Compositional contrast of biological materials in liquids using the momentary excitation of higher eigenmodes in dynamic atomic force microscopy

Fiber-Integrated Force Sensor using 3D Printed Spring-Composed Fabry-Perot Cavities with a High Precision Down to Tens of Piconewton

Developing microscale sensors capable of force measurements down to the scale of piconewtons is of fundamental importance for a wide range of applications. To date, advanced instrumentations such as atomic force microscopes and other specifically developed micro/nano-electromechanical systems face challenges such as high cost, complex detection systems and poor electromagnetic compatibility. Here, it presents the unprecedented design and 3D printing of general fiber-integrated force sensors using spring-composed Fabry-Perot cavities. It calibrates these microscale devices employing varied-diameter μ $\umu$ m-scale silica particles as standard weights. The force sensitivity and resolution reach values of (0.436 ± 0.007) nmnN-1 and (40.0 ± 0.7) pN, respectively, which are the best resolutions among all fiber-based nanomechanical probes so far. It also measured the non-linear airflow force distributions produced from a nozzle with an orifice of 2 μ $\umu$ m, which matches well with the full-sized simulations. With further customization of their geometries and materials, it anticipates the easy-to-use force probe can well extend to many other applications such as air/fluidic turbulences sensing, micro-manipulations, and biological sensing.

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

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

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

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

Effect of Ageing on the Structure and Properties of Model Liquid-Infused Surfaces

Liquid-infused surfaces (LISs) exhibit unique properties that make them ideal candidates for a wide range of applications, from antifouling and anti-icing coatings to self-healing surfaces and controlled wetting. However, when exposed to realistic environmental conditions, LISs tend to age and progressively lose their desirable properties, potentially compromising their application. The associated ageing mechanisms are still poorly understood, and results reflecting real-life applications are scarce. Here, we track the ageing of a model LIS composed of glass surfaces functionalized with hydrophobic nanoparticles and infused with silicone oil. The LISs are fully submerged in aqueous solutions and exposed to acoustic pressure waves for set time intervals. The ageing is monitored by periodic measurements of the LIS's wetting properties. We also track the changes to the LIS's nanoscale structure. We find that the LISs rapidly lose their slippery properties because of a combination of oil loss, smoothing of the nanoporous functional layer, and substrate degradation when directly exposed to the solution. The oil loss is consistent with water microdroplets entering the oil layer and displacing oil away from the surface. These mechanisms are general and could play a role in the ageing of most LISs.

Time-frequency analysis of the tip motion in liquids using the wavelet transform in dynamic atomic force microscopy

The tip motion of the dynamic atomic force microscope in liquids shows complex transient behaviors when using a low stiffness cantilever. The second flexural mode of the cantilever is momentarily excited. Multiple impacts between the tip and the sample might occur in one oscillation cycle. However, the commonly used Fourier transform method cannot provide time-related information about these transient features. To overcome this limitation, we apply the wavelet transform to perform the time-frequency analysis of the tip motion in liquids. The momentary excitation of the second mode and the phenomenon of multiple impacts are clearly shown in the time-frequency plane of the wavelet scalogram. The instantaneous frequencies and magnitudes of the second mode are extracted by the wavelet ridge analysis, which can provide quantitative estimations of the tip motion in the second mode. Moreover, the relations of the maximum instantaneous magnitude (MIM) to the amplitude setpoint and the Young's modulus of the sample surface are investigated. The results suggest that the MIM can be used to characterize the nanomechanical property of the sample surface at high amplitude setpoints.

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.

