Atomic Force Microscope Cantilever Research Articles

Cornu-Spiral-Like Organic Crystal Waveguide Providing Discriminatory Optical Pathway for Smart Organic Photonic Circuit.

In the era of artificial intelligence, developing advanced and intelligent photonic circuits has become essential. In this work, the fabrication of a smart organic photonic circuit (OPC), is illustrated which utilizes a Cornu-spiral-like waveguide (CSW) to produce discriminating optical pathways in the circuit. The mechanical flexibility of Schiff base, (E)-1-(((5-iodopyridin-2-yl)imino)methyl)naphthalen-2-ol (IPyIN) facilitates the fabrication of a first-of-its-kind, two-ring-based CSW via the atomic force microscopy cantilever tip-assisted mechanophotonics approach. The photonic studies suggest that the CSW structure routes optical signals in discriminating trajectories. To capitalize on the discriminatory properties of the CSW, two linear waveguides onto both rings of the CSW are integrated to create a smart OPC. This smart OPC can selectively route optical signals either partially or fully in the circuit, depending on the pathways determined by the CSW, thus enabling the circuit to switch ON or OFF. Such intelligent photonic circuits are essential for advancing smart technologies.

B-090 Efficient Hydrophilic Surface Coating with Low Concentrations of Bovine Gamma Globulins

Abstract Background Bovine Gamma Globulin (BGG) is a high purity immunoglobulin fraction of bovine serum. BGG is used as a blocker to prevent non-specific binding in immunoassays and, due to the mixture of immunoglobulins, its blocking capabilities differ from traditional blockers like Bovine Serum Albumin (BSA). Our objective was to evaluate the adsorption characteristics of BGG to In vitro diagnostic relevant hydrophilic surfaces compared to BSA. A bead-based immunoassay was utilized to quantify the mass of protein coating a bead surface and atomic force microscopy (AFM) to analyze physical properties of the protein-surface layer. Methods The mass of BGG bound to hydrophilic beads (Dynabeads M-270 Carboxylic Acid) was determined across varying concentrations ranging from 0.1% to 1.0% in pH 7.0 phosphate buffer. Coated beads were heated in 1x SDS loading dye to dissociate bound protein, then ran on a nonreducing SDS-PAGE gel. The total protein was measured using densitometry against a standard curve, using ImageJ, and analyzed with GraphPad Prism. This methodology was also used for BSA. AFM was used to image a topographical view of BGG binding to a silica surface. Samples were prepared at concentrations from 0.1% to 1.0% in phosphate buffer at pH 7.0. Followed by a series of washes to remove non-bound molecules, the surface was allowed to dry, then scratched with an AFM cantilever. The surface was then analyzed for roughness and thickness of BGG adsorption for each concentration. Results BGG and BSA have notable differences in their coating properties at a concentration of 1.0%. In the bead assay, the protein-surface binding is enhanced ∼4.8-fold for BGG compared to BSA. Interestingly, even at 0.1% BGG bound ∼0.8-fold more than BSA at 1.0%. Despite a 6-fold increase in mass bound to the bead surface with 1.0% BGG compared to 0.1%, AFM revealed a 1.3-fold and 1.8-fold decrease in height and roughness at the lower concentration, while maintaining effective coating. These results suggest that higher BGG concentrations result in thicker, rougher surface coating. This could lead to steric hindrance and obstruction of binding sites, affecting assay performance. Therefore, a lower concentration of BGG may lead to better surface coating and prevent reduced sensitivity and accuracy within immunoassays. Conclusions The bead binding assay demonstrates that BGG displays surface adsorption with comparable or improved results with lower concentrations compared to BSA. At 0.1%, BGG exhibits effective binding to a hydrophilic surface equivalent to that achieved by BSA at 1.0%. Additionally, AFM data suggest that even at 0.1%, BGG effectively coats the silica surface and potentially reduces steric hinderance compared to BGG at 1%. While BSA remains a reliable choice for many applications, our findings suggest that BGG can be an effective blocker for immunoassay applications. The choice of a suitable blocker varies depending on factors such as assay high background, sensitivity, and specificity. By tailoring the choice of blocker to the specific requirements of the assay, researchers can optimize assay performance by improving the accuracy and the reliability of the assay.

