As mentioned before, the measurement of friction forces dates back to da Vinci in the 15th and beginning 16th centuries. To determine the friction force necessary to initiate movement of a block resting on a substrate, da Vinci connected the block to a dead-weight by a thread (see figure 1.6). Neglecting the force necessary to rotate a pulley (roll) that diverts the thread connecting the hanging dead-weight to the block, the weight of the load equals the static friction force once movement is initiated.
Da Vinci stated the independence of the friction force of the apparent area of contact as well as the proportionality expressed in equation (1.1). Unfortunately these results were not accessible for the general public, resulting in the fact, that Guillaume Amontons (1663-1705) again stated these two laws, now called Amontons friction laws. The two laws were verified by Coulomb and extended by a third rule, the independence of the friction force on the relative sliding velocity (which is limited as already discussed, see section 1.3). The next step in friction measurements was the utilization of calibrated springs for dragging the block along a surface. Knowing the spring constant, the friction force can be directly measured by the elongation of the spring. The employment of the spring has the advantage, that thread and pulley do not have to be neglected or their contribution determined, which introduces an additional uncertainty.
More complicated is the further developed “surface force apparatus”. In a common sur-face force apparatus [2] curved glass bodies (e.g. cylinders) are coated with mica layers.
Mica is a mineral, a silicate, which strongly reflects light because the surfaces after cleav-age are very smooth. The reason for the smoothness is the layered atomic structure of
Chapter 1. Friction 1.5. Friction Measurements
normal fiber
tangential fiber
tangential mirror
normal mirror
ceramics ball
Figure 1.7.: Fiber optics and cantilever unit of the tribometer employed for the work underlying the experimental part of this thesis. A silicon nitride ball is glued underneath the cantilever. Two perpendicular mirrors reflect the light emitted by the fiber optics sensors.
the mineral. Using atomically smooth mica sheets, the contact between the two curved bodies can be studied, and the distance between them, because of condensed water vapor for example, can be measured. For the distance measurements light beam interference is employed. Upon measurement one body is pulled along the other using a spring. Result-ing from the atomic smoothness of the interactResult-ing surfaces, the influence of lubricants can be studied very accurately.
Nowadays mainly two friction measurement kinds are employed, which both are focusing on spring deflection in tangential but also in normal direction. The one measurement technique is the macroscopic tribometer, the other technique is the atomic force micro-scope (AFM).
Figure 1.7 illustrates the measurement principle: Knowing the tangential and normal force constants of the cantilever, by the displacements in tangential and normal direction the friction and normal forces are known. The displacements are determined by the voltages induced by the light emitted and received by the fiber optics sensors. This voltage depends on the distance between the end of the fiber and the mirror. The distance between mirror and fiber end can be computed by the tribometer based on the known intensity distribution relatively to the maximum of this distribution. The maximum of the distribution has to be determined before the measurement by the user.
The big advantage of course is the contact-less measurement of the acting forces.
The AFM uses the same principle, but the cantilever is so small, that it has to be handled by tweezers. Figure (1.8) schematically displays the measurement approach of an AFM. Underneath the AFM cantilever a tip with an atomically sharp profile is mounted. These tips have diameters of 10 nm and less and are usually etched to this shape by electro-etching. Typical tip materials are silicon or tungsten. The AFM cantilever deflection is measured by the deflection of a laser beam directed onto the cantilever and
1 2
3 4 (1+2)-(3+4)
(2+4)-(1+3) (1+3)-(2+4)
(3+4)-(1+2) incident
laser beam
tip specimen
cantilev er
Figure 1.8.: Schematic representation of the atomic force microscope (AFM) measure-ment unit, the probe is the tip underneath the cantilever.
reflected onto a 2x2 charge-coupled devices (CCD) array. Without any acting forces the beam directly hits the center of the array, giving approximately the same voltage for all four CCDs. Deflection in tangential and normal direction changes the different voltages which produces the measurement signal. Compared to the dimensions of the tip, the normal forces in the range of 1-100 nN are very high. This high forces on areas in the atomic dimensions often leads to the damage of the studied surface, which is why the measurement in full and constant contact of tip and surface is often referred to as “scratching mode”, although the scientifically correct term is “contact mode”. The positioning of the probe on the specimen is performed using piezo-electric materials, because mechanical positioning on nanoscopic length scales with the required accuracy is impossible. The specimen surface is then scanned for the acting forces at a given position, resulting in a two-dimensional force map, the “image”. The employment of piezo-electric materials to position a probe for scanning a certain property renders the AFM among the “scanning probe microscopies”.
The contact of an AFM tip in contact mode with the specimen is obviously direct contact of an atomically shaped tip with a surface. However, for a macroscopic body the surface roughness usually is on a scale that is a lot larger than the diameter of an AFM tip. For the contact of two bodies with surface roughness the question, whether direct contact occurs or not, and if it occurs, where and with what fraction of the surface, is far from obvious and not easily answered. To shed light on the complicated situation at the friction interface between two bodies, the following part of this thesis deals with the general topic of contact, followed by a discussion about the area of contact. Subsequently the deformation resulting from the applied in areas of contact is investigated as well as the influence of lubrication on the molecular scale and finally the squeeze-out and entrapment of lubricant molecules.
Chapter 2. Contact