Z-piezo position

Force Curve Analysis. Typical raw data are shown in Figure 3a,b, where the force is plotted as a function of the z-piezo position. Figure 3a displays the interaction between a bare Si02 microsphere and a PLL-... 

Figure 3. Raw AFM force data plots exhibiting the force experienced by the cantilever in nN as afiinction of the z-piezo position for both the approach and the retraction parts, for two polymers. PLL(20)-g[3.5]-PEG(2) (a) shows purely repulsive interaction, without hs steresis, while (b) PLL(20)-g(22.6)-PEG-(2) shows attraction on the approach curve and adhesion on the retraction.

The imaging signal in IC-AFM may be the Z-piezo position, or for phase imaging, the phase of the oscillation. In a heterogeneous sample the tip-surface interactions will generally be different for different components. This will alter the height at which a given set-point... 

Force curve gives the relationship between the z-piezo displacement and the cantilever deflection as shown in Figure 21.10b. When a cantilever approaches to a stiff sample surface, cantilever deflection. A, is equal to the z-piezo displacement, z — Zo- The value of zo is defined as the position where the tip-sample contact is realized. On the other hand, z-piezo displacement becomes larger to achieve the preset trigger value (set point) of the cantilever deflection in the case of an elastic sample due to the deformation of the sample itself. In other words, we can obtain information about a sample deformation, 8, from the force-distance curve of the elastic surface by the following relationship ... 

The output of a Nd YLF laser is focussed by a series of lenses to a spot size of 0.5 pm upon a sample which may be positioned by an x-y-z stepping motor stage and scanned by a computer-controlled high frequency x-y-z piezo stage. Ions are accelerated and transmitted through the central bore of the objective into a time-of-flight (TOF) mass spectrometer. The laser scans an area of 100 x 100 pm with a minimum step size of 0.25 pm. TOF mass spectra of each pixel are evaluated with respect to several ion signals and transformed into two-dimensional ion distribution plots. 

The appropriate force setting is performed in the force—distance mode (Fig. 2.12 for details see also Sect. 4.1 in Chap. 4). In this mode, the deflection of the cantilever is monitored as a function of sample/piezo position, while the tip is brought periodically in and out of contact with the sample surface. The measured cantilever deflection z can be converted to the corresponding force F, by applying Hooke s law, if the spring constant of the lever k is known (F = k Az). 

To begin, the tip is positioned 20 nm or more from the surface. When the tip and the surface are immersed in a solution, there is essentially no force between them at such long distances, so the cantilever is straight. The system is adjusted so that equal light falls on each photocell. As the z-piezo moves up, carrying the sample surface toward the tip, forces between tip and sample become appreciable. At distances on the order of 10 nm, the only forces between the tip and substrate are electrostatic, which can be either attractive or repulsive. Let us assume that the tip and surface have the same charge, so the force is repulsive. The upward movement of the sample and the repulsive force cause the can-... 

Figure 20.3. A schematic of the AFM set-up. The lower surface is attached to a jc> z-piezo scanner. During force measurements, the piezo device is ramped in the z-direction. The colloidal probe (not shown) is glued to the cantilever. A laser beam is reflected from the back of the cantilever. The position of the laser beam is registered by a split photodiode, thus measuring the bending of the cantilever. The inset shows a cellulose particle glued to an AFM cantilever (98). The main figure has been drawn by Lachlan Grant, Institute for Surface Chemistry, Stockholm...

SPM force curves are acquired by moving the tip toward the sample and recording the cantilever deflection as a function of the so-called Z position. Cantilever deflection is directly proportional to the force exerted on the sample by the tip. If the spring constant (fc) of the cantilever is known, the force can be calculated. The Z position defines the distance from the sample to the piezo, to which the base of the cantilever is attached (Figure 9.13). By convention the closest point of approach by the piezo is designated as zero on the x-axis. Note that for some instruments the piezo is attached to the sample stage and thus moves the sample up toward the tip however, this does not change the analysis. 

Figure 9.14 shows a typical approach force curve along with schematic drawings of the relative positions of the SPM tip and the sample surface, as related to the force curve. At the start of the experiment, i.e., position A on the right-hand side of the figure, the tip is above the surface of the sample. As it approaches the surface the Z value decreases until at position B the tip contacts the surface. With further downward movement of the piezo the cantilever starts to be deflected by the force imposed on it by the surface. If the surface is much stiffer than the cantilever, we get a straight line with a slope of — 1, i.e., for every 1 nm of Z travel we get 1 nm of deflection (Une BC in Figure 9.14). If the surface has stiffness similar to that of the cantilever, the tip wUl penetrate the surface and we get a nonlinear curve with a decreased slope (line BD in Figure 9.14). The horizontal distance between the curve BD and the line BC is equal to the penetration at any given cantilever deflection or force. The piezo continues downward until a preset cantilever deflection is reached, the so-called trigger. The piezo is then retracted a predetermined distance, beyond the point at which the tip separates from the sample.

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