Lateral Force Calibration Research Articles

Simultaneous Calibration of Axial and Lateral Radiation Forces of Ultra-High Frequency Ultrasound Acting on a Microrobot With Arbitrary Geometry

Simultaneous Calibration of Axial and Lateral Radiation Forces of Ultra-High Frequency Ultrasound Acting on a Microrobot With Arbitrary Geometry

Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy

Efforts to reliably measure AFM lateral forces have been impeded by the difficulties in obtaining appropriate calibration standards, applying those force standards to the apex of the tip, and quantifying calibration uncertainty. Here we propose a new method, Traceable Lateral Force Calibration (TLFC), which combines the reliability of direct methods with the convenience of indirect/semi-direct methods. Like other direct methods, ours comprise three essential steps: (1) fabrication of a spring (the Traceable Reference Lever or TRL); (2) calibration of the TRL spring constant; (3) conversion of measurable TRL deflections into absolute lateral force measurements based on its pre-calibrated spring constant (TLFC method). The TRL device, a simple two-axis cantilever, is easy to design, fabricate, and directly pre-calibrate with a standard laboratory microbalance. Following pre-calibration, the TRL device becomes a convenient absolute standard for AFM lateral force measurements. This paper describes the complete method and demonstrates its primary merits, which include (1) traceability to measurement standards; (2) ease of use by outside user groups; (3) absolute measurement errors 1 N/m normal stiffness); (4) robustness over a wide range of common loads, instruments, probes, and environments. While the method and proof-of-concept devices described in this paper were designed primarily for moderate to high load cantilevers (> 1 N/m), we discuss how a next generation of compliant TRL devices can be used with the TLFC method to reliably calibrate arbitrary AFM cantilevers (< < 1 N/m) and forces.

Lateral force calibration for atomic force microscope cantilevers using a suspended nanowire

Friction measurement via atomic force microscope (AFM) relies on accurate calibration for the torsional spring constant of the AFM cantilever and its lateral deflection sensitivity. Here we describe a method that employs a suspended nanowire (SNW) as a reference beam to quantify the torsional spring constant of AFM cantilevers. Based on the fact that a uniform SNW with cylindrical symmetry has an identical spring constant when bent in any direction perpendicular to its axis, the spring constant of the SNW in a normal direction is determined by an AFM cantilever with a known normal spring constant, and is subsequently used as a force transfer standard to calibrate the torsional spring constant of the AFM cantilever. The lateral deflection sensitivity can be accurately measured by pushing the AFM tip laterally on the groove edge. The calibration result is compared to the well-known diamagnetic lateral force calibrator method and shows an uncertainty of 15% or better. The presented method is applicable for the lateral force calibration of AFM cantilevers in a wide range of instruments including inverted configurations and in an ultrahigh vacuum.

Design and optimization of the diamagnetic lateral force calibration method.

The lateral force calibration is a key procedure for applications of atomic force microscopes. Among different calibration methods, the diamagnetic lateral force calibration (DLFC) method has been widely used due to its ease of use as well as being able to estimate the cross talk conversion factor and achieve very small stiffness. The lateral stiffness of the system is the only parameter in the DLFC method; however, its dependence on the properties and parameters of the DLFC system remains unexplored. In this paper, a theoretical formulation of such dependence is developed and experimentally verified. These results provide a guidance to design and optimize future DLFC systems with better applicability and precision in calibrations. As an example, we optimized a DLFC system such that it is robust against normal load, which is previously assumed impossible.

Method for lateral force calibration in atomic force microscope using MEMS microforce sensor

In this paper we present a simple and direct method for the lateral force calibration constant determination. Our procedure does not require any knowledge about material or geometrical parameters of an investigated cantilever. We apply a commercially available microforce sensor with advanced electronics for direct measurement of the friction force applied by the cantilever's tip to a flat surface of the microforce sensor measuring beam. Due to the third law of dynamics, the friction force of the equal value tilts the AFM cantilever. Therefore, torsional (lateral force) signal is compared with the signal from the microforce sensor and the lateral force calibration constant is determined. The method is easy to perform and could be widely used for the lateral force calibration constant determination in many types of atomic force microscopes.

