Dependence of Friction

Many macroscopic systems show an almost linear relationship between friction F and load L 

Integrating Eq. [4] over Areai yields the friction, which can then be divided by the load to give the following relationship for the friction coefficient  

Numerous simulations of boundary lubricants have shown that cto is indeed small, even at pressures close to the yield strengths of solids.14,21 Thus, it seems that Amontons s law should hold in a wide range of cases. However, exceptions are observed when adhesive interactions are strong, which leads to large values of cto. 

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The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

Perhaps, the most interesting observation on the molecular films is the dependence of friction on chain length. It has been reported from independent experiments conducted on different sorts of L-B films and SAMs that the friction decreases with an increasing number of carbon atoms, but once the chain length exceeds a certain limit the friction be-... 

Fig. 7—Dependence of friction force signal of Au film and Si wafer on load.

Fig. 10—Dependence of friction force of PTFE, Si3N4, and PTFE/Si3N4 film on load.

Fig. 14—Dependence of friction force signal of a triacetic acid L-B film on load.

The discussion begins below with an overview of proposed energy dissipation mechanisms that lead to friction. This is followed by brief discussions of phenomenological friction laws that describe the dependence of friction upon normal load and sliding velocity. The dependence of friction on the symmetry of the surfaces that are in contact is discussed later. 

An example of the velocity dependence of friction is given in Figure 5 for a boundary lubricant confined between two incommensurate surfaces.25 For the given choice of normal pressure and temperature, one finds four decades in sliding velocity for which Eq. [7] provides a reasonably accurate description. 

The frictional behavior of 316 stainless steel is shown in Fig. 8 for sliding in air or in different atmospheres. No clear trend in the dependence of friction coefficient on environment was observed. 

Figure 11.5 Dependence of friction on load for a single microcontact. The friction force between a silica sphere of 5 //in diameter and an oxidized silicon wafer is shown (filled symbols). Different symbols correspond to different silica particles. The solid line is a fitted friction force using a constant shear strength and the JKR model to calculate the true contact area (based on Eq. (6.68)). Results obtained with five different silanized particles (using hexamethylsililazane) on silanized silica are shown as open symbols. Redrawn after Ref. [467].

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

Fig. 5. 2. Schematic dependence of friction coefficient for MoS2 films as a function of oxygen concentration in the film. Coefficients of friction (pi) for pure MoS2 are significantly lower than for MoS2.xOx. The peak in the pi curve occurs at some relatively low concentration of oxygen in the films. Additional substitution of oxygen in the MoS2 has the combined effect of atomically smoothing the surface and reducing the coefficient of friction pi (Fleischauer and Lince, 1999)...

Figure 3. Dependence of friction factor on applied loading 1. a clay solution 2. a clay solution - SDBUR (1.0mass.%) 3. aclay solution - SDISUR (1.0 mass.%) - piperylenc bis- tetrasullide (0.1 mass.%) 4. aclay solution - SDBUR (1.0 mass.%) - piperylene bis- tetrasulfide in solvent (0.1 mass.%).

As discussed in Section I.D, the dependence of friction on past history is often modeled by the evolution of a state variable (Eq. 6) in a rate-state model [50,51]. Heslot et al. [53] have compared one such model, where the state variable changes the height of the potential in a finite-temperature PT model, to their detailed experimental studies of stick-slip motion. They slid two pieces of a special type of paper called Bristol board and varied the slider mass M, pulling... 

The linear dependence of friction on load established in solid friction, F = fiW, is explained in terms of the yielding mechanism i.e., the solid surface is not molecu-larly flat and the real contact area between two surfaces increases with an increase of load due to yielding. Thus, the friction has no dependence on the apparent contact area of the two solid surfaces, and Amonton s law holds [38]. 

Fig. 13 Velocity dependence of frictional stress for a soft gel sliding on a smooth adhesive solid substrate. The result is based on the molecular picture in Fig. 12, which considers the thermal fluctuation of adsorption and desorption of the polymer chain, (a) The elastic term of the frictional stress of a gel. See text for a description of parameter u. (b) Summation of the elastic term and the viscous term. When v -C Vf, the characteristic polymer adsorption velocity, the elastic term is dominant. At v 2> the viscose term is dominant. Therefore, transition from elastic friction to lubrication occurs at the sliding velocity characterized by the polymer chain dynamics. (Modified from figure 1 in [65])...

I feel that surface free energy is not a good parameter to correlate with surface friction. Surface free energy may be related to cohesive energy density. There is too much data which contradicts this, e.g. (1) static/dynamic friction, (2) spin effects, (3) temperature and velocity dependence of friction. 

Temperature dependence of friction and wear of some heat resistant polymers was studied. Except the one filled with glass fibers of kO wt. PPS, the specimen polymers were unfilled. 

Figure 2. Dependence of friction zone temperature (T) (curve 2) and the coefficient of friction (f) (curve l) upon PV.

Taylor and Pollet [30] reported the results of a study of friction between fabrics used for clothes, including cotton, wool, polyester fibre and acrylic fibre, and aluminium, Formica and rubber under zero or low applied normal forces. The effects of various factors, such as surface roughness, directionality, nature of table surface, pressure and velocity, on frictional force are discussed and an empirical law proposed to model the dependence of friction on velocity. 

Dependence of friction and adhesion on surface chemical species on samples has... 

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