Multifrequency AFM reveals lipid membrane mechanical properties and the effect of cholesterol in modulating viscoelasticity

The physical properties of lipid bilayers comprising the cell membrane occupy the current spotlight of membrane biology. Their traditional representation as a passive 2D fluid has gradually been abandoned in favor of a more complex picture: an anisotropic time-dependent viscoelastic biphasic material, capable of transmitting or attenuating mechanical forces that regulate biological processes. In establishing new models, quantitative experiments are necessary when attempting to develop suitable techniques for dynamic measurements. Here, we map both the elastic and viscous properties of the model system 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayers using multifrequency atomic force microscopy (AFM), namely amplitude modulation-frequency modulation (AM-FM) AFM imaging in an aqueous environment. Furthermore, we investigate the effect of cholesterol (Chol) on the DPPC bilayer in concentrations from 0 to 60%. The AM-AFM quantitative maps demonstrate that at low Chol concentrations, the lipid bilayer displays a distinct phase separation and is elastic, whereas at higher Chol concentration, the bilayer appears homogenous and exhibits both elastic and viscous properties. At low-Chol contents, the Estorage modulus (elastic) dominates. As the Chol insertions increases, higher energy is dissipated; and although the bilayer stiffens (increase in Estorage), the viscous component dominates (Eloss). Our results provide evidence that the lipid bilayer exhibits both elastic and viscous properties that are modulated by the presence of Chol, which may affect the propagation (elastic) or attenuation (viscous) of mechanical signals across the cell membrane.

Sensing in-plane nanomechanical surface and sub-surface properties of polymers: local shear stress as function of the indentation depth

Dynamic force microscopy (DFM) is an excellent tool for the study of the compositional and nanomechanical properties of polymers that exploits the flexural eigenmodes of a cantilever comprising a sharp tip vibrating perpendicular to the sample surface. However, the in-plane nanomechanical properties of a specimen cannot be detected by this technique. Here, a bimodal approach was developed where flexural and torsional eigenmodes are driven simultaneously. The corresponding vibrational amplitude and phase shift of the vertical tip motion were utilized for topographical feedback and out-of-plane dissipative interaction acquisition, respectively, whereas the frequency shift and the drive amplitude of the lateral tip motion mapped the in-plane conservative and dissipative interactions of two heterogeneous polymers: an elastomeric polypropylene (ePP) and a polystyrene-block-polybutadiene diblock copolymer (SB). The shear stress at different sub-surface levels revealed an amorphous cover layer as well as a "slipping" plane on the ePP crystallites. The imaging of SB supported by dynamic force spectroscopy experiments showed that SB exhibits considerably different in- and out-of-plane nanomechanical properties at certain areas due to the complex polymer conformation of this diblock copolymer accompanied by inter- and intramolecular interactions that give rise to its viscoelastic behavior.

Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems

Analytical equations to estimate the peak force will facilitate the interpretation and the planning of amplitude-modulation force microscopy (tapping mode) experiments. A closed-form analytical equation to estimate the tip-sample peak forces while imaging soft materials in liquid environment and within an elastic deformation regime has been deduced. We have combined a multivariate regression method with input from the virial-dissipation equations and Tatara's bidimensional deformation contact mechanics model. The equation enables to estimate the peak force based on the tapping mode observables, probe characteristics and the material properties of the sample. The accuracy of the equation has been verified by comparing it to numerical simulations for the archetypical operating conditions to image soft matter with high spatial resolution in tapping-mode AFM.

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

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

Sub-nanometer Resolution Imaging with Amplitude-modulation Atomic Force Microscopy in Liquid

Atomic force microscopy (AFM) has become a well-established technique for nanoscale imaging of samples in air and in liquid. Recent studies have shown that when operated in amplitude-modulation (tapping) mode, atomic or molecular-level resolution images can be achieved over a wide range of soft and hard samples in liquid. In these situations, small oscillation amplitudes (SAM-AFM) enhance the resolution by exploiting the solvated liquid at the surface of the sample. Although the technique has been successfully applied across fields as diverse as materials science, biology and biophysics and surface chemistry, obtaining high-resolution images in liquid can still remain challenging for novice users. This is partly due to the large number of variables to control and optimize such as the choice of cantilever, the sample preparation, and the correct manipulation of the imaging parameters. Here, we present a protocol for achieving high-resolution images of hard and soft samples in fluid using SAM-AFM on a commercial instrument. Our goal is to provide a step-by-step practical guide to achieving high-resolution images, including the cleaning and preparation of the apparatus and the sample, the choice of cantilever and optimization of the imaging parameters. For each step, we explain the scientific rationale behind our choices to facilitate the adaptation of the methodology to every user's specific system.