Lateral Force Calibration in Atomic Force Microscopy: Minireview

Lateral Force Calibration in Atomic Force Microscopy: Minireview

Quantitative assessment of contact and non-contact lateral force calibration methods for atomic force microscopy

Atomic Force Microscopy (AFM) has been widely used for measuring friction force at the nano-scale. However, one of the key challenges faced by AFM researchers is to calibrate an AFM system to interpret a lateral force signal as a quantifiable force. In this study, five rectangular cantilevers were used to quantitatively compare three different lateral force calibration methods to demonstrate the legitimacy and to establish confidence in the quantitative integrity of the proposed methods. The Flat-Wedge method is based on a variation of the lateral output on a surface with flat and changing slopes, the Multi-Load Pivot method is based on taking pivot measurements at several locations along the cantilever length, and the Lateral AFM Thermal-Sader method is based on determining the optical lever sensitivity from the thermal noise spectrum of the first torsional mode with a known torsional spring constant from the Sader method. The results of the calibration using the Flat-Wedge and Multi-Load Pivot methods were found to be consistent within experimental uncertainties, and the experimental uncertainties of the two methods were found to be less than 15%. However, the lateral force sensitivity determined by the Lateral AFM Thermal-Sader method was found to be 8–29% smaller than those obtained from the other two methods. This discrepancy decreased to 3–19% when the torsional mode correction factor for an ideal cantilever was used, which suggests that the torsional mode correction should be taken into account to establish confidence in Lateral AFM Thermal-Sader method.

Probing fibronectin-antibody interactions using AFM force spectroscopy and lateral force microscopy.

The first experiment showing the effects of specific interaction forces using lateral force microscopy (LFM) was demonstrated for lectin–carbohydrate interactions some years ago. Such measurements are possible under the assumption that specific forces strongly dominate over the non-specific ones. However, obtaining quantitative results requires the complex and tedious calibration of a torsional force. Here, a new and relatively simple method for the calibration of the torsional force is presented. The proposed calibration method is validated through the measurement of the interaction forces between human fibronectin and its monoclonal antibody. The results obtained using LFM and AFM-based classical force spectroscopies showed similar unbinding forces recorded at similar loading rates. Our studies verify that the proposed lateral force calibration method can be applied to study single molecule interactions.

A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy.

Calibration of lateral forces and displacements has been a long standing problem in lateral force microscopies. Recently, it was shown by Wagner et al. that the thermal noise spectrum of the first torsional mode may be used to calibrate the deflection sensitivity of the detector. This method is quick, non-destructive and may be performed in situ in air or liquid. Here we make a full quantitative comparison of the lateral inverse optical lever sensitivity obtained by the lateral thermal noise method and the shape independent method developed by Anderson et al. We find that the thermal method provides accurate results for a wide variety of rectangular cantilevers, provided that the geometry of the cantilever is suitable for torsional stiffness calibration by the torsional Sader method, in-plane bending of the cantilever may be eliminated or accounted for and that any scaling of the lateral deflection signal between the measurement of the lateral thermal noise and the measurement of the lateral deflection is eliminated or corrected for. We also demonstrate that the thermal method may be used to characterize the linearity of the detector signal as a function of position, and find a deviation of less than 8% for the instrument used.

AFM lateral force calibration for an integrated probe using a calibration grating

Atomic force microscopy (AFM) friction measurements on hard and soft materials remain a challenge due to the difficulties associated with accurately calibrating the cantilever for lateral force measurement. One of the most widely accepted lateral force calibration methods is the wedge method. This method is often used in a simplified format but in so doing sacrifices accuracy. In the present work, we have further developed the wedge method to provide a lateral force calibration method for integrated AFM probes that is easy to use without compromising accuracy and reliability. Raw friction calibration data are collected from a single scan image by continuous ramping of the set point as the facets of a standard grating are scanned. These data are analysed to yield an accurate lateral force conversion/calibration factor that is not influenced by adhesion forces or load deviation. By demonstrating this new calibration method, we illustrate its reliability, speed and ease of execution. This method makes accessible reliable boundary lubrication studies on adhesive and heterogeneous surfaces that require spatial resolution of frictional forces.

기준 외팔보를 이용한 액체 환경에서 Colloidal Probe의 수평방향 힘 교정

There is an indispensable need for force calibration for quantitative nanoscale force measurement using atomic force microscopy. Calibrating the normal force is relatively straightforward, whereas doing so for the lateral force is often complicated because of the difficulty in determining the optical lever sensitivity. In particular, the lateral force calibration of a colloidal probe in a liquid environment often has a larger uncertainty as a result of the effects of the epoxy, the location of the colloidal particle on the cantilever, and a decrease in the quality factor. In this work, the lateral force of a colloidal probe using a reference cantilever with a known spring constant was calibrated in a liquid environment. By obtaining the spring constant and the lateral sensitivity at the equator of a spherical colloidal particle, the damage to the bottom surface of the colloidal particle could be eliminated. Further, it was shown that the effect of the contact stiffness on the determination of the lateral spring constant of the cantilever could be minimized. It was concluded that this method can be effectively used for the lateral force calibration of a colloidal probe in a liquid environment.