Femtogram-Sensitive Cantilever Platform for Dynamic Graphene Oxide Nanosheet Monitoring.

This study introduces a new approach to optimizing graphene oxide (GO) properties using liquid-phase plasma treatment in a microenvironment. Our innovation exploits atomic force microscopy (AFM) cantilever frequency tracking to monitor mass variations in GO, which are indicative of surface oxidation-reduction processes or substituent doping (boron/nitrogen). Complementary in situ Raman spectroscopy has observed D/G band shifts, and X-ray photoelectron spectroscopy (XPS) determined the C/O ratio and B/N doping levels pre- and post-treatment, confirming chemical tuning to GO. We can achieve femtogram-level precision in detecting nanomaterial mass changes by correlating elemental ratios with AFM cantilever frequency measurements. This multifaceted approach not only enhances our understanding of the chemical properties of GO but also establishes a new, versatile method for monitoring, modifying, and optimizing the properties of nanomaterials.

Exploring the Challenges of Characterising Surface Topography of Polymer-Nanoparticle Composites.

Nanomechanical testing plays a crucial role in evaluating surfaces containing nanoparticles. Testing verifies surface performance concerning their intended function and detects any potential shortcomings in operational standards. Recognising that nanostructured surfaces are not always straightforward or uniform is essential. The chemical composition and morphology of these surfaces determine the end-point functionality. This can entail a layered surface using materials in contrast to each other that may require further modification after nanomechanical testing to pass performance and quality standards. Nanomechanical analysis of a structured surface consisting of a poly-methyl oxazoline film base functionalised with colloidal gold nanoparticles was demonstrated using an atomic force microscope (AFM). AFM nanomechanical testing investigated the overall substrate architecture's topographical, friction, adhesion, and wear parameters. Limitations towards its potential operation as a biomaterial were also addressed. This was demonstrated by using the AFM cantilever to apply various forces and break the bonds between the polymer film and gold nanoparticles. The AFM instrument offers an insight to the behaviour of low-modulus surface against a higher-modulus nanoparticle. This paper details the bonding and reaction limitations between these materials on the application of an externally applied force. The application of this interaction is highly scrutinised to highlight the potential limitations of a functionalised surface. These findings highlight the importance of conducting comprehensive nanomechanical testing to address concerns related to fabricating intricate biomaterial surfaces featuring nanostructures.

Direct Determination of Torsion in Twisted Graphite and MoS2 Interfaces.

The design space of two-dimensional materials is undergoing significant expansion through the stacking of layers in non-equilibrium configurations. However, the lack of quantitative insights into twist dynamics impedes the development of such heterostructures. Herein, we utilize the lateral force sensitivity of an atomic force microscope cantilever and specially designed rotational bearing structures to measure the torque in graphite and MoS2 interfaces. While the extracted torsional energies are virtually zero across all angular misfit configurations, commensurate interfaces of graphite and MoS2 are characterized by values of 0.1533 and 0.6384 N-m/m2, respectively. Furthermore, we measured the adhesion energies of graphite and MoS2 to elucidate the interplay between twist and slide. The adhesion energy dominates over the torsional energy for the graphitic interface, suggesting a tendency to twist prior to superlubric sliding. Conversely, MoS2 displays an increased torsional energy exceeding its adhesion energy. Consequently, our findings demonstrate a fundamental disparity between the sliding-to-twisting dynamics at MoS2 and graphite interfaces.

