Atomic Force Microscope Cantilever Research Articles

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.

Exploring the Surface Oxidation and Environmental Instability of 2H-/1T'-MoTe2 Using Field Emission-Based Scanning Probe Lithography.

An unconventional approach for the resistless nanopatterning 2H- and 1T'-MoTe2 by means of scanning probe lithography is presented. A Fowler-Nordheim tunneling current of low energetic electrons (E = 30-60eV) emitted from the tip of an atomic force microscopy (AFM) cantilever is utilized to induce a nanoscale oxidation on a MoTe2 nanosheet surface under ambient conditions. Due to the water solubility of the generated oxide, a direct pattern transfer into the MoTe2 surface can be achieved by a simple immersion of the sample in deionized water. The tip-grown oxide is characterized using Auger electron and Raman spectroscopy, revealing it consists of amorphous MoO3 /MoOx as well as TeO2 /TeOx . With the presented technology in combination with subsequent AFM imaging it is possible to demonstrate a strong anisotropic sensitivity of 1T'-/(Td )-MoTe2 to aqueous environments. Finally the discussed approach is used to structure a nanoribbon field effect transistor out of a few-layer 2H-MoTe2 nanosheet.

Simultaneous quantification of Young’s modulus and dispersion forces with nanoscale spatial resolution

Many advances in polymers and layered materials rely on a precise understanding of the local interactions between adjacent molecular or atomic layers. Quantifying dispersion forces at the nanoscale is particularly challenging with existing methods often time consuming, destructive, relying on surface averaging or requiring bespoke equipment. Here, we present a non-invasive method able to quantify the local mechanical and dispersion properties of a given sample with nanometer lateral precision. The method, based on atomic force microscopy (AFM), uses the frequency shift of a vibrating AFM cantilever in combination with established contact mechanics models to simultaneously derive the Hamaker constant and the effective Young’s modulus at a given sample location. The derived Hamaker constant and Young’s modulus represent an average over a small (typically <100) number of molecules or atoms. The oscillation amplitude of the vibrating AFM probe is used to select the length-scale of the features to analyse, with small vibrations able to resolve the contribution of sub-nanometric defects and large ones exploring effectively homogeneous areas. The accuracy of the method is validated on a range of 2D materials in air and water as well as on polymer thin films. We also provide the first experimental measurements of the Hamaker constant of HBN, MoT2, WSe2 and polymer films, verifying theoretical predictions and computer simulations. The simplicity and robustness of the method, implemented with a commercial AFM, may support a broad range of technological applications in the growing field of polymers and nanostructured materials where a fine control of the van der Waals interactions is crucial to tune their properties.

Graphene‐Enhanced Single Ion Detectors for Deterministic Near‐Surface Dopant Implantation in Diamond

AbstractDiamond color centers with applications to single photon sources, quantum computation, and magnetic field sensing down to the nanoscale have been investigated using ensembles of near‐surface implanted atoms. Deterministic ion implantation for ions stopping between 30 and 130 nm deep is demonstrated by configuring an electronic‐grade diamond substrate with a biased surface graphene electrode connected to charge sensitive electronics. The thin graphene electrode has a negligible surface dead layer, so implantation events are signaled from the drift of electron–hole pairs induced by the dissipation of ion kinetic energy in the substrate. Ion beam induced charge maps from a scanned 1 MeV He microbeam show the graphene electrode is highly effective with a charge collection efficiency up to 86% compared to an O‐terminated diamond surface of 30%. For lower energy ions, applicable to near surface implantation, single ion detection confidence is &gt;99(1)% for 19.5 keV H and 85(2)% for 24 keV N ions to allow maps of device surface features by employing a focused ion beam microscope or an atomic force microscope cantilever incorporating a nanostencil beam collimator. In the near‐term, this system can be used to investigate the annealing dynamics for the conversion of single implanted ions into diamond color centers.