Fast Stiffness Mapping of Cells Using High-Bandwidth Atomic Force Microscopy

The cytoskeleton controls cellular morphology and mediates the mechanical interactions between a cell and its environment. Atomic force microscopy (AFM) has the unique capability to map cytoskeletal mechanics and structures with nanometer resolution. However, whole-cell cytomechanical imaging with conventional AFM techniques is limited by low imaging speed. Here, we present fast nanomechanical mapping of cells using high-bandwidth AFM (HB-AFM), where >10(6) nanoindentation measurements were acquired in ∼10 min-a task that would take weeks to finish using conventional AFM. High-bandwidth measurements enabled capture of the entire tip-sample interaction for each tap on cells, engendering a new measurement ("force phase") that exceeds the contrast of conventional tapping mode and enabling spectral visualization of >10 harmonics. The abundance of measurements allowed discovery of subtle cytomechanical features, including the stiffness of fibers of the cellular spectrin network in situ. This approach bridges HB-AFM and high-harmonic imaging and opens future opportunities for measuring the dynamic mechanical properties of living cells.

Seeing is believing: atomic force microscopy imaging for nanomaterial research

Atomic force microscopy can image nanomaterial properties such as the topography, elasticity, adhesion, friction, electrical properties, and magnetism.

Selective enhancement of individual cantilever high resonance modes

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

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.

Combination of Universal Mechanical Testing Machine with Atomic Force Microscope for Materials Research

Surface deformation and fracture processes of materials under external force are important for understanding and developing materials. Here, a combined horizontal universal mechanical testing machine (HUMTM)-atomic force microscope (AFM) system is developed by modifying UMTM to combine with AFM and designing a height-adjustable stabilizing apparatus. Then the combined HUMTM-AFM system is evaluated. Finally, as initial demonstrations, it is applied to analyze the relationship among macroscopic mechanical properties, surface nanomorphological changes under external force, and fracture processes of two kinds of representative large scale thin film materials: polymer material with high strain rate (Parafilm) and metal material with low strain rate (aluminum foil). All the results demonstrate the combined HUMTM-AFM system overcomes several disadvantages of current AFM-combined tensile/compression devices including small load force, incapability for large scale specimens, disability for materials with high strain rate, and etc. Therefore, the combined HUMTM-AFM system is a promising tool for materials research in the future.

Multi-eigenmode control for high material contrast in bimodal and higher harmonic atomic force microscopy

High speed imaging and mapping of nanomechanical properties in atomic force microscopy (AFM) allows the observation and characterization of dynamic sample processes. Recent developments involve several cantilever frequencies in a multifrequency approach. One method actuates the first eigenmode for topography imaging and records the excited higher harmonics to map nanomechanical properties of the sample. To enhance the higher frequencies' response two or more eigenmodes are actuated simultaneously, where the higher eigenmode(s) are used to quantify the nanomechanics. In this paper, we combine each imaging methodology with a novel control approach. It modifies the Q factor and resonance frequency of each eigenmode independently to enhance the force sensitivity and imaging bandwidth. It allows us to satisfy the different requirements for the first and higher eigenmode. The presented compensator is compatible with existing AFMs and can be simply attached with minimal modifications. Different samples are used to demonstrate the improvement in nanomechanical contrast mapping and imaging speed of tapping mode AFM in air. The experiments indicate most enhanced nanomechanical contrast with low Q factors of the first and high Q factors of the higher eigenmode. In this scenario, the cantilever topography imaging rate can also be easily improved by a factor of 10.

Imaging and three-dimensional reconstruction of chemical groups inside a protein complex using atomic force microscopy

Scanning probe microscopes can be used to image and chemically characterize surfaces down to the atomic scale. However, the localized tip-sample interactions in scanning probe microscopes limit high-resolution images to the topmost atomic layer of surfaces, and characterizing the inner structures of materials and biomolecules is a challenge for such instruments. Here, we show that an atomic force microscope can be used to image and three-dimensionally reconstruct chemical groups inside a protein complex. We use short single-stranded DNAs as imaging labels that are linked to target regions inside a protein complex, and T-shaped atomic force microscope cantilevers functionalized with complementary probe DNAs allow the labels to be located with sequence specificity and subnanometre resolution. After measuring pairwise distances between labels, we reconstruct the three-dimensional structure formed by the target chemical groups within the protein complex using simple geometric calculations. Experiments with the biotin-streptavidin complex show that the predicted three-dimensional loci of the carboxylic acid groups of biotins are within 2 Å of their respective loci in the corresponding crystal structure, suggesting that scanning probe microscopes could complement existing structural biological techniques in solving structures that are difficult to study due to their size and complexity.

