Tip-sample force

A change in the amphtude of oscillating AFM probe is chosen for a control of tip-sample force interactions in tapping mode. At the beginning, an operator adjusts the piezo-drive of the probe to its resonant frequency and chooses initial amphtude (Aq) and set-point amplitude (Ajp). The latter is... 

Studies on fundamental interactions between surfaces extend across physics, chemistry, materials science, and a variety of other disciplines. With a force sensitivity on the order of a few pico-Newtons, AFMs are excellent tools for probing these fundamental force interactions. Force measurements in water revealed the benefits of AFM imaging in this environment due to the lower tip-sample forces. Some of the most interesting force measurements have also been performed with samples under liquids where the environment can be quickly changed to adjust the concentration of various chemical components. In liquids, electrostatic forces between dissolved ions and other charged groups play an important role in determining the forces sensed by an AFM cantilever. 

None of these properties hold for the tip sample forces, the imaging signal of the AFM, and therefore substantial hurdles had to be overcome before atomic resolution by AFM became possible. 

With an AFM even insulating surfaces can be investigated with atomic resolution. The potential tip-sample energy Uts involves a z component of the tip-sample force Fts = —dVts/dz and a tip-sample spring constant kts = —dFts/dz. Depending on the mode of operation, the AFM uses Fts or some entity derived from l K as imaging signal. 

Fig. 10. A/ is a convolution of the weight function w with the tip-sample force gradient. For small amplitudes, short range interactions contribute heavily to the frequency shift, while long-range interactions are attenuated.

Fig. 2 Schematic representation of the basic detection elements of the scanning force microscope and of the piezoelectric transducers generating the displacement modulations for purposes of dynamic mechanical measurements. The dynamic components of the tip-sample forces resulting from the normal/lateral displacement modulations are detected via the torsion/bending of the microscopic cantilever and the deflection of the laser beam reflected off the rear side of the cantilever. The positional shift of the latter is registered by means of a segmented photo-diode...

The results of various research groups show strong differences in the thickness of the QLL. Pittenger et al. calculated the thickness of the QLL assuming that it has the viscosity of supercooled water they estimated the QLL thickness to be about 1 nm at -1°C and 0.2 nm at -10°C for a silicon tip. For a hydrophobically coated tip, the layer thicknesses were slightly smaller. Several authors have used the jump-in distance to estimate the thickness of the QLL (gradient of the tip-sample forces becomes greater than... 

The differential equation of motion of a damped oscillator, which interacts with the surface via a weak tip-sample force Fts, can be written by adding tip-sample interactions (weakly perturbed oscillator). 

Fig. 1.16 Average tip—sample force and oscillation frequency as a function of reduced amplitude (setpoint). The dashed resonance corresponds to a damped driven oscillator without sample—tip interactions. Reprinted from [16], copyright American Physical Society...

The following section describes the use of the two-timing approximation for the analysis of QCM data. The same formalism is also used in the field of non-contact atomic force microscopy [28,29]. In the latter context, the tip-sample interaction perturbs the oscillation of the cantilever. As long as the tip-sample force is weak compared to the force needed to bend the cantilever, the interaction potential can be reconstructed from the frequency of the cantilever as a function of amplitude and mean vertical distance. 

AFM imaging has been used to identify interfacial aggregate structure above the cmc for a variety of ionic, nonionic, and zwitterionic surfactants on both hydrophobic and hydrophilic surfaces. (Structures far below the cmc, corresponding to the low-density adsorption plateau, cannot be imaged readily because the tip-sample force is strongly hydrophobic and attractive in this regime.) The... 

As mentioned before, AFM can measure surface forces using two different operation modes, DC and AC. In the DC mode, one measures the deflection (AZ) of a cantilever as a function of the tip-sample distance (D) that is varied usually hy a piezoelectric transducer (Fig. 3). The tip-sample force is given by Hooke s law in terms of AZ, F = kAZ, where k is the spring constant of the cantilever. This force clearly depends on the tip-sample distance, D, which is given by D = Z — AZ, in the absence of sample deformation. Z in the expression is the displacement of the piezo and the one that can be controlled in the experiment. When the tip is far away from the sample (large D), the force is zero. When the tip approaches the sample, it experiences various forces, electrostatic, van der Waals, double-layer, solvation forces, and so on. This is the regime of interest in... 

Fortunately, performing AFM in solution eliminates capillary forces. Furthermore, in suitable fluids, tip-sample forces... 

We only mention here that the probe used in AFM is a sharp tip, which is attached to a flexible microbeam (microcantilever). In AFM various forms of interactions between the apex of the tip (with a radius between approximately 10-100 nm) and the sample surface are measured, either as a function of tip location with respect to the surface, or at a fixed (x,y) position as a function of the cantilever deflection or tip-sample distance. In most conventional instruments the cantilever-tip assembly is attached to a piezo controller, which positions the tip in the (x,y) scanned plane and adjusts the vertical position (piezo travel) to accommodate sample height, or to measure tip-sample force curves. The latest generation instruments can also be equipped with active x-y-z distance feedback control loops, which enable one to perform lithography, vertical positioning of the tip (e.g. for single molecule force spectroscopy), etc. 

A variation on the amplitude modulation technique was also used to measure oscillatory surface forces with increased sensitivity in a branched hydrocarbon, squalene. In this technique, the sample was oscillated with low amplitude (c. 1 A), and both the cantilever static and dynamic (induced oscillation from a change in the tip-sample force gradient) deflection was measured. Figure 1.13 shows the static force measurement and Fig. 1.14 the dynamic measurement, shown as an interaction stiffness. The sensitivity of the dynamic force measurement is such that the interdigitation of the branched methyl groups can be detected (indicated by arrows in Fig. 1.14). 

This procedure keeps the tip in the region where the tip-sample force is (relatively) well understood, but at the price that the force is determined by the cumulative effect of a large number of atoms - hence the resolution of individual atomic-scale features is seldom possible. In the non-contact mode, the cantilever is made to vibrate at its resonant frequency, and the interaction damps the amplitude of the vibration. NC-AFM is preferable to contact AFM for measuring soft samples such as polymers, but the spatial resolution is lower. 

This is largely because the two techniques share the same key elements - a passivated tip (H-passivated in the case of Termirov et al. s results) and operation within the Pauli repulsion regime - although the contrast mechanisms are of course rather different. For STHM, the passivated tip translates variations in tip-sample force into a modulation of the junction conductance. As can be seen from Fig. 10(b) the image resolution far exceeds that observed in conventional STM because the latter is sensitive only to variations in electron density in a relatively narrow energy window close to the Fermi level. In STHM, as pointed out by Temirov et it is variations in the total electron density - and the information on chemical structure embedded within it which are probed. 

Figure 2.9. Schematic of the intermittent contact mode AFM free oscillation with free amplitude Ao far away from sample surface, and damped oscillation with set-point amplitude A,p and phase shift AO during scanning. Asp is chosen by the operator, and feedback control is used to adjust tip-sample distance such that Asp remains at constant value. The choice of Aq and Asp has great influence on tip-sample force interaction and image formation.

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