AFM probe based nano mechanical scribing of soda-lime glass

In recent years, demands for miniature components have increased due to their reduced size, weight and energy consumption. In particular, brittle materials such as glass can provide high stiffness, hardness, corrosion resistance and high-temperature strength for various biomedical and high-temperature applications. In this study, cutting properties and the effects of machining parameters on the ductile cutting of soda-lime glass are investigated through the nano-scale scratching process. In order to understand the fundamentals of the material removal mechanism at the atomic scale, such as machined surface quality, cutting forces and the apparent friction, theoretical investigation along with experimental study are needed. Scribing tests have been performed using a single crystal diamond atomic force microscope (AFM) probe as the scratching tool, in order to find the cutting mechanism of soda-lime glass in the nano-scale. The extended lateral force calibration method is proposed to acquire accurate lateral forces. The experimental thrust and cutting forces are obtained and apparent friction coefficients are deduced. The effects of feed rates and the ploughing to shearing transition of soda-lime glass have been investigated.

The extended wedge method: Atomic force microscope friction calibration for improved tolerance to instrument misalignments, tip offset, and blunt probes

One of the major challenges in understanding and controlling friction is the difficulty in bridging the length and time scales of macroscale contacts and those of the single asperity interactions they comprise. While the atomic force microscope (AFM) offers a unique ability to probe tribological surfaces in a wear-free single-asperity contact, instrument calibration challenges have limited the usefulness of this technique for quantitative nanotribological studies. A number of lateral force calibration techniques have been proposed and used, but none has gained universal acceptance due to practical considerations, configuration limitations, or sensitivities to unknowable error sources. This paper describes a simple extension of the classic wedge method of AFM lateral force calibration which: (1) allows simultaneous calibration and measurement on any substrate, thus eliminating prior tip damage and confounding effects of instrument setup adjustments; (2) is insensitive to adhesion, PSD cross-talk, transducer/piezo-tube axis misalignment, and shear-center offset; (3) is applicable to integrated tips and colloidal probes; and (4) is generally applicable to any reciprocating friction coefficient measurement. The method was applied to AFM measurements of polished carbon (99.999% graphite) and single crystal MoS2 to demonstrate the technique. Carbon and single crystal MoS2 had friction coefficients of μ = 0.20 ± 0.04 and μ = 0.006 ± 0.001, respectively, against an integrated Si probe. Against a glass colloidal sphere, MoS2 had a friction coefficient of μ = 0.005 ± 0.001. Generally, the measurement uncertainties ranged from 10%-20% and were driven by the effect of actual frictional variation on the calibration rather than calibration error itself (i.e., due to misalignment, tip-offset, or probe radius).

Multiple Pivot loading 방법을 이용한 액체 환경에서의 수평방향 힘 교정

Quantifying the nanoscale force between the atomic force microscopy (AFM) probe of a force-sensing cantilever and the sample is one of the challenges faced by AFM researchers. The normal force calibration is straightforward; however, the lateral force is complicated due to the twisting motion of the cantilever. Force measurement in a liquid environment is often needed for biological applications; however, calibrating the force of the AFM probes for those applications is more difficult owing to the limitations of conventional calibration methods. In this work, an accurate nondestructive lateral force calibration method using multiple pivot loading was proposed for liquid environment. The torque sensitivity at the location of the integrated probe was extrapolated based on accurately measured torque sensitivities across the cantilever width along a few cantilever lengths. The uncertainty of the torque sensitivity at the location of the integrated tip was about 13%, which is significantly smaller than those for other calibration methods in a liquid environment.

원자 현미경 탐침의 수평방향 힘 교정에 미치는 접촉 강성의 영향

Atomic force microscopy (AFM) has been used for imaging surfaces and measuring surface forces at the nano-scale. Force calibration is important for the quantitative measurement of forces at the nano-scale using AFM. Normal force calibration is relatively straightforward, whereas the lateral force calibration is more complicated since the lateral stiffness of the cantilever is often comparable to the contact stiffness. In this work, the lateral force calibrations of the rectangular cantilever were performed using torsional Sader's method, thermal noise method, and wedge calibration method. The lateral optical lever sensitivity for the thermal noise method was determined from the friction loop under various normal forces as well. Experimental results showed that the discrepancies among the results of the different methods were as large as 30% due to the effect of the contact stiffness on the lateral force calibration of the cantilever used in this work. After correction for the effect of contact stiffness, all the calibration results agreed with each other, within experimental uncertainties.

V 형상을 가지는 원자현미경 Cantilever의 정량적 마찰력 교정

Atomic force microscopy (AFM) has been used as a tool, not only for imaging surfaces, but also for measuring surface forces and mechanical properties at the nano-scale. Force calibration is crucial for quantitatively measuring the forces that act between the AFM probe of a force sensing cantilever and a sample. In this work, the lateral force calibrations of a V-shaped cantilever were performed using the finite element method, multiple pivot loading, and thermal noise methods. As a result, it was shown that the multiple pivot loading method was appropriate for the lateral force calibration of a V-shaped cantilever. Further, through crosschecking of the abovementioned methods, it was concluded that the thermal noise method could be used for determining the lateral spring constants as long as the lateral deflection sensitivity was accurately determined. To obtain the lateral deflection sensitivity from the sticking portion of the friction loop, the contact stiffness should be taken into account.