Advancing Atomic Force Microscopy: Design of Innovative IP-Dip Polymer Cantilevers and Their Exemplary Fabrication via 3D Laser Microprinting

This paper presents the design and fabrication of new types of polymer-based cantilevers for atomic force microscopy. The design and fabrication are aimed at the capability of 3D laser microprinting technology based on two-photon polymerization on a standard silicon substrate. IP-Dip commercial material from the Nanoscribe company was used for the fabrication of the designed cantilevers. The fabricated microprinted cantilevers facilitate precise manipulation at the nanoscopic scale, which is essential for studying nanomaterials’ mechanical, electrical, and optical properties. The cantilevers’ flexibility allows for the integration of functional elements such as piezoelectric layers and optical fibers, enabling combined measurements of multiple physical parameters. Various cantilever geometries, including rectangular and V-shaped, are examined, and their resonance frequencies are calculated. The experimental process involves preparing the cantilevers on a silicon substrate and coating them with aluminum for enhanced reflectivity and conductivity. Scanning electron microscope analysis documents the precise form of prepared polymer cantilevers. The functionality of the probes is validated by scanning a step-height standard grating. This study demonstrates the versatility and precision of the fabricated cantilevers, showcasing their potential for large-area scans, living cell investigation, and diverse nanotechnology applications.

Cryptic Extensibility in von Willebrand Factor Revealed by Molecular Nanodissection.

Von Willebrand factor (VWF) is a multimer with a variable number of protomers, each of which is a head-to-head dimer of two multi-domain monomers. VWF responds to shear through the unfolding and extension of distinct domains, thereby mediating platelet adhesion and aggregation to the injured blood vessel wall. VWF's C1-6 segment uncoils and then the A2 domain unfolds and extends in a hierarchical and sequential manner. However, it is unclear whether there is any reservoir of further extensibility. Here, we explored the presence of cryptic extensibility in VWF by nanodissecting individual, pre-stretched multimers with atomic force microscopy (AFM). The AFM cantilever tip was pressed into the surface and moved in a direction perpendicular to the VWF axis. It was possible to pull out protein loops from VWF, which resulted in a mean contour length gain of 217 nm. In some cases, the loop became cleaved, and a gap was present along the contour. Frequently, small nodules appeared in the loops, indicating that parts of the nanodissected VWF segment remained folded. After analyzing the nodal structure, we conclude that the cryptic extensibility lies within the C1-6 and A1-3 regions. Cryptic extensibility may play a role in maintaining VWF's functionality in extreme shear conditions.

Mechanical Properties of Mouse Lung Cells and Their Effects on the Atomic Force Microscope Beam Vibrations.

In the present investigation, the mechanical properties of mouse normal and carcinomatous (LL/2) lung tissue cells were investigated using atomic force microscopy (AFM). The normal lung cells have been derived directly from C57BL mice. Initially, the elastic modulus of LL/2 cells was measured following chemotherapy with the anti-cancer drug Cisplatin and plasma treatment. MTT evaluation was used to determine the optimal dosages for 24- and 48-h incubations based on the IC50 cell viability concentration during chemotherapy treatment. After 24 and 48 h, the results demonstrated that Cisplatin-based chemotherapy increases the elastic modulus of LL/2 cells by 1.599 and 2.308 times compared to untreated cells. LL/2 cells were subsequently treated with plasma for 30 and 60 s for 24 and 48-h incubation. The plasma treatment decreased the LL/2 cell's elastic modulus, and the time duration of plasma treatment increased the reduction amount of elastic modulus. During the second section of the study, theoretical (finite element analysis [FEM]) and experimental techniques were used to examine the resonant frequencies and magnitude of the frequency response function (FRF) of the AFM cantilever's movements when applying normal and cancerous cells before and after chemo and plasma treatments as specimens. The results indicated that increasing the samples' elastic modulus raises the resonant frequency, so the resonant frequency of treated cells as a sample is greater than untreated cells. In conclusion, the FEM and experimental results were compared and found to be in good agreement.

