Reference lever

Procedures for the reliable calibration of normal forces (i.e., /iN) are well established. Several methods can be used, such as the thermal fluctuation method [11-13], the reference lever [14], or the added mass technique [15]. We will mention in the following the thermal noise and the reference lever methods in some detail. 

An alternative method relies on the acquisition of f-d curves on (1) a stiff substrate and (2) a reference lever with known spring constant. For this method, the reference lever should have a spring constant close to the one that will be calibrated. If we denote the deflection of the cantilever as Zc and the height of the piezoelectric translator as Zp (zero is defined for the situation, when the tip just touches the reference cantilever and no deflection has been detected), the spring constant is given by... 

Fig. 2.30 Schematic of cantilever calibration on reference lever. Reprinted with permission from [16]. Copyright 2005. Elsevier...

TTie force-curve mapping technique is often referred to as force-volume mapping commercially, although sample volume is not probed unless stiff levers or compliant surfaces are used. 

According to the distance from probe to the sample, three operation modes can be classified for the AFM. The first and foremost mode of operation is referred to as contact mode or repulsive mode. The instrument lightly touches the sample with the tip at the end of the cantilever and the detected laser deflection measures the weak repulsion forces between the tip and the surface. Because the tip is in hard contact with the surface, the stiffness of the lever needs to be less than the effective spring constant holding atoms together, which is on the order of 1 — 10 nN/nm. Most contact mode levers have a spring constant of <1 N/m. The defection of the lever can be measured to within 0.02 nm, so for a typical lever force constant at 1 N/m, a force as low as 0.02 nN could be detected [50]. 

The movement of the pointer may be observed with respect to a reference pointer which is sealed into the jacket from above. The pointer P can also be made to move a glass lever system which magnifies the movement (S. G. Foord, 1934). 

The foregoing discussion applies to complexes that are weak-field cases. Spectral analysis for strong-field cases is somewhat different and will not be discussed here. For complete analysis of the spectra of strong-field complexes, see the book by A. B. P. Lever, Inorganic Electronic Spectroscopy, listed in the references at the end of this chapter. 

Figure 15.6 is a schematic diagram of an AFM with an optical interferometer (Erlandsson et al., 1988). The lever is driven by a lever oscillator through a piezoelectric transducer. The detected force gradient F is compared with a reference value, to drive the z piezo through a controller. In addition to the vibrating lever method, the direct detection of repulsive atomic force through the deflection of the lever is also demonstrated. 

The main ones are described in the following, that is, those based on the Pickett s, Lever s, and Bursten s models. In the first one, the potentials have typically been quoted relative to the saturated calomel electrode (SCE), whereas in the second one they have been referred to the normal hydrogen electrode (SHE). The... 

A. B. P. Lever, Inorganic Electronic Spectroscopy, Elsevier Science Publishers, Amsterdam, The Netherlands, 1984, and references cited therein. 

Figure 10-3. Scanning electron micrograph of microgear and lever alongside red blood cells and pollen grain (courtesy of Sandia National Laboratories 2003). Reference bar is 50 micrometers in length.

For the capsule measurements, glass substrates coated with polyethyleneimine were used on which the PSS-terminated capsules showed adhesion. The capsule force deformation characteristics of individual capsules were obtained by placing a capsule under the colloidal probe and pressing onto it. Special care was taken to press onto the pole of the capsule as described in more detail in [13]. Reference curves on hard substrates were obtained before and after the experiments to determine the inverse optical lever sensitivity (InvoLS) and to derive the absolute deformation of the capsules. In rare cases when the InvoLS was found to change during the measurement, the measured data was discarded. 

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