Reference cantilever

For the pattern recognition (PARC) approach, we have coated the piezoresistive cantilevers with different selective layers. Each piezoresistive cantilever had four cantilever elements. Two of these cantilevers were coated with gold, whereas the other two served as reference cantilevers. We have used four separated chips arranged into an array in a single vapor chamber. Each cantilever chip was coated with a different selective agent. The four coatings used in our study include 4-MBA, Au (evaporated), CH3(CH2)n-SH, and a complex of (i-cyclodextrin and alkane. 

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... 

Since the spring constant of the reference cantilever k,cj is known, N can be obtained from the measured slope of the force curve Zc/Zp obtained on the reference cantilever in the contact regime (Fig. 2.30). 

Force curves are used to correlate vertical movement of the scanner with cantilever deflection. A typical force curve is depicted in Figure 7. Force curves are obtained by disabling the scanner movement in the X and y directions and oscillating the scanner in the z-direction. As the tip approaches the sample, no cantilever bending is observed until the gap between the tip and the sample is extremely small. Then, the cantilever will be pulled down due to the van der Waals interactions between the tip and the substrate (or by the presence of a thin hydration layer on the surface). Once in contact, raising the sample produces an upward bend in the cantilever. The applied load is computed by multiplying the reference cantilever deflection value times its spring constant. The force curve can also be used to identify adhesive... 

In SFMS experiments, the deflection (denoted as 5(f)) and the piezo displacement (z(f)) are recorded. These data are converted into force (F(z)) and tip-snrface distance (D(t)) plot. The tip-snrface distance is obtained from D t) = z(t) — S(t). As mentioned above, the sensitivity (displacement per voltage) is calibrated from the slope in region 2. To convert the measured deflection to force via Hook s law (F(z) = k S(z)), the cantilever spring constant must be known. By various calibration methods, including the thermal tune method, the reference cantilever approach or calculations based on the geometry of the cantilever and its measured resonance frequency, the cantilever spring constant (k) can be estimated. ... 

A simple possibflity is the use of a reference cantilever with known spring constant Kref [241, 242, 244]. Therefore, the reference cantilever is used as sample and the cantilever that should be calibrated is mounted in the AFM. Then, force curves are taken on a hard substrate and on top of the end of the reference cantilever. From the slopes of the force curves S f and Ss bs taken on the soHd substrate and the reference cantilever, respectively, one can simply obtain the spring constant from... 

If spring constant of reference cantilever was determined precisely, most of the error stems from variation in alignment of cantilevers. Cumpson et al. [243] have... 

Noncomputerized Calculation. Design charts or tables are used for hand calculations or simplified formulas such as the guided cantilever equation given ia Reference 31, described briefly below. 

Note that these stress, strain and modulus equations are given for illustration purposes. They apply to three-point bending as shown in Fig. 2.3. Other types of bending can occur (e.g. four-point bending, cantilever, etc.) and different equations will apply. Some of these are illustrated in the Worked Examples later in this chapter and the reader is referred to Benham et al. for a greater variety of bending equations. 

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]. 

To minimize effects of friction and other lateral forces in the topography measurements in contact-modes AFMs and to measure topography of the soft surface, AFMs can be operated in so-called tapping mode [53,54]. It is also referred to as intermittent-contact or the more general term Dynamic Force Mode" (DFM). A stiff cantilever is oscillated closer to the sample than in the noncontact mode. Part of the oscillation extends into the repulsive regime, so the tip intermittently touches or taps" the surface. Very stiff cantilevers are typically used, as tips can get stuck" in the water contamination layer. The advantage of tapping the surface is improved lateral resolution on soft samples. Lateral forces... 

A representative example of the upd process is copper on gold and an extremely illuminating study of this system using repulsive AFM was reported by Manne et al. (1991). The authors employed a commercially available AFM, the essentials of which are shown in Figure 2.33. The reference electrode was a copper wire in contact with the electrolyte at the outlet of the cell. The counter electrode was the stainless steel spring clip holding the AFM cantilever in place. The working electrode was a 100 nm thick evaporated Au film (which is known to expose mainly the Au(111) surface) mounted on an (x, v) translator. 

The term etching refers to the dissolution processes at OCP of silicon samples immersed in an electrolyte solution. The technique has been extensively explored for its useful applications in the fabrication of electronic devices, surface polishing, and micromachining. For example, it is widely used for the production of cantilevers for the AFM technology. 

UFM detection is obtained by measuring the cantilever deflection as the ultrasound amplitude is modulated (Fig. 13.3). The ultrasonic excitation from a longitudinal wave transducer fixed to the bottom of the sample causes normal vibration of its surface. As the ultrasonic amplitude is increased, contact is eventually broken at the pull-off point (aI = hi), giving a discontinuity in the time-averaged displacement. We refer to this ultrasonic amplitude as the threshold amplitude, and the corresponding inflection in the displacement... 

Figure 24. Integrated active-substrate system proposed by Stanford University. The system includes cantilever bonding, microcapillary die attachment, and microchannel heat exchange on a silicon substrate with active circuits. (Figure was based on reference 167.)...

Applications of cantilevers also allows label-free detection of aptamer-ligand interactions. Although it is not an optical sensor, the interferometry is used for detection of the differential bending between cantilever and reference modified with non-specific aptamer [74],... 

To determine torsion force constant and height of tip we didn t refer to cantilever passport parameters that can be significant varied. The value of kL we found used new the most precise method based on analyzing of amplitude-phase characteristic [to be published] but tip height was determined with the help of optical microscope. We got kL = 77.1 N/m ltip = 10 pm. 

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