Lever oscillator

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 Lever oscillator [39], Fig. 16, allows the application of series resonance configurations with one-side quartz electrode grounding. Since the effect of parasitic capacitance is minimized and simple shielding is possible, this circuit configuration is especially suited for under-liquid QCM. Besides the series resonance frequency, the series resonance resistance Rs can be measured. For this purpose the Lever oscillator allows a largely transistor current gain-independent measurement of the resistance. An automatic level control provides a signal proportional to Rs. 

In the contact mode, there are static modes (de-modes), and dynamic modes (ac-modes). In the former, a cantilever-type spring bends in response to the force which acts on the probing tip until a static equilibrium is established [1]. In the dynamic mode, the lever oscillates close to its resonance frequency. A distance-dependence force shifts the resonance curve. Another technique is to modulate the position of the sample at a frequency below the cantilever resonance but above the feedback-response frequency and send the response signal to a lock-in amplifier to measure the signal s amplitude and phase [4]. The lock-in output is connected to the auxiliary data acquisition channels to form an image - this approach is popularly known as force modulation (FM-mode). FM-mode imaging or force cmve is an AFM technique that identifies and maps differences in surface stiffness or elasticity. 

In the fonner, the excitation amplitude to the lever (via the piezo) is kept constant, thus, if the lever experiences a damping close to the surface the actual oscillation amplitude falls. The latter involves compensatmg the excitation amplitude to keep the oscillation amplitude of the lever constant. This mode also readily provides a measure of the dissipation during the measurement [100]. 

Other noncontact AFM methods have also been used to study the structure of water films and droplets [27,28]. Each has its own merits and will not be discussed in detail here. Often, however, many noncontact methods involve an oscillation of the lever in or out of mechanical resonance, which brings the tip too close to the liquid surface to ensure a truly nonperturbative imaging, at least for low-viscosity liquids. A simple technique developed in 1994 in the authors laboratory not only solves most of these problems but in addition provides new information on surface properties. It has been named scanning polarization force microscopy (SPFM) [29-31]. SPFM not only provides the topographic stracture, but allows also the study of local dielectric properties and even molecular orientation of the liquid. The remainder of this paper is devoted to reviewing the use of SPFM for wetting studies. 

The prime differences among the different AFM modes, such as CM (discussed above) and intermittent CM, as elucidated in the following section, are the feedback parameters and the choice of the cantilever. For intermittent contact (tapping) mode AFM, a stiff cantilever (k typically 10—50 N/m) with a resonance frequency of 100—400 kHz is chosen. The cantilever, which is inserted in an identical manner as for CM into the cantilever holder, is excited to vibrate by an integrated piezo actuator. Instead of deflection (contact force), the amplitude of the forced oscillating lever is detected, analyzed, and utilized in the feedback loop (Fig. 2.20). 

For pulsed force mode imaging, a stiff contact mode lever (kN 0.6 N/m) is selected. A modulation frequency in the range of 800 Hz is selected and the cantilever oscillations are adjusted such that the adhesive interactions between tip and surface are overcome, as monitored using an oscilloscope. The modulation must clearly show the snap-off of the tip. Next the four markers are set according to the general procedure outlined in Sect. 3.2 in Chap. 3. 

In the on-off device, the sensing element is connected to the spirally wound tube (O) and changes in pressure cause the tube to move such that a lever (P) moves the indicator (L), which indicates the temperature of the system being measured (about 150°F in the figure). Attached to indicator (L) is a contact (A). Placed either side of (L) are moveable arms, (M) and (N), which indicate the minimum and maximum temperature deviation before some corrective action is taken. These two arms are connected to (B) and (C) which also carry electrical contacts. Thus if the temperature drops to 125°F then the contact (A) (on L) makes contact with (B) and presumably results in some form of heat being supplied to the system. On-off systems result in limit cycling, in which the controlled quantity oscillates between the upper and lower limits (many room temperature control systems still work on this principle, and if the upper and lower limit are too far apart one is alternately too hot and then too cold). 

As the tip is scanned over the sample, or the sample is scanned under the tip, forces between the tip and the sample surface cause spatial deflections and oscillations of the cantilever. The key information gathered in AFM comes with measuring those deflections, quantified by means of an optical lever system, coupled with a position-sensitive photodiode (Marinello et al. 2009). 

T< Tc, isotherms show unphysical oscillations analogous to the oscillations that result from the van der Waals equation of state for real gases, which predict an LGPT [37]. The range of densities where dP/dV)r > 0 are thermodynamically unstable and indicate that the system must phase separate into LDL and HDL. The equilibrium isotherm can be obtained from the isotherms obtained in simulations by applying Maxwell s construction (see Fig. 3). At volumes V > Vldl and V < HDL. the equilibrium states are (homogeneous) LDL and HDL, respectively. At volumes Vhdl < F < Vldl> regions of HDL and LDL coexist. The fraction of the system in each phase is determined by the lever rule [37]. 

As the oscillating tip approaches the surface, it is affected by long range forces well before it comes into the range of intermittent contact. Within lOjUm of the surface, it is subjected to squeeze film damping. Motion of air near the surface is restricted and there is compression at each down-stroke of the lever. Restricted motion means more effective damping, and the effect is to reduce the Q of the system, broadening the resonance peak. 

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