can present a high topography range with significant slopes, where the local angle can be as large as  ± 50°. The non-trivial correlation between surface slope and CR-frequency hinders a straight-forward interpretation of CR-AFM indentation modulus measurements on such samples. We aim to demonstrate the significant influence of the surface slope on the CR-frequency that is caused by the local angle between sample surface and the AFM cantilever and present a practical method to correct the measurements. Based on existing analytical models of the effect of the AFM set-up's intrinsic cantilever tilt on CR-frequencies, we compute the non-linear variation of the first two (eigen)modes CR-frequency for a large range of surface angles. The computations are confirmed by CR-AFM experiments performed on a curved surface. Finally, the model is applied to directly correct contact modulus measurements on a durum wheat starch granule as an exemplary sample.

High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping

The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. This is particularly pertinent today, as the SPM community has seen a rapidly growing trend towards simultaneous capture of multiple imaging channels and complex modes of operation involving high-dimensional information-rich datasets, bringing forward the challenges of visualization and analysis, particularly for cases where the underlying dynamic model is poorly understood. To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical mapping on a mixed polymer thin film and resolving irregular hydration structure of calcite at atomic resolution. Using the proposed methodology, we can efficiently reveal and hierarchically represent salient material features with rich local details, further enabling denoising, classification, and high-resolution functional imaging.

Probing nano-scale viscoelastic response in air and in liquid with dynamic atomic force microscopy

We perform a comparative study of dynamic force measurements using an Atomic Force Microscope (AFM) on the same soft polymer blend samples in both air and liquid environments. Our quantitative analysis starts with calibration of the same cantilever in both environments. Intermodulation AFM (ImAFM) is used to measure dynamic force quadratures on the same sample. We validate the accuracy of the reconstructed dynamic force quadratures by numerical simulation of a realistic model of the cantilever in liquid. In spite of the very low quality factor of this resonance, we find excellent agreement between experiment and simulation. A recently developed moving surface model explains the measured force quadrature curves on the soft polymer, in both air and liquid.

Identification of nanoparticles and nanosystems in biological matrices with scanning probe microscopy

Identification of nanoparticles and nanosystems into cells and biological matrices is a hot research topic in nanobiotechnologies. Because of their capability to map physical properties (mechanical, electric, magnetic, chemical, or optical), several scanning probe microscopy based techniques have been proposed for the subsurface detection of nanomaterials in biological systems. In particular, atomic force microscopy (AFM) can be used to reveal stiff nanoparticles in cells and other soft biomaterials by probing the sample mechanical properties through the acquisition of local indentation curves or through the combination of ultrasound-based methods, like contact resonance AFM (CR-AFM) or scanning near field ultrasound holography. Magnetic force microscopy can detect magnetic nanoparticles and other magnetic (bio)materials in nonmagnetic biological samples, while electric force microscopy, conductive AFM, and Kelvin probe force microscopy can reveal buried nanomaterials on the basis of the differences between their electric properties and those of the surrounding matrices. Finally, scanning near field optical microscopy and tip-enhanced Raman spectroscopy can visualize buried nanostructures on the basis of their optical and chemical properties. Despite at a still early stage, these methods are promising for detection of nanomaterials in biological systems as they could be truly noninvasive, would not require destructive and time-consuming specific sample preparation, could be performed in vitro, on alive samples and in water or physiological environment, and by continuously imaging the same sample could be used to dynamically monitor the diffusion paths and interaction mechanisms of nanomaterials into cells and biological systems. This article is categorized under: Diagnostic Tools > In Vivo Nanodiagnostics and Imaging Nanotechnology Approaches to Biology > Nanoscale Systems in Biology.

Scanning speed phenomenon in contact-resonance atomic force microscopy

This work presents data confirming the existence of a scan speed related phenomenon in contact-mode atomic force microscopy (AFM). Specifically, contact-resonance spectroscopy is used to interrogate this phenomenon. Above a critical scan speed, a monotonic decrease in the recorded contact-resonance frequency is observed with increasing scan speed. Proper characterization and understanding of this phenomenon is necessary to conduct accurate quantitative imaging using contact-resonance AFM, and other contact-mode AFM techniques, at higher scan speeds. A squeeze film hydrodynamic theory is proposed to explain this phenomenon, and model predictions are compared against the experimental data.