Thermal induced deflection in atomic force microscopy cantilevers: analysis & solution

Atomic force microscopy (AFM) cantilevers are commonly made from two material layers: a reflective coating and structural substrate. Although effective, this can result in thermally induced cantilever deflection due to ambient and local temperature changes. While this has been previously documented, key aspects of this common phenomenon have been overlooked. This work explores the impact of thermally induced cantilever deflection when in- and out-of-contact, including the topographic scan artefacts produced. Scanning thermal microscopy probes were employed to provide direct cantilever temperature measurement from Peltier and microheater sources, whilst permitting cantilever deflection to be simultaneously monitored. Optical lever-based measurements of thermal deflection in the AFM were found to vary by up to 250% depending on the reflected laser spot location on the cantilever. This highlights AFM’s inherent inability to correctly measure and account for thermal induced cantilever deflection in its feedback system. This is particularly problematic when scanning a tip in-contact with the surface, when probe behaviour is closer mechanically to that of a bridge than a cantilever regarding thermal bending. In this case, measurements of cantilever deflection and inferred surface topography contained significant artefacts and varied from negative to positive for different optical lever laser locations on the cantilevers. These topographic errors were measured to be up to 600 nm for a small temperature change of 2 K. However, all cantilevers measured showed a point of consistent, complete thermal deflection insensitivity 55% to 60% along their lengths. Positioning the reflected laser at this location, AFM scans exhibited improvements of up-to 97% in thermal topographic artefacts relative to other laser positions.

On the Nonlinear Stochastic Dynamics of an Atomic Force Microscope Cantilever

AbstractAtomic force microscopy (AFM) serves characterization and actuation in nanoscale applications. We study the stochastic dynamics of an AFM cantilever under tip-sample interactions represented by the Lennard–Jones and Morse potential energy functions. In both cases, we also study the contrasting dynamic effects of additive (external) and multiplicative (internal) noise. Moreover, for multiplicative noise, we study the two sub-cases arising from the Itô and Stratonovich interpretations of stochastic integrals. In each case, we also investigate the stochastic stability of the system by tracing the time evolution of the maximal Lyapunov exponent. Additionally, we obtain stationary probability densities for the unforced dynamics using stochastic averaging.

Inner-paddled atomic force microscopy cantilever for rapid mechanical mapping

Mechanical characterization methods at the nanoscale are of critical importance for many fields including nanomaterials, micro/nano devices and nanomechanics. As a key tool in nanotechnology, atomic force microscopy (AFM) is widely used due to its high-resolution topography imaging capabilities, and is also recognized as a useful platform for nanoscale mechanical characterization. Contact-resonance AFM, which modulates the tip-sample contact with ultrasonic frequencies and then analyzes the cantilever’s resonance responses, is an important AFM method for viscoelastic characterization. However, contact-resonance AFM requires the cantilever’s contact-resonance frequency and quality factor values to quantify the elastic modulus and loss tangent of the sample. This requires time-consuming frequency sweep, which makes a quantitative scanning impractical, therefore only single-point quantitative measurement and qualitative single-frequency scanning are usually applied. To address this issue, here we present an AFM cantilever design with an integrated inner-paddle substructure, which provides an eigenmode whose resonance keeps consistent, but whose resonance amplitude varies with varying contact stiffness. With this probe, it is hoped to quantify the elastic properties of the sample with fast single-frequency amplitude imaging.