Control of quality factor of atomic force microscopy cantilever by cavity optomechanical effect

The effective quality factor of the cantilever plays a fundamental role in dynamic mode atomic force microscopy. Here we present a technique to modify the quality factor of an atomic force microscopy cantilever within a Fabry–Perot optical interferometer. The experimental setup uses two separate laser sources to detect and excite the oscillation of the cantilever. While the intensity modulation of the excitation laser drives the oscillation of the cantilever, the average intensity can be used to modify the quality factor via optomechanical force without changing the fiber-cantilever cavity length. The technique enables users to optimize the quality factor for different types of measurements without influencing the deflection measurement sensitivity. An unexpected frequency shift was observed and modelled as temperature dependence of the cantilever’s Young’s modulus, which was validated using finite element simulation. The model was used to compensate for the thermal frequency shift. The simulation provided relations between optical power, temperature, and frequency shift.

Mechanical properties of human kidney cells and their effects on the atomic force microscope beam vibrations.

In the present investigation, the mechanical properties of normal and carcinomatous cells of kidney tissue (HEK-293, ACHN, respectively) were investigated using atomic force microscopy (AFM). Initially, the elastic modulus of ACHN cells was measured following chemotherapy with the anti-cancer drug Cisplatin and plasma treatment. The MTT assay was employed to ascertain the most effective dosages for incubation periods of 12, 24, 48, 72, and 96 h, guided by the IC50 concentration for cell viability during chemotherapy treatment. Analysis at these specified time points revealed a progressive increase in the elastic modulus of ACHN cells when subjected to Cisplatin-based chemotherapy. Specifically, the elastic modulus increased by 1.847, 4.416, 6.035, 8.029, and 9.727 times in comparison to untreated cells at 12, 24, 48, 72, and 96 h, respectively. ACHN cells were subsequently treated with plasma for 30 and 60 s for 24 and 48-h incubation periods. The plasma treatment increased the ACHN cell's elastic modulus. In the subsequent phase of the research, a combination of theoretical (finite element method [FEM]) and experimental methodologies was employed to investigate the resonant frequencies and magnitude of the frequency response function (FRF) concerning the movement of the AFM cantilever. This examination was conducted using ACHN cells as specimens, both before and after exposure to chemotherapy and plasma treatments. The results showed that higher sample elastic modulus increased the resonant frequency, indicating that treated cells had a higher resonant frequency than untreated cells. In conclusion, the FEM and experimental results were compared and found to be in good agreement. HIGHLIGHTS: Using Cisplatin anti-cancer drug increases the elastic modulus of ACHN cell. Applying plasma treatment increases the elastic modulus of ACHN cell. For both of the chemo and plasma therapies, increasing the incubation time increases the influence of therapies oh the cell mechanics. Using finite element modeling (FEM) the real dynamic behavior of atomic force microscope cantilever by considering human kidney cells as the soft samples is possible.

Measuring Rolling Friction at the Nanoscale.

Colloidal probe microscopy, a technique whereby a microparticle is affixed at the end of an atomic force microscopy (AFM) cantilever, plays a pivotal role in enabling the measurement of friction at the nanoscale and is of high relevance for applications and fundamental studies alike. However, in conventional experiments, the probe particle is immobilized onto the cantilever, thereby restricting its relative motion against a countersurface to pure sliding. Nonetheless, under many conditions of interest, such as during the processing of particle-based materials, particles are free to roll and slide past each other, calling for the development of techniques capable of measuring rolling friction alongside sliding friction. Here, we present a new methodology to measure lateral forces during rolling contacts based on the adaptation of colloidal probe microscopy. Using two-photon polymerization direct laser writing, we microfabricate holders that can capture microparticles, but allow for their free rotation. Once attached to an AFM cantilever, upon lateral scanning, the holders enable both sliding and rolling contacts between the captured particles and the substrate, depending on the interactions, while simultaneously giving access to normal and lateral force signals. Crucially, by producing particles with optically heterogeneous surfaces, we can accurately detect the presence of rotation during scanning. After introducing the workflow for the fabrication and use of the probes, we provide details on their calibration, investigate the effect of the materials used to fabricate them, and report data on rolling friction as a function of the surface roughness of the probe particles. We firmly believe that our methodology opens up new avenues for the characterization of rolling contacts at the nanoscale, aimed, for instance, at engineering particle surface properties and characterizing functional coatings in terms of their rolling friction.