Combining adhesive contact mechanics with a viscoelastic material model to probe local material properties by AFM

Viscoelastic properties are often measured using probe based techniques such as nanoindentation (NI) and atomic force microscopy (AFM). Rarely, however, are these methods verified. In this article, we present a method that combines contact mechanics with a viscoelastic model (VEM) composed of springs and dashpots. We further show how to use this model to determine viscoelastic properties from creep curves recorded by a probe based technique. We focus on using the standard linear solid model and the generalized Maxwell model of order 2. The method operates in the range of 0.01 Hz to 1 Hz. Our approach is suitable for rough surfaces by providing a defined contact area using plastic pre-deformation of the material. The very same procedure is used to evaluate AFM based measurements as well as NI measurements performed on polymer samples made from poly(methyl methacrylate) and polycarbonate. The results of these measurements are then compared to those obtained by tensile creep tests also performed on the same samples. It is found that the tensile test results differ considerably from the results obtained by AFM and NI methods. The similarity between the AFM results and NI results suggests that the proposed method is capable of yielding results comparable to NI but with the advantage of the imaging possibilities of AFM. Furthermore, all three methods allowed a clear distinction between PC and PMMA by means of their respective viscoelastic properties.

Simultaneous topography imaging and broadband nanomechanical mapping on atomic force microscope

In this paper, an approach is proposed to achieve simultaneous imaging and broadband nanomechanical mapping of soft materials in air by using an atomic force microscope. Simultaneous imaging and nanomechanical mapping are needed, for example, to correlate the morphological and mechanical evolutions of the sample during dynamic phenomena such as the cell endocytosis process. Current techniques for nanomechanical mapping, however, are only capable of capturing static elasticity of the material, or the material viscoelasticity in a narrow frequency band around the resonant frequency(ies) of the cantilever used, not competent for broadband nanomechanical mapping, nor acquiring topography image of the sample simultaneously. These limitations are addressed in this work by enabling the augmentation of an excitation force stimuli of rich frequency spectrum for nanomechanical mapping in the imaging process. Kalman-filtering technique is exploited to decouple and split the mixed signals for imaging and mapping, respectively. Then the sample indentation generated is quantified online via a system-inversion method, and the effects of the indentation generated and the topography tracking error on the topography quantification are taken into account. Moreover, a data-driven feedforward-feedback control is utilized to track the sample topography. The proposed approach is illustrated through experimental implementation on a polydimethylsiloxane sample with a pre-fabricated pattern.

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.

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

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

Formation of a Crack-Free, Hybrid Skin Layer with Tunable Surface Topography and Improved Gas Permeation Selectivity on Elastomers Using Gel-Liquid Infiltration Polymerization

Surface modifications of elastomers and gels are crucial for emerging applications such as soft robotics and flexible electronics, in large part because they provide a platform to control wettability, adhesion, and permeability. Current surface modification methods via ultraviolet-ozone (UVO) and/or O₂ plasma, atomic layer deposition (ALD), plasmas deposition, and chemical treatment impart a dense polymer or inorganic layer on the surface that is brittle and easy to fracture at low strain levels. This paper presents a new method, based on gel-liquid infiltration polymerization, to form hybrid skin layers atop elastomers. The method is unique in that it allows for control of the skin layer topography, with tunable feature sizes and aspect ratios as high as 1.8 without fracture. Unlike previous techniques, the skin layer formed here dramatically improves the barrier properties of the elastomer, while preserving skin layer flexibility. Moreover, the method is versatile and likely applicable to most interfacial polymerization systems and network polymers on flat and patterned surfaces.

NANOMECHANICS OF THE RUBBER–FILLER INTERFACE

Atomic force microscope (AFM)–based nanomechanics is one of the most promising tools for accessing the rubber–filler interface while providing not only structural information but also mechanical–property evaluation. An AFM-based static modulus map is used to close in on the understanding of the filler reinforcement effect. As an example, a famous Guth–Gold equation is verified by comparing tensile testing and AFM. Two different novel methods are also introduced to visualize viscoelastic quantities such as storage and loss moduli, loss tangent, relaxation modulus, and viscosity. The difference in segmental dynamics between a rubber matrix and an interfacial region will be reviewed.

