Tip shape

Figure Bl.19.19. Examples of inaccessible features in AFM imaging. L corresponds to the AFM tip. The dotted curves show the image that is recorded in the case of (a) depressions on the underside of an object and (b) mounds on the top surface of an object. M- L andMoi correspond to convolutions of the surface features with the tip shape. (Taken from [ ], figure 2.)...

It is not easy to determine detailed properties of the tube terminations using STM or AFM. These microscopes cannot image undercut surfaces and the tip shape is convoluted with the cap shape of the nanotube. How ever, the tips may have very sharp edges... 

This probably arises from the different position of tunneling (STM) and of field enhancement (TERS) owing to the tip shape and the height of the observation object. 

An example for the field cones and equipotential surface is shown in Fig. 3.9 for d = 1.2 mm and rt= 420 A. The vertical line represents a position of 5rt away from the tip. The field lines are drawn so that their density is proportional to the field strength. Field distributions and equipotential surfaces of other tip shapes have also been investigated, particularly as regards the field emission current density distribution,24,31 but will not be discussed here. 

In atomic force microscopy the tip shape is often approximated by a parabolic shape with a certain radius of curvature R at the end. Calculate the van der Waals force for a parabolic tip versus distance. We only consider non-retarded contributions. Assume that the Hamaker constant Ah is known. 

Under ambient conditions, the atmosphere contains water and organic contamination. Depending on the relative humidity, water can condense around the contact site and result in capillary forces (Fig. 3b). The meniscus curvature varies with the relative vapour pressure and the tip shape [77,78]. For a small spherical tip, the capillary contribution to the adhesion force can be calculated as... 

As was demonstrated theoretically, a single atom at the end of a rigid tip is not stable as well as tips with an infinite aspect ratio do not exist [227,228]. Therefore, SFM tips are truncated and require a special procedure to calibrate their unknown geometry. Electron microscopy was widely employed for ex-situ examination of the tip shape [226,229,230]. This technique provides valuable information on the overall shape of the tip, however it is less suitable for characterisation of the nanometer sized probe apex. 

Several authors proposed to use a specially designed substrate for in-situ calibration of the tip shape based on extraction of the tip geometry from the topo-... 

Unlike the lattice imaging which can be performed by blunt tips, the finite size and 3D shape of the tip become important for imaging of the surface structure on the nanometer scale, where the tip shape and the surface topography may su-... 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

---