Design and fabrication of an opto-mechanical antenna in the NIR range

In this study we present a novel device for the direct transduction of optical radiation in the near-infrared region into mechanical actuation, which is based on a plasmonic optical nanoantenna integrated in a microcantilever. We propose and demonstrate the feasibility of a simple fabrication process consisting in the nano-tailoring of a commercially available Atomic Force Microscope (AFM) cantilever by means of the Focused Ion Beam (FIB) milling technique. Furthermore, the comprehensive analysis of the device performance characteristics included in this work reveals the different sensitivity values of these characteristics to the fabrication process tolerances of the most relevant geometric design parameters.

Torsional force microscopy of van der Waals moirés and atomic lattices

In a stack of atomically thin van der Waals layers, introducing interlayer twist creates a moiré superlattice whose period is a function of twist angle. Changes in that twist angle of even hundredths of a degree can dramatically transform the system's electronic properties. Setting a precise and uniform twist angle for a stack remains difficult; hence, determining that twist angle and mapping its spatial variation is very important. Techniques have emerged to do this by imaging the moiré, but most of these require sophisticated infrastructure, time-consuming sample preparation beyond stack synthesis, or both. In this work, we show that torsional force microscopy (TFM), a scanning probe technique sensitive to dynamic friction, can reveal surface and shallow subsurface structure of van der Waals stacks on multiple length scales: the moirés formed between bi-layers of graphene and between graphene and hexagonal boron nitride (hBN) and also the atomic crystal lattices of graphene and hBN. In TFM, torsional motion of an Atomic Force Microscope (AFM) cantilever is monitored as it is actively driven at a torsional resonance while a feedback loop maintains contact at a set force with the sample surface. TFM works at room temperature in air, with no need for an electrical bias between the tip and the sample, making it applicable to a wide array of samples. It should enable determination of precise structural information including twist angles and strain in moiré superlattices and crystallographic orientation of van der Waals flakes to support predictable moiré heterostructure fabrication.

Quantifying droplet–solid friction using an atomic force microscope

AbstractControlling the wetting and spreading of microdroplets is key to technologies such as microfluidics, ink‐jet printing, and surface coating. Contact angle goniometry is commonly used to characterize surface wetting by droplets, but the technique is ill‐suited for high contact angles close to . Here, we attach a micrometric‐sized droplet to an atomic force microscope cantilever to directly quantify droplet–solid friction on different surfaces (superhydrophobic and underwater superoleophobic) with sub‐nanonewton force resolutions. We demonstrate the versatility of our approach by performing friction measurements using different liquids (water and oil droplets) and under different ambient environments (in air and underwater). Finally, we show that underwater superoleophobic surfaces can be qualitatively different from superhydrophobic surfaces: droplet–solid friction is highly sensitive to droplet speeds for the former but not for the latter surface.

AFM-NSOM Nano-Polarimeter: Wide-ranging sensing device for synchronized scanning

This paper explores the use of an enhanced AFM-NSOM system tip as a nanoscale polarimeter. The tip consists of a tungsten-silicon conical photodetector modified with four differently-shaped subwavelength apertures, which enable the determination of incident light's four Stokes parameters and in turn its polarization state on the Poincaré sphere. The system is mounted on a standard Atomic Force Microscope (AFM) cantilever and can serve as a triple-mode scanning system, with complementary topography scanning, optical data analysis, and polarization state detection. The device was designed and simulated using the Comsol Multi-Physics software package, and initial steps toward fabrication were taken using the application of advanced nanotechnology tools to a commercial AFM probe. After a discussion of the advantages and drawbacks of drilled scanning tips vis-a-vis standard ones, the article presents the simulation and fabrication results of the nano-polarimeter tip.

Surface Cross-Linking by Macromolecular Tethers Enhances Virus-like Particles' Resilience to Mucosal Stress Factors.

