Calibration of atomic force microscope cantilevers using standard and inverted static methods assisted by FIB-milled spatial markers

A study on the mechanical properties of a carbon nanotube probe with a high aspect ratio

Carbon nanotube (CNT) probes are used in atomic force microscopes (AFMs) for high-resolution imaging, especially in the measurement of high aspect ratio micro/nano structures. Due to the use of a longer CNT tip leading to the degradation of image resolution, researchers have used several methods to cut CNTs. However, the principle of the selection of the cutting length has hardly been reported. Moreover, the influence of the effect of size on the mechanical properties of a CNT tip is not fully understood. In this study, an accurate model of finite element simulations is constructed on the basis of scanning electron microscopy data to investigate the mechanical properties of a CNT probe. An elastic model is employed to study the factors that influence the critical buckling force at the CNT tip during the measurement process. The calculation shows that the mechanical stiffness of the probe is affected by the diameter and the length-to-diameter ratio of the CNT tip. The changes in the von Mises stress at the bond between the AFM probe and the CNT tip as well as the variation of the strain energy at the CNT tip are discussed. It is hoped that this study will provide guidance for the selection of the cutting length of CNT-AFM probes and propose a basis for probe selection and design in practical measurements.

Characterisation of the Material and Mechanical Properties of Atomic Force Microscope Cantilevers with a Plan-View Trapezoidal Geometry

Cantilever devices have found applications in numerous scientific fields and instruments, including the atomic force microscope (AFM), and as sensors to detect a wide range of chemical and biological species. The mechanical properties, in particular, the spring constant of these devices is crucial when quantifying adhesive forces, material properties of surfaces, and in determining deposited mass for sensing applications. A key component in the spring constant of a cantilever is the plan-view shape. In recent years, the trapezoidal plan-view shape has become available since it offers certain advantages to fast-scanning AFM and can improve sensor performance in fluid environments. Euler beam equations relating cantilever stiffness to the cantilever dimensions and Young’s modulus have been proven useful and are used extensively to model cantilever mechanical behaviour and calibrate the spring constant. In this work, we derive a simple correction factor to the Euler beam equation for a beam-shaped cantilever that is applicable to any cantilever with a trapezoidal plan-view shape. This correction factor is based upon previous analytical work and simplifies the application of the previous researchers formula. A correction factor to the spring constant of an AFM cantilever is also required to calculate the torque produced by the tip when it contacts the sample surface, which is also dependent on the plan-view shape. In this work, we also derive a simple expression for the torque for triangular plan-view shaped cantilevers and show that for the current generation of trapezoidal plan-view shaped AFM cantilevers, this will be a good approximation. We shall apply both these correction factors to determine Young’s modulus for a range of trapezoidal-shaped AFM cantilevers, which are specially designed for fast-scanning. These types of AFM probes are much smaller in size when compared to standard AFM probes. In the process of analysing the mechanical properties of these cantilevers, important insights are also gained into their spring constant calibration and dimensional factors that contribute to the variability in their spring constant.

Establishment of a Standard Method for Boundary Slip Measurement on Smooth Surfaces Based on AFM

Typically, it is difficult to analyze and design a micro/nanofluid system, and the design process cannot follow the traditional law of hydrodynamics. The boundary condition is very important in the applications of a micro/nanofluid system. The existence of boundary slip can reduce the hydrodynamic resistance and enhance fluid flow. How to accurately determine the dynamic boundary conditions is increasingly concerned by researchers. Atomic force microscope (AFM) is proven to be the most advanced experimental instrument for studying the characteristics of the surface and the interaction interface. Most studies on the application of atomic force microscopy to the measurement of the boundary slip do not describe a systematic standard process, leading to many differences in the measurement results. In this paper, a standard process of measuring slip on smooth and flat surfaces is developed, including the data processing methods that minimize the interference factors in the original data as well as simplify the data expression. Thus, the boundary slip can be obtained more easily and accurately.

Improved Application of Carbon Nanotube Atomic Force Microscopy Probes Using PeakForce Tapping Mode

In this work PeakForce tapping (PFT) imaging was demonstrated with carbon nanotube atomic force microscopy (CNT-AFM) probes; this imaging mode shows great promise for providing simple, stable imaging with CNT-AFM probes, which can be difficult to apply. The PFT mode is used with CNT-AFM probes to demonstrate high resolution imaging on samples with features in the nanometre range, including a Nioprobe calibration sample and gold nanoparticles on silicon, in order to demonstrate the modes imaging effectiveness, and to also aid in determining the diameter of very thin CNT-AFM probes. In addition to stable operation, the PFT mode is shown to eliminate “ringing” artefacts that often affect CNT-AFM probes in tapping mode near steep vertical step edges. This will allow for the characterization of high aspect ratio structures using CNT-AFM probes, an exercise which has previously been challenging with the standard tapping mode.

