Transfer function analysis of a surface coupled atomic force microscope cantilever system

Current methods to study atomic force microscope (AFM) cantilever dynamics use model simplification or are based on the non-trivial solution of the equation of motion. As an alternative method, transfer function analysis gives a more complete description of system dynamics. In this work a transfer function study of two different AFM configurations, the point force and base driven cantilever, is presented. Exact analytical expressions of the infinite dimensional transfer function are derived for cantilever deflection and slope along the cantilever. Frequency response and transfer function infinite product expansion are obtained for the case where system outputs are set at the free end of the cantilever. The frequency response reflects the full complexity of cantilever dynamics affected by the presence of an infinite number of poles and zeros. An analytical expression for all the zeros and poles of the system is obtained. From the frequency response and pole-zero investigations it is shown how cantilever actuation and output measurement affect AFM operation and cantilever dynamics modelling. Transfer function analysis of AFM cantilevers opens the possibility of model based AFM operation to increase imaging and manipulation performance.

The measurement of intermolecular forces at the liquid-solid interface is key to many studies of electrochemistry, wetting, catalysis, biochemistry, and mechanobiology. The atomic force microscope (AFM) is unique in its ability to measure and map these forces with nanometer resolution using the oscillating sharp tip of an AFM cantilever. These surface forces are only measured by observing the changes they induce in the dynamics of the resonant AFM probe. However, AFM cantilever dynamics at this interface can be significantly different when compared to air/vacuum environments due to the nature of nanoscale forces at the interface and the low-quality factors in liquids. In this work, we study the nonlinear dynamics of magnetically excited AFM microcantilevers on graphite and mica immersed in deionized water, high-concentration buffers, and methanol. By combining theory and experiments, a wealth of nonlinear dynamical phenomena such as superharmonic resonance, hysteretic jumps, and multimodal interactions are demonstrated and their dependence on hydration/solvation forces is clarified. These results are expected to aid ongoing efforts to link liquid-solid interface properties to cantilever dynamics and lead to accurate interpretation of data from experiments.

This paper reports a thermal sensor assembled by two multi-walled carbon nanotubes (MWCNTs) inside a field emission scanning electron microscope (FESEM) which constructed a probe tip in order to detect the local environment of single cell. An atomic force microscope (AFM) cantilever was used for substrate which is composed by Si3N4, and double side was covered by gold layer. Two MWCNTs were assembled to both side of AFM cantilever individually by employing a nanorobotic manipulation. Then another AFM cantilever was used as an end effector to manipulate the MWCNTs to touch, and used electron beam induced deposition (EBID) to bonding the two MWCNTs. The MWCNTs probe thermal sensor was evaluation inside a thermostated container for 30°C to 60°C. The experimental results show the positive characteristics of the temperature coefficient of resistance (TCR). We hope this result will be used rapidly in future. © 2012 IEEE.

Calibration of AFM cantilever stiffness: a microfabricated array of reflective springs

We investigate in theory and experiment the intermittent contact interaction between an atomic force microscope (AFM) cantilever and a nanowire under ambient conditions. The nanowire is modeled as a spring reacting instantaneously to any change of the force between the wire and the cantilever. This implies that the cantilever is subject to an “effective” force-distance relation, containing not only the surface forces but also the deflection of the nanowire. Experimentally, CVD-grown tin oxide nanowires and lithographically structured silicon nanowire arrays were investigated by intermittent contact AFM. By comparison of experimental and simulated distance-dependent resonance curves it is found that the nanowires behave like “fast nanosprings” and that the adhesion force is one of the key factors determining distance-dependent resonance curves. The results are fully applicable to a scenario in which a cantilever equipped by a nanowire interacts with a surface.

Mechanical characterization of nanofibers using a nanomanipulator and atomic force microscope cantilever in a scanning electron microscope

This paper presents a study on the dynamic response of an atomic force microscope (AFM) cantilever with a solid state heating element in liquid and its application for measuring the temperature-dependent viscosity of liquids. A finite difference model (FDM) predicts the frequency response of a heated cantilever immersed in liquid and calibrates the liquid viscosity from the measured cantilever resonant frequency (f0) at different cantilever heater temperatures. The technique measures a wide range of liquid viscosities (0.0005–0.005 kgm−1s−1) at temperatures ranging from 20 to 55 °C with high sensitivity (7.1 × 10−7 kgm-1s-1/Hz for 50 wt% ethylene glycol/water). The measurement requires heating a liquid volume of about 10 nl, which is more than 1000X smaller than other microcantilever-based viscosity measurements.

In this study we present measurements of the hydrodynamic force exerted on a glass sphere glued to an atomic force microscopy (AFM) cantilever approaching a mica surface in water. A large sphere was used to reduce the impact of the cantilever beam on the measurement. An AFM cantilever with large stiffness was used to accurately determine the actual contact position between the sphere and the sample surface. The measured hydrodynamic force with different approach velocities is in good agreement with the Taylor force calculated in the lubrication theory with the no-slip boundary conditions, which verifies that there is no boundary slip on the glass and mica surfaces. Moreover, a detailed procedure of how to subtract the electrostatic double-layer force is presented.