Detection of stiff nanoparticles within cellular structures by contact resonance atomic force microscopy subsurface nanomechanical imaging

Detecting stiff nanoparticles buried in soft biological matrices by atomic force microscopy (AFM) based techniques represents a new frontier in the field of scanning probe microscopies, originally developed as surface characterization methods. Here we report the detection of stiff (magnetic) nanoparticles (NPs) internalized in cells by using contact resonance AFM (CR-AFM) employed as a potentially non-destructive subsurface characterization tool. Magnetite (Fe₃O₄) NPs were internalized in microglial cells from cerebral cortices of mouse embryos of 18 days by phagocytosis. Nanomechanical imaging of cells was performed by detecting the contact resonance frequencies (CRFs) of an AFM cantilever held in contact with the sample. Agglomerates of NPs internalized in cells were visualized on the basis of the local increase in the contact stiffness with respect to the surrounding biological matrix. A second AFM-based technique for nanomechanical imaging, i.e., HarmoniX™, as well as magnetic force microscopy and light microscopy were used to confirm the CR-AFM results. Thus, CR-AFM was demonstrated as a promising technique for subsurface imaging of nanomaterials in biological samples.

Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m^-1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.

CONTACT INSTABILITY OF NON-PLANAR ELASTOMERIC SURFACES

Contact surfaces between non-planar elastomers widely present in the industrial and biomedical fields, such as corrugated mats and biological fillers. Probing out the mechanical instability of these contact surfaces could greatly contribute to the efficiency, safety and durability of the related structures. In this paper, we numerically studied the contact instability of non-planar elastomeric surfaces with typical projections (i.e., circular and triangle projections) by proposing an instability criterion and using the finite element method. Moreover, we studied the effects of several key factors (e.g., the geometrical parameters and the friction coefficients of the surfaces) on the critical force of the mechanical instability. It is found that with comparable geometric sizes, the surface with circular projections is more effective to enhance the contact stability than that with triangle projections. A larger slope and curvature radius result in weaker stability while a larger friction coefficient plays a positive role for the stability. However, with increasing friction coefficient, the maximum force presents smaller and smaller changes and further improvement of contact stability mainly depends on the changes of the number of projections. These investigations may improve the understanding of the mechanical instability of non-planar elastomeric surfaces and contribute to achieve better designs of related structures.

Imaging via complete cantilever dynamic detection: general dynamic mode imaging and spectroscopy in scanning probe microscopy

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify the findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip-sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.

Generalized Hertz model for bimodal nanomechanical mapping

Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip-sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface.

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.

The importance of correcting for variable probe–sample interactions in AFM-IR spectroscopy: AFM-IR of dried bacteria on a polyurethane film

Interplay between AFM-IR probe – sample interactions and signal transduction for bacteria – PU bilayer.

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.

Nanomechanics of Cells and Biomaterials Studied by Atomic Force Microscopy

The behavior and mechanical properties of cells are strongly dependent on the biochemical and biomechanical properties of their microenvironment. Thus, understanding the mechanical properties of cells, extracellular matrices, and biomaterials is key to understanding cell function and to develop new materials with tailored mechanical properties for tissue engineering and regenerative medicine applications. Atomic force microscopy (AFM) has emerged as an indispensable technique for measuring the mechanical properties of biomaterials and cells with high spatial resolution and force sensitivity within physiologically relevant environments and timescales in the kPa to GPa elastic modulus range. The growing interest in this field of bionanomechanics has been accompanied by an expanding array of models to describe the complexity of indentation of hierarchical biological samples. Furthermore, the integration of AFM with optical microscopy techniques has further opened the door to a wide range of mechanotransduction studies. In recent years, new multidimensional and multiharmonic AFM approaches for mapping mechanical properties have been developed, which allow the rapid determination of, for example, cell elasticity. This Progress Report provides an introduction and practical guide to making AFM-based nanomechanical measurements of cells and surfaces for tissue engineering applications.