Quantitative comparison of two independent lateral force calibration techniques for the atomic force microscope

Two independent lateral-force calibration methods for the atomic force microscope (AFM)--the hammerhead (HH) technique and the diamagnetic lateral force calibrator (D-LFC)--are systematically compared and found to agree to within 5 % or less, but with precision limited to about 15 %, using four different tee-shaped HH reference probes. The limitations of each method, both of which offer independent yet feasible paths toward traceable accuracy, are discussed and investigated. We find that stiff cantilevers may produce inconsistent D-LFC values through the application of excessively high normal loads. In addition, D-LFC results vary when the method is implemented using different modes of AFM feedback control, constant height and constant force modes, where the latter is more consistent with the HH method and closer to typical experimental conditions. Specifically, for the D-LFC apparatus used here, calibration in constant height mode introduced errors up to 14 %. In constant force mode using a relatively stiff cantilever, we observed an ≈ 4 % systematic error per μN of applied load for loads ≤ 1 μN. The issue of excessive load typically emerges for cantilevers whose flexural spring constant is large compared with the normal spring constant of the D-LFC setup (such that relatively small cantilever flexural displacements produce relatively large loads). Overall, the HH method carries a larger uncertainty, which is dominated by uncertainty in measurement of the flexural spring constant of the HH cantilever as well as in the effective length dimension of the cantilever probe. The D-LFC method relies on fewer parameters and thus has fewer uncertainties associated with it. We thus show that it is the preferred method of the two, as long as care is taken to perform the calibration in constant force mode with low applied loads.

In Situ Hydrodynamic Lateral Force Calibration of AFM Colloidal Probes

Lateral force microscopy (LFM) is an application of atomic force microscopy (AFM) to sense lateral forces applied to the AFM probe tip. Recent advances in tissue engineering and functional biomaterials have shown a need for the surface characterization of their material and biochemical properties under the application of lateral forces. LFM equipped with colloidal probes of well-defined tip geometries has been a natural fit to address these needs but has remained limited to provide primarily qualitative results. For quantitative measurements, LFM requires the successful determination of the lateral force or torque conversion factor of the probe. Usually, force calibration results obtained in air are used for force measurements in liquids, but refractive index differences between air and liquids induce changes in the conversion factor. Furthermore, in the case of biochemically functionalized tips, damage can occur during calibration because tip-surface contact is inevitable in most calibration methods. Therefore, a nondestructive in situ lateral force calibration is desirable for LFM applications in liquids. Here we present an in situ hydrodynamic lateral force calibration method for AFM colloidal probes. In this method, the laterally scanned substrate surface generated a creeping Couette flow, which deformed the probe under torsion. The spherical geometry of the tip enabled the calculation of tip drag forces, and the lateral torque conversion factor was calibrated from the lateral voltage change and estimated torque. Comparisons with lateral force calibrations performed in air show that the hydrodynamic lateral force calibration method enables quantitative lateral force measurements in liquid using colloidal probes.

Shape-Independent Lateral Force Calibration

Current methods for lateral force calibration are often time-consuming, expensive, or cause significant wear of the tip. A quick and simple alternative is presented in which the linear relationship between force and voltage is exploited. The technique is independent of the shapes of the sample and cantilever and eliminates common problems, while maintaining better than 10% precision. This advance will facilitate quantitative comparisons between experiments.

Noncontact Method for Calibration of Lateral Forces in Scanning Force Microscopy

This paper describes a noncontact calibration procedure for lateral force microscopy in air and liquids. The procedure is based on the observation that the sensitivity of a force microscope may be calibrated using the raw thermal noise spectrum of the cantilever and its known spring constant, which can be found from the same uncalibrated thermal noise spectrum using Sader's method (Rev. Sci. Instrum.1999, 70, 3967-3969). In addition to the power spectrum of the cantilever thermal noise, this noncontact calibration method only requires knowledge of the plan view dimensions of the cantilever that could be measured using an optical microscope. This method is suitable for in situ force calibration even in viscous fluids through a two-step calibration procedure, where the cantilever thermal spectra are captured both in air and in the desired liquid. The lateral calibration performed with the thermal noise technique agrees well with sensitivity values obtained by the wedge calibration procedure. The approach examined in this paper allows for complete calibration of normal and lateral forces without contacting the surface, eliminating the possibility for any tip damage or contamination during calibration.