Nanoscale Dynamics of Streptococcal Adhesion to AGE-Modified Collagen

The adhesion of initial colonizers such as Streptococcus mutans to collagen is critical for dentinal and root caries progression. One of the most described pathological and aging-associated changes in collagen—including dentinal collagen—is the generation of advanced glycation end-products (AGEs) such as methylglyoxal (MGO)–derived AGEs. Despite previous reports suggesting that AGEs alter bacterial adhesion to collagen, the biophysics driving oral streptococcal attachment to MGO-modified collagen remains largely understudied. Thus, the aim of this work was to unravel the dynamics of the initial adhesion of S. mutans to type I collagen in the presence and absence of MGO-derived AGEs by employing bacterial cell force spectroscopy with atomic force microscopy (AFM). Type I collagen gels were treated with 10 mM MGO to induce AGE formation, which was characterized with microscopy and enzyme-linked immunosorbent assay. Subsequently, AFM cantilevers were functionalized with living S. mutans UA 159 or Streptococcus sanguinis SK 36 cells and probed against collagen surfaces to obtain force curves displaying bacterial attachment in real time, from which the adhesion force, number of events, Poisson analysis, and contour and rupture lengths for each individual detachment event were computed. Furthermore, in silico computer simulation docking studies between the relevant S. mutans UA 159 collagen-binding protein SpaP and collagen were computed, in the presence and absence of MGO. Overall, results showed that MGO modification increased both the number and adhesion force of single-unbinding events between S. mutans and collagen, without altering the contour or rupture lengths. Both experimental and in silico simulations suggest that this effect is due to increased specific and nonspecific forces and interactions between S. mutans UA 159 and MGO-modified collagen substrates. In summary, these results suggest that collagen alterations due to aging and glycation may play a role in early bacterial adherence to oral tissues, associated with conditions such as aging or chronic hyperglycemia, among others.

Self-Assembling Nanodiscs Technology Exploration with Single-Molecule Biophysics Experimentation using Site-Specific Attachment Atomic Force Microscopy

The relationship between membrane proteins and functional cells is not yet fully understood, in large part due to the lack of knowledge about the structure and dynamics of membrane proteins. Because of the recent advancement of biotechnology, the visualization of membrane protein dynamics and energetics has progressed significantly, in large part due to nanodisc technology. Nanodiscs allow for the formation of a native environment for membrane proteins, which is essential to learning more about their structure. Atomic force microscopy (AFM) allows for the precise imaging of membrane proteins as well as the utilization of single-molecule force spectroscopy (SMFS). When completing single-molecule experimentation, it is crucial that the covalent attachment of the probe is completed, because it allows for hundreds of force-extension traces from a single molecule to be completed. Another essential aspect of site-specific attachment is passivation is necessary for unwanted interactions between the AFM cantilever tip and a single probe molecule. The focus of my senior thesis is to work with the optimization of nanodisc technology formation embedded with the membrane protein bacteriorhodopsin (bR). The bR was inserted into nanodiscs in both wild-type and c-terminal cysteine transformed to allow for site-specific labeling. The formation of nanodiscs with c-terminal cysteine bR was then labeled with DBCO-Maleimide tagging to allow for covalent connections when utilizing AFM SMFS. Altogether, this work shows a methodology for the optimization of nanodisc formation containing c-terminal cysteine bR membrane protein and warrants further investigation utilizing AFM imaging and SMFS with varying conditions of site-specific spectroscopy to target the development of protein-membrane dynamics. To see the complete thesis, please visit https://scholar.colorado.edu/concern/undergraduate_honors_theses/xg94hq786.

Lateral force separation of biopolymers using an atomic force microscope.

The lateral force separation of long chain biomolecules is demonstrated using an atomic force microscope (AFM). This is achieved by using an AFM tip to pull molecules away from the edge of a nanofluidic solution. By monitoring the torsion on the AFM cantilever, a characteristic force-distance signal is produced when long chain molecules separate and detach from the solvent edge. This lateral force separation using AFM (LFS-AFM) is demonstrated on egg albumin proteins and synthetic DNA strands. The detected length of the protein and nucleotide biopolymers was consistent with their calculated molecular contour length. LFS AFM provides separation and detection of single polymer strands that has potential applications in biochemical analysis, paleontology, and life detection.

Hair surface interactions against different chemical functional groups as a function of environment and hair condition.