Virus-like particles (VLPs) are emerging as nanoscaffolds in a variety of biomedical applications including delivery of vaccine antigens and cargo such as mRNA to mucosal surfaces. These soft, colloidal, and proteinaceous structures (capsids) are nevertheless susceptible to mucosal environmental stress factors. We cross-linked multiple capsid surface amino acid residues using homobifunctional polyethylene glycol tethers to improve the persistence and survival of the capsid to model mucosal stressors. Surface cross-linking enhanced the stability of VLPs assembled from Acinetobacter phage AP205 coat proteins in low pH (down to pH 4.0) and high protease concentration conditions (namely, in pig and mouse gastric fluids). Additionally, it increased the stiffness of VLPs under local mechanical indentation applied using an atomic force microscopy cantilever tip. Small angle X-ray scattering revealed an increase in capsid diameter after cross-linking and an increase in capsid shell thickness with the length of the PEG cross-linkers. Moreover, surface cross-linking had no effect on the VLPs' mucus translocation and accumulation on the epithelium of in vitro 3D human nasal epithelial tissues with mucociliary clearance. Finally, it did not compromise VLPs' function as vaccines in mouse subcutaneous vaccination models. Compared to PEGylation without cross-linking, the stiffness of surface cross-linked VLPs were higher for the same length of the PEG molecule, and also the lifetimes of surface cross-linked VLPs were longer in the gastric fluids. Surface cross-linking using macromolecular tethers, but not simple conjugation of these molecules, thus offers a viable means to enhance the resilience and survival of VLPs for mucosal applications.

Nanocellulose‐Based Ink for Vertically 3D Printing Micro‐Architectures with High‐Resolution

AbstractNanocellulose has become an important renewable component for composite inks, owing to its desirable physical properties, reinforcing capabilities, and tunable self‐assembly behavior. However, it is difficult to improve the rheological performance of the nanocellulose‐based composite to meet the requirement for 3D printing high resolution microarchitectures. Herein, a strategy is proposed that incorporation of amphiphilic molecular surfactant into nanocellulose gel can increase the molecular interaction via hydrophobic bonds and enhance the ink viscoelasticity. Following the design, a composite ink is formulated by adding xylan and Nonaethylene glycol monododecyl ether (C12E9) within nanocellulose gel. A new printing program is designed to achieve vertical writing of the composite ink and obtain free‐standing micropillars and microhemispheres with high resolution in dozens of micrometers. The microhemisphere on an atomic force microscope (AFM) cantilever can be used as colloidal probe. This work proves that nanocellulose composite ink is a candidate for 3D printing functional devices with special microstructures.

Quantification of Phosphatidylserine Molecules on the Surface of Individual Cells Using Single-Molecule Force Spectroscopy.

Identification of the phosphatidylserine (PS) discrepancies occurring on the cellular membrane during apoptotic processes is of the utmost importance. However, monitoring the quantity of PS molecules in real-time at a single-cell level currently remains a challenging task. Here, we demonstrate this objective by leveraging the specific binding and reversible interaction exhibited by the zinc(II) dipyridinamine complex (ZnDPA) with PS. Lipoic acid-functionalized ZnDPA (LP-ZnDPA) was subsequently immobilized onto the surface of an atomic force microscopy cantilever to form a force probe, ALP-ZnDPA, enabling a PS-specific dynamic imaging and detection mode. By utilizing this technique, we can not only create a heat map of the expression level of PS with submicron resolution but also quantify the number of molecules present on a single cell's surface with a detection limit of 1.86 × 104 molecules. The feasibility of the proposed method is demonstrated through the analysis of PS expression levels in different cancer cell lines and at various stages of paclitaxel-induced apoptosis. This study represents the first application of a force probe to quantify PS molecules on the surface of individual cells, providing insight into dynamic changes in PS content during apoptosis at the molecular level and introducing a novel dimension to current detection methodologies.