Electro-mechano responsive properties of gelatin methacrylate (GelMA) hydrogel on conducting polymer electrodes quantified using atomic force microscopy

Electrical stimulation of hydrogels has been performed to enable micro-actuation or controlled movement of ions and biomolecules such as in drug release applications. Hydrogels are also increasingly used as low modulus, biocompatible coatings on electrode devices and thus are exposed to the effects of electrical stimulation. As such, there is growing interest in the latter, especially on the dynamic and nanoscale physical properties of hydrogels. Here, we report on the electro-mechano properties of photocrosslinkable gelatin methacrylate (GelMA) hydrogel applied as coatings on conducting polymer polypyrrole-dodecylbenze sulfonate (PPy-DBSA) electrodes. In particular, Electrochemical-Atomic Force Microscopy (EC-AFM) was used to quantify the nanoscale actuation and dynamic changes in Young's modulus as the GelMA coating was electrically stimulated via the underlying PPy-DBSA electrode. Pulsed electrical stimulation was shown to induce dynamic expansion and contraction, or nanoscale actuation, of the GelMA hydrogel due to the reversible ingress of electrolyte ions and associated changes in osmotic pressure during oxidation and reduction of the PPy-DBSA film. In addition, dynamic changes in the Young's modulus of up to 50% were observed in the hydrogel and correlated with the actuation process and ion diffusion during oxidation and reduction of the underlying PPy-DBSA film. These dynamic properties were investigated for hydrogels with varying degrees of cross-linking, porosity and modulus, the latter ranging from ≈0.2-1 kPa. The study demonstrates an AFM-based approach to quantify the dynamic physical properties of hydrogels, which are shown to be modulated via electrical stimulation. This can enable a better understanding of the electro-mechano mechanisms that are important for the controlled release of drugs or controlling cell interactions at the hydrogel-cell interface.

Number density distribution of solvent molecules on a substrate: a transform theory for atomic force microscopy

Atomic force microscopy (AFM) in liquids can measure a force curve between a probe and a buried substrate. The shape of the measured force curve is related to hydration structure on the substrate. However, until now, there has been no practical theory that can transform the force curve into the hydration structure, because treatment of the liquid confined between the probe and the substrate is a difficult problem. Here, we propose a robust and practical transform theory, which can generate the number density distribution of solvent molecules on a substrate from the force curve. As an example, we analyzed a force curve measured by using our high-resolution AFM with a newly fabricated ultrashort cantilever. It is demonstrated that the hydration structure on muscovite mica (001) surface can be reproduced from the force curve by using the transform theory. The transform theory will enhance AFM's ability and support structural analyses of solid/liquid interfaces. By using the transform theory, the effective diameter of a real probe apex is also obtained. This result will be important for designing a model probe of molecular scale simulations.

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Micro- and nanocantilevers are employed in atomic force microscopy (AFM) and in micro- and nanoelectromechanical systems (MEMS and NEMS) as sensing elements. They enable nanomechanical measurements, are essential for the characterization of nanomaterials, and form an integral part of many nanoscale devices. Despite the fact that numerous methods described in the literature can be applied to determine the static flexural spring constant of micro- and nanocantilever sensors, experimental techniques that do not require contact between the sensor and a surface at some point during the calibration process are still the exception rather than the rule. We describe a noncontact method using a microfluidic force tool that produces accurate forces and demonstrate that this, in combination with a thermal noise spectrum, can provide the static flexural spring constant for cantilever sensors of different geometric shapes over a wide range of spring constant values (≈0.8-160 N/m).

Mathematical methods on atomic force microscope cantilever systems

Mathematical modelling, comprising Lennard–Jones potential and calculus of variations, is utilized to obtain the energy equations arising from AFM probe and substrate, leading to deflection equations of AFM cantilever.

