Tip-cantilever system

A novel hybrid molecular simulation technique was developed to simulate AFM over experimental timescales. This method combines a dynamic element model for the tip-cantilever system in AFM and an MD relaxation approach for the sample. The hybrid simulation technique was applied to investigate the atomic scale friction and adhesion properties of SAMs as a function of chain length [81], The Ryckaert-Bellmans potential, harmonic potential, and Lennard-Jones potential were used. The Ryckaert-Bellmans potential, which is for torsion, has the form... 

Figure 2b Idealized approach-retract curve plot of the oscillation amplitude variation with the tip-sample distance during the approach and retraction of a sample toward an oscillating tip-cantilever system. First, when the tip is far from the sample, it oscillates with its free amplitude Af as depicted in part a. In part b, the tip-CL system interacts with the surface through an attractive field. If the drive frequency is slightly below the resonance one, the oscillation amplitude increases. Part c corresponds to the so-called AFM tapping mode where the tip comes in intermittent contact with the sample. In this part, the oscillatory amplitude A decreases linearly with the CL-surface distance d with a slope equal to 1 if the sample is hard, that is if dcAf, A(d) = d. In part d, the tip is stuck on the sample with an oscillation amplitude down to zero. The tip might be damaged this part is usually avoided.

All those experimental results can be satisfactorily described by the study (with analytical expressions or simulations) of the oscillating behavior of the tip-cantilever system in interaction with the sample through an attractive force field (20, 28). When the tip is close to the sample, the non linear dynamical behaviour of the oscillator gives a bifurcation from a monostable to a bistable state. Theoretical work shows that it is very informative to follow not only the variations of the amplitude during the approach and retraction but also the phase variations (20,29,63). 

The sample-tip-cantilever system can be modeled as a mechanical system with springs and dash-pots 11,12). Solving the motion equations of this model at low frequency (i.e. below the cantilever resonance frequency) and neglecting the damping constants (i.e. neglecting viscoelastic effects in polymers) leads to the following relation for the ratio between the sample modulation amplitude, z, and the tip response amplitude, also called the dynamic elastic response ... 

FIGURE 10.15 Schematic of the tip/sample interaction in AFM using a cantilever system. 

The AFM (Fig. 1) has been described in many reviews [14,28-30] as a relatively straightforward instrument comprising a probing tip and a detection system (laser and photo diode) used to monitor the position of the tip [31]. The tip is located on the apex of a flexible cantilever, and is conunoifly composed of silicon (Si). This tip-cantilever set-up is often described in mechanical terms as a ball (tip) on the end of a flexible spring (cantilever), which, in theory, is capable of measuring forces with a resolution down to the femtonewton range [16]. However, in reality, forces lower than around ten piconewtons are rarely detected. The AFM tip may hence be described as a nanoscopic force sensor [32], which has a terminal radius that ranges from 2-15 nm [1,33] for sharp probes to 10-50 nm [34] for unsharpened probes (often used in force-distance work). 

The more recent development concerns the use of the oscillating behavior of the tip-cantilever (CL) system when brought close to the sample surface. Two modes can be used in dynamic force microscopy. With one mode, commonly called tapping. 

Force-Curves Measurements In force curve measurements, a vertical displacement of the sample, z, is imposed and the subsequent tip displacement, d, is measured. The tip-sample interaction force, F, is deduced by means of the Hooke s relation, F = -kcd, where is the cantilever stiffness. Force curves arc generally divided into different regions (7). If the part where the electrostatic repulsion forces are dominant is only considered, with silicon tips much stiffer than polymers, tips penetrate the sample surface and an indentation depth, 5, equal to Z d, can be measured. The lower the sample elastic modulus, the greater will be the indentation depth. By using the Hertz mechanical model adapted to the geometry of the tip-sample system (8,9) surface elastic modulus could be deduced from the following equations corresponding respectively to a spherical, a paraboloid and a conical tip ... 

Figure 3.22 shows the essential elements of an atomic force microscope (AFM). These include a cantilever to support the tip, a system for detecting cantilever deflection with a feedback loop, and a scanner to control the relative... 