An atomic force microscope (AFM) cantilever based coordinate measuring probe applicable for true three dimensional measurements of microstructures is presented. The probe has a shaft glued to a commercial AFM cantilever and a probing sphere located at the free end of the shaft. A conventional optical lever method is applied to detect the bending, torsion, and the dynamic behavior of the AFM cantilever which will change dramatically when the probe sphere is in proximity to the object to be measured. The probe has advantages such as small probing force (<1μN), high probing sensitivity allowing nanometer measurement resolution, easy exchange of probing elements, and low cost. Measurements of a microgear and a fuel injection nozzle using the developed probe are demonstrated, indicating its promising application potential.

This paper explores strategies for fabricating and maintaining a sharp atomic force microscope (AFM) tip suitable for AFM data storage applications. To this end, AFM cantilevers have been incorporated into micromachined sled carriers and air-bearing sliders. These supports act to limit the maximum loading force on the AFM tip and allow for improved vibration immunity for the AFM cantilever in comparison to macroscopic loading schemes. Readback from a patterned rotating disk has been demonstrated using these devices. Silicon-carbide AFM cantilevers with diamond tips have been fabricated in a process compatible with that of the sleds and sliders. Molded silicon-nitride tips defined by the intersection of three surfaces have also been fabricated for AFM cantilevers. The molds for plane-plane-concave tips are defined by two silicon {111} planes and a silicon-dioxide curved surface. By geometry, the three surfaces necessarily have a unique intersection point, which may improve the consistency in sharpness of these tips relative to conventional pyramidal tips.

Nanomechanical test instruments can precisely measure force and displacement and produce repeatable load-unload curves that can be used in characterizing mechanical behaviour at the nanoscale. In this study, a newly developed translucent nanomechanical test instrument was used in deriving reproducible stiffness values for ultra nano crystalline diamond (UNCD)-made atomic force microscope (AFM) cantilevers that are used for mechanical properties characterization of DLC films. The instrument which is calibrated according to the ISO-14577 standard is integrated with nano/micropositioners and multi-view optical microscopes to facilitate precise manipulation of those AFM cantilevers that were dozens of micrometers in size. Experimental results on UNCD-made AFM cantilever stiffness measurements are provided and compared with theoretical and batch production values.

MRI-based cerebrovascular reactivity using transfer function analysis reveals temporal group differences between patients with sickle cell disease and healthy controls.

ObjectiveThe 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.MethodsUntreated 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).ResultsSurface 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.ConclusionResults 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.

The necessity for development of new drug delivery systems for poorly soluble drugs and therapeutics which targets directly the pathogenic area requires the design of complex systems in nanoscale. Atomic Force Microscopy (AFM) since its discovery offers a unique tool to develop novel drug delivery systems. Its capability to investigate, characterise surfaces and measure forces with spatial resolution at nano-scale respectively contributes to develop and analyse pharmaceutical systems and biomedical devices with complex structures and chemistries. Specifically, polymeric nanoparticles and liposomal drug formulation have been studied extensively by using AFM where their size and morphology where revealed [1]. However, apart from topographical information, AFM can provide details on the local compositions of the sample. There are many modes that can be used to achieve this but the most common is to monitor the phase shift of the oscillating cantilever in tapping mode Such ‘Phase imaging’ can be used to detect nanoscale variation in composition, adhesion, friction, viscoelasticity, and other properties of the materials. Changes in the phase lag often indicate changes in the properties of the sample surface. Phase imaging has proved an extremely useful tool for pharmaceutical characterization. Phase imaging has been used to reveal polymeric forms from single crystal measurements [2] to confirm phase separation of two copolymers for drug delivery [3], to establish the stability of the formulation on different environments [4] and to identify formation of amorphous domains during milling of crystalline salbutamol [5]. Moreover, the ability of AFM to operate on different conditions of temperature humidity and in liquid allows studying the kinetics of range of phenomena. An interesting work was published from Miyazaki et al. where the crystal growth rate of Nifedipine, dispersed in PEG polymer matrix, was quantified [6]. Also, the dissolution process of aspirin on different facets of the crystal was studied by Danesh et al . showing their differences in dissolution rate [7]. The ability of AFM to measure force measurements have been used to investigate interactions among the different compounds in the formulation. To achieve this, the AFM cantilever is modified by attaching a particle directly onto the probe tip and is brought in contact with the substrate of interest, the force required to separate them is the measure of their adhesion. This application of AFM has been used extensively to aerosol drug formulation where the API is associated with a carrier which is released in the site of actions. For instance, AFM has been used to investigate the adhesion force of salbutamol with different excipients [8]. Moreover, localised surface energy and young’s modulus of various compounds have been measured. For example, Young’s modulus were derived from both PLA and PLA/everolimus directly from stent surface on different temperatures. The results showed that everolimus does not affect the mechanical properties of PLA up to 1/1 (w/w) drug loading of the mixture. Also, a significant drop of the Young’s modulus in solution was observed at 36°C, suggests that in vivo the Tg of the polymer is below body temperature [9]. Furthermore, force measurements have been used to identify the encapsulation the efficiency of liposomes as the rigidity of encapsulating liposomes is higher [10].

Influence of Poisson's ratio variation on lateral spring constant of atomic force microscopy cantilevers