Establishing proper scanning conditions in atomic force microscopy on polyimide and polyurethane samples and their effect on 3D surface texture parameters

Several atomic force microscopy (AFM) tests have been carried out on both smooth (polyimide) and rough (polyurethane) surfaces so that to obtain the best results; subsequently, the optimization of experiments performed is presented. A special emphasis has been put on the effect of tip geometry, image pre-processing procedure, scanning area, resolution, pixel size, and cantilever oscillation amplitude in tapping mode, as well as on the quality of the topographical images and 3D surface texture parameters. After viewing the scanning tip and finding out its sharpness, degradation, and contamination, a simultaneous calibration in X, Y, and Z directions, lateral calibration of SPM scanners and detection of lateral non-linearity, hysteresis, creep, and cross-coupling effects has been made. We have established the following experimental parameters: proper scanning resolution (512 × 512 pixels), adequate pixel size (between 2.9 and 19.5 nm) and suitable intermittent contact region (moderate tapping) for which the AFM images present good contrast and resolution. Using these parameters, the values of 3D texture parameters remain constant. These kinds of measurements are extremely important to conduct further AFM experiments on polyimide and polyurethane surfaces under optimal conditions, thus avoiding unwanted artifacts on the morphological images or unrealistic values for the 3D surface texture parameters that might occur.

Method for Measuring the Distribution of Adhesion Forces on Continuous Nanoscale Protrusions Using Carbon Nanofiber Tip on a Scanning Probe Microscope Cantilever

The adhesion force on surfaces has received attention in numerous scientific and technological fields, including catalysis, thin-film growth, and tribology. Many applications require knowledge of the strength of these forces as a function of position in three dimensions, but until now such information has only been theoretically proposed. Here, we demonstrate an approach based on scanning probe microscopy that can obtain such data and be used to image the three-dimensional surface force field of continuous nanoscale protrusions. We present adhesion force maps with nanometer and nanonewton resolution that allow detailed characterization of the interaction between a surface and a thin carbon nanofiber (CNF) rod synthesized by plasma-enhanced chemical vapor deposition (PECVD) at the end of a tip on a scanning probe microscope cantilever in three dimensions. In these maps, the positions of all continuous nanoscale protrusions are identified and the differences in the adhesive forces among limited areas at inequivalent sites are quantified.

Interaction of silver nanoparticles with tethered bilayer lipid membranes

Silver nanoparticles are well-known for their antibacterial properties. However, the detailed mechanism describing the interaction between the nanoparticles and a cell membrane is not fully understood, which can impede the use of the particles in biomedical applications. Here, a tethered bilayer lipid membrane has been used as a model system to mimic a natural membrane and to study the effect of exposure to small silver nanoparticles with diameters of about 2 nm. The solid supported membrane architecture allowed for the application of surface analytical techniques such as electrochemical impedance spectroscopy and atomic force microscopy. Exposure of the membrane to solutions of the silver nanoparticles led to a small but completely reversible perturbation of the lipid bilayer.

Accurate calibration and uncertainty estimation of the normal spring constant of various AFM cantilevers

Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke’s law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%.

Precise and direct method for the measurement of the torsion spring constant of the atomic force microscopy cantilevers

A direct method for the evaluation of the torsional spring constants of the atomic force microscope cantilevers is presented in this paper. The method uses a nanoindenter to apply forces at the long axis of the cantilever and in the certain distance from it. The torque vs torsion relation is then evaluated by the comparison of the results of the indentations experiments at different positions on the cantilever. Next, this relation is used for the precise determination of the torsional spring constant of the cantilever. The statistical analysis shows that the standard deviation of the calibration measurements is equal to approximately 1%. Furthermore, a simple method for calibration of the photodetector's lateral response is proposed. The overall procedure of the lateral calibration constant determination has the accuracy approximately equal to 10%.

Investigation on blind tip reconstruction errors caused by sample features

Precision measurements of a nanoscale sample surface using an atomic force microscope (AFM) require a precise quantitative knowledge of the 3D tip shape. Blind tip reconstruction (BTR), established by Villarrubia, gives an outer bound with larger errors if the tip characterizer is not appropriate. In order to explore the errors of BTR, a series of simulation experiments based on a conical model were carried out. The results show that, to reconstruct the tip precisely, the cone angle of the tip characterizer must be smaller than that of the tip. Furthermore, the errors decrease as a function of the tip cone angle and increase linearly with the sample radius of curvature, irrespective of the tip radius of curvature. In particular, for sharp (20 nm radius) and blunt (80 nm radius) tips, the radius of curvature of the tip characterizer must be smaller than 5 nm. Based on these simulation results, a local error model of BTR was established. The maximum deviation between the errors derived from the model and the simulated experiments is 1.22 nm. Compared with the lateral resolution used in the above simulated experiments (4 nm/pixel), it is valid to ignore the deviations and consider the local error model of BTR is indeed in quantitative agreement with the simulation results. Finally, two simulated ideal structures are proposed here, together with their corresponding real samples. The simulation results show they are suitable for BTR.