After the Pt-coated AEM tip had been secured in the AEM fluid cell, the underside and the part of the tip holder that came into contact with the solution were electrically insulated. Depending on the solvent system employed, different insulating coatings were utilized. In particular, for the MeCN studies, a thin film of polystyrene was employed [57], while in aqueous solution a mixture of nail varnish and super glue was used [59,60], applied with a fine paint brush. This procedure leaves Pt exposed only at the tip, cantilever, and, in some cases, a small fraction of the probe body. To estimate the exposed electroactive areas, cyclic voltammograms were recorded in the presence of an appropriate mediator. 

For SFM, maintaining a constant separation between the tip and the sample means that the deflection of the cantilever must be measured accurately. The first SFM used an STM tip to tunnel to the back of the cantilever to measure its vertical deflection. However, this technique was sensitive to contaminants on the cantilever." Optical methods proved more reliable. The most common method for monitoring the defection is with an optical-lever or beam-bounce detection system. In this scheme, light from a laser diode is reflected from the back of the cantilever into a position-sensitive photodiode. A given cantilever deflection will then correspond to a specific position of the laser beam on the position-sensitive photodiode. Because the position-sensitive photodiode is very sensitive (about 0.1 A), the vertical resolution of SFM is sub-A. 

Binnig et al. [48] invented the atomic force microscope in 1985. Their original model of the AFM consisted of a diamond shard attached to a strip of gold foil. The diamond tip contacted the surface directly, with the inter-atomic van der Waals forces providing the interaction mechanism. Detection of the cantilever s vertical movement was done with a second tip—an STM placed above the cantilever. Today, most AFMs use a laser beam deflection system, introduced by Meyer and Amer [49], where a laser is reflected from the back of the reflective AFM lever and onto a position-sensitive detector. 

An important consideration for the direct physical measurement of adhesion via pull-off measurements is the influence of the precise direction of the applied force. In AFM the cantilever does not usually lie parallel to the surface, due to the risk that another part of the cantilever chip or chip holder will make contact with the surface before the tip. Another problem relates to the fact that the spot size in the optical beam deflection method is usually larger than the width of the lever. This can result in an interference effect between the reflection from the sample and the reflection from the cantilever. This is reduced if the cantilever and sample are not parallel. Most commercial AFM systems use an angle in the range of 10°-15° between the sample and the cantilever. Depending on this angle and the extent to which the cantilever is bent away from its equilibrium position, there can be a significant fraction of unintentional lateral forces applied to the contact. 

The versatility of AFM is exemplified by the number of different operation modes, which have been employed with various degrees of success for the analysis of DNA molecules on surfaces. As mentioned before, AFM operates by measuring the attractive or repulsive forces between a tip and the specimen using a feedback system, with the cantilever deflection yielding the actual topography of the specimen. Different setups of the feedback and cantilever deflection result in different AFM operation modes, as summarised in Table 1. 

The AFM has a number of elements common to STM the piezoelectrc scanner for actuating the raster scan and z positioning, the feedback electronics, vibration isolation system, coarse positioning mechanism, and the computer control system. The major difference is that the tunneling tip is replaced by a mechanical tip, and the detection of the minute tunneling current is replaced by the detection of the minute deflection of the cantilever. 

Figure 8. A molecular system of extension x is connected at its leftmost end to a bead trapped in an optical well (or to the tip of an AFM cantilever) and at its rightmost end to an immobilized surface (or a bead fixed to the tip of a micropipette). The position of the bead relative to the center of the trap, xt, gives a readout of the acting force / = KXi,. The control parameter in this setup is Z = Xb + X, whereas both xt and x are fluctuating quantities.

The scanning system is a very important part of these microscopes, and is commonly composed of a cantilever whose arms are usually made of piezoelectric quartz crystal. The electric field applied by the computer to the arms of the scanning device controls the position of the tip of the sensor to within a great spatial precision. The right variation of the electric field allows the complete scanning of the sample. 

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