The nature and magnitude of molecular interactions on hair surfaces underpin the design of formulated products, of which the application involves a competitive adsorption process between cationic surfactants, fatty alcohols and surface actives such as silicone. The knowledge of molecular interaction with hair surface will not only provide insight on the surface binding affinity but also offer an effective methodology in characterizing surface deposits. Untreated and chemically treated hair samples were treated with either conditioner chassis alone (gel network) or conditioner chassis plus silicone (chassis/TAS). Hair surface interactions against four different chemical functional groups, namely methyl (-CH3 ), acid (-COOH), amine (-NH2 ) and hydroxyl (-OH), were quantified in both ambient and aqueous environment using Chemical Force Microscopy, a method based on atomic force microscopy (AFM). Surface adhesion on hair in ambient is dominated by capillary force that is determined by both the wettability of hair fibre (hydrophobic vs. hydrophilic), presence of any deposits and the chemical functionality of the AFM cantilever. Capillary force is diminished and replaced by electrostatic interaction when polar groups are present on both hair and AFM cantilever. A distinctively different force, hydrophobic interaction, plays a major role when virgin hair and hydrophobic functionalized AFM cantilever make contact in water. Results acquired by AFM cantilevers of different functional groups show that hydrophobic interaction is a key driver for deposition on virgin hair, whilst electrostatic interaction is the most important one for bleached hair. Interfacial conformation of chassis components upon deposition is determined by the hair surface properties. Our study highlights the possibility of a range of polar groups, not necessarily negatively charged, on the damaged hair. Unlike conventional surface chemical analysis method, it is possible to quantitatively evaluate the interfacial conformation of deposited surface actives on hair, which identifies the target moieties for conditioning products on different types of hair.

Air/Water Interface Rheology Probed by Thermal Capillary Waves.

Atomic force microscopy (AFM) was used to study the interfacial rheology of air/water interfaces by investigating the thermal capillary fluctuations of surfactant-loaded interfaces. These interfaces are formed by depositing an air bubble on a solid substrate immersed in a surfactant (Triton X-100) solution. An AFM cantilever, in contact with the north pole of the bubble, probes its thermal fluctuations (amplitude of the vibration versus the frequency). The measured power spectral density of the nanoscale thermal fluctuations presents several resonance peaks corresponding to the different vibration modes of the bubble. The measured damping versus the surfactant concentration of each mode presents a maximum and then decreases to a saturation value. The measurements are in good agreement with the model developed by Levich for the damping of capillary waves in the presence of surfactants. Our results show that the AFM cantilever in contact with a bubble is a powerful tool to probe the rheological properties of air/water interfaces.

Characterization of adhesion strength between carbon nanotubes and cementitious materials

Multi-walled carbon nanotube (MWCNT) and carbon nanofiber (CNF) additions increase the elastic modulus, flexural strength, and toughness of Portland cement concrete. However, the interaction mechanism between cement constituents and these nanomaterials is not fully understood. A modified MWCNT-coated atomic force microscopy (AFM) probe is developed by coating a silica particle with oxidized MWCNT through layer-by-layer assembly and adhering it to a tipless AFM cantilever. The probe allows measurement of adhesion between MWCNT and the substrate with a force control procedure. SEM-EDS is acquired in the same region as AFM measurements through a benchmarking scheme to correlate chemistry with the measured adhesion. Statistical deconvolution shows C–S–H regions have lower adhesion to MWCNT than intermixed regions (C–S–H/Clinker). Furthermore, in C–S–H regions, the normalized adhesion strength increases with calcium concentration. This result is due to the higher interaction between the oxygen functional groups in the MWCNT surface and the calcium in the substrate.

Directional Energy Transfer in a Coupled Symmetrical Multifrequency Atomic Force Microscope Cantilever

Directional Energy Transfer in a Coupled Symmetrical Multifrequency Atomic Force Microscope Cantilever

Modelling and Parameter Estimation of Cartridge Probes for Atomic Force Microscopy

A critical challenge for industrial Atomic Force Microscopes (AFM) is automatic selection of appropriate probes required for the scanning and measurement tasks (or sequences of tasks). This challenge can be addressed by specially assigned multi-probe cartridge holders with replaceable probes. Cantilevers with different spring constants and resonant frequencies are required to make specific AFM measurements. In this paper the classical PDE of lateral vibration of bars of variable cross-sections to model dynamics of the AFM cantilevers and calculate their spring constants is used. In addition, utilizing Rayleigh method, resonant frequency can be estimated. Using software based on these models, probe designer can interactively select appropriate geometric and material parameters to achieve desired spring constants and resonant frequencies of the cantilevers to be assembled in the multi-probe cartridge holders.

Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach

Kelvin probe force microscopy (KPFM) is a powerful tool for studying contact electrification (CE) at the nanoscale, but converting KPFM voltage maps to charge density maps is nontrivial due to long-range forces and complex system geometry. Here we present a strategy using finite-element method (FEM) simulations to determine the Green's function of the KPFM probe/insulator/ground system, which allows us to quantitatively extract surface charge. Testing our approach with synthetic data, we find that accounting for the atomic force microscope (AFM) tip, cone, and cantilever is necessary to recover a known input and that existing methods lead to gross miscalculation or even the incorrect sign of the underlying charge. Applying it to experimental data, we demonstrate its capacity to extract realistic surface charge densities and fine details from contact-charged surfaces. Our method gives a straightforward recipe to convert qualitative KPFM voltage data into quantitative charge data over a range of experimental conditions, enabling quantitative CE at the nanoscale.

6H–SiC Nanoparticles Integrated with an Atomic Force Microscope for Scanning Quantum Sensors

We fabricate a quantum magnetic field sensor based on the silicon vacancy centers in 6H–SiC using atomic force microscopy technique. The quantum sensing is based on optically detected magnetic resonance. To implement quantum scanning microscopy, we attach a single 6H–SiC nanoparticle on the tip of the atomic force microscopy cantilever. Our quantum sensors are characterized using optical spectroscopy and electron microscopy. The use of such probes significantly reduces the cost of a quantum sensor and enables the extension of quantum scanning microscopes to physiological and conductive environments.

Plastically Bendable Organic Crystals for Monolithic and Hybrid Micro‐Optical Circuits

AbstractFluorescent plastically bendable crystals are a promising alternative to silicon‐based materials for fabricating photonic integrated circuits, owing to their optical attributes and mechanical compliance. Mechanically bendable plastic organic crystals are rare. Their formation requires anisotropic intermolecular interactions and slip planes in the crystal lattice. This work presents three fluorescent plastically bendable crystalline materials namely, 2‐((E)‐(6‐methylpyridin‐2‐ylimino)methyl)‐4‐chlorophenol (SB1), 2‐((E)‐(6‐methylpyridin‐2‐ylimino)methyl)‐4‐bromophenol (SB2), and 2‐((E)‐(6‐Bromopyridin‐2‐ylimino)methyl)‐4‐bromophenol (SB3) molecules. The crystal plasticity in response to mechanical stress facilitates the fabrication of various monolithic and hybrid (with a tip‐to‐tip coupling) photonic circuits using mechanical micromanipulation with an atomic force microscope cantilever tip. These plastically bendable crystals act as active (self‐guiding of fluorescence) and passive waveguides both in straight and extremely bent (U‐, J‐, and O‐shaped) geometries. These microcircuits use active and passive waveguiding principles and reabsorbance and energy‐transfer mechanisms for their operation, allowing input‐selective and direction‐specific signal transduction.

Nanoscale friction force on thin films of polymer blends and silane layers matrix

In this paper, nanoscale friction measurements are obtained from the Atomic Force Microscope (AFM) cantilever tip interaction with the layer of polymer blends of Polymethyl Methacrylate (PMMA)/ Polystyrene (PS) (2:1 and 1:2 ratios), and silane (C8, C12 and C18) layers at different proportion. The contrast of these polymer blends is investigated from the simultaneous recording of the topographic and lateral forces imaging. The resonance frequency excitation method and the wedge calibrations are used to quantify the normal and the lateral force constant respectively. Then, the quantitative frictional forces are calculated from the obtained normal and lateral force constants. The nanonewton (nN) frictions are found to be dependent on the nano-dynamic properties of the tip-sample interaction, the proportion of the polymer matrix and silane layers, and the scan speed.