Nano-rheology of hydrogels using direct drive force modulation atomic force microscopy

We present a magnetic force-based direct drive modulation method to measure local nano-rheological properties of soft materials across a broad frequency range (10 Hz to 2 kHz) using colloid-attached atomic force microscope (AFM) probes in liquid. The direct drive method enables artefact-free measurements over several decades of excitation frequency, and avoids the need to evaluate medium-induced hydrodynamic drag effects. The method was applied to measure the local mechanical properties of polyacrylamide hydrogels. The frequency-dependent storage stiffness, loss stiffness, and loss tangent (tan δ) were quantified for hydrogels having high and low crosslinking densities by measuring the amplitude and the phase response of the cantilever while the colloid was in contact with the hydrogel. The frequency bandwidth was further expanded to lower effective frequencies (0.1 Hz to 10 Hz) by obtaining force-displacement (FD) curves. Slow FD measurements showed a recoverable but highly hysteretic response, with the contact mechanical behaviour dependent on the loading direction: approach curves showed Hertzian behaviour while retraction curves fit the JKR contact mechanics model well into the adhesive regime, after which multiple detachment instabilities occurred. Using small amplitude dynamic modulation to explore faster rates, the load dependence of the storage stiffness transitioned from Hertzian to a dynamic punch-type (constant contact area) model, indicating significant influence of material dissipation coupled with adhesion. Using the appropriate contact model across the full frequency range measured, the storage moduli were found to remain nearly constant until an increase began near ∼100 Hz. The softer gels' storage modulus increased from 7.9 ± 0.4 to 14.5 ± 2.1 kPa (∼85%), and the stiffer gels' storage modulus increased from 16.3 ± 1.1 to 31.7 ± 5.0 kPa (∼95%). This increase at high frequencies may be attributed to a contribution from solvent confinement in the hydrogel (poroelasticity). The storage moduli measured by both macro-rheometry and AFM FD curves were comparable to those measured using the modulation method at their overlapping frequencies (10-25 Hz). In all cases, care was taken to ensure the contact mechanics models were applied within the important limit of small relative deformations. This study thus highlights possible transitions in the probe-material contact mechanical behaviour for soft matter, especially when the applied strain rates and the material relaxation rates become comparable. In particular, at low frequencies, the modulus follows Hertzian contact mechanics, while at high frequencies adhesive contact is well represented by punch-like behaviour. More generally, use of the Hertz model on hydrogels at high loading rates, at high strains, or during the retraction portion of FD curves, leads to significant errors in the calculated moduli.

Quantitative Contact Resonance Force Microscopy for Viscoelastic Measurement of Soft Materials at the Solid-Liquid Interface

Viscoelastic property measurements made at the solid-liquid interface are key to characterizing materials for a variety of biological and industrial applications. Further, nanostructured materials require nanoscale measurements. Here, material loss tangents (tan δ) were extracted from confounding liquid effects in nanoscale contact resonance force microscopy (CR-FM), an atomic force microscope based technique for observing mechanical properties of surfaces. Obtaining reliable CR-FM viscoelastic measurements in liquid is complicated by two effects. First, in liquid, spurious signals arise during cantilever excitation. Second, it is challenging to separate changes to cantilever behavior due to the sample from changes due to environmental damping and added mass effects. We overcame these challenges by applying photothermal cantilever excitation in multiple resonance modes and a predictive model for the hydrodynamic effects. We demonstrated quantitative, nanoscale viscoelastic CR-FM measurements of polymers at the solid-liquid interface. The technique is demonstrated on a point-by-point basis on polymer samples and while imaging in contact mode on a fixed plant cell wall. Values of tan δ for measurements made in water agreed with the values for measurements in air for some experimental conditions on polystyrene and for all examined conditions on polypropylene.

Contact resonance atomic force microscopy imaging in air and water using photothermal excitation

Contact Resonance Force Microscopy (CR-FM) is a leading atomic force microscopy technique for measuring viscoelastic nano-mechanical properties. Conventional piezo-excited CR-FM measurements have been limited to imaging in air, since the "forest of peaks" frequency response associated with acoustic excitation methods effectively masks the true cantilever resonance. Using photothermal excitation results in clean contact, resonance spectra that closely match the ideal frequency response of the cantilever, allowing unambiguous and simple resonance frequency and quality factor measurements in air and liquids alike. This extends the capabilities of CR-FM to biologically relevant and other soft samples in liquid environments. We demonstrate CR-FM in air and water on both stiff silicon/titanium samples and softer polystyrene-polyethylene-polypropylene polymer samples with the quantitative moduli having very good agreement between expected and measured values.