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

We present a simulation environment, dForce, which can be used for a better understanding of dynamic force microscopy experiments. The simulator presents the cantilever-tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the instantaneous deflection and tip-surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom effect cone correction, linear viscoelastic forces or the standard linear solid viscoelastic model. We have compared two numerical integration methods to select the one that offers optimal accuracy and speed. The graphical user interface has been designed to facilitate the navigation of non-experts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years.

Investigation of temperature induced mechanical changes in supported bilayers by variants of tapping mode atomic force microscopy

Tapping mode atomic force microscopy (AFM) is an invaluable technique for examining topographical features of biological materials in solution, and there has been a growing interest in developing techniques to provide further compositional contrast and information concerning surface mechanical properties. Phase shifts, cantilever response at higher harmonic frequencies of the drive, and time-resolved tip/sample force reconstruction have all been shown to provide additional compositional contrast of surfaces, as compared to basic tapping mode AFM imaging. This study aimed to demonstrate the relative ability of these different imaging techniques to detect temperature induced changes in the elastic modulus of supported total brain lipid extract (TBLE) bilayer patches on mica. To aid in direct comparison between the different imaging techniques, all required data was obtained simultaneously while capturing traditional tapping mode AFM topography images. While all of the techniques were able to provide compositional contrast consistent with known temperature-induced changes in the bilayer patch, interpretation of the resulting contrast was not always straightforward. Phase imaging suffered from contrast inversion. Individual harmonics responded in a variety of ways to the temperature-induced changes in elastic modulus of the bilayer. The maximum tapping force (or peak force) associated with imaging the bilayer correctly reflected the changes in elastic modulus of the lipid bilayer. Importantly, as the required data can be obtained simultaneously, combining these different imaging techniques can lead to a more complete understanding of a sample's mechanical features.

Nanomechanical spectroscopy of synthetic and biological membranes

We report that atomic force microscopy based high-speed nanomechanical analysis can identify components of complex heterogeneous synthetic and biological membranes from the measured spectrum of nanomechanical properties. We have investigated phase separated ternary lipid bilayers and purple membranes of Halobacterium salinarum. The nanomechanical spectra recorded on these samples identify all membrane components, some of which are difficult to resolve in conventional phase images. This non-destructive approach can aid the design of synthetic lipid bilayers and studies lateral organization of complex heterogeneous cellular membranes.

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.

Unlocking higher harmonics in atomic force microscopy with gentle interactions

In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

Control of the higher eigenmodes of a microcantilever: applications in atomic force microscopy

While conventional techniques in dynamic mode atomic force microscopy typically involve the excitation of the first flexural mode of a microcantilever, situations arise where the excitation of higher modes may result in image artefacts. Strong nonlinear coupling between the cantilever modes in liquid environments may result in image artefacts, limiting the accuracy of the image. Similar observations have been made in high-speed contact mode AFM. To address this issue, we propose the application of the modulated-demodulated control technique to attenuate problematic modes to eliminate the image artefacts. The modulated-demodulated control technique is a high-bandwidth technique, which is well suited to the control of next generation of high-speed cantilevers. In addition to potential improvements in image quality, a high-bandwidth controller may also find application in multifrequency AFM experiments. To demonstrate the high-bandwidth nature of the control technique, we construct an amplitude modulation AFM experiment in air utilizing low amplitude setpoints, which ensures that harmonic generation and nonlinear coupling of the modes result in image artefacts. We then utilize feedback control to highlight the improvement in image quality. Such a control technique appears extremely promising in high-speed atomic force microscopy and is likely to have direct application in AFM in liquids.

