Measuring the spring constant of atomic force microscope cantilevers: thermal fluctuations and other methods

Abstract

Knowledge of the interaction forces between surfaces gained using an atomic force microscope (AFM) is crucial in a variety of industrial and scientific applications and necessitates a precise knowledge of the cantilever spring constant. Many methods have been devised to experimentally determine the spring constants of AFM cantilevers. The thermal fluctuation method is elegant but requires a theoretical model of the bending modes. For a rectangular cantilever, this model is available (Butt and Jaschke). Detailed thermal fluctuation measurements of a series of AFM cantilever beams have been performed in order to test the validity and accuracy of the recent theoretical models. The spring constant of rectangular cantilevers can also be determined easily with the method of Sader and White. We found very good agreement between the two methods. In the case of the V-shaped cantilever, we have shown that the thermal fluctuation method is a valid and accurate approach to the evaluation of the spring constant. A comparison between this method and those of Sader-Neumeister and of Ducker has been established. In some cases, we found disagreement between these two methods; the effect of non-conservation of material properties over all cantilevers from a single chip is qualitatively invoked.

Behavior of a movable electrode in piezo-response mode of an atomic force microscope

“…Possible reasons are the inelastic response of the tip-sample system, and the hysteresis and creep of the piezoelectric ceramics which are in the scanner to move the sample. 11,12 In the present experiment, we find that the intensity of the deviation also relates to the stay time between points C and D. Figure 4 shows the curve of the stay time between points C and D versus the deviation of point DЈ from point CЈ in Fig. 3͑b͒.…”

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…Proksch et al point out that the precise position of the laser spot on the cantilever and its size can also influence the result of a thermal noise measurement [97]. The use of the thermal noise method has been confirmed experimentally [43,98]. For completeness we also consider the case that not only the first vibration mode but the total noise is measured.…”

Carbohydrate-Carbohydrate Interactions Mediated by Sulfate Esters and Calcium Provide the Cell Adhesion Required for the Emergence of Early Metazoans

“…SMFS experiments were carried out at room temperature by approaching and separating the functionalized cantilevers and substrates in CMFTSW supplemented with 10 mM CaCl 2 or 5 mM EDTA. The spring constant of each cantilever was determined using the thermal noise method (35 ) and four different retract velocities (200, 800, 2000, and 5000 nm⅐s Ϫ1 ). The force curves were analyzed with a custom-made MATLAB-based software (Math Works) to calculate the molecular adhesion forces and elasticities.…”