Visualization of polar nanoregions in lead-free relaxors via piezoresponse force microscopy in torsional dual AC resonance tracking mode

Polar nanoregions (PNRs) play a key role in the functionality of relaxor ferroelectrics; however, visualizing them in lead-free relaxor ferroelectrics with high lateral resolution is still challenging. Thus, we studied herein the local ferroelectric domain distribution of the lead-free bismuth-based (1 -x)(Bi1/2Na1/2TiO3-Bi1/2K1/2TiO3) -x(Bi1/2Mg1/2TiO3) piezoceramics which show a relaxor behavior using dual AC resonance tracking (DART) piezoresponse force microscopy (PFM). By using excitation frequencies at either side of the contact resonance peak of the torsional cantilever vibration, an enhanced contrast in the amplitude and phase images of the piezoresponse can be achieved. Additionally, this tracking technique reduces the topographical crosstalk while mapping the local electromechanical properties. The true drive amplitude, drive phase, contact resonant frequency and quality factor can be estimated from DART-PFM data obtained with vertically or torsionally vibrating cantilevers. This procedure yields a three-dimensional quantitative map of the local piezoelectric properties of the relaxor ferroelectric samples. With this approach, torsional DART allowed for the visualization of fine substructures within the monodomains, suggesting the existence of PNRs in relaxor ferroelectrics. The domain structures of the PNRs were visualized with high precision, and the local electromechanical characteristics of the lead-free relaxor ferroelectrics were quantitatively mapped.

Mapping of elasticity and damping in an α + β titanium alloy through atomic force acoustic microscopy

The distribution of elastic stiffness and damping of individual phases in an α + β titanium alloy (Ti-6Al-4V) measured by using atomic force acoustic microscopy (AFAM) is reported in the present study. The real and imaginary parts of the contact stiffness k (*) are obtained from the contact-resonance spectra and by using these two quantities, the maps of local elastic stiffness and the damping factor are derived. The evaluation of the data is based on the mass distribution of the cantilever with damped flexural modes. The cantilever dynamics model considering damping, which was proposed recently, has been used for mapping of indentation modulus and damping of different phases in a metallic structural material. The study indicated that in a Ti-6Al-4V alloy the metastable β phase has the minimum modulus and the maximum damping followed by α'- and α-phases. Volume fractions of the individual phases were determined by using a commercial material property evaluation software and were validated by using X-ray diffraction (XRD) and electron back-scatter diffraction (EBSD) studies on one of the heat-treated samples. The volume fractions of the phases and the modulus measured through AFAM are used to derive average modulus of the bulk sample which is correlated with the bulk elastic properties obtained by ultrasonic velocity measurements. The average modulus of the specimens estimated by AFAM technique is found to be within 5% of that obtained by ultrasonic velocity measurements. The effect of heat treatments on the ultrasonic attenuation in the bulk sample could also be understood based on the damping measurements on individual phases using AFAM.

Probing local bias-induced transitions using photothermal excitation contact resonance atomic force microscopy and voltage spectroscopy

Nanomechanical properties are closely related to the states of matter, including chemical composition, crystal structure, mesoscopic domain configuration, etc. Investigation of these properties at the nanoscale requires not only static imaging methods, e.g., contact resonance atomic force microscopy (CR-AFM), but also spectroscopic methods capable of revealing their dependence on various external stimuli. Here we demonstrate the voltage spectroscopy of CR-AFM, which was realized by combining photothermal excitation (as opposed to the conventional piezoacoustic excitation method) with the band excitation technique. We applied this spectroscopy to explore local bias-induced phenomena ranging from purely physical to surface electromechanical and electrochemical processes. Our measurements show that the changes in the surface properties associated with these bias-induced transitions can be accurately assessed in a fast and dynamic manner, using resonance frequency as a signature. With many of the advantages offered by photothermal excitation, contact resonance voltage spectroscopy not only is expected to find applications in a broader field of nanoscience but also will provide a basis for future development of other nanoscale elastic spectroscopies.

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.