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

The peak forces exerted on soft and rigid samples by a force microscope have been modeled by performing numerical simulations of the tip motion in liquid. The forces are obtained by using two contact mechanics models, Hertz and Tatara. We present a comparison between the numerical simulations and three analytical models for a wide variety of probe and operational parameters. In general, the forces derived from analytical expressions are not in good quantitative agreement with the simulations when the Young modulus and the set-point amplitude are varied. The only exception is the parametrized approximation that matches the results given by Hertz contact mechanics for soft materials and small free amplitudes. We also study the elastic deformation of the sample as a function of the imaging conditions for materials with a Young modulus between 25 MPa and 2 GPa. High lateral resolution images are predicted by using both small free amplitudes (less than 2 nm for soft materials) and high set-point amplitudes.

Anharmonicity, solvation forces, and resolution in atomic force microscopy at the solid-liquid interface

Solid-liquid interfaces are central to nanoscale science and technology and control processes as diverse as self-assembly, heterogeneous catalysis, wetting, electrochemistry, or protein function. Experimentally, measuring the structure and dynamics of solid-liquid interfaces with molecular resolution remains a challenge. This task can, in principle, be achieved with atomic force microscopy (AFM), which functions locally, and with nanometer precision. When operated dynamically and at small amplitudes, AFM can provide molecular-level images of the liquid solvation layers at the interfaces. At larger amplitudes, results in the field of multifrequency AFM have shown that anharmonicities in the tip motion can provide quantitative information about the solid's mechanical properties. The two approaches probe opposite aspects of the interface and are generally seen as distinct. Here it is shown that, for amplitudes A<d, the thickness of the solvation region, the tip mainly probes the interfacial liquid, and subnanometer resolution can be achieved through solvation forces. For A>d, the tip trajectory becomes rapidly anharmonic due to the tip tapping the solid, and the resolution decreases. A nonlinear transition between the two regimes occurs for A~d and can be quantified with the second harmonic of the tip oscillation. These results, confirmed by computer simulations, remain valid in most experimental conditions. Significantly, they provide an objective criterion to enhance resolution and to decide whether the results are dominated by the properties of the solid or of the liquid.

Peak forces in high-resolution imaging of soft matter in liquid

The maximum force exerted by the tip of a force microscope on the sample surface is a critical factor that determines the spatial resolution and the degree of invasiveness of the measurement, in particular, on soft materials. Here we determine the conditions needed to image soft matter in the 30-500 MPa range while applying very small forces. Imaging at sub-50 pN in the elastic regime can only be achieved under strict conditions in terms of force constant values (below 0.1 N/m) and free amplitudes (below 2 nm). The peak force depends on the operational parameters, probe properties, the elastic and/or viscoelastic response of the sample, and the contact mechanics model. Images of heterogeneous samples are never taken at a constant peak force. Under the same operational conditions, smaller forces are obtained on the more compliant materials. We also find that the viscoelastic response reduces the peak force with respect to the purely elastic regions. Our findings are summarized in three-dimensional maps that contain the operational conditions for imaging at low forces.

High-resolution nanomechanical analysis of suspended electrospun silk fibers with the torsional harmonic atomic force microscope

Atomic force microscopes have become indispensable tools for mechanical characterization of nanoscale and submicron structures. However, materials with complex geometries, such as electrospun fiber networks used for tissue scaffolds, still pose challenges due to the influence of tension and bending modulus on the response of the suspended structures. Here we report mechanical measurements on electrospun silk fibers with various treatments that allow discriminating among the different mechanisms that determine the mechanical behavior of these complex structures. In particular we were able to identify the role of tension and boundary conditions (pinned versus clamped) in determining the mechanical response of electrospun silk fibers. Our findings show that high-resolution mechanical imaging with torsional harmonic atomic force microscopy provides a reliable method to investigate the mechanics of materials with complex geometries.

