Cantilever

Drilling Jackets are small steel platform structures which are used in areas of shallow and calm water. A number of wells may be drilled from one jacket. If a jacket is too small to accommodate a drilling operation, a jack-up rig (see below) is usually cantilevered over the jacket and the operation carried out from there. Once a viable development has been proven It is extremely cost effective to build and operate jackets in a shallow... 

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

Modification of an AFM to operate in a dynamic mode aids the study of soft biological materials [58]. Here a stiff cantilever is oscillated near its resonant frequency with an amplitude of about 0.5 nm forces are detected as a shift to a new frequency... 

Use Equation VIII-1 to determine the effective mass of the cantilever if the cantilever has a spring constant C = 20 N/m, the minimum detectable force gradient is hF/dz = 4 X 10 N/m, and the frequency shift is 200 kHz. How does the frequency shift depend on distance from the surface if the force has a 1/z distance dependence ... 

AFM Atomic force microscopy [9, 47, 99] Force measured by cantilever deflection as probe scans the surface Surface structure... 

Figure Bl.19.17. Conunercially produced, microfabricated, V-shaped Si3N4 cantilever and tip for AFM (Taken from [215].)...

Detection of cantilever displacement is another important issue in force microscope design. The first AFM instrument used an STM to monitor the movement of the cantilever—an extremely sensitive method. STM detection suffers from the disadvantage, however, that tip or cantilever contamination can affect the instrument s sensitivity, and that the topography of the cantilever may be incorporated into the data. The most coimnon methods in use today are optical, and are based either on the deflection of a laser beam [80], which has been bounced off the rear of the cantilever onto a position-sensitive detector (figme B 1.19.18), or on an interferometric principle [81]. 

As the tip is brought towards the surface, there are several forces acting on it. Firstly, there is the spring force due to die cantilever, F, which is given by = -Icz. Secondly, there are the sample forces, which, in the case of AFM, may comprise any number of interactions including (generally attractive) van der Waals forces, chemical bonding interactions, meniscus forces or Bom ( hard-sphere ) repulsion forces. The total force... 

Figure Bl.19.21. A plot of cantilever displacement as a function of tip sample separation during approach and retraction with an AFM. Note the adliesive forces upon retraction from the surface.

Most NC-AFMs use a frequency modulation (FM) teclmique where the cantilever is mounted on a piezo and serves as the resonant element in an oscillator circuit [101. 102]. The frequency of the oscillator output is instantaneously modulated by variations in the force gradient acting between the cantilever tip and the sample. This teclmique typically employs oscillation amplitudes in excess of 20 mn peak to peak. Associated with this teclmique, two different imaging methods are currently in use namely, fixed excitation and fixed amplitude. 

Figure Bl.19.23. Principle of simultaneous measurement of nomial and lateral (torsional) forces. The intensity difference of the upper and lower segments of the photodiode is proportional to the z-bending of the cantilever. The intensity difference between the right and left segments is proportional to the torsion, t, of the force sensor. (Taken from [110], figure 2.)...

Figure Bl.19.24. Friction loop and topography on a heterogeneous stepped surface. Terraces (2) and (3) are composed of different materials. In regions (1) and (4), the cantilever sticks to the sample surface because of static friction The sliding friction is tj on part (2) and on part 3. In a torsional force image, the contrast difference is caused by the relative sliding friction, Morphological effects may be...

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... 

Figure Bl.19.34. Cantilever deflection and corresponding frictional force in the v-direction as a fiinction of sample position as a mica sample is scaimed back and forth under a tungsten tip. (Taken from [124], figure 2.)...

Fig. 4. Typical AFM rupture experiment (top) Receptor molecules are fixed via linker molecules to a surface (left) in the same way, ligand molecules are connected to the AFM cantilever (right). When pulling the cantilever towards the right, the pulling force applied to the ligand can be measured. At the point of rupture of t he ligand-receptor complex the measured force abruptly drops to zero so that the rupture force can be measured.

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49], Prom such force simulations rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom) the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic spring potential and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected. 

Fig. 5. Block diagram of contact atomic force microscope system in which cantilever deflection monitored optically with position-sensitive photodiode...

Fig. 2. Illustrations of forces to which adhesive bonds are subjected, (a) A standard lap shear specimen where the black area shows the adhesive. The adherends are usually 25 mm wide and the lap area is 312.5 mm. The arrows show the direction of the normal apphcation of load, (b) A peel test where the loading configuration, shown by the arrows, is for a 180° peel test, (c) A double cantilever beam test specimen used in the evaluation of the resistance to crack propagation of an adhesive. The normal application of load is shown by the arrows. This load is appHed by a tensile testing machine or other...

Fracture mechanics (qv) tests are typically used for stmctural adhesives. Thus, tests such as the double cantilever beam test (Fig. 2c), in which two thick adherends joined by an adhesive are broken by cleavage, provide information relating to stmctural flaws. Results can be reported in a number of ways. The most typical uses a quantity known as the strain energy release rate, given in energy per unit area. 

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. 

The force and moment ia a constrained system can be estimated by the cantilever formula. Leg MB is a cantilever subject to a displacement of and leg CB subject to a displacement Av. Taking leg CB, for example, the task has become the problem of a cantilever beam with length E and displacement of Av. This problem caimot be readily solved, because the end condition at is an unknown quantity. However, it can be conservatively solved by assuming there is no rotation at poiat B. This is equivalent to putting a guide at poiat B, and results ia higher estimate ia force, moment, and stress. The approach is called guided-cantilever method. 

From basic beam theory, the moment-displacement and moment-force relationships for a guided cantilever are as follows ... 

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