Cantilever spring

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. 

Thin sheets of mica or polymer films, which are coated with silver on the back side, are adhered to two cylindrical quartz lenses using an adhesive. It may be noted that it is necessary to use an adhesive that deforms elastically. One of the lenses, with a polymer film adhered on it, is mounted on a weak cantilever spring, and the other is mounted on a rigid support. The axes of these lenses are aligned perpendicular to each other, and the geometry of two orthogonally crossed cylinders corresponds to a sphere on a flat surface. The back-silvered tbin films form an optical interferometer which makes it possible... 

In a force-displacement curve, the tip and sample surfaces are brought close to one another, and interact via an attractive potential. This potential is governed by intermolecular and surface forces [18] and contains both attractive and repulsive terms. How well the shape of the measured force-displacement curve reproduces the true potential depends largely on the cantilever spring constant and tip radius. If the spring constant is very low (typical), the tip will experience a mechanical instability when the interaction force gradient (dF/dD) exceeds the... 

AFM has been used to image surfaces by probing both the attractive and repulsive forces experienced by the tip as a result of its proximity to the sample surface. In both modes, the probe tip is mounted on a cantilever spring. Three main designs have been employed metal foil with a splinter of diamond, a shaped tungsten wire that acts both as spring and tip, and microfabricated tip/cantilever composites. 

The interplay between the attractive (e.g.. Van der Waals or capillary forces) and repulsive forces involved during the approach of the tip to different surfaces under different environments are presented in Fig. 5 and discussed here. When the cantilever approaches a hard and non-compressible surface (Fig. 5a), at first the forces are too small to produce any measurable deflection of the cantilever, and therefore the position of the cantilever remains unchanged. At a certain distance the attractive forces overcome the cantilever spring constant and the tip leaps into contact with the specimen surface (Fig. 5b). As the cantilever continues to press down while the tip rests on the surface, the separation between the base of the tip and the sample decreases further, which results in the deflection of the tip with a subsequent increase... 

Another device that yields results of the same kind as STM is atomic force microscopy (AFM) (Binning, 1986). This avoids dependence on an electron stream (which cannot be obtained from insulators)58 and relies on the actual interatomic forces between a microtip and nearby surface atoms. The forces experienced at a given point by the tip are sensed by a cantilever spring. The movements of this are slight, but they can be measured by means of interf erometry and in this way the movement of the tip can be quantified. The sensitivity of the atomic force microscope is less than that of STM, but its action is independent of the electrical conductivity of the surface and it is therefore to be preferred over STM, particularly for studies in bioelectrochemistiy. 

There are different methods of measuring the electrocapillarity of solid metals. In one method the deflection of a cantilever spring, which is coated on one side with the metal, is measured [71,72], The surface tension of the metallic side changes when the applied voltage... 

Present limitations in chemical forces measurements include the need for detailed knowledge of the cantilever spring constant and the tip-sample interaction... 

The principal limitation of STM is that it cannot be used with insulating substrates. However, at the sort of distances where tunnelling currents occur, there is an attractive or repulsive force between atoms in the tip and the substrate, which is independent of the conducting or nonconducting nature of the substrate. In order to measure this, the tip is mounted on the end of a soft cantilever spring, the deflection of which is monitored optically by interferometry or beam deflection. These cantilever springs are microfabricated photolithographically from silicon, silica, or silicon nitride and have lateral dimensions of around 100 pm and thickness of 1 jum, to which tiny diamond tips are attached. 

Fig. 1. Schematic representation of the main features of the interferometric surface forces apparatus. Crossed mica sheets (1) are glued onto semi-cylinder optically polished silica discs (2). One of the discs is attached to a piezoelectric crystal tube (3), and another to the force measuring double cantilever spring (4). White light passes through the window positioned in the bottom of the apparatus and reflects between two silver mirrors. Constructive interference occurs for some wavelengths and the fringes of equal chromatic order are passed through the upper silver mirror to the spectrometer where they can be viewed and their wavelengths determined. Adapted from Ref. [9]. 1996, with permission from Elsevier.

The restriction to mica was overcome by a relatively recent technique the atomic force microscope (AFM). sometimes also called the scanning force microscope [69. AFMs are usually used to image solid surfaces. Therefore a sharp tip at the free end of a cantilever spring is scanned over a surface. Tip and cantilever are microfabricated. While scanning, surface features move the tip up and down and thus deflect the cantilever. By measuring the deflection of the cantilever, a topographic image of the surface can be obtained. 

FIG. 4 Scheme of an atomic force microscope with a particle attached to the free end of the cantilever spring. 

Current instruments differ little, in principle, front the first AFM developed over I0 years ago. The biggest changes have come in the methods used to detect the deflection of the cantilever spring, as mentioned above, and the development of microfabricated silicon nitride cantilevers with integrated pyramidal tips. 

The cantilever deflection d is related to the total force F on the particle via F = Kcd, where is the cantilever spring constant. By employing a basic distance balance... 

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