Atomic force microscopy imaging of macromolecular complexes

This chapter reviews amplitude modulation (AM) AFM in air and its applications to high-resolution imaging and interpretation of macromolecular complexes. We discuss single DNA molecular imaging and DNA-protein interactions, such as those with topoisomerases and RNA polymerase. We show how relative humidity can have a major influence on resolution and contrast and how it can also affect conformational switching of supercoiled DNA. Four regimes of AFM tip-sample interaction in air are defined and described, and relate to water perturbation and/or intermittent mechanical contact of the tip with either the molecular sample or the surface. Precise control and understanding of the AFM operational parameters is shown to allow the user to switch between these different regimes: an interpretation of the origins of topographical contrast is given for each regime. Perpetual water contact is shown to lead to a high-resolution mode of operation, which we term SASS (small amplitude small set-point) imaging, and which maximizes resolution while greatly decreasing tip and sample wear and any noise due to perturbation of the surface water. Thus, this chapter provides sufficient information to reliably control the AFM in the AM AFM mode of operation in order to image both heterogeneous samples and single macromolecules including complexes, with high resolution and with reproducibility. A brief introduction to AFM, its versatility and applications to biology is also given while providing references to key work and general reviews in the field.

Heterogeneous dissipation and size dependencies of dissipative processes in nanoscale interactions

Here, processes through which the energy stored in an atomic force microscope cantilever dissipates in the tip-sample interaction are first decoupled qualitatively. A formalism is then presented and shown to allow quantification of fundamental aspects of nanoscale dissipation such as deformation, viscosity, and surface energy hysteresis. Accurate quantification of energy dissipation requires precise calibration of the conversion of the oscillation amplitude from volts to nanometers. In this respect, an experimental methodology is presented that allows such calibration with errors of 3% or less. It is shown how simultaneous decoupling and quantification of dissipative processes and in situ tip radius quantification provide the required information to analyze dependencies of dissipative mechanisms on the relative size of the interacting bodies, that is, tip and surface. When there is chemical affinity, atom-atom dissipative interactions approach the energies of chemical bonds. Such atom-atom interactions are found to be independent of cantilever properties and tip geometry thus implying that they are intensive properties of the system; these interactions prevail in the form of surface energy hysteresis. Viscoelastic dissipation on the other hand is shown to depend on the size of the probe and operational parameters.

High-resolution dynamic atomic force microscopy in liquids with different feedback architectures

The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett. 2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip-sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.

Modelling oscillatory flexure modes of an atomic force microscope cantilever in contact mode whilst imaging at high speed

Understanding the modal response of an atomic force microscope is important for the identification of image artefacts captured using contact-mode atomic force microscopy (AFM). As the scan rate of high speed AFM increases, these modes present themselves as ever clearer noise patterns as the frequency of cantilever vibration falls under the frequency of pixel collection. An Euler-Bernoulli beam equation is used to simulate the flexural modes of the cantilever of an atomic force microscope as it images a hard surface in contact mode. Theoretical results are compared with experimental recordings taken in the high speed regime, as well as previous analytical results. It is shown that the model can capture the mode shapes and resonance properties of the first four eigenmodes.

Molecular and nanoscale compositional contrast of soft matter in liquid: interplay between elastic and dissipative interactions

We demonstrate that the phase contrast observed with an amplitude modulation atomic force microscope depends on two factors, the generation of higher harmonics components and the energy dissipated on the sample surface. Those factors are ultimately related to the chemical composition and structure of the surface. Our findings are general, but they specifically describe the results obtained while imaging soft materials in liquid. Molecular resolution experiments performed on a protein membrane surface in liquid confirm the theory.

Repulsive bimodal atomic force microscopy on polymers

Bimodal atomic force microscopy can provide high-resolution images of polymers. In the bimodal operation mode, two eigenmodes of the cantilever are driven simultaneously. When examining polymers, an effective mechanical contact is often required between the tip and the sample to obtain compositional contrast, so particular emphasis was placed on the repulsive regime of dynamic force microscopy. We thus investigated bimodal imaging on a polystyrene-block-polybutadiene diblock copolymer surface and on polystyrene. The attractive operation regime was only stable when the amplitude of the second eigenmode was kept small compared to the amplitude of the fundamental mode. To clarify the influence of the higher eigenmode oscillation on the image quality, the amplitude ratio of both modes was systematically varied. Fourier analysis of the time series recorded during imaging showed frequency mixing. However, these spurious signals were at least two orders of magnitude smaller than the first two fundamental eigenmodes. Thus, repulsive bimodal imaging of polymer surfaces yields a good signal quality for amplitude ratios smaller than A(01)/A(02) = 10:1 without affecting the topography feedback.