Reconstruction of shear force in Atomic Force Microscopy from measured displacement of the cone-shaped cantilever tip

<abstract><p>We present a new comprehensive mathematical model of the cone-shaped cantilever tip-sample interaction in Atomic Force Microscopy (AFM). The importance of such AFMs with cone-shaped cantilevers can be appreciated when its ability to provide high-resolution information at the nanoscale is recalled. It is an indispensable tool in a wide range of scientific and industrial fields. The interaction of the cone-shaped cantilever tip with the surface of the specimen (sample) is modeled by the damped Euler-Bernoulli beam equation $ \rho_A(x)u_{tt} $ $ +\mu(x)u_{t}+(r(x)u_{xx}+\kappa(x)u_{xxt})_{xx} = 0 $, $ (x, t)\in (0, \ell)\times (0, T) $, subject to the following initial, $ u(x, 0) = 0 $, $ u_t(x, 0) = 0 $ and boundary, $ u(0, t) = 0 $, $ u_{x}(0, t) = 0 $, $ \left (r(x)u_{xx}(x, t)+\kappa(x)u_{xxt} \right)_{x = \ell} = M(t) $, $ \left (-(r(x)u_{xx}+\kappa(x)u_{xxt})_x\right)_{x = \ell} = g(t) $ conditions, where $ M(t): = 2h\cos \theta\, g(t)/\pi $ is the moment generated by the transverse shear force $ g(t) $. Based on this model, we propose an inversion algorithm for the reconstruction of an unknown shear force in the AFM cantilever. The measured displacement $ \nu(t): = u(\ell, t) $ is used as additional data for the reconstruction of the shear force $ g(t) $. The least square functional $ J(F) = \frac{1}{2}\Vert u(\ell, \cdot)-\nu \Vert_{L^2(0, T)}^2 $ is introduced and an explicit gradient formula for the Fréchet derivative of the cost functional is derived via the weak solution of the adjoint problem. Additionally, the geometric parameters of the cone-shaped tip are explicitly contained in this formula. This enables us to construct a gradient based numerical algorithm for the reconstructions of the shear force from noise free as well as from random noisy measured output $ \nu (t) $. Computational experiments show that the proposed algorithm is very fast and robust. This creates the basis for developing a numerical "gadget" for computational experiments with generic AFMs.</p></abstract>

Enhancing nanoscale viscoelasticity characterization in bimodal atomic force microscopy.

Polymeric, soft, and biological materials exhibit viscoelasticity, which is a time dependent mechanical response to deformation. Material viscoelasticity emerges from the movement of a material's constituent molecules at the nano- and microscale in response to applied deformation. Therefore, viscoelastic properties depend on the speed at which a material is deformed. Recent technological advances, especially in atomic force microscopy (AFM), have provided tools to measure and map material viscoelasticity with nanoscale resolution. However, to obtain additional information about the viscoelastic behavior of a material from such measurements, theoretical grounding during data analysis is required. For example, commercially available bimodal AFM imaging maps two different viscoelastic properties of a sample, the storage modulus, E', and loss tangent, tan δ, with each property being measured by a different resonance frequency of the AFM cantilever. While such techniques provide high resolution maps of E' and tan δ, the different measurement frequencies make it difficult to calculate key viscoelastic properties of the sample such as: the model of viscoelasticity that describes the sample, the loss modulus, E'', at either frequency, elasticity E, viscosity η, and characteristic response times τ. To overcome this difficulty, we present a new data analysis procedure derived from linear viscoelasticity theory. This procedure is applied and validated by performing amplitude modulation-frequency modulation (AM-FM) AFM, a commercially available bimodal imaging technique, on a styrene-butadiene rubber (SBR) with known mechanical behavior. The new analysis procedure correctly identified the type of viscoelasticity exhibited by the SBR and accurately calculated SBR E, η, and τ, providing a useful means of enhancing the amount of information gained about a sample's nanoscale viscoelastic properties from bimodal AFM measurements. Additionally, being derived from fundamental models of linear viscoelasticity, the procedure can be employed for any technique where different viscoelastic properties are measured at different and discrete frequencies with applied deformations in the linear viscoelastic regime of a sample.