The emergence of multifrequency force microscopy

In atomic force microscopy a cantilever with a sharp tip attached to it is scanned over the surface of a sample, and information about the surface is extracted by measuring how the deflection of the cantilever - which is caused by interactions between the tip and the surface - varies with position. In the most common form of atomic force microscopy, dynamic force microscopy, the cantilever is made to vibrate at a specific frequency, and the deflection of the tip is measured at this frequency. But the motion of the cantilever is highly nonlinear, and in conventional dynamic force microscopy, information about the sample that is encoded in the deflection at frequencies other than the excitation frequency is irreversibly lost. Multifrequency force microscopy involves the excitation and/or detection of the deflection at two or more frequencies, and it has the potential to overcome limitations in the spatial resolution and acquisition times of conventional force microscopes. Here we review the development of five different modes of multifrequency force microscopy and examine its application in studies of proteins, the imaging of vibrating nanostructures, measurements of ion diffusion and subsurface imaging in cells.

Resolving structure and mechanical properties at the nanoscale of viruses with frequency modulation atomic force microscopy

Structural Biology (SB) techniques are particularly successful in solving virus structures. Taking advantage of the symmetries, a heavy averaging on the data of a large number of specimens, results in an accurate determination of the structure of the sample. However, these techniques do not provide true single molecule information of viruses in physiological conditions. To answer many fundamental questions about the quickly expanding physical virology it is important to develop techniques with the capability to reach nanometer scale resolution on both structure and physical properties of individual molecules in physiological conditions. Atomic force microscopy (AFM) fulfills these requirements providing images of individual virus particles under physiological conditions, along with the characterization of a variety of properties including local adhesion and elasticity. Using conventional AFM modes is easy to obtain molecular resolved images on flat samples, such as the purple membrane, or large viruses as the Giant Mimivirus. On the contrary, small virus particles (25-50 nm) cannot be easily imaged. In this work we present Frequency Modulation atomic force microscopy (FM-AFM) working in physiological conditions as an accurate and powerful technique to study virus particles. Our interpretation of the so called "dissipation channel" in terms of mechanical properties allows us to provide maps where the local stiffness of the virus particles are resolved with nanometer resolution. FM-AFM can be considered as a non invasive technique since, as we demonstrate in our experiments, we are able to sense forces down to 20 pN. The methodology reported here is of general interest since it can be applied to a large number of biological samples. In particular, the importance of mechanical interactions is a hot topic in different aspects of biotechnology ranging from protein folding to stem cells differentiation where conventional AFM modes are already being used.

Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator

Dynamic atomic force microscopy (dAFM) continues to grow in popularity among scientists in many different fields, and research on new methods and operating modes continues to expand the resolution, capabilities, and types of samples that can be studied. But many promising increases in capability are accompanied by increases in complexity. Indeed, interpreting modern dAFM data can be challenging, especially on complicated material systems, or in liquid environments where the behavior is often contrary to what is known in air or vacuum environments. Mathematical simulations have proven to be an effective tool in providing physical insight into these non-intuitive systems. In this article we describe recent developments in the VEDA (virtual environment for dynamic AFM) simulator, which is a suite of freely available, open-source simulation tools that are delivered through the cloud computing cyber-infrastructure of nanoHUB (www.nanohub.org). Here we describe three major developments. First, simulations in liquid environments are improved by enhancements in the modeling of cantilever dynamics, excitation methods, and solvation shell forces. Second, VEDA is now able to simulate many new advanced modes of operation (bimodal, phase-modulation, frequency-modulation, etc.). Finally, nineteen different tip-sample models are available to simulate the surface physics of a wide variety different material systems including capillary, specific adhesion, van der Waals, electrostatic, viscoelasticity, and hydration forces. These features are demonstrated through example simulations and validated against experimental data, in order to provide insight into practical problems in dynamic AFM.

"Magnetic force microscopy and energy loss imaging of superparamagnetic iron oxide nanoparticles"

We present quantitative, high spatially resolved magnetic force microscopy imaging of samples based on 11 nm diameter superparamagnetic iron oxide nanoparticles in air at room temperature. By a proper combination of the cantilever resonance frequency shift, oscillation amplitude and phase lag we obtain the tip-sample interaction maps in terms of force gradient and energy dissipation. These physical quantities are evaluated in the frame of a tip-particle magnetic interaction model also including the tip oscillation amplitude. Magnetic nanoparticles are characterized both in bare form, after deposition on a flat substrate, and as magnetically assembled fillers in a polymer matrix, in the form of nanowires. The latter approach makes it possible to reveal the magnetic texture in a composite sample independently of the surface topography.

Mapping nanomechanical properties of live cells using multi-harmonic atomic force microscopy

The nanomechanical properties of living cells, such as their surface elastic response and adhesion, have important roles in cellular processes such as morphogenesis, mechano-transduction, focal adhesion, motility, metastasis and drug delivery. Techniques based on quasi-static atomic force microscopy techniques can map these properties, but they lack the spatial and temporal resolution that is needed to observe many of the relevant details. Here, we present a dynamic atomic force microscopy method to map quantitatively the nanomechanical properties of live cells with a throughput (measured in pixels/minute) that is ∼10-1,000 times higher than that achieved with quasi-static atomic force microscopy techniques. The local properties of a cell are derived from the 0th, 1st and 2nd harmonic components of the Fourier spectrum of the AFM cantilevers interacting with the cell surface. Local stiffness, stiffness gradient and the viscoelastic dissipation of live Escherichia coli bacteria, rat fibroblasts and human red blood cells were all mapped in buffer solutions. Our method is compatible with commercial atomic force microscopes and could be used to analyse mechanical changes in tumours, cells and biofilm formation with sub-10 nm detail.

Noninvasive protein structural flexibility mapping by bimodal dynamic force microscopy

Mapping of the protein structural flexibility with sub-2-nm spatial resolution in liquid is achieved by combining bimodal excitation and frequency modulation force microscopy. The excitation of two cantilever eigenmodes in dynamic force microscopy enables the separation between topography and flexibility mapping. We have measured variations of the elastic modulus in a single antibody pentamer from 8 to 18 MPa when the probe is moved from the end of the protein arm to the central protrusion. Bimodal dynamic force microscopy enables us to perform the measurements under very small repulsive loads (30-40 pN).

Nanomechanical coupling enables detection and imaging of 5 nm superparamagnetic particles in liquid

We demonstrate that a force microscope operated in a bimodal mode enables the imaging and detection of superparamagnetic particles down to 5 nm. The bimodal method exploits the nanomechanical coupling of the excited modes to enhance the sensitivity of the higher mode to detect changes in material properties. The coupling requires the presence of nonlinear forces. Remarkably, bimodal operation enables us to identify changes of slowly varying forces (quasi-linear) in the presence of a stronger nonlinear force. Thus, unambiguous identification of single apoferritin (non-magnetic) and ferritin (magnetic) molecules in air and liquid is accomplished.

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.

Reconstructing nonlinearities with intermodulation spectroscopy

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring a large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.

Origins of phase contrast in the atomic force microscope in liquids

We study the physical origins of phase contrast in dynamic atomic force microscopy (dAFM) in liquids where low-stiffness microcantilever probes are often used for nanoscale imaging of soft biological samples with gentle forces. Under these conditions, we show that the phase contrast derives primarily from a unique energy flow channel that opens up in liquids due to the momentary excitation of higher eigenmodes. Contrary to the common assumption, phase-contrast images in liquids using soft microcantilevers are often maps of short-range conservative interactions, such as local elastic response, rather than tip-sample dissipation. The theory is used to demonstrate variations in local elasticity of purple membrane and bacteriophage 29 virions in buffer solutions using the phase-contrast images.